KS3 Scheme of Work - Year 7 - SETS 1-3: IMPACT 1R

MATHS DEPARTMENT

YEAR 7 SCHEME OF WORK

SETS 1-3: IMPACT 1R

SEPT 2004 1R PLAN

AUTUMN TERM – FIRST HALF Topic 1 Calculation & Problem Solving Additional Transition Unit Topic 2 Fractions & Ratio Additional Unit Topic 3 Understanding Number 1R Ch. 2 Topic 4 Shapes 1R Ch. 1 Topic 5 Number Patterns 1R Ch. 3 TEST 1

AUTUMN TERM – SECOND HALF Topic 6 Probability 1R Ch. 4 Topic 7 Multiplication & Division 1R Ch. 5 Topic 8 Decimals 1R Ch. 6 TEST 2

SPRING TERM – FIRST HALF Topic 9 Measuring 1R Ch. 7 Topic 10 Working with Algebra 1R Ch. 9 Topic 11 Fractions & Ratio 1R Ch. 8 Topic 12 Perimeter, Area & Volume 1R Ch. 10 TEST 3

SPRING TERM – SECOND HALF Topic 13 Formulae & Equations 1R Ch. 11 Topic 14 Negative Numbers 1R Ch. 12 Topic 15 Graphs 1R Ch. 13 TEST 4

SUMMER TERM – FIRST HALF Topic 16 Angles 1R Ch. 14 Topic 17 Handling Data 1R Ch. 15 Topic 18 Percentages 1R Ch. 16 TEST 5

SUMMER TERM – SECOND HALF Topic 19 Averages 1R Ch. 17 Topic 20 Transformations 1R Ch. 18 “Optional” Tests Topic 21 Fractions, Decimals & Percentages Additional Transition Unit Topic Investigation AUTUMN TERM A TOPIC 1 Topic: Transition Unit NC Level: Calculation & Problem Solving NC Programme of Study: Ref3agijko: Add, subtract, multiply and divide integers and then any number; multiply or divide any number by powers of 10, and any positive number by a number between 0 and 1. Recall all positive integer complements to 100 ; recall all multiplication facts to 10x10, and use them to derive quickly the corresponding division facts; recall the cubes of 2, 3, 4, 5 and 10. Develop a range of strategies for mental calculation; derive unknown facts from those they know. Use standard column procedures for addition and subtraction of integers and decimals. Use standard column procedures for multiplication of integers and decimals. Use calculators effectively and efficiently: know how to enter complex calculations using brackets; know how to enter a range of calculations, including those involving measures. Learning Objectives:  Understand and use decimal notation and place value  Multiply and divide integers and decimals by 10, 100, 1000, and explain the effect  Understand negative numbers as positions on the number line  Order, add and subtract positive and negative integers in context  Consolidate rapid recall of number facts, including positive integer complements to 100 and multiplication facts to 10x10, and quickly derive associated division facts  Use standard column procedures to add and subtract whole numbers and decimals with up to 2 places  Multiply and divide 3-digit by 2-digit whole number; extend to multiplying and dividing decimals with 1 or 2 places by single-digit whole numbers  Enter numbers in a calculator and interpret the display in different contexts  Solve word problems and investigate in the context of number  Compare and evaluate solutions Additional Notes: There are 2 Transition Units. Some pupils may have studied the first unit at the end of year 6. (The first unit should not be covered in year 7) Key Vocabulary: DIFFERENCE EXPLAIN INTEGER MINUS NEGATIVE PLUS POSITIVE REASONING SUM SYSTEMATIC Impact Reference: Other references: This unit should be done in See below (pg.24 onwards) isolation but it relates V4 – ch.1,3,4,8 V5 – ch.4,7 closely to ch.2,3 &5 Mental & Oral Starters: 1R folder: pg. 24-25,44-46,76-78 101 Starters: pg.2-6, 14-17, 24-27, 39, 41, 47-51, 58 FOR DETAILED LESSON PLANS SEE: “TRANSITION FROM Y6 TO Y7: MATHS – UNITS OF WORK” BOOK Time: 5 lessons AUTUMN TERM A TOPIC 2

Topic: Fractions & Ratio NC Level: NC Programme of Study:

Learning Objectives:  Use fraction notation to describe parts of shapes and to express a smaller whole number as a fraction of a larger one  Simplify fractions and identify equivalent fractions  Calculate simple fractions of quantities; multiply by an integer  Understand percentage as the ‘number of parts per 100’  Recognise the equivalence of percentages, fractions and decimals  Calculate simple percentages  Understand the relationship between ratio and proportion; use direct proportion in simple contexts; use ratio notation and divide a quantity into 2 parts in a given ratio; solve simple problems about ratio and proportion using informal strategies  Consolidate and extend mental methods of calculation to include decimals, fractions and percentages, accompanied where appropriate by suitable jotting; solve simple word problems mentally  Check a result by considering whether it is of the right order of magnitude and by working the problem backwards  Represent problems mathematically, making correct use of symbols, words and diagrams  Present and interpret solution in the context of the original problem; explain and justify methods and conclusions, orally and in writing. Key Vocabulary: OPERATOR MULTIPLIER INCREASE DECREASE FRACTION IMPROPER MIXED NUMBER NUMERATOR DENOMINATOR EQUIVALENT RATIO PROPORTION Impact Reference: Other references:

SEE FRACTIONS & RATIO MINI-PACK FOR FURTHER GUIDANCE

Time: 6 lessons AUTUMN TERM A TOPIC 3 Topic: Understanding Number NC Level: 2 - 4 NC Programme of Study: Ref2a: Use their previous understanding of integers and place value to deal with arbitrarily large positive numbers and round them to a given power of 10. Ref3agijko: Add, subtract integers and then any number. Recall all positive integer complements to 100. Develop a range of strategies for mental calculation; derive unknown facts from those they know. Use standard column procedures for addition and subtraction of integers and decimals. Use calculators effectively and efficiently: know how to enter complex calculations using brackets; know how to enter a range of calculations, including those involving measures. Ref4c: Use a variety of checking procedures, including working the problem backwards, and considering whether a result is of the right order of magnitude. Learning Objectives:  Consolidate rapid recall of number facts, including positive integer complements to 100  Round positive whole numbers to the nearest 10, 100, 1000  Understand addition and subtraction as they apply to whole numbers  Make and justify estimates and approximations of calculations  Use standard column procedures to add and subtract whole numbers  Solve simple word problems mentally  Check a result by considering whether it is of the right order of magnitude and by working the problem backwards EXT – Recall known facts, including fraction to decimal conversions (1R-6.6,6.7,6.8) Round positive numbers to any given power of 10 (1R-6.11) Key Vocabulary: DIGIT PLACE VALUE ORDER MENTAL ADDITION SUBTRACTION ROUND ESTIMATE Impact Reference: Other references: Book 1R – ch. 2 V4 – ch.1, 3, 4 Mental & Oral Starters: 1R folder: pg. 24-25 101 Starters: pg. 2-6, 14-17, 41, 47, 58 Discussion opportunities: Pair / Group Work: Emphasise the importance of discussing Set each other sets of problems different methods ICT Links: Many internet games Spiritual/Moral/Citizenship Links: We all have different ideas and methods – it is important that we respect each other’s Investigation: Different methods for different calculations Time: 10 lessons AUTUMN TERM A TOPIC 4 Topic: Shapes NC Level: 2 - 4 NC Programme of Study: Ref2cdfjk: Use parallel lines. Use angle properties of equilateral, isosceles and right-angled triangles. Recall the essential properties of special types of quadrilateral, including square, rectangle, parallelogram, trapezium and rhombus. Explore the geometry of cuboids (including cubes), and shapes made from cuboids. Use 2D representations of 3D shapes and analyse 3D shapes through 2D projections and cross-sections, including plan and elevation. Ref3ab: Understand that reflections are specified by a mirror line. Recognise and visualise reflections, including reflection symmetry of 2D and 3D shapes, and rotation symmetry of 2D shapes. Learning Objectives:  Identify parallel and perpendicular lines  Begin to use angle, side and symmetry properties of triangles and quadrilaterals  Use 2D representations to visualise 3D shapes and deduce some of their properties EXT – Classify quadrilaterals by their geometric properties (1R-1.7) Key Vocabulary: SHAPE SYMMETRY REGULAR IRREGULAR REFLECT TRIANGLE PARALLEL PERPENDICULAR SOLID PRISM PYRAMID Impact Reference: Other references: Book 1R – ch. 1 V4 – ch.14 V5 – ch.20 V6 – ch.14,15 Mental & Oral Starters: 1R folder: pg. 4-5 101 Starters: pg. 73-78 Discussion opportunities: Pair / Group Work: Compare the symmetry properties of shapes, Classify shapes into a number of categories sorting shapes, etc. ICT Links: LOGO Maths Mansion programmes 33 & 34 Spiritual/Moral/Citizenship Links: We need to look at 3-D shapes from all angles – similar to conflicts / confrontations – consider everyone’s opinion. Investigation: Activities Book 1R pg.3 Time: 6-7 lessons AUTUMN TERM A TOPIC 5 Topic: Number Patterns NC Level: 2 - 4 NC Programme of Study: Ref6abc: Generate common integer sequences. Find the first terms of a sequence given a rule arising naturally from a context; find the rule (and express it in words) 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, justifying its form by referring to the activity or context from which it was generated. Learning Objectives:  Generate and describe simple integer sequences  Generate terms of a simple sequence, given a rule  Generate sequences from practical contexts and describe the general term in simple cases  Express simple functions in words EXT – Generate terms of a linear sequence using term-to-term and position-to-term definitions of the sequence (1R-3.6) Begin to use linear expressions to describe the nth term of an arithmetic sequence (1R-3.6) Key Vocabulary: PATTERN NUMBER MACHINES SEQUENCE RULE Impact Reference: Other references: Book 1R – ch. 3 V4 – ch.8 V5 – ch.8 V6 – ch.6 Mental & Oral Starters: 1R folder: pg. 44-46 Discussion opportunities: Pair / Group Work: Discuss the rule which produces the next term Develop different sequences – partner has to identify the rule ICT Links: EXCEL produces number patterns when programmed C4 