Westfield Community School - Mathematics

Year 81 – Scheme of Work

 Long term planning – NC & NNS Year 8

 Medium term planning – Key Maths 81, divided into 4 units

 Short term planning – Lesson by lesson planning. Note this is a guide only: it enables staff to check pace & coverage of topics.

You are welcome to use any of these materials if you wish. Any ideas/ thoughts are welcomed. This is a working document and is by no means complete.

1 07/04/18 Westfield Community School - Mathematics

Attainment Target 1: Using & Applying Mathematics

3  Try different approaches & find ways of overcoming difficulties that arise when solving problems.  Beginning to organise work & check results.  Discuss mathematical work & begin to explain thinking.  Use & interpret mathematical symbols & diagrams.  Show understanding of a general statement by finding particular examples that match it. 4  Developing strategies for solving problems & are using these strategies both in working within maths & in applying maths to practical contexts.  Present information & results in a clear & organised way.  Search for a solution by trying out ideas. 5  In order to carry through tasks & solve mathematical problems, identify & obtain necessary information.  Check their results, considering whether these are sensible.  Show understanding of situations by describing them mathematically using symbols, words & diagrams.  Draw simple conclusions & give an explanation of reasoning. 6  Carry through substantial tasks & solve quite complex problems by independently breaking them down into smaller, more manageable tasks.  Interpret, discuss & synthesise information presented in a variety of mathematical forms.  Writing explains & informs their use of diagrams.  Beginning to give mathematical justifications. 7  Starting from problems or contexts that have been presented, progressively refine or extend the maths used to generate fuller solutions.  Give a reason for their choice of mathematical presentation, explaining features selected.  Justify generalisations, arguments or solutions, showing some insight into the mathematical structure of the problem.  Appreciate the difference between mathematical explanation & experimental evidence. 8  Develop & follow alternative approaches.  Reflect on own lines of enquiry when exploring mathematical tasks; in doing so introduce & use a range of mathematical techniques.  Convey mathematical or statistical meaning through precise & consistent use of symbols that is sustained throughout the work.  Examine generalisations or solutions reached in an activity, commenting constructively on the reasoning & logic or the process employed, or the results obtained, & make further progress in the activity as a result.

Attainment Target 2: Number & Algebra

3  Show understanding of place value in nos. up to 1000 & use this to make approximations.  Begin to use decimal notation & to recognise negative nos., in contexts such as money & temperature.  Use mental recall of addition & subtraction facts to 20 in solving problems involving larger nos.  Add & subtract nos. with two digits mentally & nos. with three digits using written methods.  Use mental recall of the 2, 3, 4, 5 & 10 multiplication tables & derive the associated division facts.  Solve whole-nos. problems involving multiplication or division, including those that give rise to remainders.  Use simple fractions that are several parts of a whole & recognise when two simple fractions are equivalent. 4  Use their understanding of place value to multiply & divide whole nos. by 10 or 100.  In solving nos. problems, use a range of mental methods of computation with the four operations, including mental recall of multiplication facts up to 10 × 10 & quick derivation of corresponding division facts.  Use efficient written methods of addition & subtraction & of short multiplication & division.  Add & subtract decimals to two places & order decimals to three places.  In solving problems with or without a calculator, check the reasonableness of results by reference to knowledge of the context or to the size of the nos.  Recognise approximate proportions of a whole & use simple fractions & percentages to describe these.  Recognise & describe nos. patterns, & relationships including multiple, factor & square.  Begin to use simple formulae expressed in words.  Use & interpret coordinates in the first quadrant. 5  Use understanding of place value to multiply & divide whole nos. & decimals by 10, 100 & 1000.  Order, add & subtract negative nos. in context.  Use all four operations with decimals to two places.  Reduce a fraction to its simplest form by cancelling common factors & solve simple problems involving ratio & direct proportion.  Calculate fractional or percentage parts of quantities & measurements, using a calculator where appropriate.  Understand & use an appropriate non-calculator method for solving problems that involve multiplying & dividing any three-digit nos. by any two-digit nos.  Check solutions by applying inverse operations or estimating using approximations.  Construct, express in symbolic form, & use simple formulae involving one or two operations.  Use brackets appropriately.  Use & interpret coordinates in all four quadrants. 6  Order & approximate decimals when solving numerical problems & equations, using trial-&-improvement methods.  Are aware of which nos. to consider as 100 per cent, or a whole, in problems involving comparisons, & use this to evaluate one nos. as a fraction or percentage of another.  Understand & use the equivalences between fractions, decimals & percentages, & calculate using ratios in appropriate situations.  Add & subtract fractions by writing them with a common denominator.  When exploring nos. sequences, find & describe in words the rule for the next term or nth term of a sequence where the rule is linear.  Formulate & solve linear equations with whole-nos. coefficients.  Represent mappings expressed algebraically, & use Cartesian coordinates for graphical representation interpreting general features. 7  In making estimates, round to one significant figure & multiply & divide mentally.  Understand the effects of multiplying & dividing by nos. between 0 & 1.  Solve numerical problems involving multiplication & division with nos. of any size, using a calculator efficiently & appropriately.  Understand & use proportional changes, calculating the result of any proportional change using only multiplicative methods.  Find & describe in symbols the next term or nth term of a sequence where the rule is quadratic  Multiply two expressions of the form (x + n) & simplify the corresponding quadratic expressions.  Use algebraic & graphical methods to solve simultaneous linear equations in two variables.  Solve simple inequalities. 8  Solve problems involving calculating with powers, roots & nos. expressed in standard form, checking for correct order of magnitude.  Choose to use fractions or percentages to solve problems involving repeated proportional changes or the calculation of the original quantity given the result of a proportional change.  Evaluate algebraic formulae, substituting fractions, decimals & negative nos.  Calculate one variable, given the others, in formulae.  Manipulate algebraic formulae, equations & expressions, finding common factors & multiplying two linear expressions.  Solve inequalities in two variables.  Sketch & interpret graphs of linear, quadratic, cubic & reciprocal functions, & graphs that model real situations.

Attainment Target 3: Shape, Space & Measures

3  Classify 3-D & 2-D shapes in various ways using mathematical properties such as reflective symmetry for 2-D shapes.  Use non-standard units, standard metric units of length, capacity & mass, & standard units of time, in a range of contexts 4  Make 3-D mathematical models by linking given faces or edges, draw common 2-D shapes in different orientations on grids.  Reflect simple shapes in a mirror line.  Choose & use appropriate units & instruments, interpreting, with appropriate accuracy, nos. on a range of measuring instruments.  Find perimeters of simple shapes & find areas by counting squares. 5  When constructing models & when drawing or using shapes, measure & draw angles to the nearest degree, & use language associated with angle.  Know the angle sum of a triangle & that of angles at a point.  Identify all the symmetries of 2-D shapes.  Know the rough metric equivalents of imperial units still in daily use & convert one metric unit to another.  Make sensible estimates of a range of measures in relation to everyday situations.  Understand & use the formula for the area of a rectangle. 6  Recognise & use common 2-D representations of 3-D objects.  Know & use the properties of quadrilaterals in classifying different types of quadrilateral.  Solve problems using angle & symmetry properties of polygons & angle properties of intersecting & parallel lines, & explain these properties.  Devise instructions for a computer to generate & transform shapes & paths.  Understand & use appropriate formulae for finding circumferences & areas of circles, areas of plane rectilinear figures & volumes of cuboids when solving problems.  Enlarge shapes by a positive whole-nos. scale factor. 7  Understand & apply Pythagoras' theorem when solving problems in two dimensions.  Calculate lengths, areas & volumes in plane shapes & right prisms.  Enlarge shapes by a fractional scale factor, & appreciate the similarity of the resulting shapes.  Determine the locus of an object moving according to a rule.  Appreciate the imprecision of measurement & recognise that a measurement given to the nearest whole nos. may be inaccurate by up to one half in either direction.  Understand & use compound measures, such as speed. 8  Understand & use congruence & mathematical similarity.  Use sine, cosine & tangent in right-angled triangles when solving problems in two dimensions.  Distinguish between formulae for perimeter, area & volume, by considering dimensions.

Attainment Target 4: Handling Data

3  Extract & interpret information presented in simple tables & lists.  Construct bar charts & pictograms, where the symbol represents a group of units, to communicate information gathered, & interpret information presented to them in these forms. 4  Collect discrete data & record them using a frequency table.  Understand & use the mode & range to describe sets of data.  Group data, where appropriate, in equal class intervals, represent collected data in frequency diagrams & interpret such diagrams.  Construct & interpret simple line graphs. 5  Understand & use the mean of discrete data.  Compare two simple distributions, using the range & one of the mode, median or mean.  Interpret graphs & diagrams, including pie charts, & draw conclusions.  Understand & use the probability scale from 0 to 1.  Find & justify probabilities, & approximations to these, by selecting & using methods based on equally likely outcomes & experimental evidence, as appropriate.  Understand that different outcomes may result from repeating an experiment. 6  Collect & record continuous data, choosing appropriate equal class intervals over a sensible range to create frequency tables.  Construct & interpret frequency diagrams.  Construct pie charts.  Draw conclusions from scatter diagrams, & have a basic understanding of correlation.  When dealing with a combination of two experiments, identify all the outcomes, using diagrammatic, tabular or other forms of communication.  In solving problems, use knowledge that the total probability of all the mutually exclusive outcomes of an experiment is 1. 7  Specify hypotheses & test them by designing & using appropriate methods that take account of variability or bias.  Determine the modal class & estimate the mean, median & range of sets of grouped data, selecting the statistic most appropriate to line of enquiry.  Use measures of average & range, with associated frequency polygons, as appropriate, to compare distributions & make inferences.  Draw a line of best fit on a scatter diagram, by inspection.  Understand relative frequency as an estimate of probability & use this to compare outcomes of experiments. 8  Interpret & construct cumulative frequency tables & diagrams, using the upper boundary of the class interval.  Estimate the median & interquartile range & use these to compare distributions & make inferences.  Understand how to calculate the probability of a compound event & use this in solving problems.

National Numeracy Strategy Programme of Study – Year 81

Numbers & the Number System Place value, ordering & rounding . Multiply & divide integers and decimals by 0.1, 0.01 . Order decimals . Round positive numbers to any given power of 10 and decimals to 0, 1 or 2 decimal places Integers, powers & roots . Add, subtract, multiply & divide integers . Recognise & use multiples, factors (divisors), common factor, highest common factor, lowest common multiple & primes; find the prime factor decomposition of a number (e.g. 8000 = 26  53) . Use squares, positive and negative square numbers, cubes and cube roots, and index notation for small positive integer powers Fractions, decimals, percentages, ratio & proportion . Know that a recurring decimal is a fraction; use division to convert a fraction to a decimal; order fractions by writing them with a common denominator or by converting them to decimals . Add & subtract fractions by writing them with a common denominator; calculate fractions of quantities (fraction answers); multiply & divide an integer by a fraction . Interpret percentage as the operator ‘so many hundredths of’ and express one given number as a percentage of another; use the equivalence of fractions, decimals & percentages to compare proportions; calculate percentages and find the outcome of a given percentage increase or decrease . Extend understanding of the relationship between ratio & proportion; reduce a ratio to its simplest form, including a ratio expressed in different units, recognising links with fraction notation; divide a quantity in a given ratio; use the unitary method to solve simple word problems involving ratio & direct proportion

Calculations Number operations & the relationship between them . Understand the operations of addition & subtraction of fractions and integers, and multiplication & division of integers; use the laws of arithmetic . Use the order of operations, including brackets, with more complex calculations Mental methods and rapid recall of number facts . Recall known facts, including fraction to decimals conversions; use known facts to derive unknown facts, including products such as 0.7 and 6, 0.03 and 8 . Consolidate & extend mental methods of calculation, working with decimals, fractions & percentages, squares & square roots, cubes & cubes roots . Make & justify estimates & approximations of calculations Written methods . Consolidate standard column procedures for addition & subtraction of integers & decimals with up to 2 places . Use standard column procedures for multiplication and division of integers and decimals, including by decimals such as 0.6 or 0.06; understand where to position the decimal point by considering equivalent calculations For calculations with fractions & percentages, see above Calculator methods . Carry out more difficult calculations effectively and efficiently using the function keys for sign change, powers, roots & fractions; use brackets & the memory . Enter numbers & interpret the display in different contexts (negative numbers, fractions, decimals, percentages, money, metric measures, time) Checking results . Use checking procedures, including working the problem backwards & considering whether the result is of the right order of magnitude

Algebra Equations, formulae & identities . Begin to distinguish the different roles played by letter symbols in equations, formulae & functions; know the meanings of the words formula & function . Know that algebraic operations follow the same conventions & order as arithmetic operations; use index notation for small positive integer powers . Simplify or transform linear expressions by collecting like terms; multiply a single term over a bracket . Construct linear equations with integer coefficients (unknown on either or both sides, without & with brackets); solve them by using an appropriate method, such as inverse operations or transforming both sides in same way . Set up & use linear equations to solve simple word problems involving direct proportion . Use formulae from mathematics and other subjects; substitute integers into formulae, including examples that lead to an equation to solve, and positive integers into expressions involving small powers (e.g. 3x2 + 4 or 2x3) Sequences, functions & graphs . Generate & describe integer sequences . Generate terms of a linear sequence using term-to-term & position-to-term definitions of the sequence, on paper and using a spreadsheet . Begin to use linear expressions to describe the nth term of an arithmetic sequence, justifying its form by referring to the activity or context from which it was generated . Express simple functions in symbols; represent mappings expressed algebraically . Generate points in all four quadrants and plot the graphs of linear functions, where y is given explicitly in terms of x, on paper and using ICT; recognise that equations of the form y=mx + c correspond to straight line graphs . Construct linear functions arising from real-life problems and plot their corresponding graphs; discuss and interpret graphs arising from real situations

Using & applying mathematics to solve problems . Solve problems & explore pattern & symmetry in a range of contexts (number, algebra, shape, space & measures; handling data) . Identify the necessary information to solve a problem; represent problems and solutions in algebraic, geometric or graphical form, using correct notation and appropriate diagrams . Solve more complex problems by breaking them into smaller steps or tasks, choosing and using efficient techniques for calculation, algebraic manipulation and graphical representation, and also resources, including ICT . Explain & justify inferences and reasoning, using step-by-step deduction; give solutions to an appropriate degree of accuracy in the context of the problem . Suggest extensions by asking ‘What if…?’ or ‘Why?’, conjecture & generalise; identify exceptional cases or counter-examples

Shape, space & measures Geometric reasoning; lines, angles & shapes . Use correctly the vocabulary, notation & labelling conventions for lines, angles & shapes . Identify alternate & corresponding angles; understand a proof that: - the sum of the angles of a triangle is 180º and of a quadrilateral is 360º - the exterior angle of a triangle equals the sum of the two interior opposite angles . Know that if two 2D shapes are congruent, corresponding sides & angles are equal; know & use side & angle properties of equilateral, isosceles and right-angled triangles and of special quadrilaterals; classify quadrilaterals by their geometric properties . Solve simple problems using known geometric properties; explain and justify inferences, deductions & conclusions using mathematical reasoning . Know and use geometric properties of cuboids and shapes made from cuboids; begin to use plans and elevations Transformations . Transform 2D shapes by simple combinations of rotations, reflections & transformations, on paper and using ICT; identify all the symmetries of 2D shapes and reflection symmetry in 3D shapes . Understand and use the language and notation associated with enlargement; enlarge 2D shapes, given a centre of enlargement and a positive whole-number scale factor; explore enlargement using ICT Co-ordinates . Given the co-ordinates of points A and B, find the mid-point of the line segment AB Construction . Use straight edge and compasses to construct: -the perpendicular from a point to a line – the perpendicular from a point on a line – the mid- point and perpendicular bisector of a line segment; - the bisector of an angle; construct a triangle, given three sides (SSS); use ICT to explore these constructions . Find simple loci, both by reasoning and by using ICT, to produce shapes and paths, e.g. an equilateral triangle Measures and mensuration . Use units of measurement to measure, estimate, calculate and solve problems in everyday contexts involving length, area, volume, capacity, mass and time; know rough metric equivalents of imperial measures in daily use (feet, miles, pounds, pints, gallons) . Use bearings to specify direction . Deduce and use formulae for the area of a triangle, parallelogram and trapezium; calculate perimeters and areas of plane rectilinear figures . Know and use the formula for the volume of a cuboid; calculate volumes and surface areas of cuboids and compound shapes made from cuboids

Handling Data Specifying a problem, planning & collecting data . Discuss a given problem that can be addressed by statistical methods and identify related questions to explore . Decide which data to collect to answer a question, and the degree of accuracy needed; identify possible sources; decide how to collect the data, including sample size . For sets of continuous data, construct frequency tables with given equal class intervals . Design and use two-way tables for discrete data . Collect data using a suitable method, such as observation, controlled experiment, including data logging using ICT, or questionnaire Processing & representing data, using ICT as appropriate . Calculate statistics: - for continuous data, find the range and, for grouped data, the modal class; - for discrete data, find the mode, mean, median and range . Draw and produce, on paper and using ICT: - diagrams and graphs for continuous data, including bar charts and frequency diagrams; - stem & leaf diagrams; pie charts for categorical data; - simple scattergraphs; identify which are most useful in the context of the problem Interpreting and discussing results . Interpret tables, graphs and diagrams for both discrete and continuous data and draw inferences that relate to the problem being discussed; relate summarised data to the questions being explored . Compare two distributions using the range and one or more of the measures of average . Communicate orally and on paper the results of a statistical enquiry and the methods used, using ICT as appropriate; justify the choice of what is being presented Probability . Use the vocabulary of probability when interpreting the results of an experiment; appreciate that random processes are unpredictable . Know that if the probability of an event occurring is p, then the probability of it not occurring is 1  p; find and record all possible outcomes for single events and two successive events in a systematic way, using diagrammatic and tabular forms of presentation . Estimate probabilities from experimental data; understand that: - if an experiment is repeated there may be, and usually will be, different outcomes; - increasing the sample size generally leads to better estimates of probability . Compare experimental & theoretical probabilities in different contexts

7 07/04/18 Westfield Community School - Mathematics Year 8 : Unit 1 : 83

Topic Time NC Descriptors Resources Notes Key Words 1 Graphs 1 Conversion graphs 1 H5 Interpret graphs & diagrams..& draw Find temp/currency chart in Conversion conclusions newspaper – draw conversion graph Kilometres for homework. Miles etc.

