MATHS DEPARTMENT

YEAR 9SCHEME OF WORK

SET 1: IMPACT 3R

SEPT 2004

3R PLAN

AUTUMN TERM – FIRST HALFTopic 1 Number + Place Value 3R Ch. 1 + Additional

UnitTopic 2 Working with Algebra 3R Ch. 2Topic 3 Area, Volume & Measure 3R Ch. 3Topic 4 Averages & Spread 3R Ch. 4Topic 5 Formulae, Equations & Inequalities 3R Ch. 5

TEST 1

AUTUMN TERM – SECOND HALFTopic 6 Angles 3R Ch. 6Topic 7 Fractions, Ratio & Proportion 3R Ch. 8Topic 8 Graphs 3R Ch. 7Topic 9 Number Sequences 3R Ch. 16Topic 10 Problem Solving Additional Unit

TEST 2

SPRING TERM – FIRST HALFTopic 11 Geometrical Reasoning + unit 3R Ch. 10 + Additional

UnitTopic 12 Proportional Reasoning Additional UnitTopic 13 Decimals 3R Ch. 11Topic 14 Probability 3R Ch. 14

TEST 3

SPRING TERM – SECOND HALFTopic 15 Handling Data + unit 3R Ch. 9 + Additional

UnitTopic 16 Using a Calculator Additional UnitTopic 17 Percentages 3R Ch. 12Topic 18 Pythagoras’ Theorem 3R Ch. 13

TEST 4

SUMMER TERM – FIRST HALFTopic 19 Transformations 3R Ch. 15Topic 20 Trigonometry 3R Ch. 17Topic 21 Revision for SATs CGP Packs & Past Papers

SAT’s WEEK

SUMMER TERM – SECOND HALFStart KS4 Higher Tier Scheme of Work immediately after SATs have taken place.

AUTUMN TERM A TOPIC 1

Topic: Number NC Level: 6 - 8

NC Programme of Study:Ref2ab: Use previous understanding of integers and place value to deal with large numbers and

round to given powers of 10. Use the terms square, positive and negative square root, cube, cube root; use index notation and index laws.Ref3gh: Recall all positive integer complements to 100, all multiplication facts to 10 x 10 and use to quickly derive division facts; recall cubes of 2, 3, 4, 5, 10.Round to the nearest integer and to 1 sig. fig.Ref4c: Use a variety of checking procedures including working through the problem backwards.Ref5c: Use index notation for simple integer powers and simple instances of index laws.Learning Objectives: Use laws of arithmetic and inverse operations Make and justify estimates and approximations of calculations Check results using appropriate methods Round positive numbers to any given power of 10, and significant figures Move from one form to another to gain a different perspective on the problem Use ICT to estimate square roots and cube roots Use index notation for integer powers and simple instances of the index laws Give solutions to problems to an appropriate degree of accuracyEXT – Estimate calculations by rounding numbers to 1 sig. fig. and multiplying or dividing mentally; know and use index laws for multiplication and division of positive integer powers; recognise that index laws can be applied to negative and fractional powers; recognise limitations on the accuracy of data and measurementsAdditional Notes: The Place Value lesson should be used as part of this chapter (Booster Lesson 1)Key Vocabulary:INDICES INDEX SIGNIFICANT BOUNDS INVERSE SQUARE CUBE ROOTImpact Reference:Book 3R – ch.1

Other references: Booster L1 V8 – ch4

Mental & Oral Starters:3R folder: pg. 4-7 101 Starters: pg. 11-13, 33-35, 46, 57Discussion opportunities:Explain methods; discuss whether an answer is ‘sensible’

Pair / Group Work:Give each other questions to calculate or estimate.

ICT Links:EXCEL – trial and improvement for square / cube rootsC4 Video “Primes & Powers”Spiritual/Moral/Citizenship Links:We should all respect each other’s different methods and ideasInvestigation:Why do we need to round numbers?Time: 4-5 lessons

ADDITIONAL LESSON

Topic: Place Value NC Level: 5 & 6

Learning Objectives: Understand and use decimal notation and place value

Multiply and divide integers and decimals by 10, 100, 1000 Explain the effects of the above multiplication and division Extend knowledge of integer powers of 10 Multiply and divide integers and decimals by 0.1, 0.01 etc.

