MATHS DEPARTMENT

YEAR 8SCHEME OF WORK

SET 4: IMPACT 2G

SEPT 2004

2G PLAN

AUTUMN TERM – FIRST HALFTopic 1 Understanding Number 2G Ch. 1Topic 2 Symmetry & Angles 2G Ch. 2Topic 3 Multiplication & Division 2G Ch. 3Topic 4 Working with Algebra 2G Ch. 4

AUTUMN TERM – SECOND HALFTopic 5 Fractions 2G Ch. 6Topic 6 Probability 2G Ch. 7Topic 7 Decimals & Percentages 2G Ch. 8

SPRING TERM – FIRST HALFTopic 10 Number Patterns 2G Ch. 5Topic 11 Multiplicative Relationships Additional UnitTopic 12 Shape & Measure 2G Ch. 9

SPRING TERM – SECOND HALFTopic 13 Handling Data + unit 2G Ch. 12 + Additional

UnitTopic 14 Formulae & Equations 2G Ch. 13Topic 16 Positive & Negative Numbers 2G Ch. 10

SUMMER TERM – FIRST HALFTopic 17 Graphs 2G Ch. 11Topic 18 Problem Solving Additional UnitTopic 19 Perimeter, Area & Volume 2G Ch. 14

SUMMER TERM – SECOND HALFTopic 20 Averages 2G Ch. 15Topic 21 Calculation & Problem Solving Additional lessons (8N4.1

& 8N4.2)Topic 22 Fractions, Decimals & Percentages Additional Lessons

(8N5.1 & 8N5.2)“OPTIONAL TESTS”

Topic 21 Investigation

AUTUMN TERM A TOPIC 1

Topic: Understanding Number NC Level: 3 & 4

NC Programme of Study:Ref2a: 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.Ref3agij: add, subtract integers and then any number. Recall all positive complements to 100 (e.g. 37+62=100). Develop a range of strategies for mental calculation. Use standard column methods for addition and subtraction of integers.

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. add and subtract integers extend mental methods of computation for addition and subtraction consolidate standard column procedures for addition and subtraction mentally estimate and approximate solutions to numerical calculations; justify such

estimates use the laws of arithmetic and inverse operations use checking procedures, including working through the problem backwards and

considering whether the answer is sensible round positive numbers to any given power of 10.

Key Vocabulary:PLACE VALUE ORDER MENTAL ROUND NEAREST CHECK ESTIMATEImpact Reference:Book 2G – ch. 1

Other references:L4 to L5 Lesson 8N1.1 V3 – ch. 1 – 5 V4 – ch. 2 – 4 V5 – ch. 2 KM81 – ch. 1 - 2

Mental & Oral Starters:2G folder: pg. 4 – 6 101 Starters: pg. 14-18, 22, 47, 58Discussion opportunities:Perhaps do some place value work verbally as a class / whiteboards?Spend time allowing pupils to explain their methods for addition / subtraction.Discuss whether an answer is ‘sensible’.Discuss how to use the number line to help mental calculations.Pair / Group Work:Students can show each other their methods or check each other’s answers; compare estimations.ICT Links:SMILE.. Outware: “Balloon” , “Coin It”Spiritual/Moral/Citizenship Links:We should all respect each other’s different methods and viewsInvestigation:Activity 2G pg.10 – using activity sheet 1Time: 6 lessons

AUTUMN TERM A TOPIC 2

Topic: Symmetry & Angles NC Level: 4 & 5

NC Programme of Study:Ref2abc: 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. Ref3b: recognise and visualise rotations, reflections, including the reflection and rotation symmetry of 2D shapes; transform 2D shapes by rotation and reflection, recognising that these transformations preserve length and angle.