2 Graphs & rules 2 H4 Construct & interpret simple line graphs Gradient is not mentioned, but idea Formula H5 is used – introduce gradient? Gradient? N6 Represent mappings expressed Intercept? algebraically

3 Time 2 S5 Use of scientific calculator – Am/pm N7 Using a calculator efficiently & degrees, mins, secs button 24 hour clock appropriately Get some timetables – plan a trip

4 Travel graphs 1 H5 Please do not teach speed formula Travel graph S7 Understand & use compound measures, as triangle. Can use idea that Average speed such as speed everyone knows mph as a speed – formulae can be remembered by miles (distance) per () hour (time) Test Yourself 1 Pupils mark and fill in pupil assessment booklet. 2 Estimating your mental power 1 Powers & roots 2 N4 Recognise & describe nos. patterns & GC-1/GC-2 Calculator functions needed - x2, Square relationships including multiple, factor & ICT:excel  , xy, x1/y Square root square Useful investigation- choose a Power N6 Approx. decimals when solving number greater than 1 and to 4th root numerical problems & equations consider the effect of multiple 5th root N7 Solve numerical problems..using a applications of the  key. Multiple calculator efficiently & appropriately Then do the same starting with Factor a number between 0 and 1

2 Mental maths 2 N4 In solving nos. problems use a range of GC-3/GC-4 P34/36 Game Dice per 4-6 players Add mental & written methods of CAME lesson No 3 Fizz-Buzz/ Countdown etc. Subtract computation with 4 operations, including ‘Operating on Numbers’ Multiply mental recall of  facts upto 10  10 Extra Game WS 2:1 Divide Use efficient written methods of +/ -/ /

3 Estimation 2 N4 P44 Dice, 2 colours of counters (5 Round 8 07/04/18 Westfield Community School - Mathematics N5 Check solutions by..estimating using of each) per 2 players WS 2:2 not Significant approximations. required. figure N7 In making estimates, round to 1sf and Could discuss rounding problems Estimate / mentally such as 0.0999 to 1sf/ 2sf etc. Test Yourself 1 Pupils mark and fill in pupil assessment booklet. 3 Statistics: questions and answers 1 Diagrams and charts 2 H3 Construct bar charts & pictograms, ICT – EXCEL/Omnigraph X-curr: Geog/ Science Statistics where the symbol represents a group of Find pie chart etc. in media, Bar chart units..& interpret info presented in a interpret them Pictogram variety of forms NB: bars have gaps for non- Pie chart H4 Group data, where appropriate, in class numerical data! Tally chart intervals, represent collected data in frequency diagrams and interpret such diagrams H5 Interpret graphs and diagrams, including pie charts, and draw conclusions

2 Pie charts 1 H6 Construct pie charts * need to agree teaching approach! Pie chart Sector

3 Designing a questionnaire 1 H3 Construct bar charts & pictograms..to ICT – Pinpoint/database X-curr: humanities etc. Questionnaire communicate info. gathered Support materials p302-304 Bias H4 Collect discrete data & record them in a WS 3:1-3:2 Copy one as Exercise 3:10 as activity, else Hypothesis frequency table example? leave? H7 Specify hypothesis & test them by designing & using appropriate methods that take account of variability or bias Test Yourself 1 Pupils mark and fill in pupil assessment booklet. 4 Algebra 1 Number patterns 3 N4 Recognise & describe nos. patterns. ICT – EXCEL Key Maths 7 has 2 chapters of basic Formula Begin to use simple formulae expressed GC-5 algebra - use as intro/ more Term in words practise? (Sept 2000 only) Rule N5 Construct, express in symbolic form & Number use simple formulae involving 1 or 2 sequence operations N6 When exploring number sequences, find & describe in words the rule for the next term or nth term of a sequence where the rule is linear

2 Reversing rules 1 N6 Formulate & solve linear equations with ICT – LOGO/EXCEL (teacher Inverse 9 07/04/18 Westfield Community School - Mathematics whole nos. coefficients guide year 7) Formula WS 4:1 for more practise Equation

3 Substitution 1 N8 Evaluate algebraic formulae.. GC-6/GC-7 X-curr – Science Power N8 Calculate one variable, given the others, ICT – LOGO/EXCEL 4:12 As extra AT1 or leave? in formulae such as V = r²h Test Yourself 1 Pupils mark and fill in pupil assessment booklet. Mental work 10 N3 Use mental recall of +/- facts to 20 See mental starters on short term mins +/- nos. with 2 digits mentally planning for exact coverage every Use mental recall of the 2,3,4,5 & 10  tables & derive the associated  lesson facts N4 Use their understanding of place value to  &  whole nos. by 10 or 100 Use a range of mental methods of computation with the four operations, including mental recall of  facts up to 10  10 & quick derivation of corresponding division facts +/- decimals to 2 decimal places N5 Use understanding of place value to /  whole nos. & decimals by 10, 100 & 1000 Calculate fractional or percentage parts of quantities & measurements N6 Understand & use the equivalences between fractions, decimals & percentages S3 Classify 2D shapes in various ways using mathematical properties such as reflective symmetry for 2D shapes Use standard units of time S5 Use language associated with angle H4 Construct simple line graphs H5 Find & justify probabilities, by selecting & using methods based on equally likely outcomes Activities 5 Choose from above ideas or make up some of your own (but share!) AT1 task 1 3 Link to 4 Algebra? Houses Investigation Revision and unit test 3 Use ‘Questions’ section for revision

Topic Time NC Descriptors Resources Notes Key Words 5 Transformations 1 Reflections 1 S4 Reflect simple shapes in a mirror line ICT- Omnigraph P96 Need multi-link and  dotty Reflection WS 5:1-5:2 pupils can draw so paper (WS 5.1/5.2 not needed, Mirror line do not copy! pupils can draw for themselves) Islamic patterns X-curr: Art/RE

2 Movement - translations 1 S4 ICT- Omnigraph P99/100 Game Board/2 dice/2 Translation . counters per 2 players

3 Rotation 1 S4 .Identify orders of rotational symmetry ICT- Omnigraph Good displays for all of these Rotation Centre of rotation Rotational symmetry

4 Enlargement 2 S4 Enlarge shapes by a positive whole nos. ICT-Omnigraph Enlargement scale factor Support material p305 Test Yourself 1 Pupils mark and fill in pupil assessment booklet. 6 Don’t be negative! 1 Replay 1 N3 Recognise neg. nos. in context such as P118 Need calculator key +/- Positive ..temp & calculator display Negative N4 Explore & describe nos. patterns N5 Order, add & subtract neg. nos. in context

2 The rules for directed nos. 2 N5 Negative number snap Walking on a number line

3 Using negative numbers 2 N8 Evaluate algebraic formulae GC-8 In extension section: P131 substituting…neg. nos. Dice/coin per 4-6 players, use for early finishers? Test Yourself 1 Pupils mark and fill in pupil assessment booklet. 7 Angles 1 Replay 2 S5 Measure & draw angles to the nearest More key words: Right angle degree & use language associated with Angles at a point, angles on a Acute, Obtuse angles straight line, opposite angles, angles Reflex in a triangle, scalene, isosceles, 11 07/04/18 Westfield Community School - Mathematics equilateral

2 Parallel lines 1 S6 Solve problems using angle.. properties Parallel Alternative of intersecting & parallel lines.. & Intercept Corresponding explain these properties P149 Use investigation as Interior homework?

3 Polygons 2 S6 WS 7:17:2 for tessellations?, Regular polygon, interior & Pentagon but perhaps use tiles in shapes exterior angles, tessellation Hexagon of regular polygons Octagon

4 Bearings 2 S6 Compass Bearing Test Yourself 1 Pupils mark and fill in pupil assessment booklet. 8 Probability 1 Replay 1 H4 Understand & use simple vocab. Key Maths 7 has a chapter of P163 33 counters in 3 colours/ box Probability Associated with prob., including fair, probability - use as intro/ more per 4/5 players certain & likely practise? (Sept 2000 only) Loads of games ‘n’ stuff. RD has H5 Understand & use prob. Scale from 0 to information on a ‘circus’ of 1. Find prob. using equally likely experiments outcomes. Understand that different outcomes may result from repeating an experiment

2 It always adds up to 1 1 H5 H6 In solving problems, use knowledge that the total prob. of all the mutually exclusive outcomes of an experiment is 1

3 Probability: how to make it look 1 H5 P173 2 Dice per 2 players Prob. of difficult something not happening

b 4 Sample space diagrams 2 H6 When dealing with combinations of 2 Calculator keys a /c Sample space experiments, identify all the outcomes, Sample space using diagrammatic or other forms diagram Test Yourself 1 Pupils mark and fill in pupil assessment booklet. Mental work N3 +/- nos. with 2 digits mentally Use mental recall of the 2,3,4,5 & 10  tables & derive the associated  facts Use simple fractions that are several parts of a whole & recognise when 12 07/04/18 Westfield Community School - Mathematics two simple fractions are equivalent N4 Use a range of mental methods of computation with the four operations, including mental recall of  facts up to 10  10 & quick derivation of corresponding division facts Recognise & describe nos. patterns, & relationships including multiple, factor & square N5 Use understanding of place value to /  whole nos. & decimals by 10, 100 & 1000 Order, add & subtract negative numbers in context N6 Understand & use the equivalences between fractions, decimals & percentages S4 Find perimeters of simple shapes & find areas by counting squares S5 Understand & use the formula for the area of a rectangle S6 Know and use the properties of quadrilaterals in classifying different types of quadrilateral H4 Understand & use the mode & range to describe sets of data H5 Understand & use the mean of discrete data Activities 4 Choose from above ideas or make up some of your own (but share!) AT1 task 2 3 Area & Borders Revision and unit test 3 Use ‘Questions’ as revision

Topic Time NC Descriptors Resources Notes Key Words 9 Percentages and fractions 1 Simple percentages 2 N5 Calculate percentage parts of quantities Percentage bingo Percentage & measurements

2 Calculating percentages 2 N5 Calculate percentage parts of quantities ICT-EXCEL P189/190 Board/ 50 counters in 2 Percentage & measurements, using a calculator Support material p310-311 colours per 2 players where appropriate (Maybe on board girls Vs boys N6 Understand & use the equivalences lesson finisher?) between fractions, decimals & percentages N7 Understands effects of  by a nos. between 0 & 1

b 3 Fractions 2 N5 WS 9:1 pupils can use square Calculator key a /c N6 paper so do not copy? P194 Cuisenaire Rods (RD has set) N7 Fractions, % ratio crossword

Test Yourself 1 Pupils mark and fill in pupil assessment booklet. 10 Straight lines 1 Lines of the grid 1 N4 Use & interpret co-ordinates in the first GC-9 Lines of the quadrant grid N5 Express in symbolic form & use simple Co-ordinates formulae involving one.. operation Point of N6 Represent mappings expressed intersection algebraically interpreting features & using graphs in 4 quadrants

2 Patterns of lines 3 N5 Construct, express in symbolic form & ICT- Omnigraphs/EXCEL y= mx + C is not specifically Equation of a use simple formulae, involving 1 or 2 GC-10 mentioned- introduce anyway? line operations P205/208 Counters needed N6 N8 Sketch & interpret graphs of linear.. functions

3 Finding the equation 2 N5 ICT- Omnigraph Use ‘Can’t see the wood for the N6 trees’ for faster pupils only? N8 14 07/04/18 Westfield Community School - Mathematics Test Yourself 1 Pupils mark and fill in pupil assessment booklet. 11 Ratio Milli, kilo, 1 The metric system 2 S5 Know the rough metric equivalents of X-Curr: Science metre,etc. imperial units still in daily use & convert inch, yard, one metric unit to another ounce etc.

2 Introduction to ratio 1 N6 Calculate using ratios in appropriate Giants – class activity P235 Multi-link needed Ratio situations S6 Enlarge shapes by a positive whole number scale factor

3 Proportion 2 N6 Calculate using ratios in appropriate X-Curr: Food Proportion situations N7 Understand & use proportional change

4 Maps and scales 2 S6 X-Curr: Geog/DT Scale P241 String needed Test Yourself 1 Pupils mark and fill in pupil assessment booklet. 12Area: Covering The Ground 1 Perimeter and area (replay) 2 S4 Find perimeters of simple shapes, find Homework – design a poster for Perimeter areas by counting squares formulae – put up on bedroom wall Area S6 Understand & use appropriate formulae and learn? Cm2, m2 etc. for finding areas of plane rectilinear Practical approach to finding figures..when solving problems formula for a triangle/parallelogram

2 More ideas 2 S6 WS 12:1 as an activity? Use 12:8 as homework or for faster workers? 3 Enlargement and area 2 S6 Enlarge shapes by a positive whole Scale factor number scale factor Test Yourself 1 Pupils mark and fill in pupil assessment booklet. Mental work N3 Begin to use decimal notation & recognise negative numbers in context such as money & temp. Solve whole number problems involving /, including those that give rise to remainders Use simple fractions that are several parts of a whole & recognise when two simple fractions are equivalent N4 Add & subtract decimals to two places & order to three decimal places Recognise approximate proportions of a whole & use simple fractions & percentages to describe these N5 Order, add & subtract negative numbers in context Reduce a fraction to its simplest form by cancelling common factors & 15 07/04/18 Westfield Community School - Mathematics solve simple problems involving ratio & direct proportion N6 Are aware of which number to consider as 100 per cent, or a whole, in problems involving comparisons, & use this to evaluate one number as a fraction or percentage of another Understand & use the equivalences between fractions, decimals & percentages S3 Use non-standard units, standard metric units of length, capacity & mass S5 Know the sum of a triangle & that of angles at a point Know the rough metric equivalents of imperial units still in daily use & convert one metric unit to another S6 Solve problems using angle & symmetry properties of polygons & angle properties of intersecting & parallel lines H4 Interpret simple line graphs H5 Interpret graphs & diagrams, including pie charts, & draw conclusions Draw conclusions from scattergraphs & have a basic understanding of correlation Activities 4 Choose from above ideas or make up some of your own (but share!) Revision and unit test 3 Use ‘Questions’ as revision

Topic Time NC Descriptors Resources Notes Key Words 13 Statistics: getting it together 1 Averages and range 2 H4 Understand & use mode & median Key Maths 7 has a chapter of Mean H5 Understand & use the mean of discrete averages & range - more Median data. Compare 2 simple distributions practice? (Sept 2000 only) Mode using the range & one of the averages GC-12 Range

2 Grouping data 2 H4 Collect discrete data & record them ICT Perhaps a library activity here? Grouping using a frequency table. Group data, GC-13/GC-14 Questions repetitive – miss some Discrete data where appropriate, in equal class Leave out exercises 13:5 & out? Continuous intervals, represent collected data in 13:6 (with WS 13:1 & 13:2) data frequency diagrams & interpret such and do CAME lesson no.5 Tally H6 diagrams ‘Length of Words’ instead? Sentence Collect & record continuous data, length choosing appropriate equal class intervals over a sensible range to create frequency tables H7 Estimate the mean..of sets of grouped data

3 Frequency polygons 3 H6 Construct & interpret frequency Questions repetitive – miss some Frequency diagrams out? polygon Test Yourself 1 Pupils mark and fill in pupil assessment booklet 14 Volume: filling the space 1 Pack it in! 1 S4 Find volumes by counting cubes Pupils poor at capacity – visual aids Volume would help Capacity Litres Cubic cm

2 Stacking 2 S4 Find volumes by counting cubes WS 14:1 not required Volume S6 Recognise & use common 2D Stack representations of 3D objects

