Key Stage 3
Sample medium term plans for maths using Impact Maths
Year 8
Contents
Planning with the Framework
1
Year 7 planning chart
2
Autumn term
Number/algebra 1
Shape, space and measures 1
Handling data 1
Number 2
Algebra 2
Shape, space and measures 2
3
3
4
5
6
7
8
Spring term
Algebra 3
Number 3
Shape, space and measures 3
Algebra 4
Handling data 2
10
10
11
12
13
14
Summer term
Number 4
Algebra 5
Solving problems
Shape, space and measures 4
Handling data 3
16
16
17
19
20
21
 We have given references to the sections in 2G, 2B and 2R.
 For ease of reference, the layout is very similar to the DfES sample medium-term
plans, with the Impact sections in the column(s) alongside.
 We have repeated the DfES’s columns of ‘support’, ‘core’ and ‘extension’ to help
with differentiation across sets.
 We have also retained the dependencies between topics as the DfES sample
plans.
How to use this document
This is a reproduction of the sample medium-term plans produced by the National
Numeracy Strategy, reproduced with permission and acknowledgement to the DfES.
Details of how these charts can be used for planning are given on p1. In addition to
the material provided by the NNS, detailed cross-references in the teaching
objectives for the main activities refer to the Impact maths student books and pupil
performance packs. The cross-references in the teaching objectives for the oral and
mental activities refer to the lesson starters in the 1R pupil performance pack. There
is also a short narrative for each topic of work, giving advice on using Impact and
other resources.
All cross-references refer to material in 1G and 1R. Not all of the extension objectives
are covered in Impact 1R, and you may need to use resources from higher years to
provide extension material.
A matching guide for Year 7 is now available, and Year 9 will be available in the
spring term.
Notes on tables
(in pt)
(pt)
section covers point in part.
part of section covers point.
Working with the Impact guide
About the author
The Impact maths KS3 scheme has been used in schools since 1998. It has been
continually updated to meet the requirements of the Framework for Teaching
Mathematics. This document provides a detailed guide of how to deliver the
framework using Impact materials.
Acknowledgement
Heinemann Educational has the permission of the DfES to reproduce their objectives
in this matching guide. We have retained all the elements of the DfES sample plans
to make it very easy for you to plan your schemes of work for Year 8 using Impact.
For example:
 Core objectives are in bold as in the medium-term plans.
Impact maths sample medium-term plans for mathematics
Derek Huby is an experienced primary and secondary numeracy consultant, as well
as being an experienced maths teacher and head of department.
We would like to thank Derek Huby and Jim Newall for their work in the preparation of
this document.
Planning with the Framework
[The text of this page is reproduced with permission from the Department for
Education and Skills.]
The Framework for teaching mathematics: Years 7, 8 & 9 provides teachers with
guidance on meeting the National Curriculum requirements for mathematics. It sets
out yearly teaching programmes showing how objectives for teaching mathematics
can be planned from Year 7 to Year 9. A key task in developing medium-term plans
for Key Stage 3 mathematics is to identify the objectives for the units of work that are
going to be taught. In doing this, schools may choose to start from their existing
schemes of work, or alternatively, may find that these sample plans provide a useful
starting point.
The sample plans are designed to continue the progression and expectations
established in the yearly teaching programmes up to Year 6. They are based on the
examples of planning charts in the Framework. There are many other ways to
organise the mathematics curriculum in Key Stage 3. The planning charts indicate
dependencies between topics but the order and content of the units can be adjusted.
Each sample plan identifies core objectives that define a minimum expectation
for the majority of pupils in a particular year group. Plans for particular year
groups are designed to show:
 Progression in the teaching objectives for each strand of the curriculum;
 Links between the teaching objectives, bringing together related ideas across the
strands;
 Opportunities to revisit topics during the year (the pitch of the second and
subsequent units of a topic need careful adjusting in the light of teachers’
assessment of pupils’ progress);
 How objectives for using and applying mathematics can be incorporated into units.
For each term, suggested objectives for oral and mental mathematics are also
identified. Oral and mental work can both support the main teaching programme as
well as providing a means of regularly revisiting important elements.
Many schools set pupils for mathematics. Teachers of higher sets may well base their
pupils’ work on the programme for a later year group, while teachers of lower sets
may need to draw on objectives in the teaching programmes from a previous year
group. As always, the success of setting depends on teachers in the mathematics
department being involved in careful monitoring, close teamwork and co-operative
planning to make sure that expectations for all pupils are suitably high and that lower
expectations are not justified simply because pupils are in a lower set.
There are some secondary schools where, at present, relatively few pupils attain level
5 or above at the end of Key Stage 3. Pupils may lack a secure understanding of
Impact maths sample medium-term plans for mathematics
Page 1
some of the work they have been taught earlier. To begin with, these schools should
look carefully at the programmes for Year 5 and Year 6 and draw suitable teaching
objectives from them when they are planning work for Year 7, making corresponding
adjustments for Years 8 and 9. A decision like this would need to be reviewed before
the start of the next school year to allow for improving standards over time.
How the plans are set out
Teaching objectives for oral and mental activities are placed at the beginning of the
plan for each term. Objectives for the main activities are set out in four main columns:
 The first identifies the areas of mathematics studied in the unit and identifies links
to the supplement of examples in the Framework.
 The second identifies support objectives from previous yearly teaching
programmes. These are linked to the core objectives for each unit.
 The third column sets out the core objectives for the year group, the ones you
would expect to focus on for the majority of pupils.
 The fourth provides extension objectives, to stretch able pupils, drawn from the
next year’s teaching programme. These are linked to the core objectives for the unit.
Key Stage 3 National Strategy
YEAR 8 PLANNING CHART
Autumn
36 hours
Number/algebra 1
Integers, powers and roots
Sequences functions and graphs
6 hours
Handling data 1
Probability
6 hours
Algebra 2
Equations and
formulae
6 hours
Number 2
FDPRP
6 hours
Spring
33 hours
Algebra
3
Integers, powers and
roots
Sequences, functions
and graphs
6 hours
Number 3
Place value
Calculations
Calculator methods
FDPRP
Solving problems
9 hours
Number 4
Calculations
Measures
6 hours
Handling data 3
Handling data, including
probability
7 hours
35 weeks
SSM 3
Transformations
Geometrical reasoning:
lines, angles and shapes
6 hours
Solving problems
Solving problems,
including FDPRP
6 hours
Algebra
5
Sequences, functions and
graphs
Equations and formulae
8 hours
SSM 4
Geometrical reasoning: lines, angles and shapes
Transformations
Mensuration
9 hours
105 hours
Using and applying mathematics to solve problems should be integrated into each unit.