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: Identify all symmetries of 2D shapes – reflective and rotational Transform 2D shapes by simple rotations about a given point and reflections in a given

mirror line Use correct vocabulary, notation and labelling for lines, angles and shapes. 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 angles, to the nearest degree 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

Key Vocabulary:SYMMETRY MEASURE TURN ANGLE DEGREE PROTRACTOR ACUTE OBTUSE REFLEX CONSTRUCT ESTIMATE LINE AT A POINT SHAPE SUMImpact Reference:Book 2G – ch. 2

Other references:V3 – ch. 9 V4 – ch. 13, 18 V5 – ch. 15 KM81 – ch. 5, 7

Mental & Oral Starters:2G folder: pg. 24 – 26 101 Starters: pg. 73, 79, 80Discussion opportunities:Categorise shapes: no. of lines of symmetry and order of rotational symmetry – poster?Pair / Group Work:Discuss how to categorise shapesICT Links:SMILE – Angle 360, Snooker. LOGO can be used to construct shapes, experiment with angles. Maths Mansion programme 35, 38 & 39Spiritual/Moral/Citizenship Links:Reflection on own characterInvestigation: Find a shape with 4, 5, 6 lines of symmetry etc.Time: 5 lessons

AUTUMN TERM A TOPIC 3

Topic: Multiplication & Division NC Level: 3 - 5

NC Programme of Study:Ref2ab: Use concepts and vocabulary of factor, multiple, common factor, highest common factor, least common multiple, prime number and prime number decomposition. Use the terms square, positive square root.Ref3agk: multiply and divide integers; multiply or divide any number by powers of 10; find the prime factor decomposition of positive integers. Recall all multiplication facts to 10 x 10, and use them to derive quickly the corresponding division facts. Use standard column procedures for multiplication of integers.Ref4b: Select appropriate operations, methods and strategies to solve number problems.

Learning Objectives: multiply and divide integers use standard column procedures for multiplication and division of integers mentally estimate and approximate solutions to numerical calculations recognise and use multiples, factors and primes use squares and square roots

Key Vocabulary:MULTIPLY DIVIDE TIMES TABLES REMAINDER MULTIPLE FACTOR SQUARE SQUARE ROOT ODD EVENImpact Reference:Book 2G – ch. 3

Other references:L4 to L5 lesson 8N2.1V3 – ch. 2 - 3 V4 – ch. 3, 4, 8 V5 – ch. 2 - 3 KM81 – ch. 2

Mental & Oral Starters:2G folder: pg. 50-52 101 Starters: pg. 7, 24-31, 39, 48-51Discussion opportunities:Pupils can explain their methods of computation.Using a counting stick encourages discussion.Pair / Group Work:Check each others’ methods/ answers.Dice Bingo – multiply the 2 scores on 12 sided dice together.ICT Links:SMILE. “Balloon” (Outware)Maths Mansion programmes 23 & 24Spiritual/Moral/Citizenship Links:Sharing equally – we are all entitled to the same. Does it always happen?Investigation:Find all numbers that sum to 13 – which give the largest product? Etc.Time: 7 – 8 lessons

AUTUMN TERM A TOPIC 4

Topic: Working With Algebra NC Level: 5

NC Programme of Study:Ref5ab: 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.’

Learning Objectives: use letter symbols to represent unknown numbers or variables 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 simplify linear expressions by collecting like terms and by multiplying terms together

Key Vocabulary:LETTER COLLECT TERM SIMPLIFY EXPRESSION MULTIPLY Impact Reference:Book 2G – ch. 4

Other references:L4 to L5 lesson 8A2.1V4 – ch. 9 V5 – ch. 8, 9 KM81 – ch. 4

Mental & Oral Starters:2G folder: pg. 66-67 101 Starters: pg. 65Discussion opportunities:Discuss what the expressions can represent. Verbally substitute in values.Pair / Group Work:Pupils can make up their own word / algebraic equations and test each other.Match up expressions when simplified – card-like game. ICT Links:EXCEL – inputting formulae to get the desired output, rather than typing in numbers.Spiritual/Moral/Citizenship Links:We tend to be close to people who are similar to ourselvesInvestigation:What happens when we change the value of the variable?Time: 5 lessons

AUTUMN TERM B TOPIC 5

Topic: Fractions NC Level: 3 & 5

NC Programme of Study:Ref2c: Use fraction notation; understand equivalent fractions, simplifying a fraction by cancelling all common factors; order fractions by rewriting then with a common denominator. Ref3c: 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.