Additional Notes: Booster lesson 1 should be covered as a stand-alone lesson here

Key Vocabulary:PLACE VALUE TENTHS HUNDREDTHS THOUSANDTHS EQUIVALENT POWER INDEX MULTIPLY DIVIDEImpact Reference:This links closely to ch.1

Other references: Booster lesson 1

Mental & Oral Starters:

SEE LESSON PLAN 1 FOR DETAILED INFORMATION

Time: 1 lesson

AUTUMN TERM A TOPIC 2

Topic: Working with Algebra NC Level: 6 - 8

NC Programme of Study:Ref5bc: Understand 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, by expanding the product of 2 linear expressions, including squaring a linear expression. Use index notation for simple integer powers and simple instances of index laws; substitute positive and negative numbers into expressions.Learning Objectives: Simplify or transform algebraic expressions by taking out single term common factors Multiply and divide powers Add and subtract expressions involving brackets Combine simple algebraic fractionsEXT – Square a linear expressions, expand the product of 2 linear expressions of the form xn; establish identities such as a2-b2 = (a+b)(a-b)Key Vocabulary:INDICES POWERS FACTORISE EXPAND ALGEBRAIC FRACTIONS COMMON FACTORImpact Reference:Book 3R – ch.2

Other references: Booster L6 V8 – ch6

Mental & Oral Starters:3R folder: pg. 24-26 101 Starters: pg. 69 - 71Discussion opportunities:What expressions can represent, relate to real life.

Pair / Group Work:Develop expressions to represent real life situations

ICT Links:EXCEL – input formulae, substitute values into expressionsSpiritual/Moral/Citizenship Links:Each letter can take many different values; symbolises different numbers – in life things change, objects symbolise significant meanings.Investigation:What happens as the variables change?Time: 4 lessons

AUTUMN TERM A TOPIC 3

Topic: Area, Volume & Measure NC Level: 5 - 8

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 and perimeter of simple shapes. Find volumes of cuboids; 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 and volume measures.Learning Objectives: Use units of measure to calculate, estimate, measure and solve problems in a variety of

contexts Convert between area measures (mm2 to cm2, cm2 to m2 and vice versa) and between volume

measures (mm3 to cm3, cm3 to m3 and vice versa) Deduce and use formulae for the area of a triangle, parallelogram and trapezium Calculate areas of compound shapes made from rectangles and triangles Know and use the formulae for the circumference and area of a circle Know and use the formula for the volume of a cuboid Calculate volumes and surface areas of cuboids and shapes made from cuboids Calculate the surface area and volume of right prismsEXT – Recognise that measurements given to the nearest whole unit may be inaccurate by up to ½ unit in either direction; understand and use compound measures to solve problems; know and use formulae for lengths of arc and area of sectors; calculate lengths, areas and volumes in right prismsKey Vocabulary:AREA VOLUME CIRCUMFERENCE CONVERSION SURFACE AREA CAPACITY ACCURACY COMPOUND UNITSImpact Reference:Book 3R – ch.3

Other references: Booster L9 & 10 V6 – ch11 V7 – ch15 V8 – ch12

Mental & Oral Starters:3R folder: pg. 40-44 101 Starters: pg. 83 - 86Discussion opportunities:Discuss known formulae

Pair / Group Work:Find areas of complicated composite shapes

ICT Links:EXCEL – finding max area of different shapesSpiritual/Moral/Citizenship Links:Some countries have a larger surface area – does that mean they are better off?Investigation:Discover the formulae for circles.Compare surface area of shapes with same volume. The ‘Fencing Problem’Time: 5 lessons

AUTUMN TERM A TOPIC 4

Topic: Averages & Spread NC Level: 6 - 8

NC Programme of Study:Ref4bg: Calculate mean, range and median of small data sets with discrete then continuous data;

identify 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 Recognise when it is appropriate to use the range, mean, median and mode Recognise when it is appropriate to use the modal class for grouped data Find summary values that represent the raw data and select the statistics most appropriate to

the problem Construct and use stem-and-leaf diagrams Find the mean and median of grouped or continuous dataEXT – Find the median and quartiles for large data sets; estimate the mean, median and IQR of a large set of grouped data; generate fuller solutions to increasingly demanding problemsKey Vocabulary:MEAN MODE MEDIAN RANGE CONTINUOUS GROUPED DATA QUARTILES CUMULATUVE FREQUENCYImpact Reference:Book 3R – ch. 4

Other references: Booster L14V7 – ch19

Mental & Oral Starters:3R folder: pg. 64-66 101 Starters: pg. 96Discussion opportunities:Discuss which measure is most appropriate.Interpretation of results

Pair / Group Work:Compare averages, draw inferences

ICT Links:EXCEL for representing data, analysis of statistics – pupils can then focus on inferencesSpiritual/Moral/Citizenship Links:Pupils can draw inferences from data which relates to the class as a whole; use statistics from current affairsInvestigation:Plenty of real life topics/statistics can be investigated hereTime: 5 lessons