3 Prisms 2 S6 Understand & use appropriate formulae GC-15 Volume for finding…..volumes of cuboids when ICT-EXCEL P311 Scissors and  dotty paper Prism solving problems Support material p312-313 Cross section S7 Calculate..volumes in ..right prisms Test Yourself 1 Pupils mark and fill in pupil assessment booklet. 17 07/04/18 Westfield Community School - Mathematics 15 More or less? 1 Trial & Improvement 2 N6 Solving numerical problems & equations ICT from year 7 file Trial & such as x2 = 20, using trial & GC-16 improvement improvement methods Inequality 2 Inequalities 2 N7 Solve simple inequalities Inequality 3 Solving simple linear N7 Solve simple inequalities ICT from year 7 file Inverse equations 1 Algebraic snakes & ladders 16 The crossing point 1 Intersecting lines 1 N6 Represent mappings expressed Points of algebraically intersection

2 Solving problems with 2 N7 Use ..graphical methods to solve ICT: EXCEL/Omnigraph lines simultaneous equations in two variables

3 Using algebra 2 N7 Use algebraic & graphical methods to 16:5 works orally and as Simultaneous solve simultaneous equations in 2 demonstration purposes equations variables Test Yourself 1 Pupils mark and fill in pupil assessment booklet. Mental work N3 Begin to use decimal notation & recognise negative numbers in context such aas money & temp. Solve whole number problems involving /, including those that give rise to remainders N4 Add & subtract decimals to two places & order to three decimal places N5 Order, add & subtract negative numbers in context Reduce a fraction to its simplest form by cancelling common factors & solve simple problems involving ratio & direct proportion N6 Are aware of which number to consider as 100 per cent, or a whole, in problems involving comparisons, & use this to evaluate one number as a fraction or percentage of another Understand & use the equivalences between fractions, decimals & percentages Add & subtract fractions with a common denominator S3 Use non-standard units, standard metric units of length, capacity & mass S4 Find perimeters of simple shapes & find areas S5 Make sensible estimates of a range of measures in relation to everyday situations Understand & use the formula for the area of a rectangle S6 Solve problems using angle & symmetry properties of polygons & angle properties of intersecting & parallel lines 18 07/04/18 Westfield Community School - Mathematics H5 Understand & use the probability scale from 0 to 1 Find & justify probabilities, & approximations to these, by selecting & using methods based on equally likely outcomes & experimental evidence, as appropriate H6 When dealing with a combination of 2 experiments, identify all the outcomes, using diagrammatic, tabular or other forms of communication AT1 3 Rows of Cubes Activities 5 Choose from above ideas or make up some of your own (but share!) Revision and unit test 3 Use ‘Questions’ as revision

19 07/04/18 Westfield Community School - Mathematics 83: Unit 1: Chapter 1: Graphs Lesson 1 Lesson 2 Lesson 3 Lesson 4 l

a Using the number cards: *Using some card 2D shapes, hide behind Pupils stand up with arms out wide.

t Using /  only: if the answer was 24,

n tables and slowly show to pupils. As they Teacher calls out a graphs and they have to e what could the question have been? /  questions up to 10  10

M +/- decimals see more of the shape, ask them to identify make the shape of it with their arms. 64? 120? 4.8? +/- two digit numbers it and explain why they think that. y = 5, y = x, x = 3, y = x + 3 etc.

Push for correct use of vocabulary: regular, polygon, quadrilateral etc.

S . Interpret graphs, and draw inferences . Interpret graphs & tables, and draw . Substitute integers into simple formulae . Calculate and solve problems in N that relate to the problem being inferences that relate to the problem . Interpret graphs & tables, and draw everyday contexts, involving time N discussed being discussed inferences that relate to the problem being . Know the meaning of the words discussed formula . Construct linear functions arising from . Generate points and plot the graphs real life problems, and plot their corresponding graphs; discuss & interpret of linear functions graphs arising from real life situations .

e Introduce idea of conversion graph. Show how to draw graphs from tables. Recap writing of formulae from words and Explain 12 hour (am & pm) and 24 hour m

e Show how to read in both directions. Encourage good size graphs, use of graph drawing of graphs. clock. h t

Discuss uses and units such as miles. paper, sensible axes and labelling of Go through substituting numbers into Discuss ways of working out time n i graphs. formulae. problems (strategies and ways of writing a

M Do p2-4 exercises 1:1 & 1:2. Show how rules can be written in algebra. Introduce idea of gradient and intercept workings) NB: both exercises could be done orally (y = mx + c) as appropriate Do p5-7 exercises 1:3 & 1:4 Do p11-14 exercises 1:6 & 1:7 Extension: p24 Q1 NB: Exercise1:3 lots of similar questions- Do p9-10 exercise 1:5 Reinforce drawing and labelling of axis choose some. Exercise1:4 could be done Extension: orally Extension:

Extension: do remaining questions from exercise 1:3

k Find temperature/currency chart in media- Finish any outstanding questions from w draw a conversion graph and label. exercises 1:3 – 1:5 H And/or learn key words – spelling and definitions y

r *On prepared axis, have a conversion Orally around the room: 2  a is ? 3m is? *Question similar to exercise 1:5. Pupils *Clock- what’s the time? What other ways a

n graph drawn. For more able, use ab and 3ab. take it in turns to fill in table and plot could we say that? e l Ask questions, pupils point out answers or Describe everyday ‘billing’, ask for points etc. (Use question bank for P give answers, what was the question! formulae. What would it look like on a questions?) graph? E.g telephone billing

Lesson 5 Lesson 6 Lesson 7 l

a 18 20 11 Checklist for chapter 1:

t Starting with the question: 8  10 = 80

n Use a conversion graph to change units e What other questions can you work out

M 15 2 3 e.g 4  20 = 80, 2  40 = 80, 16  5 = 80, Read values from a graph 80  1 = 80, 800  0.1 = 80 etc. Draw a graph from a rule & formula 12 10 4 Reverses too: 80  10 = 8 etc. Write a formula in algebra Write times using am/pm & 24 hr clock Target = 33 Use a calculator for time calculations Read information from a travel graph

S . Calculate and solve problems in . Interpret graphs & tables, and draw Draw a travel graph N everyday contexts, involving time inferences that relate to the problem Calculate average speed N . Enter numbers & interpret the display being discussed in different contexts (time) . Discuss & interpret graphs arising from real life situations . e Show pupils how to use calculator keyº   Introduce travel graphs. Include idea of Do p26 ‘Test Yourself’ section. m

e Explain how to convert hours to minutes gradient and what it represents. h t and visa versa, without button too! Discuss average speed formula and ways Mark and correct answers. n i to remember it.

a Go through reading timetables/ two way

M tables. Include reading scales briefly. Fill in pupil assessment booklet.

Do p14-16 exercises 1:8 & 1:9 Do p17-18 exercise 1:10 NB: could do 1:9 orally Extension: p24 Q2,3, 4 Extension:

Key Words: k Using a variety of timetables, plan a day Do exercise 1:11 and complete any w trip. Include a timed schedule, with details unfinished questions from 1:10 conversion H of trains, buses etc. kilometres Include length of time spent at different miles etc attractions. formula gradient intercept am/pm 24 hour clock travel graph 21 07/04/18 average speed Westfield Community School - Mathematics y

r *Enlarged timetable on board- ask Information learnt today: etc. Test pupils on key words – spellings and

a Speed = d/t n questions about it. Especially time Travel graphs definitions. e l calculations, like train journey length. *Use match cards for an introduction/ P discussion etc. Time on x axis Gradient = speed

22 07/04/18 Westfield Community School - Mathematics 83: Unit 1: Chapter 2: Estimating your mental power Lesson 1 Lesson 2 Activity 1 Lesson 3 l

a Trick for multiplying some numbers Hold up a bag of counters, say if the Counting up in squares, cubes, triangular, Using the number cards: t

n 2 probability of picking out a red counter is prime numbers etc. either as class, or Halving & doubling numbers, include e 25 = 1225 (2  3=12 then 5  5=25) 2 M 37  33 = 1221(3  4= 12 then 7  3 = 21) what can you tell me about the bags around room. whole numbers & decimals 5 Encourage correct vocabulary, use factor/ Could also do halfway betweens e.g. 3 & Does this work for all numbers? contents? Percentage of red counters =40% multiple where appropriate too. 4, 0.3 and 0.4, 0.03 & 0.04 etc. Ratio other colours: red = 3:2 etc.

S . Use squares, positive & negative . Use cubes, cube roots & index . Carry out more difficult calculations . Add & subtract integers N squares roots. notation for small positive integer effectively & efficiently, using the . Use checking procedures, including N . Carry out calculations using the powers function keys for powers, roots working the problem backwards function keys for powers & roots . Carry out calculations using functions . Round decimals to 0, 1 & 2 decimal . Understand the operations of + &  of . Mental methods for squares & square keys for powers & roots places integers roots . Round decimals to 0,1 & 2 decimal . Round decimals to 0,1 & 2 decimal places places . Recognise & use multiples, factors . e Introduce squares numbers. Introduce powers and different powered *Graphical calculators, using GC-1  Experiment with strategies for ‘quick’ m

e Discuss relationship between squaring and roots. Explain relationship. GC-4 addition and subtraction. Discuss h

t y 1/y square rooting. Include 4 = 2 or 2, Show x and x buttons on calculators. relationship between addition & n i multiples & factors. subtraction. a 2

M Show x and  buttons on calculators. Do p31-33 exercises 2:3 & 2:4 (Q1 & 2) Do p34-36 exercises 2:5 &2:6 Do p28-30 exercises 2:1& 2:2 Extension: p33 exercise 2:4 Q4 onwards & *Play games p34 &38 (dice required) NB: Lots of repetition, select questions. p47 Q3 Parts of exercise 2:1 & 2:2 can be done *Extension: use 8/10 sided dice for game orally

Extension: P47 Q1 & 2

k Choose a number greater than 1. See what happens Complete any unfinished work from w when you keep square rooting it. exercises 2:1-2:6 H Now pick a number between 0 and 1- keep square rooting it. What happens? Can you predict what will And/ or learn key words- spellings and happen with other numbers? Is it always true? definitions, and what others can you find that have the same meaning? Help yourself section 1 exercises 1 & 2 y

r *Round Robin cards- two colours to Put 16 on the board. Here’s an answer, *Hold up 2 bags of numbers, pupil picks a a

n identify harder & simpler questions what could the question have been, using number from each bag, then +/-. Discuss e l powers & roots only? E.g. 42, 24, 256 strategies used for each set of numbers. P Use other numbers such as 9, 64, 100 etc.

23 07/04/18 Westfield Community School - Mathematics Lesson 4 Lesson 5 Lesson 6 Lesson 7 l

a Multiplying by 10, 100 & 1000 *Hold up various 2D shapes. Discuss *Split pupils into small groups. Two Checklist for chapter 2: t

n with whole numbers & the properties of each shape e.g. line/ dice & operation dice. Target is 200? 2 y 1/y e Can use x , , x &x keys.

M decimals. Include recap on place rotational symmetry, parallel sides, Which group can break the target Can round numbers using value and use proper vocabulary acute/ obtuse angles etc. first? decimal places. for million, ten thousand, etc. Include spellings of shape names. Can round nos using significant figures.

S . Multiply & divide integers . Round positive numbers to any . Consolidate & extend mental Can add simple nos. in your N . Use checking procedures, given power of 10 & decimals to 0, methods of calculation, working head. N including working the 1 & 2 decimal places with square roots Can subtract simple nos. in your problem backwards . Use checking procedures including . Make & justify estimates and head. . Understand the operations considering whether the result is of approximations of calculations Can multiply in your head. of  &  of integers the right magnitude Can divide in your head. . Make & justify estimates and Can estimate answers to check approximations of calculations my calculator answers.

e Experiment with strategies for Recap rounding numbers to any Quick recap of significant figures and Do p50 ‘Test Yourself’ section. m

e multiplication and division. number of decimal places. how to use them for estimating. h t

Discuss how their relationship Introduce significant figures and how Mark and correct answers. n i can help to solve problems. these can be used for estimating. *Do p43-44 exercises 2:11 & 2:12 a

M Play game p44 (counters & dice Fill in pupil assessment booklet. Do p36-39 exercises 2:7 & 2:8 Do p40-42 exercises 2:9 & 2:10 required) NB: lots of this can be done NB: Could do some/most of this orally Key Words: orally square Extension: p48 Q5 & 6 Extension: p38 ‘month’s choice’ square root & power P48 Q4 4th root 5th root multiple k Help yourself sections 2 & 3 exercises Complete any unfinished

w factor 3 & 4 exercises from 2:7 to 2:12 H add subtract multiply y

r Answers like 24 000. What Put up some questions on the board. *Starting number and rounding Test pupils on key words –

a divide

n could the multiplication and Pupils have to estimate the answers, required is put on the board. Pupils spellings and definitions. e

l round division questions have been to discussing the methods used. Who gets have to take it in turns to fill in the Include other words for + /- / / P get that answer? the closest? answers.  such as product, quotient, sum significant figure etc. estimate

83: Unit 1: Chapter 3: Statistics: questions & answers Lesson 1 Lesson 2 Lesson 3 Lesson 4 l

a Using the number cards: work on Pupils using their hands as lines, estimate Countdown (with a difference) t 100% = 240 n equivalent fractions, decimals & 100 6 5 9 2 3 target 518 e the size of angles. Call out 45/ acute/

M percentages, such as what is 25% as a obtuse and they make that size using their Find as many different ways of making the What else can you say? 50% = 120, decimal? etc. hands. target as you can. ½ = 120 etc. Use other starters such as 25% = 12…

S . Draw diagrams, including bar . Draw diagrams, including bar . Draw pie charts from categorical . Decide which data to collect to N charts charts and frequency diagrams data answer a question, decide how to N . Justify the choice of what is presented . Construct frequency tables with given collect the data, including the sample . Identify which charts are most equal class intervals size useful in the context of the problem . Collect data using a suitable method, . Interpret tables, graphs & diagrams including questionnaires for discrete data

e Discuss bar charts and pictograms - what Recap of tallying and scales/ labelling for Use p58 exercise 3:5 Q1 to explain method Discussion on questionnaires- what are m

e are the advantages/ disadvantages of each bar charts. Reminder that bars have gaps for drawing pie charts. Include ‘quick’ considered good or bad questions/ the h t

type of chart? for non-numerical data. methods e.g. when total = 90, 1 = 4º different styles of questions? n i Emphasise the importance of scales, keys, a

M labelling and titles. Do p54-55 exercises 3:3 & 3:4 Do p58-59 exercise 3:5 (Q2-6) Do p60-62 exercises 3:6  3:8 NB: could do questions orally/discussion Do p52-54 exercises 3:1& 3:2 Extension: Extension: p66 Q1 & 2 Pick a hypothesis, and design a Extension: questionnaire

k Complete unfinished questions from Complete your design for a questionnaire w exercises 3:1 to 3:4 and ask at least 20 people to participate in H And/ or learn key words- spellings and it. definitions Use p63 exercise 3:10 for help on what to do

25 07/04/18 Westfield Community School - Mathematics y

r *On an OHP, have examples of graphs & Go through points to remember when *Having some unlabelled pie charts and Share questionnaires and discuss ways of a

n charts from media. Discuss the advantages drawing graph. Information comes from the initial information. Get the pupils to improving them. e l & disadvantages of each, how could they pupils. decide which sector is representing which P improve the presentation? What do the piece of information. scales represent/ what is the graph telling us…etc.

Activity 2 Activity 3 Lesson 5 l

a Counting on… *Questions on time. Checklist for chapter 3: t

n e.g. start at 3, + 0.2 Include am/pm for 12 hour clock, 24 hour Draw and answer questions on bar charts e

M start at 4.7, + 0.2 clock, time calculations & timetables. Draw & answer questions on pictograms start at 10, +¾ Draw & answer questions on pie charts start at 12, 4 etc. Make a tally chart Draw a bar chart for grouped data Write a questionnaire which does not break

S . Draw & produce, on paper & using . Identify which charts are most the rules, to test a hypothesis N ICT: diagrams, including bar charts useful in the context of the problem Can draw diagrams & explain results of N and frequency diagrams; pie charts . Interpret graphs & diagrams and draw survey inferences that relate to the problem being discussed

e Using questionnaire responses from Continue with write-up: write about your Do p68 ‘Test Yourself’ section. m

e survey; write up results. charts and explain whether or not your h t

Include: tally chart, bar chart & pie hypothesis was right. Mark and correct answers. n i chart. a

M Could use ICT: Word for write-up and Fill in pupil assessment booklet. paste in charts for EXCEL Could use ICT: EXCEL for charts Or use pinpoint for whole exercise!

Key Words: k Complete write up, include ways you w could have improved your survey, charts statistics H & therefore your conclusions. bar chart Hand your survey in named, stapled and pictogram with the pages numbered! pie chart tally chart sector 26 07/04/18 questionnaire bias hypothesis Westfield Community School - Mathematics y

r Pull together- what they should done? How far should they have got? Test pupils on key words – spellings and a

n What the important points are? definitions. e l What they need to do next session P Homework? Final product should look like….