Learning Objectives: recognise proportions of a whole and use simple fractions to describe these recognise equivalent fractions

find equivalent fractions by multiplying or dividing cancel fractions to their lowest terms understand & interpret ‘mixed numbers’ and ‘improper fractions’ understand addition and subtraction of fractions add & subtract fractions by writing them with a common denominator calculate fractions of quantities

Key Vocabulary:MIXED NUMBER IMPROPER FRACTION QUANTITY NUMERATOR DENOMINATOR EQUIVALENT ADD SUBTRACT Impact Reference:Book 2G – ch. 6

Other references:L4 to L5 lesson 8N3.1V4 – ch. 6 V5 – ch. 5 KM81 – ch. 9

Mental & Oral Starters:2G folder: pg. 96 - 97 101 Starters: pg. 36-37Discussion opportunities:Discuss different ways of writing fractions of certain quantitiesPair / Group Work:Change the quantities of a recipe.ICT Links:Maths Mansion programmes 25 & 26Spiritual/Moral/Citizenship Links:Everything is significant no matter how smallInvestigation:

Time: 5 -6 lessons

AUTUMN TERM B TOPIC 6

Topic: Probability NC Level: 3 – 5

NC Programme of Study:Ref4cd: 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.

Learning Objectives: understand and use the probability scale from 0 to 1 – in words and numbers. find and justify probabilities based on equally likely outcomes in simple contexts. calculate probabilities with one or more successful outcomes 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.

Key Vocabulary:IMPOSSIBLE POSSIBLE CERTAIN SCALE EVENT OUTCOMEImpact Reference:Book 2G – ch. 7

Other references:V4 – ch. 22 V5 – ch. 22 - 24 KM81 – ch. 8

Mental & Oral Starters:2G folder: pg. 114-115 101 Starters: pg. 99 - 101Discussion 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:SMILESpiritual/Moral/Citizenship Links:Morality of gamblingInvestigation:Investigate the probability of various real events – e.g. rain, red car in car park etc.Time: 5 lessons – perhaps more, depending on practical work

AUTUMN TERM B TOPIC 7

Topic: Decimals & Percentages NC Level: 4 - 6

NC Programme of Study:Ref2de: Use decimal notation and recognise that each terminating decimal is a fraction. Understand that ‘percentage’ means ‘number of parts per 100’ and use this to compare proportions; interpret percentage as the operators ‘so many hundredths of’.Ref3acejk: add, subtract, multiply and divide integers and then by any number; multiply or divide any number by powers of 10, and any positive number between 0 and 1. Perform short division to convert a simple fraction to a decimal. Convert simple fractions of a whole to percentages of the whole and vice versa, then understand the multiplicative nature of percentages as operators. 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 fractions; solve a problem involving division by an integer.

Learning Objectives: order decimals use standard column procedures for addition and subtraction of decimals with up to two

places multiply and divide decimals by powers of 10 use standard column procedures for multiplication and division of decimals by single digit

whole numbers; understand where to position the decimal point by considering equivalent calculations

use division to convert a fraction to a decimal interpret percentage as the operator ‘so many hundredths of’ express one given number as a percentage of another calculate simple percentages use the equivalence of fractions, decimals and percentages to compare proportions

Key Vocabulary:PLACE VALUE WHOLE NUMBER FRACTION DECIMAL PERCENTAGE ORDER AMOUNTImpact Reference:Book 2G – ch. 8

Other references:V4 – ch. 6 V5 – ch. 4 - 5 KM81 – ch. 9

Mental & Oral Starters:2G folder: pg. 126-127 101 Starters: pg. 38Discussion opportunities:Where do we use decimals and percentages?Pair / Group Work:Human number lineICT Links:EXCEL for interest rates, discounts etc; perhaps set up a shop.Outware: “Coin It”Maths Mansion programmes 21, 22, 27, 29 & 30. C4 Video “Not all There”Spiritual/Moral/Citizenship Links:No matter how small, everything is significant. Tax – where does it go?Investigation:Investigate the equivalence of fractions, decimals & percentages – which is more useful?Time: 8 - 9 lessons

