KS3 Scheme of Work - Year 8 - SET 1: IMPACT 2R

MATHS DEPARTMENT

YEAR 8 SCHEME OF WORK SET 1: IMPACT 2R

SEPT 2004 2R PLAN

AUTUMN TERM – FIRST HALF Topic 1 Number 2R Ch. 1 Topic 2 Angles 2R Ch. 2 Topic 3 Fractions, Decimals & Percentages Additional Transition Unit Topic 4 Fractions & Ratio 2R Ch. 3 Topic 5 Probability 2R Ch. 4 TEST 1

AUTUMN TERM – SECOND HALF Topic 6 Decimals 2R Ch. 5 Topic 7 Shape & Measure 2R Ch. 7 Topic 8 Percentages 2R Ch. 6 TEST 2

SPRING TERM – FIRST HALF Topic 9 Positive & Negative Numbers 2R Ch. 8 Topic 10 Multiplicative Relationships Additional Unit Topic 11 Working with Algebra 2R Ch. 10 TEST 3

SPRING TERM – SECOND HALF Topic 12 Handling Data + unit 2R Ch. 13 + Additional Unit Topic 13 Number Patterns 2R Ch. 9 Topic 14 Perimeter, Area & Volume 2R Ch. 15 TEST 4

SUMMER TERM – FIRST HALF Topic 15 Averages 2R Ch. 16 Topic 16 Graphs 2R Ch. 12 Topic 17 Problem Solving Additional Unit TEST 5

SUMMER TERM – SECOND HALF Topic 18 Formulae & Equations 2R Ch. 14 Topic 19 Transformations 2R Ch. 11 “OPTIONAL TESTS“ Topic 20 Thinking Proportionally Additional Transition Unit Topic 21 Investigation AUTUMN TERM A TOPIC 1 Topic: Number NC Level: 4 - 7 NC Programme of Study: Ref2ab: use previous understanding of integers and place value to deal with arbitrarily large positive numbers and round them to a given power of 10; order integers. Ref3h: round to the nearest integer and to one significant figure; estimate answers to problems involving decimals. Ref4c: use a variety of checking procedures, including working through the problem backwards, and considering whether the result is of the right order of magnitude. Learning Objectives:  understand place value, recognising HTU etc with large numbers.  recognise and use multiples, factors, common factor, HCF, LCM and primes  use squares, positive and negative square toots, cubes and cube roots, and index notation for small positive integer powers  round positive numbers to any given power of 10  make and justify estimates and approximations of calculations  round numbers to 1 significant figure  use inverse operations to check calculations Key Vocabulary: MILLIONS BILLIONS MULTIPLE FACTOR PRIME POWER ROUND NEAREST SIGNIFICANT FIGURE CHECK ESTIMATE INVERSE OPERATION Impact Reference: Other references: Book 2R – ch. 1 V4 - ch.2-4 V5 – ch. 2 V8 – ch. 2 KM83 – 1-2 Mental & Oral Starters: 2R folder: pg. 4 – 5 101 Starters: pg. 14-18, 22, 47, 58 Discussion opportunities: Discuss whether an answer is ‘sensible’. Pair / Group Work: Students can show each other their methods or check each others’ answers; compare estimations. ICT Links: SMILE Spiritual/Moral/Citizenship Links:

Investigation:

Time: 4 – 5 lessons AUTUMN TERM A TOPIC 2 Topic: Angles NC Level: 4 - 6 NC Programme of Study: Ref 2abcdg: recall and use properties of angles at a point, angles on a straight line, perpendicular lines and opposite angles at a vertex. Distinguish between acute, obtuse, reflex and right angles; estimate the size of an angle in degrees. Use parallel lines; the angle sum of a triangle is 180 degrees. Use angle properties of equilateral, isosceles, and right-angled triangles; understand congruence, recognising when 2 triangles are congruent; explain why the angle sum of any quadrilateral is 360 degrees. Calculate and use the sums of interior and exterior angles of quadrilaterals, pentagons and hexagons; calculate and use the angles of regular polygons. Ref4bd: understand angle measure, using the associated language. Measure and draw lines to the nearest millimetre and angles to the nearest degree; draw triangles and other 2D shapes using a ruler and protractor, given information about their side lengths and angles. Learning Objectives:  Use angle measure; distinguish between and estimate the size of acute, obtuse and reflex angles.  Identify parallel and perpendicular lines; know the sum of right angles, angles at a point, on a straight line and in a triangle. Recognise vertically opposite angles.  Identify alternate angles and corresponding angles  Understand the proof that : - the sum of the angles of a triangle is 180 and quadrilateral is 360 - the exterior angle of a triangle is equal to the sum of the 2 interior opposite angles  Find the interior and exterior angles of different polygons  solve the geometrical problems of side and angle properties or equilateral, isosceles and right angled triangles and special quadrilaterals, explaining reasoning with diagrams and text  classify quadrilaterals by their geometric properties Key Vocabulary: MEASURE DRAW ESTIMATE LINE AT A POINT TRIANGLE QUADRILATERAL POLYGON REGULAR PARALLEL Impact Reference: Other references: Book 2R – ch. 2 V4 - ch. 13, 18 V5 – ch. 15 V6 - ch. 12, 13 KM83 – 5, 7 Mental & Oral Starters: 2R folder: pg. 20 - 22 101 Starters: pg. 73, 79, 80 Discussion opportunities:

Pair / Group Work:

ICT Links: SMILE – Angle 360, Snooker. LOGO can be used to construct shapes; experiment with angles. Spiritual/Moral/Citizenship Links:

Investigation:

Time: 8 lessons AUTUMN TERM A TOPIC 3 Topic: Fractions, Decimals & NC Level: Percentages NC Programme of Study:

Learning Objectives:  Begin to use the equivalence of fractions, decimals and percentages to compare proportions  Recall known facts including fraction to decimal conversions  Use known facts to derive unknown facts, including products such as 0.7 & 6, and 0.03 & 8  Consolidate and extend mental methods to include decimals, fractions and percentages  Solve word problems mentally Key Vocabulary: EQUIVALENT FRACTION DECIMAL PERCENTAGE CONVERT NUMERATOR DENOMINATOR PROPORTION

Impact Reference: Other references: Transition Unit lessons N2.1 & N2.2

Mental & Oral Starters: See lesson plans Discussion opportunities: Pair / Group Work:

ICT Links:

Spiritual/Moral/Citizenship Links:

Investigation:

Time: 2 lessons AUTUMN TERM A TOPIC 4 Topic: Fractions & Ratio NC Level: 5 & 6 NC Programme of Study: Ref2cd: Use fraction notation; understand equivalent fractions, simplifying a fraction by cancelling all common factors; order fractions by rewriting then with a common denominator. Use decimal notation and recognise that each terminating decimal is a fraction. Ref3cdf: Calculate a given fraction of a given quantity, expressing the answer as a fraction; express a given number as a fraction of another; add and subtract fractions by writing them with a common denominator; perform short division to convert a simple fraction to a decimal. Understand and use unit fractions as multiplicative inverses; multiply and divide a given fraction by an integer, by a unit fraction and by a general fraction Divide a quantity in a given ratio. Learning Objectives:  know that a recurring decimal is a fraction  use division to convert a fraction to a decimal  understand addition and subtraction of fractions  use the laws of arithmetic and inverse operations  add and subtract fractions by writing them with a common denominator  calculate fraction of quantities (fraction answers)  multiply and divide an integer by a fraction  consolidate understanding of the relationship between ratio and proportion  reduce a ratio to its simplest form, including a ratio expressed in different units, recognising links with fraction notation  divide a quantity into 2 or more parts in a given ratio  use the unitary method to solve simple word problems involving ratio and direct proportion Key Vocabulary: MIXED NUMBER IMPROPER EQUIVALENT CANCEL SIMPLIFY LOWEST TERMS NUMERATOR DENOMINATOR DECIMALS COMPARE RATIO SCALE Impact Reference: Other references: Book 2R – ch. 3 V4 - ch.6 V5 – ch. 5 V6 - ch.2, 4 KM83 – ch. 9 Mental & Oral Starters: 2R folder: pg. 42 - 44 101 Starters: pg. 36-38, 56, 60 Discussion opportunities:

Pair / Group Work: Adapting recipes – enough to feed the whole class – display work. ICT Links:

Investigation: Find ratios in real life – e.g. no. of boys to girls in school, in population. Time: 9 – 10 lessons AUTUMN TERM A TOPIC 5