Video “Primes & powers” Spiritual/Moral/Citizenship Links: Each term in the sequence follows the same rule – links to the rules followed at school Investigation: Number patterns in real life – e.g. Fibonacci numbers Time: 4-5 lessons AUTUMN TERM B TOPIC 6 Topic: Probability NC Level: 2 - 4 NC Programme of Study: Ref4cde: 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 two successive events, in a systematic way. Ref5hij: Use the vocabulary of probability in interpreting results involving uncertainty and prediction. Compare experimental data and theoretical probabilities. Understand that if they repeat an experiment, they may and usually will get different outcomes, and that increasing sample size generally leads to better estimates of probability and population characteristics. Learning Objectives:  Use vocabulary and ideas of probability, drawing on experience  Understand and use the probability scale from 0 to 1  Find and justify probabilities based on equally likely outcomes in simple contexts  Identify all the possible mutually exclusive outcomes of a single event  Collect data from a simple experiment and record in a frequency table  Estimate probabilities based on this data EXT – Know that if the probability of an event occurring is p then the probability of it not occurring is 1-p (1R-4.9) Find and record all possible mutually exclusive outcomes for 2 successive events in a systematic way using diagrams and tables Key Vocabulary: CERTAIN IMPOSSIBLE POSSIBLE LIKELY UNLIKELY EVEN CHANCE SCALE EVENT OUTCOME EXPERIMENTAL Impact Reference: Other references: Book 1R – ch. 4 V4 – ch.22 V5 – ch.28,29 V6 – ch.20 Mental & Oral Starters: 1R folder: pg. 62-63 Discussion opportunities: Pair / Group Work: Discuss the probability of real life events Probability experiments ICT Links: Random number generators. Internet games Spiritual/Moral/Citizenship Links: Morality of gambling, Lottery Investigation: Investigate probabilities within the class – e.g. the probability of having blue eyes in the class Time: 5-6 lessons AUTUMN TERM B TOPIC 7 Topic: Multiplication & Division NC Level: 3 - 5 NC Programme of Study: Ref2ab: Use the concepts and vocabulary of factor (divisor), multiple, common factor, highest common factor, least common multiple, prime number and prime factor decomposition. Use the terms square, positive and negative square root, cube, cube root; use index notation for small integer powers and index laws for multiplication and division of positive integer powers. Ref3agik: Multiply and divide integers and then any number; multiply or divide any number by powers of 10, and any positive number by a number between 0 and 1; find the prime factor decomposition of positive integers. Recall all multiplication facts to 10x10, and use them to derive quickly the corresponding division facts; recall the cubes of 2, 3, 4, 5 and 10. Develop a range of strategies for mental calculation; derive unknown facts from those they know. Use standard column procedures for multiplication of integers and decimals. Ref4c: Use a variety of checking procedures, including working the problem backwards, and considering whether a result is of the right order of magnitude. Learning Objectives:  Multiply and divide integers by 10, 100, 1000 and explain the effect  Consolidate the rapid recall of number facts, including multiplication facts to 10x10, and quickly derive associated division facts  Enter numbers into a calculator and interpret the display in different contexts  Know how to use the laws of arithmetic and inverse operations  Multiply and divide 3-digit by 2-digit whole numbers  Recognise and use multiples, factors, common factor, HCF, LCM in simple cases and primes (<100)  Use simple tests of divisibility  Use the square root key  Recognise the squares of numbers to at least 12x12 EXT – Recall known facts including fraction to decimal conversions (1R-6.6,6.7,6.8) Use known facts to derive unknown facts including products such as 0.7 and 6, 0.03 and 8 Multiply and divide integers and decimals (1R-6.8,6.9) Find the prime factor decomposition of a number (1R-5.5) Use squares and positive and negative square toots Key Vocabulary: MULTIPLY DIVIDE MULTIPLE FACTOR SQUARE ROOT CUBE PRIME HALFWAY POWER Impact Reference: Other references: Book 1R – ch. 5 V4 – ch.3,4,8 V5 – ch.4,7 Mental & Oral Starters: 1R folder: pg. 76-78 101 Starters: pg.24-27, 39, 48-51 Discussion opportunities: Pair / Group Work: Different ways of learning times tables (e.g. Set each other problems using the fingers for the 9 times table). ICT Links: Many internet games Maths Mansion programmes 23 & 24 Spiritual/Moral/Citizenship Links: Discuss how different factors play a part in our lives each day Investigation: Number patterns produced. AUTUMN TERM B TOPIC 8 Topic: Decimals NC Level: 4 & 5 NC Programme of Study: Ref2d: Use decimal notation and recognise that each terminating decimal is a fraction; order decimals. Ref3ahijk: Add, subtract, multiply and divide integers and then any number; multiply or divide any number by powers of 10, and any positive number by a number between 0 and 1. Round to the nearest integer and to one significant figure; estimate answers to problems involving decimals. Develop a range of strategies for mental calculation; derive unknown facts from those they know; add and subtract mentally numbers with up to two decimal places; multiply and divide numbers with no more than one decimal digit, using factorisation when possible. Use standard column procedures for addition and subtraction of integers and decimals. 