SPRING TERM A TOPIC 8

Topic: Number Patterns NC Level: 4

NC Programme of Study:Ref5d: set up simple equation; solve simple equations by using inverse operations.Ref6bc: 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 terms of a simple sequence given by a rule generate sequences from practical contexts and describe the general term in simple

cases use number machines – including inverse use the laws of arithmetic and inverse operations when generating terms and describing

the sequence

Key Vocabulary:PATTERN SEQUENCE NUMBER MACHINE INVERSE OPERATION RULE OPERATION INPUT OUTPUTImpact Reference:Book 2G – ch. 5

Other references:V3 – ch. 3 V4 – ch. 8 KM81 – ch. 5, 7

Mental & Oral Starters:2G folder: pg. 80 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.C4 Video “Primes & Powers”Spiritual/Moral/Citizenship Links:We all have to follow rules at school and in lifeInvestigation:See group workTime: 4 lessons

SPRING TERM A TOPIC 9

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 quantities; 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 UNITARYImpact Reference: Other references:

Phase 3 Problem BankSEE MULTIPLICATIVE RELATIONSHIPS MINI-PACK FOR FURTHER GUIDANCE

Time: 9 lessons

SPRING TERM A TOPIC 10

Topic: Shape & Measure NC Level: 4 - 6

NC Programme of Study:Ref2fik: 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. Use “2D representations of 3D shapes and analyse 3D shapes through 2D projections and cross sections including plans and elevation.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; 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.

Learning Objectives: classify quadrilaterals by their geometric properties recognise parts of a circle recognise and draw common 3D solids recognise and produce 2D representations of 3D shapes - nets

use units of measurement to estimate, calculate and solve problems in everyday contexts – involving length, area, volume, capacity, mass, time and angle

convert one metric unit to another know rough equivalents of imperial measures in daily use (feet, miles, pounds, pints,

gallons) read and interpret scales on a range of measuring instruments

Key Vocabulary:POINT LINE SHAPE QUADRILATERAL CIRCLE SOLID NET MEASURE CAPACITY UNITS IMPERIAL METRIC TIMEImpact Reference:Book 2G – ch. 9

Other references:V3 – ch. 8, 10 V4 – ch. 14, 16 V5 – ch. 11 – 13, 16

Mental & Oral Starters:2G folder: pg. 138-141 101 Starters: pg. 74, 75, 77, 78, 83-86Discussion opportunities:Discuss properties of shapes, where metric / imperial units are used.Pair / Group Work:Classify shapes into categoriesICT Links:LOGOMaths Mansion programmes 33 & 34Spiritual/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:Activity sheet 2 (rhombus) and 3 (trapezium)Time: 6 lessons

SPRING TERM B TOPIC 11

Topic: Handling Data NC Level: 3 & 4

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.

Learning Objectives: construct on paper and using ICT:

- bar charts and frequency diagrams for discrete data- simple line graphs for time series

interpret tables, graphs and diagrams for discrete data and draw inferences that relate to the problem being discussed

collect data from a simple experiment and record in a frequency table construct frequency tables with equal class intervals for sets of continuous data

Key Vocabulary:COLLECT DATA PICTOGRAM BAR CHART FREQUENCY DUAL

DISCRETE CONTINUOUS GROUPED DATAImpact Reference:Book 2G – ch. 12

Other references:V3 – ch. 14 V4 – ch. 21 V5 – ch. 20 KM81 – ch. 3, 13

Mental & Oral Starters:2G folder: pg. 186 - 187 Discussion opportunities:Discuss which methods of representation are most suitable. Draw inferences from diagrams, explain findingsPair / Group Work:Collecting data.ICT Work.ICT Links:EXCEL for producing graphs / charts. Internet for sets data to analyse.Maths Mansion programme 40Spiritual/Moral/Citizenship Links:Use real life dataInvestigation:Conduct a survey relevant to the pupils’ livesTime: 8 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 DISTRIBUTIONSTEM-AND-LEAF DIAGRAM LINE GRAPH FREQUENCY TABLE PRIMARY SOURCE SECONDARY SOURCE RAW DATA HYPOTHESISImpact Reference:Book 2G – ch. 12