AUTUMN TERM A TOPIC 5

Topic: Formulae, Equations & Inequalities

NC Level: 6 - 8

NC Programme of Study:Ref5defhij: Understand that the transformation of algebraic expressions obeys and generalises the

rules of arithmetic; simplify or transform algebraic expressions by collecting like terms and by expanding the product of 2 linear expressions; distinguish in meaning between the words ‘equation’ ‘formula’ ‘identity’ ‘expression’. 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 appear on either side or on both sides of the equation; solve linear equations that require prior simplification of brackets. Link a graphical representation of an equation to is algebraic solution; find an approx. solution of a pair of linear simultaneous equations by graphical methods, then find the exact solution by eliminating one variable; consider the graphs of cases with no solution or an infinite number of solutions. Use formulae from maths and other subjects; substitute numbers into formulae; derive a formula and change its subject. Solve simple linear inequalities in one variable and represent the solution on a number line.Learning Objectives: Distinguish the different roles played by letter symbols in equations, identities, formulae and

functions Construct and solve linear equations with integer coefficients (unknown on either or both

sides) using appropriate methods Use systematic trial and improvement methods and ICT tools to find approximate solutions of

equations such as x3 + x = 20 Use formulae from maths and other subjects Substitute numbers into expressions and formulae Derive a formula, and in simple cases, change its subject Simplify non-linear equationsEXT – Solve a pair of simultaneous linear equations by eliminating 1 variable; link a graphical representation of an equation or pair of equations to the algebraic solution; solve linear inequalities in 1 and 2 variables; derive and use more complex formulae, and change the subject of a formulaKey Vocabulary:SOLVE LINEAR EQUATION VARIABLE UNKNOWN REARRANGE SUBSTITUTE TRIAL AND IMPROVEMENTImpact Reference:Book 3R – ch. 5

Other references: Booster L13V6 – ch7 V7 – ch6-8 V8 – ch6 & 8

Mental & Oral Starters:3R folder: pg. 86-91 101 Starters: pg. 69-72Discussion opportunities:Discuss different methods

Pair / Group Work: Can set each other equations to solve

ICT Links:EXCEL for trial and improvement. Graphical equations for solving equations graphically?C4 Video “Orders please”Spiritual/Moral/Citizenship Links:Treat both sides equally. Can set up formulae that model real life issues.Investigation:Investigate what happens as the values changeTime: 6-8 lessons

AUTUMN TERM B TOPIC 6

Topic: Angles NC Level: 5 - 7

NC Programme of Study:Ref2abcdg: Recall and use properties of angles at a point, on a straight line, perpendicular lines and opposite angles at a vertex. Distinguish between acute, obtuse, reflex and right angles;

estimate the size in degrees. Use parallel line rules; understand properties of parallelograms and proof that the angle sum of a triangle is 180; understand proof that the exterior angle of a triangle is equal to the sum of the interior angles at the other 2 vertices. 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. Calculate and use the sums of the interior and exterior angles of quadrilaterals, pentagons and hexagons; calculate and use the angles of regular polygons.Learning Objectives: Solve problems using properties of angles, of parallel and intersecting lines Justify inferences and explain reasoning with diagrams and text Identify alternate angles and corresponding angles Understand the proof that:

- the sum of the angles of a triangle is 180 and of a quadrilateral is 360- the exterior angle of a triangle is equal to the sum of the 2 interior opposite

angles Explain how to find, calculate and use:

- the sums of the interior and exterior angles of quadrilaterals, pentagons and hexagons

- the interior and exterior angles of regular polygons Distinguish between conventions, definitions and properties Recognise and use three figure bearingsEXT – Distinguish between practical demonstration and proof

Key Vocabulary:STRAIGHT INTERSECTING LINE PARALLEL SUPPLEMENTARY ALTERNATE CORRESPONDING VERTICALLY OPPOSITE INTERIOR EXTERIOR BEARINGImpact Reference:Book 3R – ch. 6

Other references: Booster L8 V6 – ch12-14

Mental & Oral Starters:3R folder: pg. 110-113 101 Starters: pg. 82-83Discussion opportunities:Explain angle rules

Pair / Group Work:Proof of angle facts

ICT Links:

Spiritual/Moral/Citizenship Links:Everything has its own rules to followInvestigation:Investigate angle rules by measurementTime: 3-4 lessons