Impact maths sample medium-term plans for mathematics
Page 2
SSM 2
Measures and mensuration
6 hours
Algebra
4
Equations and formulae
Graphs
6 hours
Handling data 2
Handling data
6 hours
Summer
36 hours
SSM1
Geometrical reasoning: lines,
angles and shapes
Construction
6 hours
Key Stage 3 National Strategy
Impact maths sample medium-term plans for mathematics
Page 3
Key Stage 3 National Strategy
Year 8: Autumn term
Numbers in the LH column refer to the supplement of examples for the core teaching programme
YEAR 8 – AUTUMN TERM
Teaching objectives for the oral and mental activities
 Order, add, subtract, multiply and divide integers.
 Multiply and divide decimals by 10, 100, 1000.
 Count on and back in steps of 0.4, 0.75, 3/4…
 Round numbers, including to one or two decimal places.
 Know and use squares, positive and negative square roots, cubes of
numbers 1 to 5 and corresponding roots.
 Convert between fractions, decimals and percentages.
 Find fractions and percentages of quantities.
 Know or derive complements of 0.1, 1, 10, 50, 100, 1000.
 Add and subtract several small numbers or several multiples of 10,
e.g. 250 + 120 – 190.
 Use jottings to support addition and subtraction of whole numbers and
decimals.
 Calculate using knowledge of multiplication and division facts and
place value, e.g. 432  0.01, 37  0.01.
 Recall multiplication and division facts to 10  10.
 Use factors to multiply and divide mentally, e.g. 22  0.02, 420  15.
2R
5.3 (pt),
8.1–8.4
5.3
3.5
3.1B, 6.2
2R
 Multiply and divide a two-digit number by a one-digit number.
 Use partitioning to multiply, e.g. 13  1.4.
 Use approximations to estimate the answers to calculations, e.g. 39
 2.8.
 Solve equations, e.g. 3a – 2 = 31.
14.3, 14.5
 Visualise, describe and sketch 2-D shapes.
 Estimate and order acute, obtuse and reflex angles.
7.3
 Use metric units (length, mass, capacity) and units of time for
calculations.
 Use metric units for estimation (length, mass, capacity).
 Convert between m, cm and mm, km and m, kg and g, litres and ml,
cm² and mm².
5.3, 5.5
 Discuss and interpret graphs.
5.3, 5.5
 Apply mental skills to solve simple problems.
12.1, 12.3,
12.6A&B,
12.7, 13.5
Teaching objectives for the main activities
Number/
Algebra 1 (6
hours)
Integers,
powers and
roots (48–59)
SUPPORT from the Y7 teaching 2G
programme
2B
2R
CORE from the Y8 teaching
programme
2G
2B
2R
 Understand negative
numbers as positions on a
number line.
10.2
8.2
 Add, subtract, multiply and
divide integers.
8.1,
8.3
1.3,
1.8,
1.9,
3.1,
3.2,
3.7–
3.11,
10.4
8.3,
8.4,
8.5
10.1,
10.3
10.4
1.6,
1.8,
1.11–
1.14,
3.1–
3.4,
3.8–
3.11,
10.4–
10.9
3.5,
3.6
See
notes
3.3–
3.5
1.2
10.1,
10.3,
10.4,
10.7
10.2,
 Order, add and subtract
positive and negative integers in 10.5
10.6
context.
10.8
10.9
 Use tests of divisibility.
See
See
See
 Recognise and use multiples,
notes notes notes factors (divisors), common factor,
highest common factor, lowest
common multiple and primes.
Impact maths sample medium-term plans for mathematics
Page 4
EXTENSION from the Y9 teaching
programme
2R
 Use the prime factor
decomposition of a number
–
Key Stage 3 National Strategy
 Recognise the first few
triangular numbers, squares of
numbers to at least 12 x12 and
the corresponding roots.
Year 8: Autumn term
Numbers in the LH column refer to the supplement of examples for the core teaching programme
3.7
3.6
1.3
 Generate and describe integer
sequences.
Sequences and
functions (144–
157)
 Generate terms of a simple
sequence, given a rule.
5.4
5.4
9.4
 Generate sequences from
practical contexts and describe
the general term in simple
cases.
16.1
16.1
9.1,
9.4
Notes (2G)
 Tests of divisibility are covered in 1G.
 HCF, LCM and prime factors are covered in 3G.
 Cubes and index notation are covered in 3G.
Shape, space
and measures
1 (6 hours)
Geometrical
reasoning:
lines, angles
and shapes
(178–189)
 Find the prime factor
decomposition of a number (e.g. 8000
= 2³ x5³).
 Use squares, positive and negative
square roots, cubes and cube roots,
and index notation for small positive
integer powers.
SUPPORT from the Y7 teaching
programme
2G
2B
2R
 Use correctly the vocabulary, 2.9,
9.1–
notation and labelling
conventions for lines, angles and 9.4
shapes.
2.9
9.1–
9.3
2.5,
7.1
 Identify parallel and
perpendicular lines.
 Know the sum of angles at
a point, on a straight line and
in a triangle, and recognise
vertically opposite angles.
 Use angle measure.
9.1
9.1
2.10
2.7,
2.8
2.7
2.8
2.4
Impact maths sample medium-term plans for mathematics
Page 5
–
–
3.6,
3.6,
3.7
3.11
(in pt)
see
notes
5.1–
5.4
5.1–
5.4
5.4,
5.4,
 Generate terms of a linear
17.2, 17.3,
sequence using term-to-term and
17.4 17.5
position-to-term definitions of the
sequence, on paper and using a
spreadsheet or graphical calculator.
5.4
 Begin to use linear expressions to –
describe the nth term of an arithmetic
sequence, justifying its form by
referring to the activity or practical
context from which it was generated.
Notes (2B)
 Tests of divisibility are covered in 1G and 1R.
–
1.3
 Use ICT to estimate square
roots and cube roots.
 Use index notation for integer
powers and simple instances of the
index laws.
 Know and use the index laws in
generalised form for multiplication
and division of integer powers.
9.5
Notes (2R)
 Tests of divisibility are covered in 1R.
2G
2B
2R
EXTENSION from the Y9 teaching
programme
 Identify alternate angles and
corresponding angles.
–
–
2.10
2.10
2.6
 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.