Other references: Data Library CD-ROMInteracting with Data Handling Pack from LEA

SEE HANDLING DATA MINI-PACK FOR FURTHER GUIDANCE

Time: 6 lessons

SPRING TERM B TOPIC 12

Topic: Formulae & Equations NC Level: 4 – 6

NC Programme of Study:Ref5adf: 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. Set up simple equations; solve simple equations, by using inverse operations or by transforming both sides in the same way. Use formulae from maths and other subjects; substitute numbers into a formula; derive a formula and change its subject.

Learning Objectives: 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 method (e.g. inverse operations) begin to use graphs and set up equations to solve simple problems involving direct

proportion

Key Vocabulary:WORD FORMULAE LETTER REPRESENT OPERATION ALGEBRA SUBSTITUTE SOLVE EQUATION NUMBER MACHINE BALANCEImpact Reference:Book 2G – ch. 13

Other references:L4 to L5 lessons 8A4.1V4 – ch. 9 V5 – ch. 8 - 9 KM81 – ch. 4

Mental & Oral Starters:2G folder: pg. 204 - 205 101 Starters: pg. 62-67Discussion opportunities:Using algebra to model real lifePair / Group Work:Set up problems to test each other. Create formulae ‘stories’ICT Links:Use EXCEL to change the variable of a formulaC4 Video “Orders Please”Spiritual/Moral/Citizenship Links:Treat both sides and each other equally; fairnessInvestigation:Investigate what happens to the formula as the values changeTime: 7 - 8 lessons

SUMMER TERM A TOPIC 13

Topic: Positive & Negative Numbers

NC Level: 4 & 5

NC Programme of Study:Ref2a: Understand and use negative numbers, both as positions and translations on a number line; order integersRef3a: Add, subtract, multiply and divide integers

Learning Objectives: Understand negative numbers as temperatures Understand negative numbers as positions on a number line – both vertical and

horizontal lines Order positive and negative integers in context Continue number patterns involving negative numbers

Key Vocabulary:POSITIVE NEGATIVE ORDER NUMBER LINE TEMPERATURE NUMBER PATTERN SEQUENCEImpact Reference:Book 2G – ch. 10

Other references:L4 to L5 lesson 8N1.2V3 – ch. 6 V5 – ch. 6 KM81 – ch. 6

Mental & Oral Starters:2G folder: pg. 156 - 157 101 Starters: pg. 19-21, 23Discussion opportunities:

Where do negative numbers occur in real life?Pair / Group Work:Human number lineICT Links:EXCEL can be used to generate number patternsC4 Video “Walking Backwards”Spiritual/Moral/Citizenship Links:Positive qualities can balance out the negative. Debt – 3rd WorldInvestigation:How often are negative numbers used in real life?Time: 7 -8 lessons

SUMMER TERM A TOPIC 14

Topic: Graphs NC Level: 4 & 5

NC Programme of Study:Ref6ef: use the conventions for co-ordinates in the plane; plot points in al 4 quadrants; recognise that equations of the form y=mx+c correspond to straight line graphs; plot graphs of functions in which y is given explicitly in terms of x, or implicitly. Construct linear functions arising from real life problems and plot their corresponding graphs; discuss and interpret graphs arising from real situations

Learning Objectives: generate points in all four quadrants generate co-ordinate pairs that satisfy a simple linear rule recognise straight line graphs parallel to the x and y axes plot the graphs of linear functions where y is given explicitly in terms of x construct linear functions arising from real-life problems and plot the corresponding

graphs discuss and interpret graphs from real situations find co-ordinates of points determined by geometric informationKey Vocabulary:COORDINATE QUADRANT PLOT LINE GRAPH AXES SCALE CONVERSION TEMPERATURE IMPERIAL METRICImpact Reference:Book 2G – ch. 11