83: Unit 1: Chapter 4: Algebra Lesson 1 Lesson 2 Lesson 3 Activity 4 l

a Quick mental methods for 50%, 25%, ½ , 17 3 10 *Oral probability questions. Hold up cards Quick oral recap of: if a pattern goes up in t

n ¼ etc. with diagrams on and ask related e fours, the first part of the rule is to  4, 2 14 1

M Write starting number on the board, probability questions to pupils (could use then adjust by +/  as appropriate discuss answers and how they were found 13 5 8 number cards for answers). (could use numbers cards) Target = 39

S . Generate & describe integer . Generate terms of a linear sequence . Generate terms of a linear sequence . Begin to use linear expressions to N sequences using term to term and position to term using term to term and position to term describe the nth term of an arithmetic N . Generate terms of a linear sequence definitions of the sequence definitions of the sequence sequence using term to term definitions of the . Begin to use linear expressions to . Begin to use linear expressions to sequence on paper describe the nth term of an arithmetic describe the nth term of an arithmetic sequence, justifying its form by sequence referring to the activity or context from which it was generated

e Introduce idea of patterns (term to term Show how numbers can be substituted into Recap proper vocabulary: number *ICT: Excel – patterns and their rules m

e rules). Explain difference of term to term formulae, to find answers without drawing sequences, term, term to term, nth term h t

rules and nth term rules. Show how patterns. Remember 3a means 3  a. rule (formulae/position to term) n i patterns can help find nth term rules. Try to get pupils to explain rules in a

M Discuss how rules can be written in relation to diagrams. Do p76/77 exercise 4:5 algebra. Do p73-76 exercise 4:3 & 4:4 Extension: p88 Q 4 & 5 Do p70-71 exercise 4:1 Extension: p88 Q1 & 3 Extension: for Q1-3, can you write the nth term rules in algebra

k Do p 72-73 exercise 4:2 Complete any unfinished questions from w exercises 4:1 – 4:5 H And/ or learn key words- spellings and definitions y

r *Have some ready drawn patterns, decide *Several formulas on the board and a pupil *Same as lesson before, but make the Draw together ideas very briefly. Quick a

n what the pattern would be by looking at throws the dice, chooses which formula to formulas slightly harder and include questions around the class- who got the e l diagram only! Then working out the rule. put it into and in the 5 minutes the class squaring. furthest on the programme? P Go through nth rule at end as it is in the must try to reach the target of e.g 200. homework!

Lesson 4 Activity 5 Lesson 5 Lesson 6 l

a Using the number cards, Using the number cards, questions Checklist for chapter 4: t

n questions on multiplication on halfway between: Find patterns and term to term e

M facts up to 10  10, +/  of 0.2 & 0.3, 0.05 & 0.06, 1000 & rules two digit numbers and 2000 etc. Find nth term rules, in algebra decimals Use rules to find further pattern

S . Linear equations with . Find simple loci, both by . Substitute integers into numbers N integer coefficients reasoning and by using ICT, to simple formulae, including Solve equations by reversing N (unknown on either or produce shapes and paths, e.g. an examples that lead to an rules both sides); solve them by equilateral triangle equation to solve, and positive Substitute numbers into using an appropriate . Solve simple problems using integers into expressions formulae method, such as inverse known geometric properties involving small powers (e.g. Can use powers appropriately operations 3x2 or 2x3) and can substitute numbers into powers e Discuss ‘reversing’ is ICT- LOGO Go through substituting numbers Do p90 ‘Test Yourself’ m

e ‘undoing’. Go through inverse Use ideas from ICT section of year 7 into formulae. Recap 3a is 3  a, ab h

t 2 functions for +/ -/ / . teacher’s guide is a  b, 4y is y  y then  4, Mark and correct n i For multiple functions, 2 a whereas (4y) is 4  y then square

M explain backwards and Draw a triangle, square, pentagon- answer. Fill in pupil assessment booklet reverse. regular polygons. Do p81-83 exercises 4:9 & 4:10 Do p78-80 exercises 4:6 – 4:8 Extension: tessellate shapes NB: some of the easier questions NB: can do 4:6 & some of 4:7 can be done orally orally Extension: p85 exercise 4:12 Extension: p88 Q2 ‘Traffic light squares’

k *Do WS 4:1 P 83-85 complete 4:10 and do w exercise 4:11 H Key Words: formula term rule y

r *I thin k of a number ….. my Draw ideas together by showing off *Several formulas on the board and Test pupils on key words – number sequence a

n answer is …, what was the the best work and discussing how a pupil throws the dice, chooses spellings and definitions.

e equation l number I started with? they did it. which formula to put it into and in P the 5 minutes the class must try to power reach the target of e.g 200. term to term Formulas need to be of the sytle of position to term exercise 4:9/4:10 etc. nth term

83: Unit 1: AT1, revision and test Lesson 1 Lesson 2 Lesson 3 Lesson 4 l

a *Find a way. (see additional sheet) *Have some ready prepared sequences on *Unlucky Sum (see additional sheet) Using the number cards, work on t

n a sheet, what are the term to term rules and complements of 10/ 20/ 50/ 100 e

M the position to term rules.

S . Reviewing – see earlier sections . Solve problems & explore number . Solve more complex problems by . Suggest extensions by asking ‘What N patterns breaking into smaller steps or tasks if?’ or ‘Why?’ N . Identify the necessary information to solve a problem; represent problems and solutions in algebraic form

e Review main points from chapters 1 to 4. Introduce ‘Houses’ investigation. Explain about making problem more Explain about pulling ideas together to get m

e Explain criteria (in pupil assessment difficult. So the same again, but this time overall rule. h t

Do P22 &23 Questions section in chapter booklet) with two storeys. Start three storeys. Predict the rule for 4 storeys. n i 1 Use exemplar for personal guidance only. Test to check. a

M Diagrams Rule for any number for storeys. Table of results Patterns and predictions Rules Explanation of rules, relating to diagrams Graphs

k P45 & 46 Questions section from chapter Complete one storey buildings, using list Complete investigation. w 2. above. Number pages, staple neatly and name H before handing in! y

r Divide the board into 4 sections, pupils Pull together, by explaining what pupils Pull together.. what are you looking for.. Explain to pupils what is expected for a a

n write up what they can remember of each should have done and how far they should what should you have noticed?.. finished piece of work. e l of the four chapters. Discuss what is have got. What else is required for This is finished when you have done….. P written and what the main points are. homework.

Lesson 5 Lesson 6 l

a Test knowledge of pupils around the room t

n by asking questions related to chapters 1 to e

S . Reviewing – see earlier sections Testing of: N . Substitute integers into simple formulae N . Interpret graphs, and draw inferences that relate to the problem being discussed . Calculate and solve problems in everyday contexts, involving time . Round decimals to 0,1 & 2 decimal places . Begin to use linear expressions to describe the nth term of an arithmetic sequence . Carry out calculations using the function keys for powers & roots . Draw pie charts from categorical data . Linear equations with integer coefficients (unknown on either or both sides); solve them by using an appropriate method, such as inverse operations . Substitute integers into simple formulae

30 07/04/18 Westfield Community School - Mathematics e Recap main points for chapters 1 to 4. Test 83: Unit 1 m e h t

Do p64 & 65 Questions section from Non-calculator section first. n i chapter 3 a

M Remove non-calculator test paper once complete, pupil may get out calculator.

Give out test paper for calculator section.

k P86 & 87 Questions section from chapter 4 w H y

r Take questions from pupils regarding a

n chapters 1 to 4 e l Deal with any remaining issues P

31 07/04/18 Westfield Community School - Mathematics Houses Investigation Question:

People that can live in house: 1 2 3 Number of rooms in the house: 2 4 … Number of beams that make the house: 6 11 …

Investigate!

Diagrams:

Table of results:

Number of people (P) Number of Rooms (R) Number of Beams (B) 1 2 6 2 4 11 3 6 16 4 8 21 5 10 26

Predictions: P = 6 R = 12 B = 31 P = 7 R = 14 B = 36

 I have predicted that for 6 and 7 people, there will be 12 and 14 rooms, as the number of rooms increases by 2 each time.  I have predicted that for 6 and 7 people, there will be 31 and 36 beams, as the number of beams increases by 5 each time.

Testing Predictions:

People: 6 7 Rooms: 12 14 Beams: 31 36 

 My predictions were correct!

Rules:

 Number of people times by 2 equals number of rooms

P  2 R so 2P = R

 Number of people times by 5, then add 1 equals number of beams

P  5 + 1 so 5P + 1 = B

Reversing the rules: R P  2 R so  P 2

P  1 ÷ 5 B 1 so  P 5

Testing the rules:  If P=3 B should equal 6 and R equals 16 So 2P = R 2  3 = 6  And 5P + 1 = B (5  3) + 1 = 16 

 If R = 10 and B = 26, then P should equal 5 R 10 So  P  5  2 2 B 1 26 1 And  P  5  5 5

Graphs:

Houses Investigation Houses Investigation

12 30 s s m m a o 10 25 o e R B

f 8 f 20 o o

r r e e

6 b 15 b m m u 4 u 10 N N 2 5

0 0 1 2 3 4 5 6 7 1 2 3 4 5 6 7 Num ber of People Num ber of People

 The first graph shows that the number of rooms goes up in 2s.  The second graph shows that the number of beams goes up in 5s.

Explaining my Rules:

 Each house is made of two rooms, since each person lives in one house, each person has two rooms. This explains why you multiply the number of people by two to get the total number of rooms.  Each house is made up of 5 beams. But then you need to add one beam to finish the first house off.

Each house represents one person, so you need to multiply the number of people by 5 and then add.

I am now going to extend my investigation by looking at houses that have another storey.

Diagrams:

Table of results:

Number of people (P) Number of Rooms (R) Number of Beams (B) 1 3 9 2 6 16 3 9 23 4 12 30 5 15 37

Predictions: P = 6 R = 18 B = 44 P = 7 R = 21 B = 51

 I have predicted that for 6 and 7 people, there will be 18 and 21 rooms, as the number of rooms increases by 3 each time.  I have predicted that for 6 and 7 people, there will be 44 and 51 beams, as the number of beams increases by 7 each time.

Testing Predictions:

People: 6 7 Rooms: 18 21 Beams: 44 51 

 My predictions were correct!

Rules and Testing:

 3P = R For P = 6, R = 18 3  6 = 18   7P + 2 = B For P = 6, B = 44 (7  6) + 2 =44 

Graphs:

Tw o Storey Houses Tw o Storey Houses

20 50 s s

m m 40 o a

o 15 e R B

f f 30 o o

r 10 r e e

b b 20 m m u u N 5 N 10

0 0 0 2 4 6 8 0 2 4 6 8 Num ber of People Num ber of People

 Both graphs are straight line graphs, showing a linear connection.  The first graph has a gradient of 3, and the second has a gradient of 7.

Explaining my Rules:

 There are three rooms per house now, so each person has three rooms. Therefore the number of people are multiplied by 3.  Each house is now made from seven beams, and the first house will require two beams to finish it off.

Trying to find a connection in my work so far…

Number of Storeys (S) Rule for Number of Rooms Rule for Number of Beams 1 2P = R 5P + 1 = B 2 3P = R 7P + 2 = B

I think for 3 storeys 4P = R 9P + 3 = B

 I have noticed that the coefficient of P, for the number of rooms rule, goes up in 1s.  I have noticed that the coefficient of P, for the number of beams rule, goes up in 2s and the number added on is going up in 1s.

Testing my Rules: For a 3 storey house, for 6 people:

Number of people = 6 Number of rooms = 24 Number of beams = 57  4P = R 4  6 = 24   9P + 3 = B (9  6) + 3 = 57 

An Overall Rule:  (S + 1)P = R The coefficient of P is always 1 more than S.  (2S + 3)P + S = B The coefficient of P has the pattern 2  S, + 3 and then added on the value of S.

Year 81: Unit 1 Test: Non-calculator Section

1. Paul is doing a sponsored swim. He gets £2 a length. a) This table shows how much Paul gets. Copy and complete the table on the answer sheet.

Number of lengths 1 2 3 4 5

Total (£)

c) On the answer sheet is a graph, fill in the points and join the points up with a straight line. Continue the line to the edge of the graph. d) Use the graph to help your answer this question. How much does Paul get for 6 lengths?

2. a) Convert 19:30 to an am or pm time b) Convert 6:00pm into 24 hour clock c) If a train leaves at 9:40 am and takes 45 minutes, what time does it arrive?

3. a) Round 75 to the nearest 10. b) Round 660 to the nearest 100. c) Round 6.4 to the nearest whole number

4. Stephen is making patterns with tiles. Here is his table:

Number of red tiles 1 2 3 4 5

Number of blue 8 10 12 14 16 tiles

a) How many blue tiles does he add each time? b) Fill in the first part of the formula number of blue tiles = ……× number of red tiles c) Fill in the full formula number of blue tiles = ……× number of red tiles + ……

Year 81: Unit 1 Test: Calculator Section

5. Work out the following, using the x² button on your calculator: a) 14² b) 2.4²

6. Work out the following, using the  button on your calculator: a)  8 b) 17.4

7. Mohammed asked about their flavour of ice cream. Their answers were: vanilla 12 strawberry 6 chocolate 5 other 7 He decided to draw a pie chart of his results. a) Copy and complete the following: 360 ÷ 30 = …… for each pupil b) Fill in the table below. Flavour Number of pupils Working Angle Vanilla 12 12 × 144º Strawberry 6 6 × Chocolate 5 5 × Other 7 7 ×

c) Use the table to help you draw a pie chart on the answer sheet.

8. Draw the inverse for each of these:

a)  5 b) 3

9. Emma puts some numbers into the function machine.

A? 70 B? 10 120 C? 1000

Work out the numbers Emma used.

37 07/04/18 Westfield Community School - Mathematics NAME: Year 81: Answer Sheet: Non-calculator Section

1. a) Number of lengths 1 2 3 4 5

Total (£)

b) c) Paul gets …………

2. a) ………… b) ………… c) …………

3. a) ………… b) ………… c) …………

4. a) Paul adds ………… each time.

b) Number of blue tiles = …………  Number of red tiles

c) Number of blue tiles = ……  Number of red tiles + ………

38 07/04/18 Westfield Community School - Mathematics NAME: Year 81: Answer Sheet: Calculator Section

5. a) ………… b) …………

6. a) ………… b) …………

7. a) 360  30 = …………

b) Flavour Number of pupils Working Angle Vanilla 12 12 × 144º Strawberry 6 6 × Chocolate 5 5 × Other 7 7 × c)

8. a ) b)

9 . A is ……………? 70 B is ……………? 10 120 C is…………….? 1000

39 07/04/18 Westfield Community School - Mathematics 83: Unit 2: Chapter 5: Transformations Lesson 1 Lesson 2 Lesson 3 Lesson 4 l

a Using the number cards, + /- questions Guess the quadrilateral. Have some clues, Using 1 – 100 grids, pupils aim is to get Match the cards up – each team is given a t

n with upto two decimal places. progressively getting easier. Pupils have to four numbers in a row. Teacher calls out set of cards with equivalent fractions, e

M decide what the shape is by listening to the “even number”, pupil can choose any even decimals and percentages. clues. When they are sure they have the number and put a counter on it. “Multiple Once cards are sorted, discuss with other right answer, they write it down and on of 3” etc, “prime number”, “square groups and amend answers where which clue they guessed it on. If 5 clues, 5 number”. First pupil to get four counters in necessary. points for guess on first clue etc. Work in a straight line wins! teams and see who gets the most points.

S . Transform 2D shapes by reflections . Transform 2D shapes by translations . Transform 2D shapes by rotations . Understand & use the language & N . Identify reflection symmetry in 3D notation associated with N shapes enlargement

e Go through reflection and how to ways Discuss rotations and translations. Use p97 Recap idea of rotation, include direction Go through basic enlargement and scale m

e that can help (tracing paper, mirror and Exercise 5:4 to aid discussion. Focus and size of rotation. Use p101 – 102 factors. Explain how the scale factor h t

measuring from the mirror line) mostly on translations. Exercise 5:7 to help discussion. affects the lengths of the shapes. n i Extend rotation into rotational symmetry a

M Do p94 – 95 Exercise 5:2 Do p98 – 99 Exercises 5:5 & 5:6 and order of. Do p106 Exercises 5:10 & 5:11

Extension: p96 Exercise 5:3 Extension: p99- 100 Game ‘Translate a Do 103 –104 Exercises 5:8 & 5:9 Extension: cube’ Extension: p112 Q4

k Do p92 – 94 Exercise 5:1. Tracing paper Look at p104 ‘Patterns with reflections, w needed translations & rotations’ & p111 Q1 & 2. H

Use these ideas to create at least one coloured pattern for display. y

r Have a variety of pictures and 3D objects, A T H Discuss & display patterns that involve Have some shapes and there enlargements a

n class discussion about the lines of rotational symmetry (introduce Asian art – drawn, can you work out the scale factor?

e S E l symmetry. regularly use order of 5 rotational How did you work that out? How could P Who can name an object that has 2 lines of R C B symmetry) you do it if the numbers were not so symmetry etc? (for 2D & 3D) Translate the letters to make as many simple? words as you can. Write down the translations and the words you make!

