MATHS DEPARTMENT
YEAR 9
SCHEME OF WORK
SET 1: IMPACT 3R
SEPT 2004
3R PLAN
AUTUMN TERM – FIRST HALF
Topic 1
Number + Place Value
Topic 2
Working with Algebra
Topic 3
Area, Volume & Measure
Topic 4
Averages & Spread
Topic 5
Formulae, Equations & Inequalities
3R Ch.
3R Ch.
3R Ch.
3R Ch.
3R Ch.
1 + Additional Unit
2
3
4
5
TEST 1
AUTUMN TERM – SECOND HALF
Topic 6
Angles
Topic 7
Fractions, Ratio & Proportion
Topic 8
Graphs
Topic 9
Number Sequences
Topic 10
Problem Solving
3R Ch. 6
3R Ch. 8
3R Ch. 7
3R Ch. 16
Additional Unit
TEST 2
SPRING TERM – FIRST HALF
Topic 11
Geometrical Reasoning + unit
Topic 12
Proportional Reasoning
Topic 13
Decimals
Topic 14
Probability
3R Ch. 10 + Additional Unit
Additional Unit
3R Ch. 11
3R Ch. 14
TEST 3
SPRING TERM – SECOND HALF
Topic 15
Handling Data + unit
Topic 16
Using a Calculator
Topic 17
Percentages
Topic 18
Pythagoras’ Theorem
3R Ch. 9 + Additional Unit
Additional Unit
3R Ch. 12
3R Ch. 13
TEST 4
SUMMER TERM – FIRST HALF
Topic 19
Transformations
Topic 20
Trigonometry
Topic 21
Revision for SATs
3R Ch. 15
3R Ch. 17
CGP Packs & Past Papers
SAT’s WEEK
SUMMER TERM – SECOND HALF
Start KS4 Higher Tier Scheme of Work immediately after SATs have taken place.
AUTUMN TERM A
Topic:
Number
TOPIC 1
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 accuracy
EXT – 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
measurements
Additional 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 ROOT
Other references: Booster L1
Impact Reference:
Book 3R – ch.1
V8 – ch4
Mental & Oral Starters:
3R folder: pg. 4-7
101 Starters: pg. 11-13, 33-35, 46, 57
Discussion opportunities:
Pair / Group Work:
Explain methods; discuss whether an answer is Give each other questions to calculate or
‘sensible’
estimate.
ICT Links:
EXCEL – trial and improvement for square / cube roots
C4 Video “Primes & Powers”
Spiritual/Moral/Citizenship Links:
We should all respect each other’s different methods and ideas
Investigation:
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
POWER INDEX
MULTIPLY
DIVIDE
Impact Reference:
Other references:
This links closely to ch.1
Booster lesson 1
Mental & Oral Starters:
THOUSANDTHS
SEE LESSON PLAN 1 FOR DETAILED INFORMATION
Time:
1 lesson
EQUIVALENT
AUTUMN TERM A
Topic: Working with Algebra
TOPIC 2
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 fractions
EXT – Square a linear expressions, expand the product of 2 linear expressions of the form xn; establish
identities such as a2-b2 = (a+b)(a-b)
Key Vocabulary:
INDICES POWERS FACTORISE EXPAND ALGEBRAIC FRACTIONS
COMMON FACTOR
Other references: Booster L6
Impact Reference:
Book 3R – ch.2
V8 – ch6
Mental & Oral Starters:
3R folder: pg. 24-26
101 Starters: pg. 69 - 71
Discussion opportunities:
Pair / Group Work:
What expressions can represent, relate to real
Develop expressions to represent real life
life.
situations
ICT Links:
EXCEL – input formulae, substitute values into expressions
Spiritual/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:
Area, Volume & Measure
TOPIC 3
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 prisms
EXT – 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 prisms
Key Vocabulary:
AREA VOLUME CIRCUMFERENCE CONVERSION SURFACE AREA
CAPACITY ACCURACY COMPOUND UNITS
Other references: Booster L9 & 10
Impact Reference:
Book 3R – ch.3
V6 – ch11 V7 – ch15 V8 – ch12
Mental & Oral Starters:
3R folder: pg. 40-44
101 Starters: pg. 83 - 86
Discussion opportunities:
Pair / Group Work:
Discuss known formulae
Find areas of complicated composite shapes
ICT Links:
EXCEL – finding max area of different shapes
Spiritual/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:
Averages & Spread
TOPIC 4
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 data
EXT – 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 problems
Key Vocabulary:
MEAN MODE MEDIAN RANGE CONTINUOUS GROUPED DATA
QUARTILES CUMULATUVE FREQUENCY
Other references: Booster L14
Impact Reference:
Book 3R – ch. 4
V7 – ch19
Mental & Oral Starters:
3R folder: pg. 64-66
101 Starters: pg. 96
Discussion opportunities:
Pair / Group Work:
Discuss which measure is most appropriate.