AUTUMN TERM B TOPIC 7

Topic: Fractions, Ratio & Proportion NC Level: 6 & 8+

NC Programme of Study:Ref2fg: Use ratio notation, including reduction to its simplest form and its various links to fraction notation. Recognise where fractions are needed to compare proportions.Ref3cfn: 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; perform short division to convert a simple fraction to a decimal. Divide a quantity in a given ratio. Solve word problems about ratio and proportion, including using informal strategies and the unitary method.Ref5fg: 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.Ref3d(shape): recognise that enlargements preserve angle and not length; identify the scale factor of an enlargement as the ratio of the lengths of any 2 corresponding line segments and apply this to triangles; understand the implications of enlargement for perimeter; use and interpret maps and scale drawings.Learning Objectives: Calculate fractions of quantities Use efficient methods to add, subtract, multiply and divide fractions, interpreting division as a

multiplicative inverse Cancel common factors before multiplying or dividing Reduce a ratio to its simplest form, including a ratio expressed in different units 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 Use proportional reasoning to solve a problem, choosing the correct numbers to take as 100% or as a

whole Compare 2 ratios; interpret and use ratio in a range of contexts, involving solving word problems Solve problems involving direct proportion using algebraic methods, relating algebraic methods,

relating algebraic solutions to graphical representations of the equations Use and interpret maps and scale drawings Consolidate understanding of the relationship between ratio and proportionEXT – Understand and use proportionality and calculate the result of any proportional change using only multiplicative methodsAdditional Notes: THIS CHAPTER SHOULD BE USED TO PREPARE FOR THE PROPORTIONAL REASONING UNIT IN THE SPRING TERM.Key Vocabulary:FRACTION RATIO DIRECT PROPORTION CONSTANT SIMPLIFYImpact Reference:Book 3R – ch. 8

Other references: Booster L5 & 15 V6 – ch2 & 4 V8 – ch1 & 10

Mental & Oral Starters:3R folder: pg.158-162 Discussion opportunities:Dividing quantities

Pair / Group Work:e.g Adapt a recipe using ratio

ICT Links:C4 Video “Scaling the Heights”Spiritual/Moral/Citizenship Links:Can keep the problems relevant to pupils/ current issuesInvestigation:What happens to quantities as the ratio changes and vice versa?Time: 3- 4 lessons

AUTUMN TERM B TOPIC 8

Topic: Graphs NC Level: 7 & 8

NC Programme of Study:Ref5d: Set up simple equations.Ref6efgh:Use the conventions for co-ordinates in the plane; plot points in all 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. 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: Find the inverse of a linear function 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 Given values for m and c, find the gradient of lines given by equations of the form y=mx+c Construct functions arising from real-life problems and plot their corresponding graphs Interpret graphs arising from real situations including distance-time graphs Represent problems and synthesise information in algebraic, geometric or graphical form Communicate interpretations and results of a statistical enquiry using selected tables, graphs

and diagrams in support, using ICT as appropriate Analyse 3D shapes through 2D projections, including plans and elevationsEXT – Plot the graph of the inverse of a linear function; consider cases that have no solution or an infinite no. of solutions; investigate the gradients of parallel and perpendicular lines; plot graphs of simple quadratic and cubic functionsKey Vocabulary:GRADIENT INTERCEPT COORDINATE AXESImpact Reference:Book 3R – ch. 7

Other references: V6 – ch9 V7 – ch9 & 10 V8 – ch7 & 9

Mental & Oral Starters:3R folder: pg. 128-132 101 Starters: pg. 72Discussion opportunities:The relationship between the equations and their graphs

Pair / Group Work:Spot relationships using ICT

ICT Links:Omnigraph, Autograph, EXCEL, graphical calculators. “Carpark” (Outware)Spiritual/Moral/Citizenship Links:Can study conversion graphs, or graphs from current issues.Investigation:Investigate the effects of changing m and c – find y=mx+c + c for themselves by plotting several graphsTime: 4-6 lessons

AUTUMN TERM B TOPIC 9

Topic: Number Sequences NC Level: 7

NC Programme of Study:Ref5d: Set up simple equations; solve simple equations by using inverse operations or by transforming both sides in the same way.Ref6abc: Generate common integer sequences. Find the first terms of a sequence given a rule arising naturally from a context; find the rule for the nth term. 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 integer sequences Generate term of a sequence using term-to-term and position-to-term definitions of the

sequence, on paper and using ICT Generate sequences from practical contexts and write an expression to describe the nth term

of an arithmetic sequence Find the inverse of a linear function Represent mappings expressed algebraically Generate non-linear sequencesEXT – Quadratic sequences, deduce properties of sequences of triangular and square nos. from spatial patternsKey Vocabulary:DIFFERENCE GENERAL RULE LINEAR INVERSE MAPPINGImpact Reference:Book 3R – ch. 16

Other references: Booster L7 V6 – ch6 V7 – ch5

Mental & Oral Starters:3R folder: pg. 304-307 101 Starters: pg. 72Discussion opportunities:Discuss the rules of sequences; how to generate the next no.