40 07/04/18 Westfield Community School - Mathematics Lesson 5 Lesson 6 l

a How many different rectangles can you Checklist for chapter 5: t

n make that have a perimeter of 24cm? Can reflect an object in a mirror line e

M How many different rectangles can you Understand that a translation is a make that have an area of 36cm squared? movement in a straight line Discuss answers once pupils have got Understand that a rotation is a movement their answers. around a point

S . Understand & use the language & Know clockwise and anticlockwise N notation associated with Know fractions of turn N enlargement Understand the term scale factor . Enlarge 2D shapes, given a centre Can enlarge an object by a scale factor of enlargement & a positive scale factor

e Extend enlargement to be about a point Do p114 Test Yourself m

e and centre of enlargement. h t

Mark and correct n i Do p107 – 108 Exercises 5:12 a

M Fill in pupil assessment booklet Extension: p112 Q5

k Ensure chapter is up-to-date and w corrections are completed. H AND Choose a simple shape- enlarge the same Key words: shape 3 times, but move the centre of Reflection enlargement (once inside the shape) What do you notice? Mirror line Translation Rotation y r OHP with diagrams on – predict where Test pupils on key words, spellings and Centre of rotation a

n the centre of enlargement is, predict how definitions

e Rotational symmetry l large the shape will be, Now get pupils P to draw on OHP – who is right? How did Enlargement they work it out?

41 07/04/18 Westfield Community School - Mathematics 83: Unit 2: Chapter 6: Don’t be negative! Lesson 1 Lesson 2 Activity 1 Lesson 3 l

a 7 3 9 Guess the number. Have clues which get

t Staring with 25  100 = 2500

n progressively easier and pupils have to e 4 6 10 What other questions can you make up e.g

M write down the answer and the clue they 5 8 2 2.5  1000 = 2500 Can reverse questions too: 2500  25 = have guessed it on. If 5 clues, 5 points for Target = 45 100 guessing the answer on the first clue. Use terms such as square, multiple, prime etc in the clues.

S . Carry out calculations effectively & . Understand the operations of +/  of . Understand the operations of +/  of . Understand the operations of /  of N efficiently using the function keys for integers integers integers N sign change . Enter numbers & interpret the display in different contexts (negative numbers)

e Discuss the number line, inequality signs Recap work from year 7.Go through Negative number snap Go through multiplying and dividing m

e and where negative numbers are found in adding & subtracting. Draw a number line negative numbers and the rules. h t

real life situations. for those that need it. RD has sets of cards n i Do p 122 – 124 Exercise 6:3 a

M Do p116– 117 Exercise 6:1 Q1- 8 Do p121 Exercise 6:2 Extension: p132 Q5 Extension: p132 Q3 Extension: p132 Q4

k Do p118 - 119 Exercise 6:1 Q 9 – 13 Do p124 – 125 Exercise 6:4 w H y

r Large number line on the board going up Using –1, 2, -3 and 4, how many different Class counting the –2 times tables, -3 times a

n in tens, place the inbetween numbers on it. answers can you make, using the signs + table etc. Then reverse the times tables i.e. e l Then have some statements on the board and – only. You can use as many of the dividing! P e.g. –3 …..-8 and pupils have to fill in the numbers in the questions as you like, but correct sign. Harder version –3 + 5…..-3 you can only use them once each time. etc.

42 07/04/18 Westfield Community School - Mathematics ¯1 + 5 ¯5 + 1 4 + 0 ¯2 + 7 ¯1 + 5 2 + 3 ¯3 + 7 ¯3 + 8 ¯2 – 2 5 + 0 ¯3 – 1 ¯7 + 2

43 07/04/18 Westfield Community School - Mathematics ¯1 – 4 5 + 1 ¯6 + 1 ¯3 – 3 ¯8 + 3 ¯5 + 2 ¯3 + 9 ¯5 – 1 ¯1 + 7 ¯7 + 1 ¯2 + 8 ¯2 – 4

44 07/04/18 Westfield Community School - Mathematics ¯3 + 2 ¯5 + 8 ¯1 + 0 2 + 1 ¯1 + 3 ¯5 + 2 ¯3 + 5 ¯4 + 1

¯4 + 6 ¯2 - 1 1 + 1 ¯7 + 4

45 07/04/18 Westfield Community School - Mathematics ¯3 + 4 ¯2 + 0 ¯2 + 3 ¯5 + 3 0 + 1 ¯4 + 2 ¯1 + 2 ¯3 + 1 ¯2 + 1 ¯3 + 6 ¯6 + 5 ¯2 + 5

47 07/04/18 Westfield Community School - Mathematics Lesson 4 Lesson 5 Lesson 6 l

a Quick fire tables test. Reverse the Pupils call out some numbers, then race Checklist for chapter 6: t

n questions too! each other to find the mean, mode and Understand positive and negative numbers e

M Go through answers and pupils identify range. Understand 0 is not negative or positive the tables they do not know as well and Add an extra number to the list, discuss Know the inequality signs and their learn for extra homework. how this will effect the mean, mode and meaning range. Can they guess what will happen Be able to do ‘shopkeepers’ addition’ before they work it out? Be able to write money from a calculator Be able to use the FIX and memory

S . Use the order of operations with . Use the order of operations with buttons on the calculator N more complex calculations more complex calculations N . Substitute integers into formulae.. and integers into expressions involving small powers

e Explain formulae and how to substitute Go through formula including squares Do p134 Test Yourself m

e numbers into them. Recap order of and powers. h t

operations (BODMAS). Mark and correct n i Do p129 Exercise 6:8 a

M Do p126 - 127 Exercises 6:5 & 6:6 Fill in pupil assessment booklet Extension: p132 Q6, 7, 8 Extension: p132 Q2, 9

k Do p128 Exercise 6:7 Design a poster to help pupils remember w

H the rules for +/-// You do not have to do all the operations. Best ones can be copied for pupils to put into the books! y

r Using the numbers –1, 2, 3, -4, -5, can Have some formulae on the board, roll a Test pupils on key words, spellings and a

n you make all the answers between 1 – dice for numbers to substitute (maybe a definitions e l 20? You can use any of the four blank dice with +/- on too). Working in P Key words: operations, and brackets. Work in pairs, or groups work out the answers. groups, which table can get the most? Positive Negative

48 07/04/18 Westfield Community School - Mathematics 83: Unit 2: Chapter 7: Angles Lesson 1 Lesson 2 Lesson 3 l

a Using the numbers -1, -2, -3, -4, and using the How many fractions can you make equivalent to half, Dice with multiply 10, 100, 1000, divide 10, 100, 1000. t

n operations - / +, how many questions and answers cant three-quarters etc. Start with a number e.g. 8. Pupils roll the dice and work e

M he pupils make? Have pairs of cards, pupils have to find their partner out the answer. Using the latest answer, the next pupil Work in groups or pairs, then share their questions with and display their pairs. rolls the dice and works out the next answer, keep the the rest of the class. change going until they get it wrong. Work in small groups!

S . Use correctly the vocabulary, notations and . Understand a proof that – the sum of the angles in a . Identify alternate and corresponding angles N labelling conventions for angles triangle is 180º and of a quadrilateral is 360º . Use correctly the vocabulary, notation & labelling N conventions for lines & angles

e Go through language associated with angles. Use p137 Introduce rule for angles in a triangle. Must show By using p142 – 143 Exercise 7:5 see how many of the m

e Exercise 7:1 to help. proof:- draw a triangle, cut off corners and put together rules for parallel and intersecting lines the pupils can h t

Explain the difference between drawing & measuring to make a straight line first. (Show proper proof once work out. n i and using the rules. Introduce rules for around a point alternate angle & corresponding angles rules are taught) Bring groups together to reinforce rules. a

M and straight line. Show quadrilateral too

Do p139 – 140 Exercise 7:3 Do p140 – 141 Exercise 7:4 Do p143 –144 & p146 Exercises 7:6 & 7:8 Write some quadrilateral questions on board! Extension: Extension: p158 Q2 & 3

Extension: p158 Q1

k Do p137 – 139 Exercise 7:2 Copy out the rules on p144 carefully and learn them w AND do p145 Exercise 7:7 H y

r Pupils standing up, using their arms display an acute OHP of some test questions, include special cases such Match the diagrams with the names of the rules. a

n angle, obtuse angle etc. as isosceles, equilateral triangles too. Perhaps have cards for each table, discuss answers – e l Using the rules they have leant – pupils design Also do some with quadrilateral questions too, have tables agree, disagree, then correct any incorrect P questions for each other- and then hand them back for emphasising special cases here too! answers. checking Finally reinforce correct answers before pupils leave

49 07/04/18 Westfield Community School - Mathematics Lesson 4 Activity 2 Activity 3 l

a Have some cards with pictures of polygons & t

n properties of polygons. Pupils have to work in pairs and e

M match the cards up. Then discuss with their table their answers until they all agree. Then discuss with the whole class.

S . Use correctly the vocabulary, notation & labelling . Know & use side & angle properties of equilateral, . Know & use side & angle properties of equilateral, N conventions for lines, angles & shapes isosceles & right angled triangles & of special isosceles & right angled triangles & of special N . Understand a proof that the exterior angle of a quadrilaterals, classify quadrilaterals by geometric quadrilaterals, classify quadrilaterals by geometric triangle equals the sum of the two interior opposite properties properties angles

e Discuss polygons and their names and properties. In the computer room, using LOGO. Draw the different Investigate interior and exterior of polygons. m

e quadrilaterals & regular polygons. h t

Do p147 – 148 exercise 7:9 Find the connections: n i Extension: tessellate the shapes. 360  number of sides = exterior a

M Extension: exterior and interior = 180

k Do p149 Exercise 7:10 Design a table with the polygons down one side, and the w AND properties across the top e.g number of sides, sets of H P149 ‘An investigation into tessellating shapes’ parallel sides, pairs of angles, lines of symmetry, order of rotational symmetry etc. Then fill it in! y

r Guess the polygon. Give a list of clues gradually getting a

n easier. Pupils write answer down when they think they e l have worked it out with the number clue they guessed it P on. Once they have written an answer down, they must turn over their piece of paper. If 5 clues, 5 marks for guessing it one the first clue etc. Keep score running for all the shapes – who gets the most points?

a How many shapes can you find that have How many shapes can you make with an Checklist for chapter 7: t

n a perimeter of 18cm? Allow all regular area of 24cm squared? Understand the terms relating to angles e

M polygons and label the lengths of the Allow triangles, parallelograms, Know the rule for angles on a straight line sides. rectangles, and any other shapes that Know the rule for angles around a point they know the rules. Know the rule for angles in a triangle Know corresponding and vertically opposite angles

S . Use bearings to specify direction . Use bearings to specify direction Know the polygons- names and angles N Understand tessellation N Know the points of a compass Know bearings are measured clockwise and have three figures Key words: Right angle

e Go through compass points and idea of Recap homework and discuss pupil’s Do p158 Test Yourself Acute m

e bearings. answers to Q 1 – 6. Obtuse h t

Explain how to work out bearings and Mark and correct

n Reflex i the significance of the word ‘from’ in Continue p152 – 153 Exercise 7: 12 Q7 – a Angles about a point

M bearing questions. 11 Fill in pupil assessment booklet Angles about a straight line Do p150 – 151 exercise 7:11 Extension: p158 Q5 Opposite angles + additional questions from the board on Angles in a triangle bearings Scalene triangle Isosceles triangle Extension: Equilateral triangle Alternate angles

k P151 – 152 Exercise 7:12 Q1 - 6 Worksheet: Angles (year 8) Corresponding angles w

H Interior and exterior angles Parallel Intercept y

r Pupil standing up, facing north – turn to Have a map on OHT/ on a sheet, work Test pupils on key words Regular polygon a

n face south, west etc, out the bearing of …. Tessellations e l Estimate the bearings from one pupil’s Explain to everyone else what you are

P Pentagon desk to another – then testing estimates doing. Hexagon by measuring! Octagon Compass Bearing

51 07/04/18 Westfield Community School - Mathematics 83: Unit 2: Chapter 8: Probability Lesson 1 Activity 4 Activity 5 Lesson 2 l

a Countdown: Roll a 6 sided dice and a dice with t

n 25, 8, 4, 5, 1, 7 multiply 10,100,1000 and divide 10, 100, e

M Target number = 195 1000 on. Pupils roll both dice and work out How many different ways can you make answer. Pupils keep a running total of their the target? scores, who is the first to reach 5000? Work in small groups.

S . . Use the vocabulary of probability . Use the vocabulary of probability when . Know that if a probability of an event N when interpreting the results of an interpreting the results of an experiment; occurring is p, then the probability of N experiment; appreciate the random appreciate the random processes are it not occurring is 1 - p unpredictable processes are unpredictable . Estimate probabilities from experimental data; understand that:- if an experiment is repeated there may be, & usually will be, different outcomes;- increasing the sample size generally leads to better estimates of probability . Compare experimental & theoretical probabilities in different contexts

e Recap idea of probability and words Explain how by using outcomes we can Practical experiments: Explain idea of probability adding up to 1. m

e associated with it. Link words to values 0 work backwards to work out what is Some theoretical probabilities – see if the Use probability scale to help emphasis the h t

to 1. Go through working out probabilities probably in the bag/ box etc. answers come out right and some point. Use fractions mostly, but include n i for equally likely outcomes and predicting Also explain these are experimental experimental - similar to day before. decimals and percentages. a

M outcomes based on probabilities. probabilities and may well change when repeated or the experiment is continued. Work in small groups, and rotate around Do P164 – 165 Exercise 8:4 Do probability questions similar to the stations. Can do some or all of it orally/ on the exercises 8:1 – 8:3 orally with whole Do p163 Game ‘Holder of the box’ board. group Counters and bags are needed. Extension: p176 Q 3 & 4 Extension: p176 Q1 & 2 Extension: Change the number of counters, or numbers of colours

k Do p161 – 163 Exercises 8:2 & 8:3 Write up the experiments, with any w probabilities that you have found. Were H there any unexpected results? Did everything go as planned? y

r Teacher has some cards with pictures on If there were counters in a bag and the Have some cards with pictures on, what is a

n e.g bag with colour counters and asks for probability of getting a green one is a the probability of this not happening? e l simple probabilities- pupils use white third, what could be in the bag? What would that be in decimals, fractions, P boards to write answers. Discuss the ideas that pupils suggest. percentages?

a Roll a dice twice to make two 2 How many different ways can Give the mean = 5, and the range Checklist for chapter 8: t

n digit numbers. Add or subtract you make 36, using multiplying = 4. If there are 4 numbers, what Know the terms impossible, even e

M them. Pupils work out the and dividing only? You can use could they be? chance and certain answers. two or three numbers, or more! Same idea, but give different Know that probabilities are Discuss answers with whole information median, mode etc. between 0 and 1 class Be able to work out equally

S . Know that if a probability of . Know that if a probability of an . Know that if a probability of an likely outcome questions, using N an event occurring is p, then event occurring is p, then the event occurring is p, then the fractions N the probability of it not probability of it not occurring is probability of it not occurring is Know that probabilities add up to occurring is 1 – p 1 – p; find & record all 1 – p; find & record all 1 . Enter & interpret the display possible outcomes for single possible outcomes for single events & 2 successive events in events & 2 successive events in (fractions) a systematic way, using a systematic way, using diagrammatic & tabular forms diagrammatic & tabular forms of presentation of presentation

e Discuss notation for probability, Go through exercise 8:6 and how Play p177 Game ‘It’s not fair’ Do p178 Test Yourself m

e and events happening and not the pupils worked out the several times with different h t

happening, and how they are answers and how they displayed partners. Mark and correct n i related. their answers. In small groups, discuss who a

M Go through probabilities sin Go through idea of sample won the most. Can you explain Fill in pupil assessment booklet fractions mostly, but include spaces and diagrams, and how why? decimals and percentages. Go these help with a logical Continue discussion with whole through cancelling fractions on a approach. class. calculator. How can you prove this? Do p171 – 173 Exercise 8:7 In pairs, change the game so that Do 166 – 168 Exercise 8:5 it is fair. Extension: Find all the outcomes As whole class, discuss the Extension: for throwing 3 coins. different ideas – what are the P176 Q5 advantages/ disadvantages of the rules?

k Finish any outstanding work and Design a simple game for a fair. w do the corrections Work out all of the probabilities H AND p169 Exercise 8:6 (ensure the probability is in your favour as you would like to make Key words: money!!) and then try out your Probability game on at least two people. Probability of something not happening Sample space Sample space diagram

r Match the pictures of probability Discuss ways of displaying Continue from class discussion Test pupils on key words, a

n questions and the answers in outcomes for different questions or use to time to give an example spellings and definitions e l simplest fractions, decimals & of the homework P percentages

83: Unit 2: AT1, revision and test Lesson 1 Lesson 2 Lesson 3 l

a -5 3 -1 Have a variety of shapes, rectangles, rectilinear Quick fire tables test, using the number cards, Checking t

n compound shapes, triangles, parallelograms.. on speed and recollection of times tables upto 10 times e

M -7 -4 8 In a time limit, how many of them can they work out the 10. perimeter and the area? 6 2 -3