2.10
(in pt)
10.3
9.1,
9.2,
9.4
9.1–
9.4,
18.3,
18.5
CORE from the Y8 teaching
programme
 Understand a proof that:
 the sum of the angles of a
18.1
(in pt)
10.2
2R
2.9
2.8
Key Stage 3 National Strategy
 Distinguish between and
estimate the size of acute,
obtuse and reflex angles.
Construction
(220–223)
Year 8: Autumn term
Numbers in the LH column refer to the supplement of examples for the core teaching programme
2.2
2.3–
2.6
 Use a ruler and protractor to:

measure and draw lines 2.4,
to the nearest millimetre and 2.5
angles, including reflex
angles, to the nearest degree.

construct a triangle given –
two sides and the included
angle (SAS) or two angles
and the included side (ASA).
2.2
2.3–
2.6
2.1
2.2,
2.3
2.4,
2.5
2.2,
2.3
–
–
Solving
problems
(14–17)
Notes (2G)
 Side and angle properties of triangles are not covered.
Handling data
1 (6 hours)
Probability
(276–283)
SUPPORT from the Y7 teaching
programme
2G
–
–
9.2
9.1,
(in pt) 9.2
see
notes
9.2
9.2
2.7
7.3
7.4
–
–
–
–
–
–
–
7.5
–
–
–
–
9.4
7.3
17J
Notes (2B)
2B
2R
 Understand and use the
probability scale from 0 to 1.
7.3
7.1,
7.2
4.1
 Find and justify
probabilities based on equally
7.4
7.3,
7.4
4.2
Impact maths sample medium-term plans for mathematics
Page 6
triangle is 180º and of a
quadrilateral is 360º
 the exterior angle of a triangle is
equal to the sum of the two interior
opposite angles.
 Solve geometrical problems using
side and angle properties of
equilateral, isosceles and right-angled
triangles and special quadrilaterals,
explaining reasoning with diagrams
and text.
 Classify quadrilaterals by their
geometric properties.
 Use straight edge and
compasses to construct:
 the mid-point 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.
 Investigate in a range of contexts:
shape and space.
 Solve problems using
properties of angles, of parallel
and intersecting lines, and of
triangles and other polygons.
 Know the definition of a circle
and the names of its parts.
2.10
 Use straight edge and
compasses to construct a triangle,
given right angle, hypotenuse and
side (RHS).
–
7.1
Notes (2R)
CORE from the Y8 teaching
programme
 Use the vocabulary of probability
when interpreting the results of an
experiment.
 Appreciate that random processes
are unpredictable.
 Know that if the probability of an
event occurring is p, then the
probability of it not occurring is 1 – p.
2G
2B
2R
7.1–
7.5
7.1,
7.6
4.1,
4.5
–
–
–
7.4
7.5,
(in pt) 7.6
see
notes
4.3–
4.5
 Identify all the mutually exclusive 4.5
outcomes of an experiment.
 Find and record all possible
mutually exclusive outcomes for
single events and two successive
–
4.6
 Know that the sum of
probabilities of all mutually
exclusive outcomes is 1 and use
–
EXTENSION from the Y9 teaching
programme
2R
4.6
Key Stage 3 National Strategy
likely outcomes in simple
contexts.
 Identify all the possible
mutually exclusive outcomes of
a singe event.
 Collect data from a simple
experiment and record in a
frequency table.
 Estimate probabilities based
on this data.
Year 8: Autumn term
Numbers in the LH column refer to the supplement of examples for the core teaching programme
7.5,
7.6
7.4
4.2
–
7.6
7.5
–
7.6
7.5
Notes (2G)
 (1 – p) is covered in 3G.
Number 2 (6
hours)
Fractions,
decimals,
percentages
(60 – 77)
SUPPORT from the Y7 teaching
programme
 Use fraction notation to
express a smaller whole number
as a fraction of a larger one.
 Simplify fractions by
cancelling all common factors
and identify equivalent
fractions.
 Convert terminating decimals
to fractions.
 Add and subtract simple
fractions and those with common
denominators
 Calculate fractions of
quantities (whole-number
answers).
 Multiply a fraction by an
integer.
 Understand percentage as
the 'number of parts per 100'
2G
2B
2R
6.1
6.1
3.1
6.5
6.2
3.2
3.3
 Calculate simple
percentages.
–
–
–
6.3,
6.6
6.5
3.6
6.4
6.5
3.1
–
6.4
3.9
8.8
8.9
8.9,
8.11
–
17.3
8.8
(pt),
8.9,
6.2
Impact maths sample medium-term plans for mathematics
Page 7
events in a systematic way, using
diagrams and tables.
this when solving problems.
see
7.6
 Estimate probabilities from
notes
experimental data.
 Understand that:
7.6
 if an experiment is repeated there
may be, and usually will be,
different outcomes.
–
 increasing the number of times an
experiment is repeated generally
leads to better estimates of
probability.
Notes (2B)
4.5
CORE from the Y8 teaching
programme
 Know that a recurring decimal is a
fraction.
 Use division to convert a fraction to
a decimal.
4.5
–
4.5
4.5
Notes (2R)
2G
2B
2R
–
–
3.4
–
3.5,
5.6
6.3
5.6,
5.8
 Add and subtract fractions by
writing them with a common
denominator
 Calculate fractions of quantities
(fraction answers)
 Multiply and divide an integer by a
fraction.
6.6
6.5
(in pt)
–
–
–
–
3.6,
3.7
 Interpret percentage as the
operator 'so many hundredths of' and
express one given number as a
percentage of another.
 Use the equivalence of fractions,
decimals and percentages to
compare proportions.
8.7–
8.9
8.8,
8.9
8.8
(pt),
17.7
 Order fractions by writing them with –
a common denominator or by
converting them to decimals.
 Compare experimental and
theoretical probabilities in a range
of contexts.
 Appreciate the difference
between mathematical explanation
and experimental evidence.
EXTENSION from the Y9 teaching
programme
2R
3.8
3.10
3.9
 Use efficient methods to add,
subtract, multiply and divide
fractions, interpreting division as a
multiplicative inverse.
 Cancel common factors before
multiplying or dividing.
8.9–
8.12
6.1,
6.2
 Solve problems involving
percentage changes.
6.7,
6.8
8.14
6.4,
6.5
3.8
3.12
Key Stage 3 National Strategy
Year 8: Autumn term
Numbers in the LH column refer to the supplement of examples for the core teaching programme
 Calculate percentages and find
the outcome of a given percentage
increase or decrease.