Pair / Group Work:Create sequences and describe the rule

ICT Links:EXCEL may be useful hereSpiritual/Moral/Citizenship Links:Sequences / patterns that occur in natureInvestigation:Sequences that occur in the worldTime: 4 lessons

AUTUMN TERM B TOPIC 10

Topic: Problem Solving NC Level:

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

Additional Notes: Booster lessons 12 and 14 his should be used as a stand-alone Problem

Solving unitKey Vocabulary:EXPLAIN REASONS JUSTIFYImpact Reference: Other references:

Booster lesson 12 & 16Mental & Oral Starters:

SEE LESSON PLAN 12 & 16 FOR DETAILED INFORMATION

Time: 2 lessons

SPRING TERM A TOPIC 11

Topic: Geometrical Reasoning & Construction

NC Level: 6 - 8

NC Programme of Study:Ref2fik:Recall the essential properties of special types of quadrilateral; classify quadrilaterals by their geometric properties. Recall the definition of a circle and the meaning of related terms; understand that the tangent at any point on a circle is perpendicular to the radius at that point; explain why the perpendicular from the centre to a chord bisect the chord; understand that inscribed regular polygons can be constructed by equal division of a circle. Use 2D representations of 3D shapes and analyse 3D shapes through 2D projections and cross-sections.Ref4ej: Use straight edge and compasses to do standard constructions. Find loci both by reasoning and by using ICT to produce shapes and paths.Learning Objectives:

Solve problems using properties of angles, of parallel and intersecting lines, and of triangles and other polygons

Justify inferences and explain reasoning with diagrams and text Classify quadrilaterals by their geometric properties Know the definition of a circle and the names of its parts Explain why inscribed regular polygons can be constructed by equal division of a circle Use straight edge and compasses to construct:

- 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- a triangle give 3 sides (SSS)- a triangle given right angle, hypotenuse and side (RHS)

use ICT to explore constructions of triangles and other 2D shapes Find the locus of a point that moves according to a simple rule, both by reasoning and by

using ICT Visualise and use 2D representations of 3D objectsEXT – Know that a tangent at any point on a circle is perpendicular to the radius at that point; find the locus of a point which moves according to a more complex ruleAdditional Notes: GEOMETRICAL REASONING UNIT TO BE DONE AFTER OR ALONGSIDE THIS CHAPTERKey Vocabulary:CROSS SECTION CONSTRUCTION LOCI TESSELLATIONImpact Reference:Book 3R – ch. 10

Other references: V6 – ch15 V7 – ch13

Mental & Oral Starters:3R folder: pg. 200-202 Discussion opportunities:Discuss the paths of various objects / situations

Pair / Group Work:

ICT Links:Spiritual/Moral/Citizenship Links:

Investigation:Investigate loci of different objectsTime: 4-5 lessons

ADDITIONAL UNIT

Topic: Geometrical Reasoning Unit

Learning Objectives: Distinguish between conventions, definitions and derived properties Distinguish between practical demonstration and proof; know underlying assumptions,

recognising their importance and limitations, and the effect of varying them. Explain how to find, calculate and use:

- the sums of the interior and exterior angles of quadrilaterals, pentagons and hexagons

- the interior and exterior angles of regular polygons Solve problems using properties of angles, parallel and intersecting lines, and triangles and

other polygons, justifying inferences and explaining reasoning with diagrams and text.

Visualise and use 2D representation so of 3D objects; analyse 3D shapes through 2D projections, including plans and elevations

Transform 2D shapes by combinations of translations and rotations Know that translations and rotations preserve length and angle and map objects on to

congruent images Present a concise, reasoned argument, using symbols, diagrams and related explanatory text Give reasons for choice of presentation, explaining selected features and showing insight into

the problem’s structure Suggest extensions to problems, conjecture and generalise Identify exceptional cases or counter examples, explaining why Justify generalisations, arguments or solutions Pose extra constraints and investigate whether particular cases can be generalised further.Additional Notes: This should be used as a follow-on to chapter 10

Key Vocabulary:CONVENTION DEFINITION JUSTIFY DEDUCE GENERALISE PROVE PROOF VERTICALLY OPPOSITE ALTERNATE CORRESPONDING INTERIOR EXTERIOR SUPPLEMENTARY PLAN ELEVATION PROJECTIONImpact Reference:Ch.10