Target = 10

S . See previous references to NNS . Solve problems & explore them in a range of . Solve more complex tasks by breaking them into N contexts (shape, space & measures) smaller steps or tasks, choosing & using efficient N . Identify the necessary information to solve a techniques for calculation, algebraic manipulation & problem; represent problems & solutions in graphical representation algebraic, geometric & graphical form, using correct notation & appropriate diagrams

e Review main points of chapters 5 & 6 Introduce Area and border investigation. Explain about making problem more difficult. Extend to m

e Do p109 –110 Questions sections in chapter 5 Recap criteria (in pupil assessment booklet) rectangles, but be logical and break down the problem. h t

Diagrams e.g. height of 2, then height of 3 etc. n i Table of results a

M Patterns and predictions Rules Explanation of rules, relating to diagrams Graphs

k Do p130 Questions sections in chapter 6 Continue for 40 minutes with the investigation w H y

r Divide the board into two parts- pupils write all the key Go through what should have been achieved in the Set completion targets for homework. a

n facts for each chapter on the board. lesson. Discuss pupil criteria for investigations and then Again look at pupil criteria and look at each others’ e l Discussion of facts, types of questions that might be get pupils to analyse their work and decide what levels work and mark it so far! P asked- pupils do most of the talking. they have achieved

a How many facts can you write down about 36? Using multiplying and dividing by 10, 100, 1000 Testing of: t

n Pupils get one point for each correct fact. E.g square only, how many ways can you make the answer 340? . Understand operations of +/ / /  of integers e . Substitute integers into formulae

M number, multiple of 6, has factors of…. Etc. Pupils get 1 point for each right answer, who gets the most points? . Use correct vocab & notation for lines & angles . Identify alternate & corresponding angles

S . See previous references to NNS . Explain & justify inferences & reasoning, . Understand that the angles of a triangle are 180º N using step-by-step deduction . Use bearings to specify direction N . Use correct vocab for shapes . Suggest extensions by asking ‘What if..? or . Solve simple problems using known geometric ‘Why?’, conjecture & generalise properties . Know that if the probability of an event occurring is p, then the probability of it not occurring is 1 – p; find & record all possible outcomes for single events & 2 successive events in a systematic way . Transform 2D shapes by rotations, reflections and transformations . Enlarge 2D shapes, given a centre of enlargement & a positive whole number scale factor e Review main points of chapters 7 & 8 Finalise investigation by trying to pull together Tests 82: Unit 2 m

e formulas for height of 2, 3 and 4. Try to predict h t

Do p154 – 155 Questions sections in chapter 7 formulas for height of 5 and then ‘n’ Non-calculator section only. n i Answer sheet for diagram questions – will need a

M Pupils need to check against the criteria to ensure they copying. have covered all the points.

k Do p174 – 175 Questions section from chapter 8 w H

r Divide the board into two parts – pupils write up key A final look at pupil criteria and a final marking of a

n points/ facts of chapter 7 & 8. work by pupils before teacher collects for official e l Pupils suggest types of questions that might arise in marking. P the test. Discuss the key words/ facts.

56 07/04/18 Westfield Community School - Mathematics Area & Border Investigation

Question: Border

Garden

A square garden has a length of: L 1 2 And a garden area of: G 1 4 A border area of: B 8 12 So a total area of: A 9 16 Investigate!

Basic problem:

 Diagrams  Table of results L² = G  Predictions and testing them 4L + 4 = B  Rules, in algebra; and testing them (L + 2)² = A  Graphs  Explanations of rules (relating to diagrams)

Extending the problem:

Go onto rectangles: height (H), length (L), area of garden (G), area of border (B) and total area (A). Follow the bullet points for the basic problem for each of these:  H = 2 2L = G 2L + 8 = B 3(L+1) = A  H = 3 3L = G 2L + 10 = B 4(L+1) = A  H = 4 4L = G 2L + 12 = B 5(L+1) = A

 For any size H HL = G 2L + 2H + 4 = B (H+1)(L+1) = A

Year 81: Unit 2 Test: Non-calculator Section

1. Put these temperatures into order, lowest first. a) 4ºC, 9ºC, 3ºC, 3ºC b) 15ºC, 18ºC, 0ºC, 13ºC, 21ºC

2. Round these sums of money to the nearest penny a) £3.782 b) £10.955

3. Work out the answers to these a) £4.36 + 82p + £1.95 b) £5  75p c) £2.40  6 d) £4  5

4. Write these sums of money in pounds correctly a) £1.8 b) £6.36p c) 96p

5. Find the marked angles:

a b 65 11 2

6. a) Measure the bearing of the Flag (F) from the Tent (T) …

b) What is the bearing of the tent from the flag?

7. A set of snooker balls consist of fifteen reds, one white, a yellow, a green, a brown, a blue, a pink and a black. a) What is the probability of the ball being white? b) What is the probability of the ball being red? c) What is the probability of the ball being purple?

8. Michael wants to choose his lunch. He has to choose a dinner and a pudding

Dinner Pudding Sausage and mash (S) Apple pie and custard (A) Vegetable curry and rice (V) Yoghurt (Y) Chicken salad (C) Jam doughnut (J)

Make a list of all the possible lunches he could have. Use the letters in brackets to save you writing all the lunches out in full e.g. S and A

9. Use the separate answer sheet for this question.

a) Draw triangle ABC : A(-2 , 0) B(0 , 2) C(-3 , 3)

b) Draw triangle A'B'C' so that it is a reflection of triangle ABC in the mirror line.

10. Use the separate answer sheet for this question.

a) Draw triangle ABC : A(1 , 1) B(5 , 1) C(1 , 4)

b) Draw the image of triangle ABC under a rotation of 90o anticlockwise, about A.

c) Draw triangle DEF: D( 1 , 1) E( 1 , 3) F(2 , 1)

d) Translate triangle DEF by 3 squares left and 4 squares down.

59 07/04/18 Westfield Community School - Mathematics 83: Unit 3: Chapter 9: Percentages and fractions Lesson 1 Lesson 2 Lesson 3 Activity 1 l

a Have a straight line graph drawn. Ask True or false: Pupils recap the rules of angles with lines How many ways can you split up then t

n pupils question about the line – e.g what is Have some statements about imperial and and triangles. Then design 5 questions for number 5 into decimals with one and two e

M the equation of the line, does this point fit metric units and the conversion. their partner, swap questions, do them, decimal places. E.g. 2.25 + 2.75 i.e. onto the line, name a line that would be a Discuss in pairs/ small groups, agree on then return for marking by the partner. compliments of 5 parallel line, name a line that intercepts the true or false, then share with the rest of the Pupils volunteer to demonstrate their y axis at the same place as the line drawn class. Discuss outcomes. questions and answers on the board. etc.

S . Interpret percentage as the operator . Interpret percentage as the operator . Enter numbers & interpret the display . Use the equivalence of fractions, N ‘so many hundredths of’ ‘so many hundredths of’ in different contexts (percentages) decimals & percentages N . Consolidate & extend mental methods . Consolidate & extend mental methods . Carry out more difficult calculations of calculation, working with of calculation, working with effectively & efficiently using the percentages percentages function keys: percentage . Use the equivalence of fractions, decimals & percentages to compare proportions e Discuss percentages – what they mean and Explain how if you work out 1%, you can Introduce calculator methods – 38% = To emphasise fractions, decimals & m

e where pupils might come across them. work out any other percentage (recap  0.38, so 38% of 240 = 0.38  240 etc. And percentages conversions, play bingo. h t Include working out 10% without using a 100 without a calculator) show 38/100  240 and cancelling etc. n i calculator. Extend non-calculator methods Pupils draw 5  5 grid and fill in a Also introduce percentage buttons on the

M for other percentages, e.g. 25%, 50%, Do p185 - 186 Exercise 9:4 calculator!! percentages. Teacher calls out a fraction or 75%, 33.3% etc. Emphasise different methods and decimal, and pupils cross out the Extension: p198 Q4 connection between fractions, decimals & equivalent percentage. Do p180 – 183 Exercises 9:1 & 9:2 percentages And in pairs p189 – 190 Four in a row Extension: Do p188 – 189 Exercise 9:5 game

Extension: p198 Q1, 2 & 3

k Do p184 exercise 9:3 Do p191 – 192 Exercise 9:6 w And H Write down a list of ‘quick’ methods for working out percentages y

r Match up questions with methods of Put 240 on the board. Hand out cards with How many ways can you work out 25%, Match cards with percentages, fractions a

n working out. E.g 50% of .. and on another percentages on e.g 1%, 50%, 25% - any with and without a calculator. Write up and decimals. Give pupils a card and they e l card divide by 2! that can be easily completed mentally (use methods on board and discuss. Go onto have to find their matching partner(s). P Discuss answers, can be completed in 2%, 20% etc for brighter pupils) Pupils other percentages. Discuss groups of answers. small groups or as a class write up their question and answer on board

61 07/04/18 Westfield Community School - Mathematics 0.29 0.7 0.86 0.16 0.5 0.79

0.03 0.31 0.92 0.01 0.24 0.87

0.07 0.46 0.74 0.08 0.33 0.54

0.15 0.4 0.52 0.12 0.3 0.41

0.68 0.81 0.99 0.47 0.63 0.95

0.23 0.59 0.71 0.2 0.53 0.8

0.09 0.27 0.89 0.05 0.26 0.83

0.1 0.37 0.6 0.06 0.39 0.61

0.18 0.35 0.42 0.13 0.32 0.45

0.51 0.66 0.94 0.48 0.73 0.91

0.28 0.75 0.93 0.19 0.57 0.72

0.02 0.34 0.97 0.04 0.21 0.85

0.11 0.56 0.78 0.09 0.38 0.64

0.22 0.49 0.6 0.14 0.36 0.43

0.62 0.84 1.0 0.5 0.69 0.9

0.25 0.76 0.82 0.15 0.58 0.88

0.01 0.3 0.96 0.06 0.27 0.91

0.17 0.55 0.77 0.08 0.37 0.65

0.22 0.43 0.58 0.1 0.32 0.44

0.67 0.8 0.98 0.51 0.75 1.0

0.03 0.28 0.4 0.07 0.24 0.41

0.46 0.61 0.87 0.49 0.62 0.84

0.33 0.52 0.93 0.36 0.53 0.9

0.19 0.67 0.99 0.11 0.68 0.95

0.2 0.38 0.71 0.18 0.38 0.7

0.02 0.17 0.31 0.04 0.23 0.42

0.39 0.54 0.76 0.48 0.59 0.82

0.2 0.47 0.89 0.3 0.55 0.9

0.05 0.66 0.92 0.12 0.63 0.94

0.13 0.26 0.7 0.16 0.34 0.72

0.02 0.25 0.44 0.01 0.21 0.45

0.5 0.64 0.73 0.57 0.74 0.88

0.29 0.56 0.86 0.33 0.69 0.96

0.1 0.68 0.98 0.07 0.79 1.0

0.14 0.35 0.7 0.12 0.4 0.81

0.03 0.25 0.42 0.08 0.22 0.59

0.49 0.6 0.83 0.65 0.71 0.86

0.29 0.56 0.85 0.3 0.69 0.93

0.11 0.63 0.97 0.1 0.78 0.97

0.16 0.38 0.77 0.15 0.48 0.81

0.04 0.28 0.67 0.05 0.2 0.57

0.09 0.72 0.82 0.14 0.64 0.76

0.32 0.46 0.91 0.23 0.41 0.82

0.58 0.8 0.99 0.47 0.7 0.96

0.13 0.4 0.61 0.18 0.34 0.5

0.06 0.32 0.73 0.01 0.24 0.69

0.19 0.75 0.87 0.07 0.74 0.87

0.39 0.53 0.9 0.36 0.43 0.92

0.6 0.83 0.98 0.54 0.77 0.97

0.21 0.44 0.68 0.13 0.4 0.62

0.06 0.35 0.68 0.02 0.2 0.55

0.17 0.7 0.89 0.09 0.6 0.79

0.37 0.45 0.95 0.24 0.43 0.84

0.5 0.85 1.0 0.49 0.65 0.91

0.26 0.41 0.52 0.11 0.36 0.51

0.03 0.12 0.59 0.04 0.26 0.61

0.08 0.66 0.75 0.15 0.73 0.85

0.23 0.34 0.8 0.3 0.42 0.9

0.45 0.72 0.92 0.48 0.81 0.94

0.1 0.29 0.53 0.19 0.37 0.52

0.39 0.54 0.71 0.51 0.64 0.89

0.05 0.2 0.45 0.01 0.22 0.55

0.07 0.5 0.62 0.1 0.6 0.78

0.14 0.25 0.84 0.16 0.32 0.95

0.31 0.69 0.97 0.46 0.83 0.99

0.47 0.68 0.86 0.4 0.76 0.87

0.04 0.21 0.56 0.08 0.23 0.58

0.09 0.63 0.7 0.11 0.65 0.79

0.17 0.3 0.88 0.18 0.27 0.93

0.35 0.74 0.96 0.38 0.8 0.98

0.45 0.72 0.9 0.38 0.6 0.78

0.02 0.28 0.57 0.03 0.17 0.42

0.06 0.67 0.76 0.1 0.59 0.61

0.19 0.32 0.91 0.14 0.26 0.84

0.33 0.84 1.0 0.3 0.73 0.95

0.43 0.54 0.86 0.49 0.69 0.89

0.01 0.24 0.47 0.03 0.29 0.51

0.12 0.52 0.62 0.07 0.6 0.74

0.2 0.32 0.9 0.15 0.3 0.94

0.39 0.7 0.94 0.41 0.81 1.0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

67 07/04/18 Westfield Community School - Mathematics Lesson 5 Activity 2 Lesson 7 l

a Have some pie charts drawn, discuss what ¼ of a number = 8 Checklist for chapter 9: t

n They represent if there are 100 pupils, … What other facts can you work out? Work out 10% by dividing by 10 e

M What fraction of the circle is it? What ½ = , ¾ = , 25% = , 10% = etc. Work out multiples of 10% e.g 20% angle does this represent? Etc Find 25%, 50% etc by using simple mental methods Be able to turn percentages into decimals

S . Use the equivalence of fractions, . Add & subtract fractions by writing Be able to work out percentages with a N decimals & percentages to compare them with common denominator calculator N proportions Be able to work out fractional quantities . Calculate fractions of quantities e.g quarter divides by 4 . Enter numbers & interpret the display Three quarters, divide by 4, then multiply in different contexts (fractions) by 3 Be able to use that fraction button on the calculator

e Go through finding a fraction of a quantity Recap fraction work: +  Do p200 Test yourself m

e (did a bit last year). h t

Do p363 Help yourself 15 Adding Mark and fill in pupil assessment booklet n i Do p193 – 195 Exercises 9:8 & 9:10 fractions a

M (Can do exercise 9:9, but need Cuisenaire Do P364 Help yourself 16 Subtracting rods – RD has some) fractions & 17 Simplifying fractions

Extension: p198 Q5 Extension:

k Fraction, percentage and ratio crossword Ensure all exercises are completed and w corrected. H And/or Learn fractions and decimal equivalents, P191 Exercise 9:7 especially one third, one eight etc. y

r One eight = 5, go through the eight times Match up questions and answers on OHT. Test pupils on key words, spellings and a

n table. Pupils discuss pairs and then discuss as a definitions e l Then extend so 1 whole = 80, so do fifth class. P Key words: times tables! Percentage

68 07/04/18 Westfield Community School - Mathematics Fractions, Ratios and Percentages.

1 2 3 4

8 9 10

11 12 13

16 17 18

19 20 21

Across Down 1 What is ½ of 2884? 2 What is the larger amount of 60 in the ratio of 1 : 3 ? 4 What is the larger amount of 3 What is 75% of 280? 150 in the ratio 2 : 3 ? 1 6 What is 10% of 1920? 4 What is /3 of 276? 4 8 What is /5 of 70? 5 The ratio of 2 : 5 is the same as 100 : ? 9 What is the smaller amount of 7 What is 90% of 1010? 3000 in the ratio of 2 : 13 ? 1 11 What is 25% of 196? 9 What is /10 of 49870? 1 12 What is /3 of 2769? 10 The ratio of 3 : 7 is the same as 27 : ? 14 What is the larger amount of 11 What is 5% of 820? 3980 in the ratio 1 : 4 ? 3 16 What is 20% of 160? 13 What is /4 of 3828? 4 17 What is /5 of 95470? 14 What is the smaller amount of 981 in the ratio of 1 : 2 ? 19 The ratio of 3 : 11 is the same 15 What is 50% of 9284? as 21 : ? 1 21 What is 1% of 1000? 18 What is /4 of 2420? 7 22 What is /10 of 3040? 20 What is the larger amount of 132 in the ratio 6 : 5 ?