Compare averages, draw inferences
Interpretation of results
ICT Links:
EXCEL for representing data, analysis of statistics – pupils can then focus on inferences
Spiritual/Moral/Citizenship Links:
Pupils can draw inferences from data which relates to the class as a whole; use statistics from
current affairs
Investigation:
Plenty of real life topics/statistics can be investigated here
Time:
5 lessons
AUTUMN TERM A
Topic:
Formulae, Equations
& Inequalities
TOPIC 5
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 equations
EXT – 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 formula
Key Vocabulary:
SOLVE LINEAR EQUATION VARIABLE UNKNOWN REARRANGE
SUBSTITUTE TRIAL AND IMPROVEMENT
Other references: Booster L13
Impact Reference:
Book 3R – ch. 5
V6 – ch7 V7 – ch6-8 V8 – ch6 & 8
Mental & Oral Starters:
3R folder: pg. 86-91
101 Starters: pg. 69-72
Discussion opportunities:
Pair / Group Work:
Discuss different methods
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 change
Time:
6-8 lessons
AUTUMN TERM B
Topic:
Angles
TOPIC 6
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 bearings
EXT – Distinguish between practical demonstration and proof
Key Vocabulary:
STRAIGHT INTERSECTING LINE PARALLEL SUPPLEMENTARY ALTERNATE
CORRESPONDING VERTICALLY OPPOSITE INTERIOR EXTERIOR BEARING
Other references: Booster L8
Impact Reference:
Book 3R – ch. 6
V6 – ch12-14
Mental & Oral Starters:
3R folder: pg. 110-113
101 Starters: pg. 82-83
Discussion opportunities:
Pair / Group Work:
Explain angle rules
Proof of angle facts
ICT Links:
Spiritual/Moral/Citizenship Links:
Everything has its own rules to follow
Investigation:
Investigate angle rules by measurement
Time:
3-4 lessons
AUTUMN TERM B
Topic: Fractions, Ratio & Proportion
TOPIC 7
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 proportion
EXT – Understand and use proportionality and calculate the result of any proportional change using only
multiplicative methods
Additional Notes:
THIS CHAPTER SHOULD BE USED TO PREPARE FOR THE
PROPORTIONAL REASONING UNIT IN THE SPRING TERM.
Key Vocabulary:
FRACTION RATIO DIRECT PROPORTION CONSTANT SIMPLIFY
Other references: Booster L5 & 15
Impact Reference:
Book 3R – ch. 8
V6 – ch2 & 4 V8 – ch1 & 10
Mental & Oral Starters:
3R folder: pg.158-162
Discussion opportunities:
Pair / Group Work:
Dividing quantities
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 issues
Investigation:
What happens to quantities as the ratio changes and vice versa?
Time:
3- 4 lessons
AUTUMN TERM B
Topic:
Graphs
TOPIC 8
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 elevations
EXT – 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 functions
Key Vocabulary:
GRADIENT INTERCEPT COORDINATE AXES
Impact Reference:
Other references:
Book 3R – ch. 7
V6 – ch9 V7 – ch9 & 10 V8 – ch7 & 9
Mental & Oral Starters:
3R folder: pg. 128-132
101 Starters: pg. 72
Discussion opportunities:
Pair / Group Work:
The relationship between the equations and
Spot relationships using ICT
their graphs
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
graphs
Time:
4-6 lessons
AUTUMN TERM B
Topic:
Number Sequences
TOPIC 9
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 sequences
EXT – Quadratic sequences, deduce properties of sequences of triangular and square nos. from spatial
patterns
Key Vocabulary:
DIFFERENCE
GENERAL RULE LINEAR INVERSE MAPPING
Other references: Booster L7
Impact Reference:
Book 3R – ch. 16
V6 – ch6 V7 – ch5
Mental & Oral Starters:
3R folder: pg. 304-307
101 Starters: pg. 72
Discussion opportunities:
Pair / Group Work:
Discuss the rules of sequences; how to generate Create sequences and describe the rule
the next no.