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; solve a problem involving division by a decimal by transforming it to a problem involving division by an integer. Learning Objectives:  Understand and use decimal notation and place value  Multiple and divide decimals by 10, 100, 1000 and explain the effect  Compare and order decimals in different contexts  Use standard column procedures to add and subtract decimals with up to 2 places  Consolidate and extend mental methods of calculation to include decimals, fractions and percentages accompanied where appropriate by suitable jottings  Solve simple word problems mentally  Round decimals to the nearest whole number or one decimal place  Know and use the laws of arithmetic and inverse operations  Make and justify estimates and approximations of calculations  Multiply and divide decimals with 1 or 2 places by single digit whole numbers  Check a result by considering whether it is of the right order of magnitude and by working the problem backwards EXT – Recall fraction to decimal conversions (1R-8.8) Round decimals to one or two decimal places (1R-6.11) Multiply and divide integers and decimals including decimals such as 0.6 and 0.06; and understand where to position the decimal point by considering equivalent calculations(1R-6.8,6.9) Key Vocabulary: PLACE VALUE DECIMAL POINT PLACE ORDER HALFWAY ROUND NEAREST APPROXIMATE ESTIMATE Impact Reference: Other references: Book 1R – ch. 6 V4 – ch.12 V5 – ch.1 V6 – ch.2 Bridging Units lessons 11 – 16 (Fractions, Decimals & Percentages) Mental & Oral Starters: 1R folder: pg. 98-100 101 Starters: pg. 40-52 Discussion opportunities: Pair / Group Work: Share different ways of solving problems Posters – shop prices/ discounts Where do decimals occur in real life? ICT Links: EXCEL can be used for rounding decimals. Maths Mansion programmes 21, 22, 29 & 30 Spiritual/Moral/Citizenship Links: Everything is significant no matter how small Investigation: Investigate use of decimals in real life. What happens when multiplied/divided? Time: 8 lessons SPRING TERM A TOPIC 9 Topic: Measuring NC Level: 3 & 4 NC Programme of Study: Ref4ad: 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; recognise that measurements given to the nearest whole unit may be inaccurate by up to one half in either direction; convert measurements from one unit to another; know rough metric equivalents of pounds, feet, miles, pints and gallons; make sensible estimates of a range of measures in everyday settings. Measure and draw lines to the nearest millimetre. Learning Objectives:  Know that when comparing measurements they must be in the same units  Use names and abbreviations of units of measurement to measure, estimate, calculate and solve problems in everyday contexts involving length, area, mass, capacity, time and angle  Convert one metric unit to another  Read and interpret scales on a range of measuring instruments  Use a ruler to draw and measure lines to the nearest millimetre EXT – Make simple scale drawings Know rough metric equivalents of imperial measures in daily use Key Vocabulary: MEASURE LENGTH DISTANCE UNIT ORDER WEIGHT READ SCALE TIME TIMETABLE Impact Reference: Other references: Book 1R – ch. 7 V4 – ch.12 V5 – ch13-16 Mental & Oral Starters: 1R folder: pg.116-118 101 Starters: pg.93 Discussion opportunities: Pair / Group Work: Where are Imperial units still used? Why have Develop a unit conversion manual/poster/story we changed to metric? ICT Links: There are several ‘unit converters’ on the internet; EXCEL, Spiritual/Moral/Citizenship Links: The effects of changing from Imperial to metric units – have we benefited? Investigation: Investigate the conversions between different units Time: 5-6 lessons SPRING TERM A TOPIC 10 Topic: Working With Algebra NC Level: 4 NC Programme of Study: Ref5abc: Distinguish the different roles played by letter symbols in algebra, knowing that letter symbols represent definite unknown numbers in equations, defined quantities or variables in formulae general, unspecified and independent numbers in identities and in functions they define new expressions or quantities by referring to known quantities. Understand that the transformation of algebraic expressions obeys and generalises the rules of arithmetic; simplify or transform algebraic expressions by collecting like terms, by multiplying a single term over a bracket, by taking out single term common factors; 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 positive and negative numbers into expressions. Learning Objectives:  Use letter symbols to represent unknown numbers or variables  Know the meanings of the words term, expression