Fractions, Ratios and Percentages..Answers

1 2 3 4 1 4 4 2 9 0 5 6 7 2 5 1 9 2 8 9 10 5 6 4 0 0 6 11 12 13 0 4 9 9 2 3 14 15 3 1 8 4 8 16 17 18 3 2 7 6 3 7 6 19 20 21 7 7 4 1 0 22 2 1 2 8 5

Across Down 1 What is ½ of 2884? 2 What is the larger amount of 60 in the ratio of 1 : 3 ? 4 What is the larger amount of 3 What is 75% of 280? 150 in the ratio 2 : 3 ? 1 6 What is 10% of 1920? 4 What is /3 of 276? 4 8 What is /5 of 70? 5 The ratio of 2 : 5 is the same as 100 : ? 9 What is the smaller amount of 7 What is 90% of 1010? 3000 in the ratio of 2 : 13 ? 1 11 What is 25% of 196? 9 What is /10 of 49870? 1 12 What is /3 of 2769? 10 The ratio of 3 : 7 is the same as 27 : ? 14 What is the larger amount of 11 What is 5% of 820? 3980 in the ratio 1 : 4 ? 3 16 What is 20% of 160? 13 What is /4 of 3828? 4 17 What is /5 of 95470? 14 What is the smaller amount of 981 in the ratio of 1 : 2 ? 19 The ratio of 3 : 11 is the same 15 What is 50% of 9284? as 21 : ? 1 21 What is 1% of 1000? 18 What is /4 of 2420? 7 22 What is /10 of 3040? 20 What is the larger amount of 132 in the ratio 6 : 5 ?

70 07/04/18 Westfield Community School - Mathematics 83: Unit 3: Chapter 10: Straight lines Lesson 1 Activity 3 Lesson 2 Lesson 3 l

a Sketch the polygons, divide up into the Ratio questions: have the questions and the Using the number cards, go through some t

n triangles. Work out the interior and answers written in the board, match up the decimal addition and subtraction questions e

M exterior angels for each of these shapes. pairs. Complete the workings to match the with upto two decimal places. Which table can complete the list upto questions with the answers. octagon first!

S . . Recognise that equations of the . Recognise that equations of the . Recognise that equations of the N form y = mx + c correspond to form y = mx + c correspond to form y = mx + c correspond to N straight line graphs straight line graphs straight line graphs . Plot the graphs of linear functions, . Generate points in all 4 quadrants and . Generate points in all 4 quadrants and where y is explicitly in terms of x plot the graphs of linear graphs, plot the graphs of linear graphs, using ICT where y is explicitly in terms of x, on where y is explicitly in terms of x, on paper paper

e Go through plotting points on a straight Computer room: Omnigraph Reinforce facts learnt from yesterday. Show pupils how to substitute a co- m

e line on 4 quadrant axis. Write down the Introduce y = mx + c and what m and c ordinate into a linear equation to see if the h t

co-ordinates, what do you notice? What Get pupils to plot lines y = x, y = 2x, y = stand for point is on the line. Also show how to n i could that line be called, so that everyone 3x. What do you notice? linear – straight line graph substitute a value of x into the equation to a

M will know what line we are talking about? What happens if you have a fraction of x? gradient – steepness find a value of y, so the graph can be Do lines in both x and y direction. What happens if x is negative? intercept of the y axis – where it cuts plotted.

Do p202 –204 Exercises 10:1 & 10:2 Plot y = x +1, y = x + 2, y = x + 3 etc. Do p208 – 211 Exercise 10:4 Do p211 – 213 Exercises 10:5 & 10:6 What do you notice? What happens if you Use graph paper to draw graphs!! Extension: take away a number rather than add? Extension: p222 Q1, 2 & 3 Extension: p222 Q6 & 7 Ensure that pupils keep notes and sketch graphs that they draw.

k Do p205 – 207 Exercise 10:3 Do p214 Exercise 10:7 w Use graph paper and draw rather than use Use graph paper and stick in properly. H counters. Remember to label axis and give the graphs titles. y

r Have a large axes drawn on the board. Ask On an OHT have some equations of lines, Have equations of lines and some co- a

n pupils to come to the front and draw on using the white boards, pupils answer ordinates and match them up. Have some e l lines such as y = 3 etc questions about the gradients and unfinished co-ordinates e.g (3, …) and get P intercepts of the lines. pupils to fill in the missing numbers. Can draw go through drawing a line on the board if there is time.

a Using at least one negative number and One 1- 100 grid divide the numbers by 5, Checklist for chapter 10: t

n addition/ subtraction only, how many write on the remainders. Can you spot the Know the lines x = are vertical e

M different ways can you make 5? pattern? What would happen if you divide Know the lines y = are horizontal Pupils come to the front and write their by another number? Try it and see if you Know that where the two line cross is answers on the board. are right. called point of intersection Understand the rule of a line is called the equation of a line Know that the co-efficient of x is the

S . Recognise that equations of the form . Solve problems & explore patterns in a gradient N y = mx + c correspond to straight range of contexts (shape, space & Know the number is the intercept of the y N line graphs measures) axis

e Recap y = mx + c and discuss the effects of Mini- investigation: Do p 224 Test yourself m

e m and c on the graph. h t

P219 Can’t see the wood for the tree. Mark and fill in pupil assessment booklet. n i Do p215 – 218 Exercise 10:18 a M Extension: p222 Q4 & 5

k Write up investigation on paper. w H

Key words:

y Line of the grid

r Have some lines drawn on some axes. Discuss pupil’s results for the investigation. Test pupils on key words, spellings and a

n Match the lines with the equations of the Go through how to write up the definitions Co-ordinates e l lines. Discuss the answers and encourage investigation, with hopefully most of the Points of intersection P proper use of the vocabulary for intercept input from the pupils. Equation of a line and gradient Linear Gradient Intercept

72 07/04/18 Westfield Community School - Mathematics 83: Unit 3: Chapter 11: Ratio Lesson 1 Lesson 2 Activity 4 Lesson 3 Lesson 4 l

a Have a scattergraph drawn on How many conversions can you How many fractions, decimal Using the number cards, t

n an OHT, pupils describe write down? Metric to metric and percentage questions can answers some negative number e

M correlation. Give real life lengths, then include imperial to you make up and work out with questions. Subtraction and examples of what the graph imperial, and then metric to the number 60. E.g 10% of 60 addition! could represent. What would the imperial! 1 point for each = 6, ¾ of 60 = 45 etc. axis be labelled? Title? correct answer! Check your question sand answers with your partner!

S . Know rough metric . Use units of measurement . Extend understanding of . Reduce a ratio to its . Extend understanding of the N equivalents of imperial to measure, calculate & the relationship between simplest form relationship between ratio N measures in daily use (feet, solve problems in everyday ratio and proportion and proportion miles, pounds, pints, contexts involving length, . Divide a quantity in a gallons) volume and capacity given ratio . Know rough metric . Reduce a ratio to its equivalents of imperial simplest form, recognising measures in daily use (feet, links with fraction notation miles, pounds, pints, gallons) e Go through metric and imperial Recap conversions relating to Giants – a class activity on ratio. Recap idea of ratios and how Discuss how proportions and m

e units. Discuss conversions mass and capacity. they can be written. Go through ratios can be used to solve h t

between metric and approximate Explain difference between See additional teacher notes. how to cancel them down. problems. Cross-curricular ideas n i conversion from metric to metric tonne and imperial ton! – food and recipes a

M imperial and visa and versa Do p232 – 235 Exercise 11:6 Do p229 – 231 Exercise 11:3 & Do 236 – 237 Exercise 11:7 Do p 227 – 228 Exercise 11:2 11:4 Extension: Extension: Extension: Extension:

k Do p227 Exercise 11:1 Write up today’s activity Do p238 – 239 Exercise 11:8 w H y

r Match cards – pupils are given a Have some packages or pictures Go through some questions on Have a recipe on the board, a

n card with one part of a pair of of items. Estimate the capacity cancelling ratios with the pupils. working in pairs/ groups, rewrite e l conversion. Have to go around or mass, using the appropriate Use the whiteboards to allow all the recipe for a different number P the room to find their partner! units. the pupils to answer the of people. questions. Discuss the answers.

74 07/04/18 Westfield Community School - Mathematics Giants.

My hand span is ...... long.

The giant's hand span is ...... long.

Body Parts I Number of J Size of handspans Giant Head: length : width Arms: lower : upper Neck

Trunk: upper : lower Leg: upper : lower Foot

a Have a straight line graph drawn Questions on angles in a triangle. If 25% of a number is 15, what is Checklist for chapter 11: t

n on an OHT. Discuss what the table Scalene, isosceles, and equilateral the number? Know the metric conversions e

M would look like, what points triangles – what are the rules? Having worked out the answer to Know the imperial and metric would fit on the line, what would What are the answers to the that, work out as many other conversions a parallel line’s equation be? questions on the board? percentages of the number as you Understand the terms length, mass What could this line represent? can. E.g 10%, 1%, 50%, 75% etc and capacity Be able to use proportion to solve

S . Use the unitary method to . Reduce a ratio to its simplest . Reduce a ratio to its simplest problems N solve simple word problems form, including a ratio form, including a ratio Understand and use scale. N involving ratio and direct expressed in different units expressed in different units proportion

e Show how ratios can be written Discuss scales and where pupils Go through converting units and Do p248 Test yourself m

e into the form 1:n or n:1. might come across them. how this relates to ratios. h t

Mark and fill in pupil assessment n i Do p239 Exercise 11:9 Do p240 – 241 Exercise 11:10 Do p242 – 243 Exercise 11:11 booklet. a M Extension: Extension: Extension:

k Design a front room/ dinning Ensure all work on the chapter is w room, whose dimensions are 10m completed and the corrections are H by 8m. From a catalogue, choose also completed fully. furniture to put into your room. Complete the worksheet from this Now draw a scale drawing (floor lesson. plan) of your room and its furniture. Include all details in your write up. Key words: Metre –milli, centi,

y kilo etc

r Have some ratios on the board and Have some maps, with 1:n ratios. Pupils design some questions of Test pupils on key words, a

n them written in the form of 1:n or Work out some distances on the their own and give them to a spellings and definitions Inch, yard, foot etc e l n:1. Pupils have to match them up map. partner to solve. Return for Ounce etc P or find the odd one out. checking – discuss the answers as Worksheet: Units (fill the gaps) Ratio a whole group. Proportion Scale

76 07/04/18 Westfield Community School - Mathematics 83: Unit 3: Chapter 12: Area Lesson 1 Lesson 2 Lesson 3 Lesson 4 l

a Answers around the room. Pupils are given On an OHT, have some questions on Negative number question on a card given Teacher calls out some equation of lines t

n a question and have to blue tack their angles with intersecting and parallel lines. to each pupil. They have to find the and pupils use their arms to demonstrate e

M question underneath the right answer. Pupils work in pairs to work out the person who has the same answer. the line e.g x = y, x = 6, y = 3, y = 2x. y = Once everyone has done that, teacher answers and write them onto the Blue tack up answers and then go through 3x, y = x + 2, y = x + 5 etc discusses positions of questions with whiteboards. Discussion of answers and as class – do they agree on pairs. Can Ensure that pupils realise basic ideas of pupils. (fractions, %, decimals) methods with whole class. always try to catch them out by having lines. more than two same answers.

S . Calculate perimeters & areas of plane . Deduce & use formulae for the . Deduce & use formulae for the . Deduce & use formulae for the N rectilinear figures triangle, parallelogram triangle, parallelogram and triangle, parallelogram N trapezium

e Recap briefly area and perimeter of Recap triangles and parallelograms Introduce trapeziums and the formula for Go through how to work out areas of m

e rectangles, compound shapes made of formula. Emphasise perpendicular heights! working out their areas. Can show how compound shapes and how to set out h t

rectangles, triangles and parallelograms Remind how the formulae are found. formula is created practically. carefully. Encourage drawing of diagrams n i and labelling. a

M Do p250 –253 Exercises 12:1 & 12:2 Do p254 Exercise 12:3 Do p255 – 257 Exercises 12:4 & 12:5 Go through area of a kite, showing how formula works practically. Extension: Extension: Extension: Do p258 – 261 Exercises 12:6 & 12:7

Extension: p268 Q2, 3, 4, 5 & 6

k Design a poster for the formulae learnt Finish work from today w today. And H And finish any incomplete work. P261 Exercise 12:8 y

r On an OHT have some shapes drawn and Have some triangles and parallelograms on Who can write down the formula of the On the board, pupils put as many of the a

n work out the perimeters and the areas. an OHT and some perimeters/ areas. area of a trapezium. Now draw a trapezium formulas as they can. e l Working backwards find a shapes that has Match up the shapes with the answers. and label the sides. Design a shape, and label the sides, get P a perimeter of .. or an area of .., discuss your partner to find the area. and look at answers of pupils. Discuss the answers on your table.

77 07/04/18 Westfield Community School - Mathematics Lesson 5 Lesson 6 Activity 5 Lesson 7 l

a Each pupil is given a decimal Describe a real life situation that Checklist for chapter 12: t

n number with a maximum of two would be a negative correlation, Understand the term perimeter e

M decimal places, pupils have to positive correlation, no correlation. Understand the term area get into numerical order. What would the axis be labelled as? Know the formula for area of a rectangle Be able to work out the area of

S . Understand & use the . Understand & use the . Understand & use the compound shapes N language & notation language & notation language & notation Know and use the formula for N associated with associated with enlargement; associated with enlargement; area of a triangle enlargement; enlarge 2D enlarge 2D shapes enlarge 2D shapes shapes

e Go through enlargement and Recap work from yesterday and Find a simple picture, and cut into Do p270 Test yourself m

e scale factors. Explain how scale show how process can be reversed. pieces. Give each pupil a piece of h t

factor affects areas the picture. Mark and fill in pupil n i – use p262 – 263 exercise 12:9 Do p264 – 265 Exercises 12:11 & Pupils have to enlarge the piece and assessment booklet a

M 12:12 draw. Then put all the pieces back Do p263 exercise 12:10 together to make whole picture! Extension: Extension: p268 Q1

k Finish the exercises 12:10 – 12:12. Complete picture from w Correct any incorrect questions. yesterday for next lesson. H And/or learn key words from the And learn formulae for test. chapter. y

r Have some shapes and scale Give two shapes, one an Test pupils on key words, a

n factors, predict the area of the enlargement of the other, ask what spellings and definitions e l enlargement – draw it and see if was the scale factor. Key words: P you are right. Discuss the answers given by the Perimeter pupils. Area Cm2, m2 etc Scale factor

78 07/04/18 Westfield Community School - Mathematics 83: Unit 3: Revision and test Lesson 1 Lesson 2 Lesson 3 l

a Pupils given a card with a fraction, Have some pictures of real objects, Testing of: t

n decimal or percentage. Pupils have to peg estimate their length/ mass/ capacity, using e  Consolidate & extend mental methods of calculation,

M up their card in the correct order on a the correct units either in metric or working with percentages number line. Discussing cards as they are imperial. . Carry out more difficult calculations effectively & placed onto the line. efficiently using the function keys: percentage  Use the equivalence of fractions, decimals &

S . See previous references to NNS . See previous references to NNS percentages to compare proportions N

N  Calculate fractions of quantities  Know rough metric equivalents of imperial measures in daily use (feet, miles, pounds, pints, gallons)  Calculate perimeters & areas of plane rectilinear figures  Deduce & use formulae for the triangle, parallelogram . Recognise that equations of the form y = mx + c correspond to straight line graphs  Generate points in all 4 quadrants and plot the graphs of linear graphs, where y is explicitly in terms of x, on paper

e Review main points of chapters 9 & 10 Review main points of chapters 11 & 12 Test unit 3 m

e Do p196 - 197 Questions sections in Do p224 Questions sections in chapter 11 h t

chapter 9 Calculator section only. n i a M

k Do p220 - 221 Questions sections in Do p266 – 267 Questions section in w chapter 10 chapter 12 H y

r Divide the board into 2 parts and pupils Divide the board into 2 parts and pupils a

n write up as much as they know about write up as much as they know about e l chapters 9 & 10. Discuss key points/ words chapters 11 & 12. Discuss key points/ P words

Year 81: Unit 3 Test: Calculator allowed

1. Work out the following: a) 50% of 320 b) 10% of 675 c) 30% of 80

2. What are these numbers as percentages: a) 68 out of 100 b) 23 out of 50 c) 16 out of 25

3. What is: a) 54% of £685 b) 37% of 288g

4. Work out: 3 5 a) of £108 b) of848 cm 7 8

5. Convert the units in each of these: a) 470cm into m b) 1375mm to cm c) 1.7m into cm

6. Work out the area of the following shapes: 12cm a) b) c) 3cm 3cm 5cm 10cm 6cm

8cm 5cm

7. Copy the axisa) on the right. 8 a) Drawb) the line y = 3 on your axis 7 b) Drawc) the line x = 5 on your axis 6 c) Writed) down the co-ordinate where the lines 5 cross. e 4 d) Write down the co-ordinates of the point of intersection of these lines: x = 2 and y = 6 3 e) Write down the rules of the two lines that 2 cross at the point (4 , 7) 1 f) Draw the line y = 3x on your axis 0

80 0 1 2 3 4 507/04/18 6 7 8 Westfield Community School - Mathematics 83: Unit 4: Chapter 13: Statistics: getting it together Lesson 1 Lesson 2 Activity 1 l

a Pupils draw a 3 by 3 grid and fill it in with % of their A bag has counters of different colours. The probability t

n choice. Teacher calls out decimal equivalents and of getting a blue one is ¼. What counters could be in e

M pupils cross out percentages. First one to cross them all the bag? What happens if there are 16 / 24 etc counters? out wins. What can you say for definite? What other information do you need to decide what is in the bag?