 Understand addition and
subtraction of fractions.
 Use the laws of arithmetic and
inverse operations.
8.14
Calculations
(82–85, 88–
101)
 Consolidate the rapid recall of
number facts, including positive
integer complements to 100 and
multiplication facts to 10 x10,
and quickly derive associated
division facts.
3.1,
3.1,
3.2,
3.2
3.4
(in pt)
–
Notes (2G)
 Mental methods of calculation are covered by starters 1.3, 1.5, 1.7,
1.11, 1.12, 6.1, 6.2, 6.5, 8.1–8.3.
Algebra 2 (6
hours)
Equations and
formulae
(112-119, 138143)
SUPPORT from the Y7 teaching
programme
 Use letter symbols to
represent unknown numbers
or variables.
 Know the meanings of the
words term, expression and
equation.
2G
2B
2R
4.1,
13.3
13.2
10.1
4.3,
13.6
4.1,
13.4
10.1
8.13,
17.4
6.3
6.6
(in pt)
1.11–
1.14,
5.2–
5.4
6.5
3.6,
3.7
3.8–
3.10
1.3,
1.7–
1.9,
3.1,
3.2,
3.7–
3.11
1.7
1.5
5.5
 Recall known facts, including
fraction to decimal conversions.
5.5
 Use known facts to derive unknown 1.12 1.7
facts, including products involving
numbers such as 0.7 and 6, and 0.03
and 8.
see
see
5.1,
 Consolidate and extend mental
notes notes 5.5
methods of calculation, working with
see
decimals, fractions and percentages.
notes
 Solve word problems mentally.
Notes (2B)
 Mental methods of calculation are covered by starters 8.2
and 8.3.
 Use known facts to derive
unknown facts.
5.5
 Extend mental methods of
calculation, working with factors,
powers and roots.
–
CORE from the Y8 teaching
programme
 Begin to distinguish the different
roles played by letter symbols in
equations, formulae and functions.
 Know the meanings of the words
formula and function.
EXTENSION from the Y9 teaching
programme
2G
2B
2R
4.1,
4.2
Ch 4
start
10.1
13.1
(pt)
13.1
(pt)
14.1
4.1,
 Know that algebraic operations
follow the same conventions and order 4.2,
4.5,
as arithmetic operations.
4.6,
13.4
4.2,
4.5
10.4,
14.1
 Use index notation for small
positive integer powers.
Impact maths sample medium-term plans for mathematics
Page 8
–
3.11 see
10.1,
(in pt) notes 10.2
see
notes
Notes (2R)
 Mental methods of calculation are
covered by starters 5.1, 5.3–5.5.
2R
10.3
 Use index notation for integer
powers and simple instances of the
index laws.
Key Stage 3 National Strategy
 Simplify linear algebraic
expressions by collecting like
terms.
Year 8: Autumn term
Numbers in the LH column refer to the supplement of examples for the core teaching programme
4.2
4.1–
4.3
10.1
Notes (2G)
 Index notation is covered in 3G.
 Powers are covered in 3G.
Shape, space
and measures
2 (6 hours)
Measures and
mensuration
(228-231, 234241)
Solving
Problems
(18–21)
 Simplify or transform linear
expressions by collecting like
terms.
 Multiply a single term over a
bracket.
 Use formulae from mathematics
and other subjects.
 Substitute integers into simple
formulae, and positive integers into
expressions involving small powers
(e.g. 3x² + 4 or 2x³).
 Derive simple formulae.
4.3
4.4
4.1
4.3
10.4,
14.6
–
4.4
10.5,
14.7
13.1
13.1
14.1
13.3–
13.6,
see
notes
13.3
(pt)
13.3– 14.3
13.6
13.3
(pt)
2B
 Convert one metric unit to
another (e.g. grams to
kilograms).
 Read and interpret scales
on a range of measuring
instruments.
9.8
9.9
2R
CORE from the Y8 teaching
programme
 Use units of measurement to
estimate, calculate and solve
problems in everyday contexts
involving length, area, volume,
capacity, mass, time and angle.
 Know rough metric equivalents of
imperial measures in daily use (feet,
miles, pounds, pints, gallons).
 Know and use the formula for 14.2 14.2 –
 Deduce and use formulae for
the area of a rectangle.
the area of a triangle,
 Calculate the perimeter and 14.4 14.4
parallelogram and trapezium.
area of shapes made from
 Calculate areas of compound
rectangles.
shapes made from rectangles and
triangles.
see
see
 Calculate the surface area of see
 Know and use the formula for
notes notes notes the volume of a cuboid.
cubes and cuboids.
Calculate volumes and surface
areas of cuboids and shapes made
from cuboids.
 Investigate in a range of contexts:
measures.
9.7
9.8
9.10
–
Impact maths sample medium-term plans for mathematics
Page 9
–
10.6
10.7
14.2
Notes (2B)
 Index notation is covered in 3B.
SUPPORT from the Y7 teaching 2G
programme
 Simplify or transform algebraic
expressions by taking out singleterm common factors.
Notes (2R)
2G
2B
2R
9.7,
9.8,
9.10
9.8,
9.9,
9.11
15.3
(in pt)
9.9
9.10
see
 Convert between area
notes measures (mm² to cm², cm² to m²,
and vice versa) and between
volume measures (mm³ to cm³,
cm³ to m³, and vice versa).
7.10
15.1–  Know and use the formulae
15.3 for the circumference and area
of a circle.
15.2
15.4
see
14.3–
notes 14.5
14.1–
14.5
14.6,
14.7
–
14.10,
14.11
–
15.5
–
–
–
see
notes
EXTENSION from the Y9 teaching
programme
 Calculate the surface area and
volume of right prisms.
2R
–
Key Stage 3 National Strategy
Notes (2G)
 For area of a triangle etc., see starters 14.1 and 14.3.
 Surface area of a cuboid is covered in 1G.
Impact maths sample medium-term plans for mathematics
Page 10
Year 8: Autumn term
Numbers in the LH column refer to the supplement of examples for the core teaching programme
Notes (2B)
 Surface area of a cuboid is covered in 1G and 1R.
Notes (2R)
 Using units of measurement in everday
contexts is covered in 1R.
 Surface area of a cuboid is covered in
1R.
Key Stage 3 National Strategy
Year 8: Spring term
Numbers in the LH column refer to the supplement of examples for the core teaching programme
YEAR 8 – SPRING TERM
Teaching objectives for the oral and mental activities
 Order, add, subtract, multiply and divide integers.