and equation  Understand that algebraic operations follow the same conventions and order as arithmetic operations  Simplify linear algebraic expressions by collecting like terms  Begin to multiply a single term over a bracket (integer coefficients) EXT – Begin to distinguish the different roles played by letter symbols in equations, formulae and functions Know the meanings of the words formula and function (1R-11.1) Use index notation for small positive integer powers (1R-9.9) Key Vocabulary: LETTER REPRESENT COLLECT TERM SIMPLIFY MULTIPLY BRACKETS FACTORISE EXPRESSION POWER Impact Reference: Other references: Book 1R – ch. 9 V4 – ch.8 V5 – 9,10 V6 – ch.7 Bridging Units lessons 11 – 16 (Algebra) Mental & Oral Starters: 1R folder: pg.150 101 Starters: pg. 41, 62-64 Discussion opportunities: Pair / Group Work: Discuss situations which can be represented by Set equations for partner to solve – each expressions equation can have its own ‘story’ ICT Links: EXCEL for trial and improvement methods, Spiritual/Moral/Citizenship Links: It is only fair to treat both sides equally Investigation: Investigate the effects of substituting different values into an expression – develop a sequence; relate to number machines Time: 5-6 lessons SPRING TERM A TOPIC 11 Topic: Fractions & Ratio NC Level: 4 - 6 NC Programme of Study: Ref2cfg: Use fraction notation; understand equivalent fractions, simplifying a fraction by cancelling all common factors; order fractions by rewriting them with a common denominator. Use ratio notation, including reduction to its simplest form and its various links to fraction notation. Recognise where fractions or percentages are needed to compare proportions. Ref3cdef: 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. Convert simple fractions of a whole to percentages of the whole and vice versa, then understand the multiplicative nature of percentages as operators. Divide a quantity in a given ratio. Learning Objectives:  Use fraction notation to describe parts of shapes and express a smaller whole number as a fraction of a larger one; use a diagram to compare 2 or more simple fractions  Simplify fractions by cancelling all common factors and identify equivalent fractions  Begin to add and subtract simple fractions and those with common denominators  Calculate simple fractions of quantities and measurements (whole number answers)  Multiply a fraction by an integer  Recognise the equivalence of percentages, fractions and decimals  Understand the relationship between ratio and proportion; use direct proportion in simple contexts  Use ratio notation, reduce a ratio to its simplest form and divide a quantity into 2 parts in a given ratio  Solve simple problems about ratio and proportion using informal strategies EXT – Know that a recurring decimals is a fraction Use division to convert a fraction to a decimal (1R-8.8) Order fractions by converting them to decimals (1R-6.3) Calculate fractions of quantities and measurements with fraction answers Multiply and divide an integer by a fraction (1R-8.10) Use the equivalence of fractions, decimals, percentages to compare proportions (1R-8.11) Divide a quantity into 2 or more parts in a given ratio (1R-8.13) Use the unitary method to solve simple word problems involving ratio and proportion Key Vocabulary: FRACTION MIXED NUMBER IMPROPER QUANTITY NUMERATOR DENOMINATOR EQUIVALENT DECIMAL CONVERT COMPARE ORDER RATIO CALCULATE Impact Reference: Other references: Book 1R – ch. 8 V4 – ch.6 V5 - ch.2,3,16 V6 – ch.2,4 Bridging Units lessons 11 – 16 (Fractions, Decimals & Percentages) Mental & Oral Starters: 1R folder: pg. 132-133 101 Starters: pg. 36, 52 Discussion opportunities: Pair / Group Work: Discuss where fractions are used in everyday Display work – converting fractions to life? Are they more useful than decimals/percentages, reducing prices in a sale, decimals/percentages? calculating recipe quantities using ratios ICT Links: C4 Video “Scaling the Heights”. Maths Mansion programmes 25 & 26 Spiritual/Moral/Citizenship Links: Everything is significant no matter how small Investigation: Equivalence of all 3 types of numbers – which is more useful? Time: 10 lessons SPRING TERM A TOPIC 12 Topic: Perimeter, Area & Volume NC Level: 4 & 6 NC Programme of Study: Ref4fg: 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. Learning Objectives:  Use names and abbreviations of units of measurements to measure, estimate, calculate and solve problems in everyday contexts involving length and area  Know and use the formula for the area of a rectangle  Calculate the perimeter and area of shapes made from rectangles  Use the formula for the area of a triangle and parallelogram  Calculate the surface area of cubes and cuboids EXT – Deduce and use formulae for the area of a trapezium (1R-10.6,10.7) Know and use the formula for the volume of a cuboid (1R-10.10,10.11) Key Vocabulary: PERIMETER AREA VOLUME LENGTH WIDTH ESTIMATE FORMULA COMPOSITE CAPACITY SURFACE AREA Impact Reference: Other references: Book 1R – ch. 10 V4 – ch.19 V6 – ch.11 Mental & Oral Starters: 1R folder: pg. 166-168 101 Starters: pg. 94 