ICT Links:
EXCEL may be useful here
Spiritual/Moral/Citizenship Links:
Sequences / patterns that occur in nature
Investigation:
Sequences that occur in the world
Time:
4 lessons
AUTUMN TERM B
Topic:
Problem Solving
TOPIC 10
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 unit
Key Vocabulary:
EXPLAIN REASONS JUSTIFY
Impact Reference:
Other references:
Booster lesson 12 & 16
Mental & Oral Starters:
SEE LESSON PLAN 12 & 16 FOR DETAILED INFORMATION
Time:
2 lessons
SPRING TERM A
Topic:
TOPIC 11
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 objects
EXT – 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 rule
Additional Notes:
GEOMETRICAL REASONING UNIT TO BE DONE AFTER OR
ALONGSIDE THIS CHAPTER
Key Vocabulary:
CROSS SECTION
CONSTRUCTION LOCI TESSELLATION
Impact Reference:
Other references:
Book 3R – ch. 10
V6 – ch15 V7 – ch13
Mental & Oral Starters:
3R folder: pg. 200-202
Discussion opportunities:
Pair / Group Work:
Discuss the paths of various objects / situations
ICT Links:
Spiritual/Moral/Citizenship Links:
Investigation:
Investigate loci of different objects
Time:
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
VERTICALLY OPPOSITE ALTERNATE CORRESPONDING INTERIOR
EXTERIOR SUPPLEMENTARY PLAN ELEVATION PROJECTION
Impact Reference:
Other references:
Ch.10
Year 9 Geometrical Reasoning mini-pack
SEE MINI-PACK FOR FURTHER GUIDANCE
Time:
6-7 lessons
PROOF
SPRING TERM A
Topic:
TOPIC 12
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 further
Additional 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 SIMILAR
Impact Reference:
Other references:
Ch.8
Year 9 Proportional Reasoning mini-pack
SEE MINI-PACK FOR FURTHER GUIDANCE
Time:
9 lessons
SPRING TERM A
Topic:
Decimals
TOPIC 13
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 problem
EXT – Use algebraic methods to convert a recurring decimal to a fraction; use a calculator for standard
form
Key Vocabulary:
STANDARD FORM
RECUR
Impact Reference:
Other references:
Book 3R – ch. 11
V6 – ch2 V7 – ch2
Mental & Oral Starters:
3R folder: pg. 218-220
101 Starters: pg. 56-61
Discussion opportunities:
Pair / Group Work:
Discuss the effects of multiplying/dividing by
Convert recurring decimals to fractions
decimals
ICT Links:
Spiritual/Moral/Citizenship Links:
How much do we use decimals in everyday life?
Investigation:
Convert recurring decimals to fractions
Time:
3-4 lessons
SPRING TERM A
Topic:
Probability
TOPIC 14
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 evidence
EXT – Understand and use relative frequency as an estimate of probability and use this to compare
outcomes of experiments
Key Vocabulary:
SAMPLE SPACE
THEORETICAL EXPERIMENTAL RELATIVE TRIAL
EXPECTED
Other references: Booster L11
Impact Reference:
Book 3R – ch. 14
V6 – ch20 V7 – ch22-23 V8 – ch19
Mental & Oral Starters:
3R folder: pg. 262-264
101 Starters: pg. 101
Discussion opportunities:
Pair / Group Work:
Probability of real life events
Probability experiments
ICT Links:
Random number generators
Spiritual/Moral/Citizenship Links:
Gambling - morality
Investigation:
Experimental probability – e.g. dice, coins – write a report on findings
Time:
4 lessons
SPRING TERM B
Topic:
TOPIC 15
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 anomalies
Additional Notes:
Booster L14 should be used as an additional lesson here
Key Vocabulary: COLLECT
REPRESENT
INTERPRET
Impact Reference:
Other references: Booster L14
Book 3R – ch. 9
V6 – ch18-19 V7 – ch18-20 V8 – ch17-18
Mental & Oral Starters:
3R folder: pg. 178-181
101 Starters: pg. 97
Discussion opportunities:
Pair / Group Work:
Interpretation of diagrams. Which is most
Conduct a survey and produce and interpret
suitable?