 Round numbers, including to one or two decimal places.
 Know and use squares, positive and negative square roots, cubes of
numbers 1 to 5 and corresponding roots.
 Know or derive quickly prime numbers less than 30.
 Convert between improper fractions and mixed numbers.
 Find the outcome of a given percentage increase or decrease.
 Know complements of 0.1, 1, 10, 50, 100, 1000.
 Add and subtract several small numbers or several multiples of 10,
e.g. 250 + 120 – 190.
 Calculate using knowledge of multiplication and division facts and
place value, e.g. 432  0.01, 37  0.01, 0.04  8, 0.03  5.
 Recall multiplication and division facts to 10  10.
 Use factors to multiply and divide mentally, e.g. 22  0.02, 420  15.
 Multiply and divide a two-digit number by a one-digit number.
 Multiply by near 10s, e.g. 75  29, 8  –19.
 Use partitioning to multiply, e.g. 13  1.4.
 Use approximations to estimate the answers to calculations, e.g. 39 
2R
5.3, 8.1–8.4
2R
14.3, 14.5
 Solve equations, e.g. n(n – 1) = 56.
 Visualise, describe and sketch 2-D shapes, 3-D shapes and simple
loci.
 Estimate and order acute, obtuse and reflex angles.
3.1A
6.5
5.3, 5.5
5.3, 5.5
7.3 (in pt)
 Use metric units (length, area and volume) and units of time for
calculations.
 Use metric units for estimation (length, area and volume).
 Recall and use the formula for perimeter of rectangles and calculate
areas of rectangles and triangles.
 Calculate volumes of cuboids.
12.1, 12.3,
12.6A&B,
12.7, 13.5
 Discuss and interpret graphs.
 Apply mental skills to solve simple problems.
2.8.
Teaching objectives for the main activities
Algebra 3 (6
hours)
Sequences,
functions,
graphs
(160-177)
SUPPORT from the Y7 teaching
programme
 Express simple functions in
words.
2G
2B
2R
5.2
5.3
5.2
5.3
9.2
9.3
 Generate coordinate pairs
that satisfy a simple linear rule.
11.2,
11.3
11.2,
11.3,
17.8
11.2,
11.3
12.5
11.3
 Recognise straight-line
graphs parallel to the x-axis or yaxis.
Impact maths sample medium-term plans for mathematics
Page 11
12.3,
12.4
CORE from the Y8 teaching
programme
 Express simple functions in
symbols.
 Represent mappings expressed
algebraically.
 Generate points in all four
quadrants and plot the graphs of
linear functions, where y is given
explicitly in terms of x, on paper and
using ICT.
 Recognise that equations of the
form y = mx + c correspond to
straight-line graphs.
2G
2B
11.4
12.6,
12.7
 Plot graphs of linear functions (y 12.8
18.9
given implicitly in terms of x), e.g.
ay + bx = 0, y + bx + c = 0, on
paper and using ICT.
 Given values for m and c, find 12.7
the gradient of lines given by
equations of the form y = mx + c.
 Construct linear functions arising
11.4– 11.7
11.6
12.9
 Discuss and interpret distance–
see
5.4
notes
5.4
2R
EXTENSION from the Y9 teaching
programme
see
 Find the inverse of a linear
notes function.
11.1– 11.1– 12.1–
11.5 11.5 12.4,
12.10
18.9
–
2R
–
–
Key Stage 3 National Strategy
Year 8: Spring term
Numbers in the LH column refer to the supplement of examples for the core teaching programme
from real-life problems and plot their
corresponding graphs.
 Discuss and interpret graphs
arising from real situations.
Notes (2B)
Notes (2G)
 Expressing simple functions in symbols is covered in 3G.
Number 3 (9
hours)
Place value
(36–47)
SUPPORT from the Y7 teaching
programme
 Understand and use decimal
notation and place value.
 Multiply and divide integers
and decimals by 10, 100, 1000,
and explain the effect.
2G
2B
1.1
1.1
3.4,
8.3
3.8,
8.3
 Round positive whole
numbers to the nearest 10, 100
or 1000 and decimals to the
nearest whole number or one
decimal place.
 Consolidate and extend
mental methods of calculation
to include decimals, fractions
and percentages, accompanied
where appropriate by suitable
jottings.
1.7,
1.4,
1.9
1.5,
see
8.6
notes
1.4
1.5,
1,7,
1.12 8.1
(in pt)
5.1,
5.5
 Multiply and divide threedigit by two-digit whole
numbers.
3.8,
3.9,
3.11
3.7,
3.9,
3.10
 Extend to multiplying and
dividing decimals with one or
two places by single-digit
8.4,
8.5
8.4,
8.5
Impact maths sample medium-term plans for mathematics
Page 12
2R
CORE from the Y8 teaching
programme
see
 Read and write positive integer
notes powers of 10.
 Multiply and divide integers and
decimals by 0.1, 0.01.
 Order decimals.
 Round positive numbers to any
given power of 10.
 Round decimals to the nearest
whole number or to one or two
decimal places.
 Consolidate and extend mental
methods of calculation, working with
decimals, fractions and percentages,
squares and square roots, cubes and
cube roots.
 Solve word problems mentally.
 Make and justify estimates and
approximations of calculations.
 Consolidate standard column
procedures for addition and
subtraction of integers and decimals
with up to two places.
time graphs.
11.6
12.9
Notes (2R)
 See starter 12.6B for expressing simple
functions in symbols. This topic is also
covered in 1R.
2G
2B
see
–
notes
8.6
1.7,
1.9
–
8.8
1.4
8.6
2R
EXTENSION from the Y9 teaching
programme
see
 Extend knowledge of integer
notes powers of 10.
 Multiply and divide by any
integer power of 10.
1.7–
1.10
1.13,
1.14,
8.2
8.4,
8.5
2R
5.8
5.2
1.4–
1.6
5.7–
5.9
see
see
5.1,
notes notes 5.5
see
notes
 Use standard column procedures 3.8–
3.11
for multiplication and division of
integers and decimals, including by
decimals such as 0.6 or 0.06.
 Understand where to position
the decimal point by considering
equivalent calculations.
11.7
1.6
1.6
1.8,
1.9,
8.2
5.1
3.9,
3.10
5.3,
5.4
8.4,
8.5
5.3,
5.4
 Extend mental methods of
calculation, working with decimals,
fractions, percentages, factors,
powers and roots.