Other references: Year 9 Geometrical Reasoning mini-pack

SEE MINI-PACK FOR FURTHER GUIDANCE

Time: 6-7 lessons

SPRING TERM A TOPIC 12

Topic: Proportional Reasoning Unit

Learning Objectives: Understand the effects of multiplying and dividing numbers between 0 and 1 Use the laws of arithmetic and inverse operation Recognise and use reciprocals Enter numbers into a calculator and interpret the display in context Recognise when fractions or percentages are needed to compare proportions Solve problems involving percentage changes Use proportional reasoning to solve a problem, choosing the correct numbers to take as 100%

or as a whole

Understand and use proportionality and calculate the result of any proportional change using multiplicative methods

Understand the implications of enlargement for area and volume Compare 2 ratios Interpret and use ratio in a range of contexts, including solving word problems Enlarge 2D shapes; recognise the similarity of the resulting shapes; identify the scale factor of

an enlargement as the ratio of the lengths of any 2 corresponding line segments; recognise that enlargements preserve angle but not length

Solve increasingly demanding problems and evaluate solutions Explore connections in maths across a range of contexts Represent problems and synthesise information in algebraic, geometric or graphical form Suggest extensions to problems, conjecture and generalise Identify exceptional cases or counter-examples, explaining why Justify generalisations, arguments or solutions Pose extra constraints and investigate whether particular cases can be generalised furtherAdditional Notes: Should be used as a stand-alone unit. Can relate back to topic 8

Key Vocabulary:SCALE MULTIPLIER INVERSE OPERATION RECIPROCAL RATIO PROPORTION RATE UNITARY ENLARGE CENTRE SIMILARImpact Reference:Ch.8

Other references: Year 9 Proportional Reasoning mini-pack

SEE MINI-PACK FOR FURTHER GUIDANCE

Time: 9 lessons

SPRING TERM A TOPIC 13

Topic: Decimals NC Level: 5 & 8

NC Programme of Study:Ref3k: 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 problems involving division by a decimal by transforming it to a problem involving division by an integer.Learning Objectives: Understand the effects of multiplying and dividing by numbers between 0 and 1 Extend knowledge of integer powers of 10 Multiply and divide by any integer power of 10 Know that a recurring decimal is an exact fraction

Use standard column procedures to add and subtract integers and decimals of any size, including a mixture of large and small numbers with differing decimal places

Multiply and divide by decimals, dividing by transforming to division by an integer

Write numbers in standard form; use prefixes Move from one form to another to gain a different perspective on the problemEXT – Use algebraic methods to convert a recurring decimal to a fraction; use a calculator for standard formKey Vocabulary:STANDARD FORM RECUR Impact Reference:Book 3R – ch. 11

Other references: V6 – ch2 V7 – ch2

Mental & Oral Starters:3R folder: pg. 218-220 101 Starters: pg. 56-61Discussion opportunities:Discuss the effects of multiplying/dividing by decimals

Pair / Group Work:Convert recurring decimals to fractions

ICT Links:

Spiritual/Moral/Citizenship Links:How much do we use decimals in everyday life?Investigation:Convert recurring decimals to fractionsTime: 3-4 lessons

SPRING TERM A TOPIC 14

Topic: Probability NC Level: 6 & 7

NC Programme of Study:Ref4def: Understand and use estimates of 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.Ref5i: Compare experimental data and theoretical probabilities. Learning Objectives: Use the vocabulary of probability in interpreting results involving uncertainty and prediction Know that if the probability of an event occurring is p, then the probability of it not occurring

is 1-p

Find and record all possible outcomes for single and combined events in a systematic way using diagrams and tables

Identify all the mutually exclusive outcomes of an experiment Know that the sum of probabilities of all mutually exclusive outcomes is 1 and use this when

solving problems Understand that if an experiment is repeated there may be, and usually will be, different

outcomes Estimate probabilities from experimental data Compare experimental and theoretical probabilities in a range of contexts Appreciate the difference between mathematical explanation and experimental evidenceEXT – Understand and use relative frequency as an estimate of probability and use this to compare outcomes of experimentsKey Vocabulary:SAMPLE SPACE THEORETICAL EXPERIMENTAL RELATIVE TRIAL EXPECTEDImpact Reference:Book 3R – ch. 14

Other references: Booster L11 V6 – ch20 V7 – ch22-23 V8 – ch19

Mental & Oral Starters:3R folder: pg. 262-264 101 Starters: pg. 101Discussion opportunities:Probability of real life events