Discussion opportunities: Pair / Group Work: Derive formulae for different shapes. Prove the formulae for triangles /parallelograms Relevance of units /trapeziums ICT Links: EXCEL – using formulae Maths Mansion programmes 31 & 32 Spiritual/Moral/Citizenship Links: Areas in real life Investigation: Derive formulae for different shapes Time: 8-9 lessons SPRING TERM B TOPIC 13 Topic: Formulae & Equations NC Level: 4 - 6 NC Programme of Study: Ref5abcdef: Distinguish the different roles played by letter symbols in algebra. Understand that the transformation of algebraic expressions obeys and generalises the rules of arithmetic; simplify or transform algebraic expressions by collecting like terms, by multiplying a single term over a bracket, by taking out single term common; 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 positive and negative numbers into expressions. 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. Use formulae from mathematics and other; substitute numbers into a formula. Learning Objectives:  Express simple functions in words and then using symbols  Know the meanings of the words term, expression, equation, formula and function  Understand that algebraic operations follow the same conventions as arithmetic operations  Use simple formulae from maths and other subjects  Substitute integers into simple linear expressions and formulae, and in simple cases, derive a formula  Identify the necessary information to solve a problem  Represent problems mathematically making correct use of symbols, words, diagrams, tables and graphs  Know and use the order of operations, including brackets  Solve word problems and investigate in a range of contexts EXT – Represent mappings expressed algebraically 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, 2x3) Solve more complex problems by breaking them into smaller steps Key Vocabulary: WORD FORMULA LETTER REPRESENT OPERATION ALGEBRAIC SUBSTITUTE SOLVE EQUATION BALANCE WRITE FORM Impact Reference: Other references: Book 1R – ch. 11 V4 – ch.9 V5 – ch.9 V6 – ch.7 Bridging Units lessons 11 – 16 (Algebra) Mental & Oral Starters: 1R folder: pg. 190-191 101 Starters: pg. 62-64 Discussion opportunities: Pair / Group Work: Discuss situations which can be represented by Set equations for partner to solve – each expressions equation can have its own ‘story’ ICT Links: EXCEL for trial and improvement methods C4 Video “Orders Please” Spiritual/Moral/Citizenship Links: It is only fair to treat both sides equally Investigation: Investigate the effects of substituting different values into an expression – develop a sequence; relate to number machines Time: 8-10 lessons SPRING TERM B TOPIC 14 Topic: Negative Numbers NC Level: 3 & 5 NC Programme of Study: Ref2a: Understand and use negative numbers, both as positions and translations on a number line; order integers. Learning Objectives:  Understand negative numbers as positions on a number line  Order, add and subtract positive and negative integers in context EXT – Multiply and divide positive and negative integers Key Vocabulary: TEMPERATURE ORDER HIGHEST LOWEST POSITIVE NEGATIVE Impact Reference: Other references: Book 1R – ch. 12 V5 – ch.5 Mental & Oral Starters: 1R folder: pg. 208-210 101 Starters: pg. 19-23, 47 Discussion opportunities: Pair / Group Work: When do we use negative numbers in everyday A human number line life? ICT Links: C4 Video “Walking Backwards” Spiritual/Moral/Citizenship Links: Positive qualities can balance out the negative. Debt Investigation: Temperatures in different countries over a period of time Time: 5 lessons SPRING TERM B TOPIC 15 Topic: Graphs NC Level: 4-6 NC Programme of Study: Ref6ef: Use the conventions for coordinates in the plane; plot points in all four quadrants; recognise that equations of the form y = mx+c correspond to straight-line graphs in the coordinate plane; plot graphs of functions in which y is given explicitly in terms of x. Construct linear functions arising from real life problems and plot their corresponding graphs; discuss and interpret graphs arising from real situations. Learning Objectives:  Use correctly the vocabulary, notation and labelling conventions  Use conventions and notation for 2D coordinates in all 4 quadrants  Find coordinates or points determined by geometric information  Generate coordinate pairs that satisfy a simple linear rule in all 4 quadrants  Plot the graphs of simple linear functions where y is given explicitly in terms of x, on paper and using ICT  Recognise straight line graphs parallel to the x and y axes  Begin to plot and interpret graphs of simple linear functions arising from real life situations EXT – Recognise hat equations of the form y=mx+c correspond to straight line graphs Key Vocabulary: COORDINATE GRID AXES QUADRANT EQUATION LINE STRAIGHT CONVERSION REAL-LIFE Impact Reference: Other references: Book 1R – ch. 13 V4 – ch.10 V5 – ch.11, 27 V6 – ch.8, 9 Mental & Oral Starters: 101 Starters: pg.73, 90-92 Discussion opportunities: Pair / Group Work: Discuss importance of labelling axes etc Human axes. Set each other coordinate treasure trails/pictures