results
ICT Links:
EXCEL
Spiritual/Moral/Citizenship Links:
Examples / problems can be linked to current issues
Investigation:
There is plenty of scope here
Time:
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
SLIGHTLY
SIGNIFICANTLY
Impact Reference:
Other references:
This links closely to ch.9
Booster lesson 14
Mental & Oral Starters:
GREATER
LESS
SEE LESSON PLAN 14 FOR DETAILED INFORMATION
Time:
1 lesson
SPRING TERM B
Topic:
TOPIC 16
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
CUBE
FRACTION
Impact Reference:
UNITS
DIGIT
BRACKETS
Other references:
Booster lesson 4
SQUARE
SQUARE ROOT
Mental & Oral Starters:
101 Starters: pg.
SEE LESSON PLAN 4 FOR DETAILED INFORMATION
Time:
1 lesson
SPRING TERM B
Topic:
Percentages
TOPIC 17
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 change
Key Vocabulary:
CHANGE INCREASE
DECREASE INTEREST
Other references: Booster L2 & 3
Impact Reference:
Book 3R – ch. 12
V6 – ch3
Mental & Oral Starters:
3R folder: pg. 232-233
101 Starters: pg. 56-57
Discussion opportunities:
Pair / Group Work:
Where we use percentages. VAT, interest rates Bank accounts
ICT Links:
EXCEL can be used for investigation
C4 Video “Not all There”
Spiritual/Moral/Citizenship Links:
Tax, interest, percentage rise, the Budget
Investigation:
Investigate different bank accounts – simple and compound interest
Time:
3 lessons
SPRING TERM B
TOPIC 18
Topic: Pythagoras’ Theorem
NC Level:
7&8
NC Programme of Study:
Ref2h: Understand, recall and use Pythagoras’ theorem
Ref3e: 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 triples
Key Vocabulary:
SQUARE SQUARE ROOT
Impact Reference:
Book 3R – ch. 13
Mental & Oral Starters:
3R folder: pg. 246-248
Discussion opportunities:
Derive the rule
ICT Links:
HYPOTENUSE
Other references:
V7 – ch14
Pair / Group Work:
Discover the theorem themselves
Spiritual/Moral/Citizenship Links:
Everything has its own rules to follow – we need to be consistent
Investigation:
Pythagorean triples
Time:
3-4 lessons
SUMMER TERM A
Topic:
Transformations
TOPIC 19
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 shapes
EXT – Apply the condition SSS, SAS, ASA, RHS to establish congruence; rules for area and volume of
similar shapes; enlarge using fractional scale factor
Key Vocabulary:
TRANSLATION ROTATION REFLECTION ENLARGEMENT SCALE FACTOR
CONGRUENCE SIMILAR
Impact Reference:
Other references:
Book 3R – ch. 15
V6 – ch16 V7 – ch16 V8 – ch13
Mental & Oral Starters:
3R folder: pg. 280-285
101 Starters: pg. 89
Discussion opportunities:
Pair / Group Work:
Discuss the transformations that have taken
Combined transformations
place – giving full details
ICT Links:
LOGO.
Outware: “Carpark” “Defender”
Spiritual/Moral/Citizenship Links:
We can be transformed or reformed
Investigation:
The order of transformations – what effect does this have on the original shape?
Time:
5-6 lessons
SUMMER TERM A
Topic:
Trigonometry
TOPIC 20
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
dimensions
Key Vocabulary:
RIGHT ANGLED SINE
COSINE TANGENT RATIO
Impact Reference:
Other references:
Book 3R – ch. 17
V8 – ch14
Mental & Oral Starters:
3R folder: pg. 324-327
Discussion opportunities:
Pair / Group Work:
Derive the rules, why can’t we use Pythagoras? Set each other problems
ICT Links:
Trig Graphs can be plotted – Autograph, Omnigraph, graphical calculators
Spiritual/Moral/Citizenship Links:
We must all follow the same rules – be consistent
Investigation:
EX17B pg 343 (3R)
Fencing Problem – finding maximum area
Time:
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.