Other references:V4 – ch. 10 KM81 – ch. 1

Mental & Oral Starters:

2G folder: pg. 170 -172 101 Starters: pg. 90-92Discussion opportunities:Discuss how to label the axes and graphsPair / Group Work:Connect 4 -type gameICT Links:EXCEL, Omnigraph. Outware: “Carpark” “Defender”Maths Mansion programme 36Spiritual/Moral/Citizenship Links:Currency conversions – difference between 1st and 3rd WorldInvestigation:Can you spot a relationship between the lines and their equations?Time: 6 lessons

SUMMER TERM A TOPIC 15

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 JUSTIFYImpact Reference: Other references:

Mental & Oral Starters:

SEE PROBLEM SOLVING PACK FROM LEA

Time: 5 lessons

SUMMER TERM B TOPIC 16

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: find the perimeter of simple shapes know and use the formula for the area of a rectangle calculate the perimeter and area of shapes made from rectangles calculate the area of a triangle know and use the formula for the volume of a cuboid calculate the surface area of cubes and cuboids

Key Vocabulary:PERIMETER AREA RECTANGLE TRIANGLE COMPOSITE SHAPE CURVE VOLUME CUBOID FORMULAImpact Reference:Book 2G – ch. 14

Other references:V4 – ch. 19 KM81 – ch. 12, 14

Mental & Oral Starters:2G folder: pg. 216 - 217

101 Starters: pg. 93, 94Discussion opportunities:Discuss formulae already known, ways to estimate areasPair / Group Work:Find the area of real life objects – e.g. football pitchICT Links:Maths Mansion programmes 31 & 32Spiritual/Moral/Citizenship Links:Dimensions – finite and infiniteInvestigation:Find the max. area when the perimeter is 20cm, 50cm, 100cm etc. – similar to ‘Fencing’Time: 5 lessons

SUMMER TERM B TOPIC 17

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. Ref5d: Compare distributions and make inferences, using the shapes of distributions and measures of average and range.

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 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 COMPARE DATAImpact Reference:Book 2G – ch. 15

Other references:V5 – ch. 19 KM81 – ch. 13

Mental & Oral Starters:2G folder: pg. 236 -237 101 Starters: pg. 96Discussion opportunities:Discuss which average is the most appropriatePair / Group Work:Collect data in groupsICT Links:Perhaps for larger samples - EXCELSpiritual/Moral/Citizenship Links:

Is anyone really average?Investigation:Set a hypotheses – collect results etc.Time: 6 lessons – perhaps more depending on practical work

SUMMER TERM B TOPIC 18

Topic: Calculation & Problem Solving

NC Level:

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 solutionsAdditional Notes: There are 2 Transition Units used at the beginning of year 7 for sets 1-3. Some pupils may have studied the first unit at the end of year 6. Key Vocabulary:DIFFERENCE EXPLAIN INTEGER MINUS NEGATIVE PLUS POSITIVE REASONING SUM SYSTEMATICImpact Reference: Other references:

L4 to L5 lesson 8N4.1 & 8N 4.2

V4 – ch.1,3,4,8 V5 – ch.4,7“TRANSITION FROM Y6 TO Y7: MATHS – UNITS OF WORK”

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, 58Time: 2 lessons

SUMMER TERM B TOPIC 19

Topic: Fractions, Decimals & Percentages

NC Level:

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 mentallyKey Vocabulary:EQUIVALENT FRACTION DECIMAL PERCENTAGECONVERT NUMERATOR DENOMINATOR PROPORTION

Impact Reference: Other references: L4 to L5 lessons 8N5.1 & 8N5.2

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

ICT Links:Maths Mansion programme 27C4 Video “Not all There”Spiritual/Moral/Citizenship Links:

Investigation:

Time: 2 lessons