ICT Links: Autograph, Omnigraph, graphics calculators Maths Mansion programme 36 Spiritual/Moral/Citizenship Links: Real life conversions – e.g. currency Investigation: The relationships that exist in y=mx+c Time: 8-10 lessons SUMMER TERM A TOPIC 16 Topic: Angles NC Level: 4 & 5 NC Programme of Study: Ref2abcd: Recall and use properties of angles at a point, angles on a straight line (including right angles), 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, alternate angles and corresponding angles; understand the properties of parallelograms and a proof that the angle sum of a triangle is 180 degrees; understand a proof that the exterior angle of a triangle is equal to the sum of the interior angles at the other two vertices. Use angle properties of equilateral, isosceles and right-angled triangles; understand congruence, recognising when two triangles are congruent; explain why the angle sum of any quadrilateral is 360 degrees. Ref4bde: 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; understand, from their experience of constructing them, that triangles satisfying SSS, SAS, ASA and RHS are unique, but SSA triangles are not. 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:  Use correctly the vocabulary, notation and labelling conventions for lines and angles  Identify parallel and perpendicular lines  Know the sum of angles at a point, on a straight line and in a triangle and recognise vertically opposite angles; use angle measure  Distinguish between and estimate the size of acute, obtuse and reflex angles  Use a ruler and protractor to measure and draw lines to the nearest millimetre and angles, including reflex, to the nearest degree; construct a triangle given 2 sides and the included angle (SAS) or 2 angles and the included side (ASA); explore these constructions using ICT EXT – Identify alternate and corresponding angles Understand a proof that the sum of the angles of a triangle is 180 and of a quadrilateral is 360 (1R-14.7,14.8); and the exterior angle of a triangle is equal to the sum of the 2 interior opposite angles Use straight edge and compasses to construct the midpoint and perpendicular bisector of a line segment and the bisector of an angle Construct a triangle given 3 sides (SSS) Key Vocabulary: TURN QUARTER HALF ROTATIONAL SYMMETRY ANGLE PROTRACTOR ACUTE OBTUSE REFLEX RIGHT ESTIMATE MEASURE SUM AT A POINT SHAPE DRAW CONSTRUCT Impact Reference: Other references: Book 1R – ch. 14 V4 – ch.13 V5 – ch.17,19,21 V6 – ch.12-14 Mental & Oral Starters: 1R folder: pg. 254-255 101 Starters: pg. 73-78 Discussion opportunities: Pair / Group Work: Discuss estimations of angles. Estimation game – who is nearest? ICT Links: LOGO Maths Mansion programmes 35 Spiritual/Moral/Citizenship Links: Angles that occur in the world Investigation: Investigate the sums of different angle relationships Time: 6 lessons SUMMER TERM A TOPIC 17 Topic: Handling Data NC Level: 3, 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. 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. Ref5abcdf: Relate summarised data to the initial questions. Interpret a wide range of graphs and diagrams and draw conclusions. Look at data to find patterns and exceptions. Compare distributions and make inferences, using the shapes of distributions. Have a basic understanding of correlation. Learning Objectives:  Interpret diagrams and graphs and draw simple conclusions based on the shape of graphs and simple statistics for a single distribution  Plan how to collect and organise small sets of data  Design a data collection sheet or questionnaire to use in a simple survey  Construct frequency tables for discrete data, grouped where appropriate in equal class intervals  Construct on paper and using ICT, graphs and diagrams to represent data including: bar-line graphs, frequency diagrams for grouped discrete data; and use ICT to generate pie charts EXT – Plan how to collect the data, including sample size Construct frequency tables with equal class intervals for sets of continuous data Construct on paper and using ICT pie charts for categorical data and simple line graphs for time series (1R-15.6,15.8,20.11) Key Vocabulary: DATA COLLECT TALLY PICTOGRAM BAR CHART DUAL PIE DISCRETE CONTINUOUS LINE GRAPH SCATTER DIAGRAM CORRELATION Impact Reference: Other references: Book 1R – ch. 15 V4 – ch.21 V5 – ch.24-26 V6 – ch.18,19 Mental & Oral Starters: 1R folder: pg. 272-273 Discussion opportunities: Pair / Group Work: Discuss what to investigate, how to collect the Design an investigation – collect the data, data, what do the results mean? display and interpret the results – mini-project ICT Links: Autograph, EXCEL Maths Mansion programme 40 Spiritual/Moral/Citizenship Links: Investigate real life issues/data – keep it relevant to pupils Investigation: See above Time: 8-10 lessons SUMMER TERM A TOPIC 18 Topic: Percentages NC Level: 4 & 5 NC Programme of Study: Ref2eg: Understand that 'percentage' means 'number of parts per 100' and use this to compare proportions; interpret percentage as the operator 'so many hundredths of'. 