–
 Use standard column
procedures to add and subtract
integers and decimals of any size,
including a mixture of large and
small numbers with differing
numbers of decimal places.
 Multiply and divide by decimals,
dividing by transforming to division
by an integer.
5.1
(in pt)
–
Key Stage 3 National Strategy
Year 8: Spring term
Numbers in the LH column refer to the supplement of examples for the core teaching programme
whole numbers.
 Carry out calculations with
more than one step using
brackets and the memory.
 Use the square root and sign
change keys.
17.1
17.1
18.1
17.1
17.1
18.1
Notes (2G)
 Rounding of decimals is not covered.
 For reading and writing positive integer powers of 10, see starter 1.2.
 Mental methods of calculation are covered by starters 1.3, 1.5, 1.7,
1.11, 1.12, 6.1, 6.2, 6.5, 8.1–8.3.
Shape, space
and measures
3 (6 hours)
Geometrical
reasoning: lines
angles and
shapes
(190–191)
Transformations
(202–215)
SUPPORT from the Y7 teaching
programme
 Recognise and visualise the
transformation and symmetry of
a 2-D shape:

reflection in given mirror
lines, and line symmetry.

rotation about a given
point, and rotation symmetry.

translation.
 Explore these transformations
and symmetries using ICT.
2G
2B
2R
2.1
2.1
11.1
2.1
2.1
11.1
–
–
11.1
17.6
17.7
18.8
Impact maths sample medium-term plans for mathematics
Page 13
1.10 8.7
5.9
 Check a result by considering
(in pt) (in pt) (in pt)
whether it is of the right order of
magnitude and by working the
problem backwards.
 Carry out more difficult calculations 17.1, 17.1, 18.1,
17.3, 17.2, 18.2,
effectively and efficiently using the
function keys for sign change, powers, 17.7 17.9 18.10
roots and fractions; use brackets and
the memory.
–
17.2 18.2
 Enter numbers and interpret the
17.4 18.4
display in different contexts (negative
17.9 18.10
numbers, fractions, decimals,
percentages, money, metric
measures, time).
Notes (2B)
 Mental methods of calculation are covered by starters 8.2
and 8.3.
CORE from the Y8 teaching
programme
2G
2B
2R
 Know that if two 2D shapes are
congruent, corresponding sides and
angles are equal.
see
see
see
notes notes notes
 Transform 2D shapes by simple
combinations of rotations, reflections
and translations, on paper and using
ICT.
 Identify all the symmetries of 2D
shapes.
2.1
2.1
2.1
2.1
 Understand and use the language
and notation associated with
enlargement.
 Enlarge 2D shapes, given a
–
–
11.4,
11.5
–
–
11.6
 Use a calculator efficiently and
appropriately to perform complex
calculations with numbers of any
size, knowing not to round during
intermediate steps of a calculation.
–
Notes (2R)
 Place value is covered in 1R.
 Reading and writing of positive integer
power of 10 is covered in 1R.
 Mental methods of calculation are
covered by starters 5.1, 5.3–5.5.
EXTENSION from the Y9 teaching
programme
11.1,  Know that translations,
11.2, rotations and reflections
18.11 preserve length and angle and
map objects on to congruent
11.1, images.
11.2,  Identify reflection symmetry in
18.11 3D shapes.
2R
11.2
11.3
–
11.5,
 Enlarge 2D shapes, given a
centre of enlargement and a whole- 11.6
number scale factor, on paper.
11.4
 Identify the scale factor of an
Key Stage 3 National Strategy
Year 8: Spring term
Numbers in the LH column refer to the supplement of examples for the core teaching programme
centre of enlargement and a
positive whole-number scale factor.
–
 Explore enlargement using ICT.
 Understand the relationship
between ratio and proportion.
 Solve simple problems about
ratio and proportion using
informal strategies.
–
–
3.11
Notes (2G)
 Congruence of 2D shapes is covered in 3G.
Algebra 4 (6
hours)
Equations and
formulae
(112–113, 122–
125, 138–143)
SUPPORT from the Y7 teaching
programme
 Use letter symbols to
represent unknown numbers
or variables.
 Know the meanings of the
words term, expression and
equation.
2G
2B
2R
4.1
13.3
13.2
10.1
4.3
13.6
4.1
13.4
10.1
13.6– 13.4– 14.3
 Construct and solve simple
13.8 13.6
linear equations with integer
coefficients (unknown on one
side only) using an appropriate
method (e.g. inverse operations).
Impact maths sample medium-term plans for mathematics
Page 14
–
–
–
 Consolidate understanding of the
relationship between ratio and
proportion.
–
 Reduce a ratio to its simplest form, –
including a ratio expressed in different
units, recognising links with fraction
notation.
Notes (2B)
 Congruence of 2D shapes is covered in 3B.
CORE from the Y8 teaching
programme
 Begin to distinguish the different
roles played by letter symbols in
equations, formulae and functions.
 Know the meanings of the words
formula and function.
 Construct and solve linear
equations with integer coefficients
(unknown on either or both sides,
without and with brackets) using
appropriate methods (e.g. inverse
operations, transforming both sides in
same way.)
 Use formulae from mathematics
and other subjects.
 Substitute integers into simple
formulae, including examples that
lead to an equation to solve.
 Derive simple formulae.
2G
Notes (2R)
 Congruence of 2D shapes could be
covered using starter 2.8.
EXTENSION from the Y9 teaching
programme
4.1,
Ch4 10.1  Construct and solve linear
4.2
start
equations with integer
coefficients (with and without
13.1 13.1 14.1 brackets, negative signs anywhere
(pt)
(pt)
in the equation, positive or negative
solution), using an appropriate
method.
13.6– 13.4– 10.8,  Use formulae from mathematics
13.8 13.6 14.3– and other subjects.
(in pt) (in pt) 14.7  Substitute numbers into
expressions and formulae.
 Derive a formula and, in simple
cases, change its subject.
13.1
2B
enlargement as the ratio of the
lengths of any two corresponding
18.11 line segments.
11.4
 Recognise that enlargements
preserve angle but not length, and
understand the implications of
enlargement for perimeter.
3.11,  Use proportional reasoning to
3.13 solve a problem.
 Interpret and use ratio in a range
3.12 of contexts.