Pair / Group Work:Probability experiments

ICT Links:Random number generatorsSpiritual/Moral/Citizenship Links:Gambling - moralityInvestigation:Experimental probability – e.g. dice, coins – write a report on findingsTime: 4 lessons

SPRING TERM B TOPIC 15

Topic: Handling Data NC Level: 5 - 7

NC Programme of Study:Ref1acefh: Carry out each of the 4 aspects of the handling data cycle to solve problems. Select and organise the appropriate maths and resources to use for a task. Interpret, discuss and synthesise information presented in a variety of forms. Communicate mathematically, making use of diagrams and related explanatory text. Apply mathematical reasoning, explaining and justifying inferences and deductions.Ref3a: design and use data collection sheets; collect data using various methods.Ref4ah: Draw and produce, using paper and ICT, diagrams for discrete and continuous data. Draw lines of best fit by eye.Ref5ade: Relate summarised data to the initial questions. 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: Collect data using a suitable method, such as observation, controlled experiment, including data

logging using ICT, or questionnaire Design a survey or experiment to capture the necessary data from 1 or more sources; determine the

sample size and degree of accuracy needed; design, trial and if necessary, refine data collection sheets Construct tables for large discrete and continuous sets of raw data, choosing suitable class intervals Design and use 2 way tables Select, construct and modify, on paper and using ICT, suitable graphical representation to progress an

enquiry, including: line graphs for time series and scatter graphs to develop further understanding of correlation

Identify key features present in the data; interpret graphs and diagrams and draw inferences to support or cast doubt on initial conjectures

Have a basic understanding of correlation Compare 2 or more distributions and make inferences, using the shape of the distributions, the range of

data and appropriate statistics Communicate interpretations and results of a statistical enquiry using selected tables, graphs and

diagrams in support, using ICT as appropriate EXT – Know underlying assumptions, recognising their importance and limitations, and effect of varying them; identify possible sources of bias and plan how to minimise it; try to explain anomaliesAdditional Notes: Booster L14 should be used as an additional lesson here

Key Vocabulary: COLLECT REPRESENT INTERPRET

Impact Reference:Book 3R – ch. 9

Other references: Booster L14V6 – ch18-19 V7 – ch18-20 V8 – ch17-18

Mental & Oral Starters:3R folder: pg. 178-181 101 Starters: pg. 97Discussion opportunities:Interpretation of diagrams. Which is most suitable?

Pair / Group Work:Conduct a survey and produce and interpret results

ICT Links:EXCELSpiritual/Moral/Citizenship Links:Examples / problems can be linked to current issuesInvestigation:There is plenty of scope hereTime: 5-6 lessons

ADDITIONAL UNIT

Topic: Handling Data NC Level:

Learning Objectives: Find the mode, median, mean and range Interpret graphs, diagrams and tables for discrete and continuous data Draw inferences that relate to the problem being discussed Relate summarised data to the questions being explored Compare two distributions using the range and one or more of the mode, median and mean

Additional Notes: This should be used alongside chapter 9

Key Vocabulary:MODE MEDIAN MEAN RANGE COMPARE GREATER LESS SLIGHTLY SIGNIFICANTLY

Impact Reference:This links closely to ch.9

Other references: Booster lesson 14

Mental & Oral Starters:

SEE LESSON PLAN 14 FOR DETAILED INFORMATION

Time: 1 lesson

SPRING TERM B TOPIC 16

Topic: Using a Calculator NC Level:

Learning Objectives: Make and justify estimates and approximations of calculations Use a calculator efficiently and appropriately to perform complex calculations with numbers

of any size Use sign change keys and function keys for powers, roots, brackets and memory

Additional Notes: This should be used as a stand-alone lesson

Key Vocabulary:ESTIMATE SIGNIFICANT UNITS DIGIT SQUARE SQUARE ROOT CUBE FRACTION BRACKETS

Impact Reference: Other references: Booster lesson 4

Mental & Oral Starters:101 Starters: pg.