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. Ref3em: Convert simple fractions of a whole to percentages of the whole and vice versa, then understand the multiplicative nature of percentages as operators. Solve simple percentage problems, including increase and decrease. Learning Objectives:  Understand percentage as ‘the number of parts per 100’  Recognise the equivalence of percentages, fractions and decimals  Calculate simple percentages and use them to compare simple proportions  Convert terminating decimals to fractions EXT – Find the outcome of a given percentage increase or decrease (1R-16.6) Use the equivalence of fractions, decimals and percentages to compare proportions (1R- 8.11) Key Vocabulary: PERCENTAGE FRACTION DECIMAL EQUIVALENT CONVERT COMPARE AMOUNT INCREASE DECREASE CALCULATE Impact Reference: Other references: Book 1R – ch. 16 V4 – ch.6 V5 – ch.2 V6 – ch.3 Bridging Units lessons 11 – 16 (Fractions, Decimals & Percentages) Mental & Oral Starters: 1R folder: pg. 294-295 Discussion opportunities: Pair / Group Work: Discuss where percentages are used in Display work – converting percentages to everyday life? Are they more useful than decimals/fractions, reducing prices in a sale fractions/percentages? ICT Links: EXCEL for display work C4 Video “Not all There” Maths Mansion programme 27 & 28 Spiritual/Moral/Citizenship Links: Taxation, percentages in real life Investigation: Which are more useful – fractions/decimals/percentages? Time: 5-6 lessons SUMMER TERM B TOPIC 19 Topic: Averages NC Level: 4 & 5 NC Programme of Study: Ref4b: Calculate mean, range and median of small data sets with discrete then continuous data; identify the modal class for grouped data. Ref5cde: Look at data to find patterns and exceptions. Compare distributions and make inferences, using the shapes of distributions and measures of average and range. Evaluate and check results, answer questions, and modify their approach if necessary. Learning Objectives:  Calculate statistics for small sets of discrete data  Find the mode, median and range, and the modal class for grouped data  Calculate the mean including from a simple frequency able, using a calculator for a larger number of items EXT – Recognise when it is appropriate to use the range, mean, median and mode Calculate a mean using assumed mean Key Vocabulary: MEAN MEDIAN MODE RANGE FREQUENCY TABLE COMPARE DATA DISCRETE SET Impact Reference: Other references: Book 1R – ch. 17 Mental & Oral Starters: 1R folder: pg. 308-309 101 Starters: pg. 98 Discussion opportunities: Pair / Group Work: What do the results actually tell us? Discuss Calculate averages within the class – e.g. shoe which average is most appropriate size, height etc ICT Links: The is an Internet Census site which can be used for additional data – see website list, Spiritual/Moral/Citizenship Links: It is important that results are relevant to the class and to current issues. Which averages are used in news articles? Do averages really exist? Is anyone average? Investigation: Averages within the class Time: 4-5 lessons SUMMER TERM B TOPIC 20 Topic: Transformations NC Level: 4 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 2D and 3D shapes, and rotation symmetry of 2D shapes; transform 2D 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. Learning Objectives:  Understand and use the language and notation associated with reflections, translations and rotations  Recognise and visualise the transformation and symmetry of a 2D shape: - reflection in given mirror lines and line symmetry - rotation about a given point and rotation symmetry - translation  Explore these transformations and symmetries using ICT EXT – 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 Key Vocabulary: REFLECTION ROTATION TRANSLATION TESSELLATION CONGRUENCE Impact Reference: Other references: Book 1R – ch. 18 V4 – ch.17,18 V6 – ch.16 Mental & Oral Starters: 1R folder: pg. 321-322 101 Starters: pg.87 Discussion opportunities: Pair / Group Work: Discuss as a class the transformations that have Develop patterns involving several taken place; explain methods to each other transformations – display work ICT Links: LOGO Maths Mansion programmes 37 - 39 Spiritual/Moral/Citizenship Links: Upon reflection, we often see things in a different light Investigation: The effects of different transformations on shapes Time: 4-5 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 21 Topic: Fractions, Decimals & NC Level: Percentages NC Programme of Study:

Learning Objectives:  Consolidate and extend mental methods to include decimals, fractions and percentages, accompanied where appropriate by suitable jottings  Solve simple word problems mentally  Recognise the equivalence of percentages, fractions and decimals Key Vocabulary: EQUIVALENT RELATIONSHIP OPERATION INVERSE FRACTION DECIMAL PERCENTAGE Impact Reference: Other references: Transition Unit lessons N5.1 & N5.2 Bridging Units lessons 11 – 16 (Fractions, Decimals & Percentages) Mental & Oral Starters: See lesson plans Discussion opportunities: Pair / Group Work:

ICT Links:

Spiritual/Moral/Citizenship Links:

Investigation:

Time: 2 lessons