13.1
2R
14.1
13.3– 13.3– 14.3
13.6 13.6
13.3
(pt)
13.3
(pt)
14.2
2R
14.5
(in pt)
14.1
10.8
14.2
(in pt)
Key Stage 3 National Strategy
Year 8: Spring term
Numbers in the LH column refer to the supplement of examples for the core teaching programme
Notes (2G)
 Constructing and solving linear equations references the same
materials as ‘Algebra 5’. You will need to decide which sections will be
covered in each unit.
Notes (2R)
 Constructing and solving linear equations references the
same materials as ‘Algebra 5’. You will need to decide which
sections will be covered in each unit.
Notes (2R)
 Constructing and solving linear
equations references the same materials
as ‘Algebra 5’. You will need to decide
which sections will be covered in each unit.
Handling data
2 (6 hours)
Handling Data
(248-273)
CORE from the Y8 teaching
programme
 Discuss a problem that can be
addressed by statistical methods and
identify related questions to explore.
2G
EXTENSION from the Y9 teaching
programme
2R
 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 two-way tables for
discrete data.
–
–
13.1
–
–
–
–
–
13.1
13.1
 Discuss how data relate to a
problem; identify possible sources,
including primary and secondary
sources.
–
12.6
13.8
 Gather data from specified
secondary sources, including
printed tables and lists from ICTbased sources.
–
SUPPORT from the Y7 teaching
programme
 Given a problem that can be
addressed by statistical
methods, suggest possible
answers.
2G
2B
2R
–
–
–
 Design a data collection sheet –
or questionnaire to use in a
simple survey.
 Construct frequency tables for 12.1
discrete data.
 Calculate statistics for small
sets of discrete data:

find the mode, median
and range.

calculate the mean,
including from a simple
frequency table, using a
calculator for a larger number
of items.
 Construct, on paper and
using ICT, graphs and diagrams
to represent data, including:

bar-line graphs.
 Use ICT to generate pie
charts.
–
13.1
12.2
13.4
2B
see
see
13.1
notes notes see
notes
–
–
 Collect data using a suitable
method, such as observation,
controlled experiment, including data
logging using ICT, or questionnaire.
12.1, 15.1– 16.1–  Calculate statistics, including with a 15.1– 12.3,
15.1– 15.5 16.6 calculator.
15.5 15.1–
15.5
15.5
15.1, 15.1, 16.1,  Recognise when it is appropriate to 15.1– 15.1–
15.3, 15.3, 16.2, use the range, mean, median and
15.5 15.6,
15.5 15.5 16.4 mode.
17.6
15.4 15.4, 16.3,  Construct and use stem-and-leaf
–
–
(in pt) 15.6 16.5 diagrams.
12.3,
12.4,
12.5,
12.6
12.2
12.3
13.2
–
13.2
–
–
18.6
Impact maths sample medium-term plans for mathematics
Page 15
 Construct, on paper and using
ICT:

pie charts for categorical
data.

bar charts and frequency
diagrams for discrete data.

simple scatter graphs.
2R
13.1
16.1–
16.7
16.1–
16.7,
18.6
13.3
18.6
–
12.4,
12.5
13.6,
13.7
12.2
12.2
–
12.6
13.2,
13.4
13.8
Key Stage 3 National Strategy
Year 8: Spring term
Numbers in the LH column refer to the supplement of examples for the core teaching programme
 Identify which are most useful in the
–
context of the problem.
 Write a short report of a
statistical enquiry and illustrate
with appropriate diagrams,
graphs and charts, using ICT as
appropriate.
 Justify the choice of what is
presented.
–
–
–
–
–
–
 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.
–
–
12.1– 12.7– 13.2–  Interpret graphs and diagrams
12.6 12.8 13.8 and draw inferences to support or
cast doubt on initial conjectures.
15.2– 15.2
15.3
–
–
16.5,
16.6
–
–
–
–
 Have a basic understanding of
correlation.
–
13.8
Ch
Ch
Ch
 Solve more complex problems by
16
16
17
breaking them into smaller steps or
tasks, choosing and using resources,
including ICT.
Notes (2G)
Notes (2R)
Notes (2R)
 Discussing a problem that can be addressed by statistical methods is  Discussing a problem that can be addressed by statistical  Starter 13.1A can be used to discuss a
covered in 3G.
methods is covered in 3R.
problem that an be addresses by statistical
methods.
Solving
problems
(28–29)
Impact maths sample medium-term plans for mathematics
Page 16
Key Stage 3 National Strategy
Year 8: Summer term
Numbers in the LH column refer to the supplement of examples for the core teaching programme
YEAR 8 – SUMMER TERM
Teaching objectives for the oral and mental activities







2R
5.3, 8.1–8.4
Order, add, subtract, multiply and divide integers.
Multiply and divide decimals by 10, 100, 1000, 0.1, 0.01.
Round numbers, including to one or two decimal places.
Know and use squares, cubes, roots and index notation.
Know or derive prime factorisation of numbers to 30.
Convert between fractions, decimals and percentages.
Find the outcome of a given percentage increase or decrease.
3.5
6.5
 Know complements of 0.1, 1, 10, 50, 100.
 Add and subtract several small numbers or several multiples of 10,
e.g. 250 + 120 – 190.
 Use jottings to support addition and subtraction of whole numbers and
decimals.
 Calculate using knowledge of multiplication and division facts and
place value, e.g. 432  0.01, 37  0.01, 0.04  8, 0.03  5.
 Recall multiplication and division facts to 10  10.
 Use factors to multiply and divide mentally, e.g. 22  0.02, 420  15.
 Multiply by near 10s, e.g. 75  29, 8  –19
 Use partitioning to multiply, e.g. 13  1.4.
5.3, 5.5
5.3, 5.5
2R
 Use approximations to estimate the answers to calculations, e.g. 39
 2.8.
 Solve equations, e.g. n(n – 1) = 56,  +  = –46.
14.3, 14.5
 Visualise, describe and sketch 2-D shapes, 3-D shapes and simple
loci.
 Estimate and order acute, obtuse and reflex angles.
7.3 (in pt)
 Use metric units (length, mass, capacity, area and volume) and units
of time for calculations.
 Use metric units for estimation (length, mass, capacity, area and
volume).
 Convert between m, cm and mm, km and m, kg and g, litres and ml,
cm² and mm².
 Discuss and interpret graphs.
 Calculate a mean using an assumed mean.
12.1, 12.3,
12.6A&B,
12.7, 13.5
16.3 (in pt),
16.5 (in pt)
 Apply mental skills to solve simple problems.