SEE LESSON PLAN 4 FOR DETAILED INFORMATION

Time: 1 lesson

SPRING TERM B TOPIC 17

Topic: Percentages NC Level: 5, 6 & 8

NC Programme of Study:Ref3em:Convert simple fractions of a whole to percentages 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.Learning Objectives: Interpret percentages as the operator ‘so many hundredths of’ Express one given number as a percentage of another Recognise when fractions or percentages are needed to compare proportions Solve problems involving percentage changes – inc. VAT and interest Reverse percentage calculations – finding the original amount

Convert between fractions, decimals and percentages

EXT – repeated percentage changeKey Vocabulary:CHANGE INCREASE DECREASE INTERESTImpact Reference:Book 3R – ch. 12

Other references: Booster L2 & 3 V6 – ch3

Mental & Oral Starters:3R folder: pg. 232-233 101 Starters: pg. 56-57Discussion opportunities:Where we use percentages. VAT, interest rates

Pair / Group Work:Bank accounts

ICT Links:EXCEL can be used for investigationC4 Video “Not all There”Spiritual/Moral/Citizenship Links:Tax, interest, percentage rise, the BudgetInvestigation:Investigate different bank accounts – simple and compound interestTime: 3 lessons

SPRING TERM B TOPIC 18

Topic: Pythagoras’ Theorem NC Level: 7 & 8

NC Programme of Study:Ref2h: Understand, recall and use Pythagoras’ theoremRef3e: Find the co-ordinates of the midpoint of the line segment AB, given points A and B and then calculate the length AB.Learning Objectives: Understand and apply Pythagoras’ theorem to:

- find lengths of right-angled triangles- find the distance between 2 co-ordinates

EXT – Perigal’s dissections; applying the theorem; Pythagorean triplesKey Vocabulary:SQUARE SQUARE ROOT HYPOTENUSE

Impact Reference:Book 3R – ch. 13

Other references: V7 – ch14

Mental & Oral Starters:3R folder: pg. 246-248 Discussion opportunities:Derive the rule

Pair / Group Work:Discover the theorem themselves

ICT Links:

Spiritual/Moral/Citizenship Links:Everything has its own rules to follow – we need to be consistentInvestigation:Pythagorean triplesTime: 3-4 lessons

SUMMER TERM A TOPIC 19

Topic: Transformations NC Level: 7 & 8

NC Programme of Study:Ref3abc: Understand that rotation are specified by a centre and an angle; use right angles, fractions of 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; recognise that these transformations preserve length and angle.Ref4d: Understand from their experience of constructing them that triangles satisfying SSS, SAS, ASA and RHS are unique but SSA triangles are not.Learning Objectives: Understand congruence (SSS, SAS, AAS, RHS)

Transform 2D shapes by combinations of translations, rotations and reflections on paper and using ICT

Know that translation, rotations and reflections preserve length and angle and map objects on to congruent images

Understand and use the language and notation associated with enlargement Enlarge 2D shapes given a centre of enlargement and a whole number scale factor, on paper

and using ICT Identify the scale factor of an enlargement as the ratio of the lengths of any 2 corresponding

line segments Recognise that enlargements preserve angle but not length, and understand the implications of

enlargement for perimeter Identify similar shapesEXT – Apply the condition SSS, SAS, ASA, RHS to establish congruence; rules for area and volume of similar shapes; enlarge using fractional scale factorKey Vocabulary:TRANSLATION ROTATION REFLECTION ENLARGEMENT SCALE FACTOR CONGRUENCE SIMILARImpact Reference:Book 3R – ch. 15

Other references: V6 – ch16 V7 – ch16 V8 – ch13

Mental & Oral Starters:3R folder: pg. 280-285 101 Starters: pg. 89Discussion opportunities:Discuss the transformations that have taken place – giving full details

Pair / Group Work:Combined transformations

ICT Links:LOGO. Outware: “Carpark” “Defender”Spiritual/Moral/Citizenship Links:We can be transformed or reformedInvestigation:The order of transformations – what effect does this have on the original shape?Time: 5-6 lessons

SUMMER TERM A TOPIC 20

Topic: Trigonometry NC Level: 8

NC Programme of Study:KS4 (H) Ref2g

Learning Objectives:EXT - begin to use sine, cosine and tangent in right angled triangles to solve problems in 2 dimensionsKey Vocabulary:RIGHT ANGLED SINE COSINE TANGENT RATIOImpact Reference:Book 3R – ch. 17

Other references: V8 – ch14

Mental & Oral Starters:

3R folder: pg. 324-327 Discussion opportunities:Derive the rules, why can’t we use Pythagoras?

Pair / Group Work:Set each other problems

ICT Links:Trig Graphs can be plotted – Autograph, Omnigraph, graphical calculatorsSpiritual/Moral/Citizenship Links:We must all follow the same rules – be consistentInvestigation:EX17B pg 343 (3R)Fencing Problem – finding maximum areaTime: 6-8 lessons

Time should now be spent revising for the SATs exams – use past papers and CGP packs.

After the SATs, the KS4 Higher Tier Scheme of Work should be started.