Topic: Probability NC Level: 5 & 6

NC Programme of Study: Ref3a: Design and use data collection sheets for grouped discrete and continuous data; collect data using various methods including observation, controlled experiment, data logging, questionnaires and surveys. Ref4cdef: Understand and use the probability scale. Understand and use estimates or measures of probability from theoretical models, including equally likely outcomes, or from relative frequency. List all outcomes for single events, and for 2 successive events in a systematic way. Identify different mutually exclusive outcomes and know that the sum of the probabilities of all these outcomes is 1. Learning Objectives:  use the vocabulary of probability when interpreting the results of an experiment  appreciate that random processes are unpredictable  understand that if the probability of an event occurring is p, then the probability of it not occurring is 1 – p (numerically rather than algebraically at this level)  find and record all possible outcomes for single events and 2 successive events in a systematic way using diagrams or tables.  estimate probabilities from experimental data, understand that: - if an experiment is repeated there may be different outcomes - increasing the number of times an experiment is repeated generally leads to better estimates of probability Key Vocabulary: CALCULATE TOTAL EVENT OUTCOME NOT HAPPENING EXPERIMENTAL SAMPLE SPACE DIAGRAM Impact Reference: Other references: Book 2R – ch. 4 V4 - ch.22 V5 – ch. 22-24 V6 - ch.20 V7 – ch. 22, 23 KM83 – 8 Mental & Oral Starters: 2R folder: pg. 58 - 59 101 Starters: pg. 99 - 101 Discussion opportunities: Discuss the likelihood of things happening in everyday life. Pair / Group Work: Probability experiments can be done in pairs to ensure results are recorded carefully. ‘Play your cards right’, human probability scale, Bingo with dice. ICT Links: SMILE Spiritual/Moral/Citizenship Links: Morality of gambling. Investigation: Investigate the probability of real events occurring – set up hypotheses etc. Time: 6 lessons – perhaps more depending on practical work AUTUMN TERM B TOPIC 6 Topic: Decimals NC Level: 4, 5 & 7

NC Programme of Study: Ref2d: Use decimal notation and recognise that each terminating decimal is a fraction. Ref3chijk: Perform short division to convert a simple fraction to a decimal. Round to the nearest integer and to 1 significant figure; estimate answers to problems involving decimals. Use standard column procedures for addition and subtraction of integers and decimals. Develop a range of strategies for mental calculation; derive known facts from those they know; add and subtract mentally numbers with up to 2 decimal places; multiply and divide numbers with no more than one decimal digit using factorisation where possible. Use standard column procedures for multiplication of integers and decimals, understanding where to position the decimal point by considering what happens if they multiply equivalent fractions; solve a problem involving division by an integer. Learning Objectives:  order fractions by writing them with a common denominator or by converting them to decimals  recall known facts, including fraction to decimal conversions  use known facts to derive unknown facts, including products involving numbers such as 0.7 and 6, and 0.03 and 8  consolidate and extend mental methods of calculation, working with decimals, fractions and percentages  order decimals  use standard column procedures for addition and subtraction of decimals  multiply and divide decimals by powers of 10  round decimals to the nearest whole number, or to one or two decimal places  use standard column procedures for multiplication and division of decimals; understand where to position the decimal point by considering equivalent calculations  find approximate answers to calculations, checking a result by considering whether it is of the right order of magnitude and by working the problem backwards Key Vocabulary: ORDER DECIMAL POINT FRACTION ROUND NEAREST PLACE ESTIMATE SIGNIFICANT FIGURE Impact Reference: Other references: Book 2R – ch. 5 V4 - ch.6 V5 – ch. 4, 5 V6 - ch.2 V7 – ch. 2 KM83 – 9 Mental & Oral Starters: 2R folder: pg. 74 - 75 101 Starters: pg. 38 Discussion opportunities:

Pair / Group Work:

ICT Links:

Spiritual/Moral/Citizenship Links: No matter how small, everything is significant. Investigation:

Time: 6 – 7 lessons AUTUMN TERM B TOPIC 7

Topic: Shape & Measure NC Level: 4 - 6

NC Programme of Study: Ref 2fijk: Recall the essential properties of special types of quadrilateral, including square, rectangle, parallelogram, trapezium and rhombus; classify quadrilaterals by their geometric properties. Recall the definition of a circle and the meaning of related terms including centre, radius, chord, diameter, circumference, tangent, arc, sector, and segment. Explore the geometry of cuboids and shapes made from cuboids. Use “2D representations of 3D shapes and analyse 3D shapes through 2D projections and cross sections including plans and elevation. Ref 4ade: Interpret scales on a range of measuring instruments, including those for time and mass; know that measurements using real numbers depend on the choice of unit; convert measurements from one unit to another; know rough metric equivalents of pounds, feet, miles, pints and gallons. Measure and draw lines to the nearest millimetre and angles tot he nearest degree; draw triangles and other 2D shapes using a ruler and protractor, given information about their side lengths and angles; construct cubes, regular tetrahedra, square based pyramids and other 3D shapes from given information. Use straight edge and compasses to do standard constructions, including an equilateral triangle with a given side, the midpoint and perpendicular bisector of a line segment, the perpendicular from a point to a line, the perpendicular from a point on a line and the bisector of an angle. Learning Objectives:  solve geometrical problems using side and angle properties of equilateral, isosceles and right-angled triangles and special quadrilaterals, explaining reasoning with diagrams and text  classify quadrilaterals by their geometric properties  use straight edge and compasses to construct: - a triangle given 3 sides - the midpoint and perpendicular bisector of a line segment - the bisector of an angle - the perpendicular from a point to a line - the perpendicular from a point on a line  know and use geometric properties of cuboids and shapes made from cuboids  use plans and elevations  know rough equivalents of imperial measures in daily use (feet, miles, pounds, pints, gallons) Key Vocabulary: CIRCLE CONSTRUCTION POLYGON BISECT PERPENDICULAR SOLID NET PLAN ELEVATION METRIC IMPERIAL UNIT Impact Reference: Other references: Book 2R – ch. 7 V4 - ch.14, 16 V5 – ch. 11-13, 16 V6 - ch.13-15 Mental & Oral Starters: 2R folder: pg. 106 - 108 101 Starters: pg. 74, 75, 77, 78, 83-86 Discussion opportunities:

Pair / Group Work:

ICT Links:

Spiritual/Moral/Citizenship Links: We need to look at 3D shapes from different angles – similar to confrontations / conflicts. We need to consider everyone’s opinion. Investigation:

Time: 5 – 6 lessons AUTUMN TERM B TOPIC 8 Topic: Percentages NC Level: 5 & 6 NC Programme of Study: Ref2e: Understand that ‘percentage’ means ‘number of parts per 100’ and use this to compare proportions; interpret percentage as the operator ‘so many hundredths of’. Ref3em: Convert simple fractions of a whole to percentages of a whole and vice versa, then understand the multiplicative nature of percentages as operators. Solve simple percentage problems, including increase and decrease. Ref4b: Select appropriate operations, methods and strategies to solve number problems, including trial and improvement where a more efficient method to find the solution is not obvious. Learning Objectives:  interpret percentage as the operator ‘so many hundredths of’  use the equivalence of fractions, decimals and percentages to compare proportions  calculate percentages and find the outcome of a given percentage increase or decrease  convert percentages to decimals and fractions  express one given number as a percentage of another  calculate percentage increase and decrease – inc. profit and loss, tax, interest  solve more demanding problems and investigate in a range of contexts. Key Vocabulary: FRACTION DECIMAL AMOUNT INCREASE DECREASE PROFIT LOSS TAX CREDIT SIMPLE INTEREST Impact Reference: Other references: Book 2R – ch. 6 V6 - ch.3 KM83 – ch. 9 Mental & Oral Starters: 2R folder: pg. 90 - 92 101 Starters: pg. 38 Discussion opportunities: When/ where do percentages occur? Pair / Group Work: See ICT ICT Links: EXCEL for interest rates, discounts etc; perhaps set up a shop. Spiritual/Moral/Citizenship Links: Tax – where does it go? Investigation:

Time: 4 – 5 lessons SPRING TERM A TOPIC 9 Topic: Positive & Negative Numbers NC Level: 5 NC Programme of Study: Ref2a: Understand and use negative numbers, both as positions and translations on a number line; order integers Ref3a: Add, subtract, multiply and divide integers Learning Objectives:  order positive and negative numbers with and without a number line  continue number patterns involving negative numbers  add, subtract, multiply and divide positive and negative integers Key Vocabulary: ORDER NUMBER LINE ADD SUBTRACT MULTIPLY DIVIDE SIGN Impact Reference: Other references: Book 2R – ch. 8 V4 - ch. V5 – ch. 6 V8 – ch. 3 KM83 – 6 Mental & Oral Starters: 2R folder: pg. 126 -128 101 Starters: pg. 19-21, 23 Discussion opportunities: Where do negative numbers occur in real life? Pair / Group Work:

ICT Links:

Spiritual/Moral/Citizenship Links: Positive qualities can balance out the negative. Debt – 3rd World Investigation:

Time: 4 lessons SPRING TERM A TOPIC 10 Topic: Multiplicative Relationships NC Level: NC Programme of Study:

Learning Objectives:  Understand multiplication and division of integers and decimals; use laws of arithmetic and inverse operations  Check a result by considering whether it is of the right order of magnitude  Use division to convert a fraction to a decimal; calculate fractions of quanities; multiply and 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 equivalence of fractions, decimals and percentages to compare proportions; calculate percentages and find the outcome of a given percentage increase or decrease  Consolidate understanding of the relationship between ratio and proportion; reduce a ratio to its simplest form, including a ratio expressed in different units; recognise links with fraction notation  Divide a quantity into 2 or more parts in a given ratio; use the unitary method to solve simple word problems involving ratio and direct proportion  Identify the necessary information to solve a problem, using the correct notation and appropriate diagrams  Solve more complex problems by breaking them into smaller steps, choosing and using efficient techniques for calculation  Suggest extensions to problems, conjecture and generalise; identify exceptional cases or counter-examples Key Vocabulary: SCALE FACTOR MULIPLIER OPERATOR INVERSE MULTIPLICATIVE RATIO FRACTION PERCENTAGE PROPORTION RATE UNITARY Impact Reference: Other references: Phase 3 Problem Bank SEE MULTIPLICATIVE RELATIONSHIPS MINI-PACK FOR FURTHER GUIDANCE

Time: 9 lessons SPRING TERM A TOPIC 11

Topic: Working With Algebra NC Level: 5 - 7

NC Programme of Study: Ref5abcf: distinguish the different roles played by letter symbols in algebra, knowing that letter symbols represent definite unknown numbers in equations. Understand that the transformation of algebraic expressions obeys and generalises the rules of arithmetic; simplify or transform algebraic expressions by collecting like terms; distinguish in meaning between the words ‘equation’, ‘formula’, ‘identity’ and ‘expression.’ Use index notation for simple integer powers, and simple instances of index laws. Substitute numbers into a formula; derive a formula and change its subject. Learning Objectives:  distinguish the different roles played by letter symbols in equations, formulae and functions  know the meaning of the words ‘formula’ and ‘function’  know that algebraic operations follow the same conventions and 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 Key Vocabulary: TERM EXPRESSION POWER MULTIPLY EXPAND BRACKETS FACTORISE REARRANGE FORMULA SUBJECT Impact Reference: Other references: Book 2R – ch. 10 V4 - ch.9 V5 – ch. 8, 9 V8 – ch.6 KM83 – 4 Mental & Oral Starters: 2R folder: pg. 158 - 160 101 Starters: pg. 65 Discussion opportunities: Discuss what expressions can represent. Pair / Group Work: Pupils can make up their own expressions / equations and test each other; design algebraic problems. ICT Links: EXCEL – inputting formulae to get the desired output, rather than typing in numbers. Spiritual/Moral/Citizenship Links:

Investigation:

Time: 4 – 5 lessons SPRING TERM B TOPIC 12 Topic: Handling Data NC Level: 4, 6 & 7 NC Programme of Study: Ref2g: Recognise where fractions or percentages are needed to compare proportions; identify problems that call for proportional reasoning, and choose the correct numbers to take as 100% or as a whole. Ref3a: Design and use data collection sheets for grouped discrete and continuos data; collect data using various methods including observation, controlled experiment, data logging, questionnaires and surveys. Ref4a: Draw and produce, using paper and ICT, pie charts for categorical data and diagrams for continuous data, including line graphs for time series, scatter graphs, frequency diagrams and stem and leaf diagrams. Learning Objectives:  discuss a problem that can be addressed by statistical methods and identify related questions to explore  decide which data to collect to answer a questions, and the degree of accuracy needed  identify possible sources  plan how to collect the data, including sample size  design and use 2-way tables for discrete data  construct and use stem-and-leaf diagrams  construct on paper and using ICT: - pie charts for categorical data - bar charts and frequency diagrams for discrete data - bar charts and frequency diagrams for continuous data - simple scatter graphs - simple line graphs for time series  interpret tables, graphs and diagrams for discrete data, and draw inferences that relate to the problem being discussed  relate summarised data to the questions being explored Key Vocabulary: QUESTIONNAIRES CHART PICTOGRAM BAR LINE STEM-AND-LEAF HISTOGRAM FREQUENCY POLYGON PIE CHART ANGLE SCATTER DIAGRAM CORRELATION LINE OF BEST FIT Impact Reference: Other references: Book 2R – ch. 13 V4 - ch.21 V5 – ch. 20 V6 - ch.18, 19 KM83 – 3, 13 Mental & Oral Starters: 2R folder: pg. 236 - 239 Discussion opportunities: Discuss most appropriate methods for the purpose Pair / Group Work: Collecting data. ICT Work. ICT Links: EXCEL for producing graphs / charts. Internet for sets of data to analyse. Spiritual/Moral/Citizenship Links:

Investigation:

Time: 9 – 10 lessons – perhaps more depending on practical work ADDITIONAL UNIT Topic: Handling Data NC Level: NC Programme of Study:

Learning Objectives:  Discuss a 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  Plan how to collect the data, including sample size; design and use 2-way tables for discrete data  Collect data using a suitable method, such as observation, controlled experiment using ICT or questionnaire  Construct on paper and using ICT: pie charts, bar charts, frequency diagrams, simple scatter diagrams; identify which are most useful in the context of the problem  Interpret tables, graphs and diagrams for discrete data, and draw inferences that relate to the problem being discussed; relate summarised data to the questions being explored  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 presented  Solve more complex problems by breaking then into smaller steps or tasks choosing and using resources Key Vocabulary: MODE MEAN MEDIAN RANGE BAR CHART PIE CHART DISTRIBUTION STEM-AND-LEAF DIAGRAM LINE GRAPH FREQUENCY TABLE PRIMARY SOURCE SECONDARY SOURCE RAW DATA HYPOTHESIS Impact Reference: Other references: Data Library CD-ROM Interacting with Data Handling Pack from LEA SEE HANDLING DATA MINI-PACK FOR FURTHER GUIDANCE

Time: 6 lessons SPRING TERM B TOPIC 13

Topic: Number Patterns NC Level: 6

NC Programme of Study: Ref5d: set up simple equation; solve simple equations by using inverse operations. Ref6abc: generate common integer sequences (inc. odd or even integers, squared integers, powers of 2, powers of 10, triangular numbers). Find the first terms of a sequence given a rule arising naturally from a context; find the rule for the nth term of a sequence. Generate terms of a sequence using term-to-term and position-to-term definitions of the sequence; use linear expressions to describe the nth term of an arithmetic sequence. Learning Objectives:  generate and describe integer sequences  know the meaning of the words ‘term’, ‘expression’, ‘equation’  generate sequences from practical contexts and describe the general term in simple cases  use the laws of arithmetic and inverse operations when generating terms and describing the sequence  express simple functions in symbols  represent mappings expressed algebraically  generate terms of a linear sequence using term-to-term and position-to-term definitions of the sequence on paper and using a spreadsheet or graphical calculator  begin to use linear expressions to describe the nth term of an arithmetic sequence, justifying its form by referring to the activity or practical context from which it was generated Key Vocabulary: RULE NUMBER MACHINE PATTERN SEQUENCE INVERSE nth TERM Impact Reference: Other references: Book 2R – ch. 9 V4 - ch.8 V5 – ch. 2 V6 - ch.6 V7 – ch.5 KM83 – ch.4 Mental & Oral Starters: 2R folder: pg. 140 - 141 Discussion opportunities: Pupils should be encouraged to verbally explain the rules of sequences, share ideas. Pair / Group Work: Find sequences that occur in real life – e.g. apples, pineapples, leaves, plants ICT Links: EXCEL can be used to produce number patterns. Spiritual/Moral/Citizenship Links:

Investigation: See group work Time: 5 lessons SPRING TERM B TOPIC 14 Topic: Perimeter, Area & Volume NC Level: 6 - 7

NC Programme of Study: Ref4fghi: Find areas of rectangles, recalling the formula, understanding the connection to counting squares and how it extends this approach; recall and use the formulae for the area of a parallelogram and a triangle; find the surface area of simple shapes using the area formulae for triangles and rectangles; calculate perimeters and areas of shapes made from triangles and rectangles. Find volumes of cuboids, recalling the formula and understanding the connection to counting cubes and how it extends this approach; calculate volumes of right prisms and of shapes made from cubes and cuboids. Find circumferences of circles and areas enclosed by circles, recalling relevant formulae. Convert between area measures, including cm2 and m2, and volume measures, including cm3 and m3. Ref5f: Use formulae from maths and other subjects. Learning Objectives:  find the perimeter of simple shapes  know and use the formula for the area of a rectangle  deduce and use formulae for the area of a triangle, parallelogram and trapezium  calculate areas of compound shapes made from rectangles and triangles  convert units for area and volume – mm, cm, m  know and use the formula for the volume of a cuboid, prism and cylinder  calculate the surface area of cubes and cuboids  find the circumference and area of a circle Key Vocabulary: PERIMETER AREA UNITS PI VOLUME CAPCACITY CIRCUMFERENCE Impact Reference: Other references: Book 2R – ch. 15 V4 - ch. 19 V6 – ch.11 V7 – ch.15 KM83 – 12, 14 Mental & Oral Starters: 2R folder: pg. 290-291 101 Starters: pg. 93, 94 Discussion opportunities:

Pair / Group Work:

ICT Links:

Spiritual/Moral/Citizenship Links: Dimensions – finite and infinite Investigation: Find the max. area for a shape with perimeter 100cm, 1000cm etc – similar to ‘Fencing’ Time: 6 – 7 lessons SUMMER TERM A TOPIC 15 Topic: Averages NC Level: 5 – 7 NC Programme of Study: Ref4bg: Calculate mean, range and median of small data sets with discrete then continuous data; identify the modal class for grouped data. Find the median for large data sets and calculate an estimate of the mean for large data sets with grouped data. Learning Objectives:  calculate statistics, including with a calculator – mode, median, mean, range  recognise when it is appropriate to use the range, mean, median and mode  calculate a mean using an assumed mean  find the mean and median from frequency tables  know when it is appropriate to use the modal class for grouped data  compare 2 distributions using the range and one or more of the mode, median and mean  relate summarised data to the questions being explored Key Vocabulary: MODE MEDIAN MEAN RANGE FREQUENCY TABLE AVERAGE Impact Reference: Other references: Book 2R – ch. 16 V5 – ch. 19 V7 – ch. 19 KM83 – 13 Mental & Oral Starters: 2R folder: pg. 306 -307 101 Starters: pg. 96 Discussion opportunities: Which average is most appropriate? Pair / Group Work: Collect data in groups ICT Links: Perhaps for larger samples - EXCEL Spiritual/Moral/Citizenship Links: Is anyone really average? Investigation: Set a hypotheses – collect results etc. Time: 4 lessons - perhaps more depending on practical work SUMMER TERM A TOPIC 16 Topic: Graphs NC Level: 5 – 7 NC Programme of Study: Ref3e: Use axes and co-ordinates to specify points in all 4 quadrants; locate points with given co- ordinates. Ref6fgh: Construct linear functions arising from real-life problems and plot their corresponding graphs; discuss and interpret graphs arising from real situations. Generate points and plot graphs of simple quadratic and cubic functions. Find the gradient of lines given by equations of the form y=mx+c; investigate the gradients of parallel lines and lines perpendicular to these lines. Learning Objectives:  generate points in all 4 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 from real life situations  identify the gradient and intercept of a line  plot quadratic curves Key Vocabulary: COORDINATE LINE HORIZONTAL VERTICAL SLOPING GRADIENT INTERCEPT TABLE AXES EQUATION CURVE CONVERSION Impact Reference: Other references: Book 2R – ch. 12 V4 - ch.10 V5 – ch. 2 V6 - ch.8, 9 V7 – ch.9 V8 – ch. 7 KM83 – 1 Mental & Oral Starters: 2R folder: pg. 194 -197 101 Starters: pg. 90 - 92 Discussion opportunities:

Pair / Group Work:

ICT Links: Omnigraph, EXCEL. Outware: “Carpark” Defender” Spiritual/Moral/Citizenship Links: Currency conversions – difference between 1st and 3rd World Investigation:

Time: 8 – 9 lessons SUMMER TERM A TOPIC 17 Topic: Problem Solving NC Level: NC Programme of Study:

Learning Objectives:  Identify the necessary information to solve a problem  Solve more complex problems by breaking them down into smaller tasks/steps  Interpret the numbers on a calculator display in different contexts  Carry out more difficult calculations effectively and efficiently  Solve problems and investigate in a range of contexts  Explain and justify methods and conclusions  Identify exceptional cases or counter-examples Key Vocabulary: EXPLAIN REASONS JUSTIFY Impact Reference: Other references:

Mental & Oral Starters:

SEE PROBLEM SOLVING PACK FROM LEA

Time: 5 lessons SUMMER TERM B TOPIC 18 Topic: Formulae & Equations NC Level: 5 – 7 NC Programme of Study: Ref5defgij: Set up simple equations; solve simple equations, by using inverse operations or by transforming both sides in the same way. Solve linear equations, with integer coefficients, in which the unknown appears on either side or on both sides of the equation; solve linear equations that require prior simplification of brackets, including those that have negative signs occurring anywhere in the equation, and those with a negative solution. Use formulae from maths and other subjects; substitute numbers into a formula; derive a formula and change its subject. Set up and use equations to solve word and other problems involving direct proportion, and relate their algebraic solutions to graphical representations of the equations. Solve simple linear inequalities in one variable, and represent the solution set on a number line. Use systematic trial and improvement methods using ICT tools to find approximate solutions of equations where there is no simple analytical method. Learning Objectives:  know the meaning of the words ‘formula’ and ‘function’  use formulae from maths and other subjects  substitute integers into simple formulae, including examples that lead to an equation to solve  derive simple formulae  express simple functions in words  use letter symbols to represent unknown numbers or variables  know the meanings of the words ‘term’, ‘expression’ and ‘equation’  derive simple formulae  use the order of operations including brackets, with more complex calculations  construct and solve simple linear equations with integer coefficients (unknown on one side only) using appropriate methods (e.g. inverse operations)  begin to use graphs and set up equations to solve simple problems involving direct proportion  use inequalities  solve equations by trial and improvement Key Vocabulary: SUBSTITUTE SOLVE EQUATION OPERATION LINEAR BRACKETS INEQUALITIES TRIAL AND IMPROVEMENT Impact Reference: Other references: Book 2 – ch. 14 V4 - ch.9 V5 – ch. 8, 9 V6 - ch.7 KM83 – 4 Mental & Oral Starters: 2R folder: pg. 270 - 274 101 Starters: pg. 62-67 Discussion opportunities: Using algebra to model real life Pair / Group Work:

ICT Links:

Spiritual/Moral/Citizenship Links: Treat both sides and each other equally; fairness. Investigation: Time: 7 – 8 lessons SUMMER TERM B TOPIC 19 Topic: Transformations NC Level: 5 - 7 NC Programme of Study: Ref3abc: Understand that rotations are specified by a centre and an (anticlockwise) angle; use right angles, fractions of a turn or degrees to measure the angle of rotation; understand that reflections are specified by a mirror line, translations by a distance and direction, and enlargements by a centre and positive scale factor. Recognise and visualise rotations, reflections and translations, including reflection symmetry of 2-D and 3-D shapes, and rotation symmetry of 2-D shapes; transform 2-D shapes by translation, rotation and reflection, recognising that these transformations preserve length and angle, so that any figure is congruent to its image under any of these transformations. Recognise, visualise and construct enlargements of objects using positive integer scale factors greater than one, then positive scale factors less than one; understand from this that any two circles and any two squares are mathematically similar, while, in general, two rectangles are not. Learning Objectives:  transform 2D shapes by simple combinations of rotations, reflections and translations, on paper and using ICT  identify all symmetries of 2D 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 Key Vocabulary: REFLECTION ROTATION TRANSLATION MIRROR LINE CENTRE ENLARGEMENT SCALE FACTOR Impact Reference: Other references: Book 2R – ch. 11 V6 - ch.16 V7 – ch. 16 KM83 – ch. 5 Mental & Oral Starters: 2R folder: pg. 174-176 101 Starters: pg. 87 - 89 Discussion opportunities: Discuss how shapes have been transformed. Discuss methods. Pair / Group Work:

ICT Links: LOGO. “Carpark” (Outware) Spiritual/Moral/Citizenship Links:

Investigation:

Time: 5 lessons

Optional Tests will take place for 3 lessons . they consist of 3 tests: a mental arithmetic test and 2 papers – non- calculator and calculator SUMMER TERM B TOPIC 20 Topic: Thinking Proportionally NC Level: NC Programme of Study:

Learning Objectives:  Identify the necessary information to solve a problem  Represent problems and interpret solution in algebraic, geometric or graphical form, using correct notation  Use logical argument to establish the truth of a statement  Suggest extensions to problems; conjecture and generalise  Consolidate understanding of the relationship between ratio and proportion  Reduce a ratio to its simplest form, including a ratio expressed in different units, recognising links with fraction notation Key Vocabulary: RATIO PROPORTION DIRECT RATE PER NOTATION EQUIVALENT FRACTION DECIMAL PERCENTAGE

Impact Reference: Other references: Transition Unit lesson P1.1 & P1.2

Mental & Oral Starters: See lesson plans Discussion opportunities: Pair / Group Work:

ICT Links:

Investigation:

Time: 2 lessons