S . Calculate statistics – for discrete data, find the . Calculate statistics – for discrete data, find the . Draw & produce, on paper:- diagrams & graphs for N mode, mean, median and range mode, mean, median and range continuous data, including bar charts and frequency N . Compare 2 distributions using the range and one or . Compare 2 distributions using the range and one or diagrams more of the measures of average more of the measures of average . Interpret graphs for continuous data and draw inferences that relate to the problem being discussed

e Recap mean, median, mode and range. Discuss which Same as yesterday, but very quick. Discuss different types of data: discrete and continuous. m

e averages to use and when. Explain differences in drawing bar chart (bars not h t

Do p275 – 277 Exercises 13:2 & 13:4 together) and histogram (bars next to each other) n i Do p272 – 274 Exercise 13:1 a

M Extension: Do p280 – 282 Exercise 13:7 Q1 - 3 Extension:

k Do p276 Exercise 13:3 w H y

r Have two sets of data of 2 100m runners. You have to Have some data on wages. Explain the employees want a

n pick the runner you would choose to put into your team. a pay rise, and the employer does not want to give them e l Get pupils to work in groups and then put their one. How would they use the statistics to support their P arguments forward, using the different averages or cases. range

a Using half, quarter, eight and Pupils have some cards with Pupils have a set of cards with Checklist for chapter 13: t

n sixteen, and the operation +/- only. different lengths on in metric units. polygons on. Teacher say “lines of Be able to work out the mean, e

M How many different questions and Pupils have to put them into order, symmetry” and the pupils have to median, mode and range for answers can the pupils make? shortest first. E.g 2.4m, 215cm, group the cards, putting similar discrete data 2m, 2220mm etc.. ones together. Discuss outcomes. Be able to work out the mean of Other categories: order of grouped data rotational symmetry, sets of Be able to draw frequency polygon parallel lines etc. graph

S . Calculate statistics:- for . Draw & produce, on paper:- . Draw & produce, on paper:- Understand the term, trend N continuous data, find the range graphs, including frequency graphs, including frequency N and, for grouped data, the diagrams diagrams modal class . Interpret graphs for both . Interpret graphs for both discrete & continuous data & discrete & continuous data & draw inferences that relate to draw inferences that relate to the problem being discussed; the problem being discussed; relate summarised data to the relate summarised data to the questions being explored questions being explored

e Go through finding a mean of Explain a frequency polygon, Recap plotting of points for Do p294 Test yourself m

e grouped data. pointing out where to plot the grouped data. h t

points for grouped data. Mark and fill in pupil assessment n i Do p284 Exercise 13:8 Do p290 Exercise 13:10 booklet a

M Do p286 - 289 Exercise 13:9 Use graph paper to draw graphs. Extension: p292 Q1 Can do a lot of this orally Use graph paper to draw graphs Extension: p292 Q2

Extension:

k Do p282 Exercise 13:7 Q4 & 5 Complete any unfinished work Key words: w And .. H Mean Choose a question you did from this exercise and do it on paper for Median a display – ensure you label it Mode properly Range Grouping y r Have a table of grouped data. As a Have a large set of axes drawn on Have a frequency polygon graph Test pupils on key words, spellings Discrete data a

n class work out the approximate the board and some data. As a drawn on an OHT. Ask pupils and definitions

e Continuous data l mean. class draw the frequency polygon. questions about the graph. (Can P use the whiteboards for them to Worksheet: Statistics (year 8) Tally write their answers on) Match the words and Frequency polygon definitions/diagrams) 82 07/04/18 Westfield Community School - Mathematics 83: Unit 4: Chapter 14: Volume: filling the space Lesson 1 Lesson 2 Lesson 3 Lesson 4 l

a Using the number cards, times tables and Some probability scenarios on OHT/ cards. Have some boxes, containers.. estimate the Have a triangle, square, rectangle, t

n division question upto 10 × 10. Pupils have to work out probabilities and volumes, capacity, mass etc. parallelogram, trapezium, their rules e

M For less well known tables, group chanting then put into order, with smallest first. Pupils write estimate on the whiteboards, written in algebra and words, all on or number stick! who has the closest value? Ensure pupils separate cards. Pupils have to match up the using sensible units. cards into threes. Pupils then share answers and check they all agree – if not discuss and amend their answers.

S . Use units of measurement to measure . Know & use the formula for the . Calculate volumes of compound . Calculate volumes of compound N & estimate in everyday contexts volume of a cuboid; calculate shapes made from cuboids shapes made from cuboids N involving volume, capacity volumes of cuboids

e Recap units of volume and capacity. Go Go through volume of a cuboid. Volume of prisms, however book does not Explain a prism. Have visual aids m

e through conversions of units. use word prism yet! available. Include cross section. h t

Mini investigation: if you have 48 multi- n i Do p296 – 298 Exercises 14:1 & 14:2 link, how many different cuboids can you Do p302 – 303 Exercise 14:5 Do p305 Exercise 14:6 orally a

M Can do this orally and where possible have make? Have multi-link available! visual aids for capacity! Extension: Do p306 – 307 Exercise 14:7 Do p299 – 301 Exercises 14:3 & 14:4 Extension: Extension: p314 Q1 & 2 Extension:

k Find 10 items – find their volume/ Do p311 Exercise 14:10 Building a box w capacity. Convert the units into ml or cm3 H y

r Write up the conversions on the board. Have some cuboids drawn on an OHT. Have some 3D objects, ask the pupils to With the prisms identified from yesterdays a

n Work out the volumes. identify which are prisms. lesson, pupils identify the cross sectional e l Have some lengths in a mixture of units so areas. P that pupils have to convert the units first.

83 07/04/18 Westfield Community School - Mathematics Lesson 5 Activity 2 Lesson 6 l

a Using 0.1, 0.2 0.3, 0.4, make all tenths Checklist for chapter 14: t

n between 0 and 2 e.g 1.2, 1.4 etc Understand the terms volume and capacity e

M Can use any of the four operations. Understand the units of volume are cm To extend more able, now convert all of cubed the questions and answers into fractions. Understand the units of capacity are millilitre Know the conversion 1ml = 1cm cubed

S . Calculate volumes of compound . Use the formula for the volume of a Know that 1000ml = 1 litre N shapes made from cuboids cuboid Know the formula for volume of a cuboid N . Calculate areas of plane rectilinear figures

e Go through volume of prism, where Computer room Do p316 Test yourself m

e cross sectional area using formulae such h t

as triangle, parallelogram. Go through EXCEL Mark and fill in pupil assessment booklet n i how to reverse questions. Put results from homework on building a a

M box on to a spreadsheet. Do p308 – 310 Exercise 14:9 Plot a graph of results, what would be the optimum volume be? Extension: p314 Q3 (Max-box – see additional notes)

k Do p307 – 308 Exercise 14:8 Complete all exercises from this chapter w and correct any wrong answers. H Complete write up from computer lesson yesterday. Key words: Volume Capacity y

r Have some questions written on an OHT Test the pupils on the key words, spellings

a Litres

n that involve reversing the rules and and definitions e l working backwards. Cubic cm P Pupils work through together as a class Volume or in small groups. Stack Prism Cross section

84 07/04/18 Westfield Community School - Mathematics 83: Unit 4: Chapter 15: More or less? Lesson 1 Lesson 2 Activity 3 Lesson 3 l

a Roll a dice six times, write down the Teacher draws a shape on the board, pupils 0.24 0.6 0.15 t

n numbers. Use the numbers to make have to write down as many facts as they e 0.8 0.31 0.4

M 100. Can use any of the four can about the shape. They get 1 point for operations, can put numbers together to each correct fact. E.g name, symmetry, 0.1 0.05 0.75 make 2 digit numbers. order of rotation, parallel lines, angles, length of sides etc. Give pupils target numbers to make using the numbers above, and any of the four operations.

S . Not on year 8 NNS . Not on year 8 NNS . . Not on year 8 NNS N However important NCT topic, so However important NCT topic, so N introduce idea introduce idea

e Go through trial & improvement Go onto using decimal places for trial and EXCEL Remind pupils of inequality signs. m

e methods. Encourage good setting out. improvement. Go through how to show inequalities on h t

Put formulae onto spreadsheet and check number line (dots – filled in: equal to etc. n i Do p318 – 319 Exercise 15:1 Do p320 – 321 Exercise 15:2 answers to exercises 15:1 & 15:2 a

M Do p322 – 324 Exercises 15:3 & 15:4 Extension: Extension: p334 Q1 See additional notes. If short of time, do not cover inequalities as it is not on the NNS for year 8 and a level 8 topic

k Finish exercise 15:2 Do p325 exercise 15:5 w And H y

r Solve a question as a class using a Pupils design a question, and then they Have a pack of 1 – 100 cards. Pupils pick a

n large number line to show ‘homing in’ choose the best question. Everybody has a out two cards, and then have to write down e l on the answer. guess at the answer, then help to answer it the appropriate inequality sign to put in the P on the board. See who had the closest middle. answer.

a On triangular dotty paper, rule Have an OHT with intersecting 30% = 27 Checklist for chapter 15: t

n off 3 by 3 sets of dots. Pupils and parallel lines. Pupils have What other facts can the pupils Understand the term trial and e

M draw different triangles or to estimate the angles. Pupils work out? E.g 100% = , ½ = improvement quadrilaterals, then work out then check angles by etc. Understand the idea of inverse the areas. measuring and using rules. Know the inverses of the four operations Be able to solve equations by using the inverses of the operations

S . Not on year 8 NNS . Not on year 8 NNS . Not on year 8 NNS N N

e Recap inequalities and include Go through solving Go through how to solve Do p336 Test yourself m

e double inequalities. inequalities. double inequalities. h t

Mark and fill in pupil n i Do p326 – 327 Exercises 15:6 Do p328 – 329 Exercises 15:8 Do p331 – 332 exercises 15:11 assessment booklet a

M & 15:7 & 15:12 Extension: p334 Q7 Extension: p334 Q2, 3, 4, 5 & Extension: p334 Q8 & 9 6

Short of time? Not this then. Short of time? Not this then Short of time? Not this then

k Do p330 Exercise 15:9 Complete any unfinished work w from inequalities. H

r Fill in the gaps idea. This time Have some questions on the Have a question, get pupils to Test pupils on key words, a

n numbers on an OHT, pupils board, work through the come to the front and do a line spellings and definitions Key words: e l write down answers and hold answers together. each.

P Trial & improvement up on whiteboards. Inequality Inverse Double inequality

83: Unit 4: Chapter 16: The crossing point Lesson 1 Lesson 2 Lesson 3 Activity 4 l

a Countdown: Have some probabilities on the board, such Complete the question: t

n 75, 4, 9, 3, 1, 6 as half, quarter and pupils have to design 1.2……………………………= 2.4 e

M Target = 144 questions that would give those answers. How many ways can you complete this How many different ways can you make Pupils discuss their questions. question in one step? the target? What about in two steps? What about using different operations?

S . Represent mappings expressed . Represent mappings expressed . Substitute integers into formulae, . Generate points in all four quadrants N algebraically algebraically including examples that lead to an & plot linear functions, where y is N . Generate points in all four quadrants . Generate points in all four quadrants equation to solve explicitly in terms of x, using ICT & plot linear functions, where y is & plot linear functions, where y is explicitly in terms of x, on paper explicitly in terms of x, on paper

e Recap drawing lines. Go through idea of Recap yesterday’s work. Must use graph Go through finding points on a line. In computer room: either EXCEL or m

e simultaneous equations, solved by paper! Omnigraph h t

drawing. Do p344 Exercise 16:4 n i Do p342 – 343 Exercise 16:3 Q1 - 3 Can use the programs to check graphs and a

M Do p338 – 340 Exercise 16:1 & 16:2 Extension: p350 Q2 answers. Extension: Extension: p350 Q1 See additional notes.

k Do p343 exercise 16:3 Q4 – 6 P345 Exercise 16:5 w H y

r “John goes to the shop and buys a coke Work through a question together on the Have some lines on an OHT, name some a

n and a twix, it costs 60p. What are the board. points that are on the lines – how do you e l possible prices?” Draw on a large chart. know and how can you check that you are P “Jane goes the next day and buys 2 cokes right? and a twix, it costs £1. What does she 87 07/04/18 Westfield Community School - Mathematics think the possible prices could be?” Draw her ideas on the graph. Using both Jane and Johns’ ideas what are the prices of a coke and a twix. Could you work it out any other way?

a Using the 1- 100 grid, and two dice. Using number cards, answer fractional Checklist for chapter 16: t

n Pupils throw the two dice and add the additional and subtraction questions. Be able to find co-ordinates from the e

M score together. They then put a counter equation of the line on a multiple of that number. Aim is to Be able to plot co-ordinates and draw a get four in a row. straight line Spot patterns in tables and relate them

S . Not on year 8 NNS . Not on year 8 NNS to the gradient. N However level 7 and we should However level 7 and we should Use patterns to find rules N introduce idea introduce idea

e Go through solving simultaneous Recap work, especially checks. Do p352 Test yourself m

e equations algebraically. Explain how h t

to check their answers. Do p347 Exercise 16:8 Mark and fill in pupil assessment n i booklet a

M Do p346 – 347 Exercises 16:6 & 16:7 Extension:

Extension:

k Do p348 Exercise 16:9 w H y

r 1 coke and 1 twix = 60p Similar to yesterday, but with harder Test pupils on key words, spellings a

n 2 cokes and 1 twix = £1 numbers. and definitions e l How can you work out the answer? P How did you do it? Can you do it with different numbers? Key words: How can you check your answers? Points of intersection Simultaneous equations 88 07/04/18 Westfield Community School - Mathematics

83: Unit 4: AT1, revision and test Lesson 1 Lesson 2 Lesson 3 l

a Using 1- 100 grid, and dice. Pupil rolls the dice and Have some numbers on the board e.g 2¼, 1¾ etc. 8 5 2 t

n moves that number of spaces starting at 1. Make up Ask how many quarters are in those numbers, how many e

M additional rules such as if land on a prime number, move halves?, how many eighths? What fraction is left over?? 1 9 7 a space backwards, land on a square move one square forwards. 3 6 4 Can have each group make up their own rules – are they are equally likely – who has the best rules? Who has the fairest rules etc.? Target = 56 How many ways can you make the target, usign the 4 operations?

S . See previous references to NNS . Solve problems & explore them in a range of . See previous references to NNS N contexts (shape, space & measures) N . Identify the necessary information to solve a problem; represent problems & solutions in algebraic, geometric & graphical form, using correct notation & appropriate diagrams

e Go through work in chapters 13 & 14 Start investigation ‘Rows of cubes’ Go through chapters 15 & 16 m e h t

Do p291 Questions for chapter 13 See additional teacher notes. Do p333 Questions from chapter 15 n i a M

k Do p312 – 313 Questions from chapter 14 Do p349 Questions from chapter 16 w H y

r Divide board into two pieces and pupils write up all they Go through pupils friendly investigation criteria – what Divide the board into two pieces and pupils write up all a

n know about these chapters have they completed so far – what marks have they got? they know about these chapters. e l What do they need to do to get the next level for the P three strands?

a Staring with ¼, how many different ways can you get Testing of: t 2 n the answers of 2¾? You can use any of the four of a number is 6. What is the number? e 7

M operations, also one step. Two step operations etc. Pupils need to discuss how to work this out, write some of their own questions and answer each other’s questions.

S . Solve more complex tasks by breaking them into . Explain & justify inferences & reasoning, N smaller steps or tasks, choosing & using efficient using step-by-step deduction N techniques for calculation, algebraic manipulation . Suggest extensions by asking ‘What if..? or & graphical representation ‘Why?’, conjecture & generalise

e Continue with investigation. Continue with extensions Test Unit 4 m

e Finish first part and go onto extensions. h t

n i a M

k Complete the write up of the investigation. w H y

r Go through pupil friendly criteria and discuss ways Go through what a perfect investigation would look a

n forward to improve their work. Get your partner to like. What should it include, what should it be handed e l look at your work and see what else you have to do to in looking like? P get the next level.

91 07/04/18 Westfield Community School - Mathematics Rows of Cubes Investigation

Question:  You need to look at how many faces of a row can be seen when they are laid on a table. E.g.

5 faces 8 faces 11 faces

 You also need to think about the number of faces which cannot be seen, and the total number of faces.

Investigate!

 Some answers for you:

Number of Number of Faces Number of Faces Total Number of Cubes in a Row Visible Hidden Faces C V H F 1 5 1 6 2 8 4 12 3 11 7 18 4 14 10 24 5 17 13 30

 Rules: 3C + 2 = V 3C  2 = H 6C = F

 Ideas for extensions:

Squares: Cubes: Corners:

Pyramids: These are all stage 2 shapes. For all of these patterns, shape 1 is a single cube.

 An example table for the above ideas:

Stage Number of Number of faces that Number of faces that Total number of cubes used can be seen can’t be seen faces

93 07/04/18