Teaching objectives for the main activities
Number 4 (6
hours)
Calculations
(82–87, 92–
107, 110–111)
SUPPORT from the Y7 teaching
programme
2G
Impact maths sample medium-term plans for mathematics
Page 17
2B
2R
CORE from the Y8 teaching
programme
 Understand addition and
subtraction of fractions and integers,
and multiplication and division of
integers.
 Use the laws of arithmetic and
inverse operations.
2G
2B
2R
3.1–
3.11,
6.6
3.1–
3.11,
6.5
3.6
3.7
1.11–
1.14,
5.2–
5.4
1.3,
1.7–
1.9,
3.1,
3.2,
3.7–
3.11
3.8–
3.10
 Use the order of operations,
13.4
13.3
14.4
EXTENSION from the Y9 teaching
programme
 Understand the effects of
multiplying and dividing by
numbers between 0 and 1.
2R
 Understand the order of
–
–
Key Stage 3 National Strategy
Year 8: Summer term
Numbers in the LH column refer to the supplement of examples for the core teaching programme
1.5,
1.7,
 Consolidate and extend
mental methods of calculation 1.12 8.1
to include decimals, fractions (in pt)
and percentages, accompanied
where appropriate by suitable
jottings.
 Multiply and divide threedigit by two-digit whole
numbers.
 Extend to multiplying and
dividing decimals with one or
two place by single digit
numbers.
Measures
(228–231)
 Convert one metric unit to
another (e.g. grams to
kilograms).
5.1,
5.5
3.9,
3.11
3.9,
3.10
–
8.4,
8.5
8.4,
8.5
5.3,
5.4
9.7,
9.8,
9.10,
14.5
9.8,
9.9
–
including brackets, with more complex
calculations.
 Consolidate and extend mental
methods of calculation, working with
decimals, fractions and percentages,
squares and square roots, cubes and
cube roots.
 Solve word problems mentally.
 Make and justify estimates and
approximations of calculations.
 Consolidate standard column
procedures for addition and
subtraction of integers and decimals
with up to two places.
 Use standard column procedures
for multiplication and division of
integers and decimals, including by
decimals such as 0.6 or 0.06.
 Understand where to position
the decimal point by considering
equivalent calculations.
 Check a result by considering
whether it is of the right order of
magnitude and by working the
problem backwards.
 Use units of measurement to
estimate, calculate and solve
problems in everyday contexts.
precedence and effect of powers.
see
see
5.1,
notes notes 5.5
 Extend mental methods of
calculation, working with decimals,
fractions, percentages, factors,
powers and roots.
–
1.7–
1.10
1.13,
1.14,
8.2
1.6
1.6
1.8,
1.9,
8.2
5.1
 Use standard column
procedures to add and subtract
integers and decimals of any size.
5.1
(in pt)
3.8–
3.11
3.9,
3.10
5.3,
5.4
 Multiply and divide by decimals,
dividing by transforming to division
by an integer.
–
8.4,
8.5
8.4,
8.5
5.3,
5.4
1.10 8.7
5.9
(in pt) (in pt) (in pt)
9.7,
9.8,
9.10
9.8,
9.10,
9.11
see
notes
Notes (2G)
 Mental methods of calculation are covered by starters 1.3, 1.5, 1.7,
1.11, 1.12, 6.1, 6.2, 6.5, 8.1–8.3.
Notes (2B)
Notes (2R)
 Mental methods of calculation are covered by starters 8.2  Mental methods of calculation are
and 8.3.
covered by starters 5.1, 5.3–5.5.
 Using units of measurement is covered
in 1R.
Algebra 5 (8
hours)
Equations and
formulae
(116–137)
CORE from the Y8 teaching
programme
 Simplify or transform linear
expressions by collecting like
terms.
 Multiply a single term over a
bracket.
 Construct and solve linear
SUPPORT from the Y7 teaching
programme
 Simplify linear algebraic
expressions by collecting like
terms.
 Construct and solve simple
2G
2B
2R
4.2
4.1–
4.3
10.1
13.6– 13.4– 14.3
Impact maths sample medium-term plans for mathematics
Page 18
2G
2B
2R
4.3,
4.4
4.1,
4.3
10.4,
14.6
–
4.4
10.5
14.7
13.6– 13.4– 10.8,
EXTENSION from the Y9 teaching
programme
 Simplify or transform algebraic
expressions by taking out singleterm common factors.
2R
 Construct and solve linear
14.5
10.6,
10.7
Key Stage 3 National Strategy
linear equations with integer
coefficients (unknown on one
side only) using an appropriate
method (e.g. inverse
operations).
 Generate coordinate pairs
that satisfy a simple linear rule.
Year 8: Summer term
Numbers in the LH column refer to the supplement of examples for the core teaching programme
13.8
11.3
11.2,
 Recognise straight-line
graphs parallel to the x-axis or y- 11.3
axis.
13.6
11.2,
11.3,
17.8
11.2,
11.3
equations with integer coefficients
(unknown on either or both sides,
without and with brackets) using
appropriate methods (e.g. inverse
operations, transforming both sides in
same way.)
12.5
12.3,
12.4
13.8 13.6 14.3– equations with integer
(in pt) (in pt) 14.7 coefficients (with and without
brackets, negative signs anywhere
in the equation, positive or negative
solution), using an appropriate
method.
 Use systematic trial and
improvement methods and ICT
tools to find approximate solutions
to equations such as x³ + x = 20.
13.8 13.3 14.2  Solve problems involving direct
 Begin to use graphs and set up
equations to solve simple problems
proportion using algebraic methods,
involving direct proportion.
relating algebraic solutions to
graphical representations of the
equations.
 Use ICT as appropriate.
11.5 11.4 12.4,  Plot graphs of linear functions (y
 Plot the graphs of linear
(in pt) 11.5 12.6, given implicitly in terms of x), e.g.
functions, where y is given
12.7 ay + bx = 0, y + bx + c, on paper
explicitly in terms of x, on paper and
and using ICT.
using ICT.
Notes (2G)
 Constructing and solving linear equations references the same
materials as ‘Algebra 4’. You will need to decide which sections will be
covered in each unit.
11.4– 11.7 12.9
 Construct linear functions arising
11.6
from real-life problems and plot their
corresponding graphs.
11.4– 11.7 12.9
 Discuss and interpret graphs
11.6
arising from real situations.
Ch
Ch
Ch
 Solve more demanding problems
16
17
and investigate in a range of contexts: 16
algebra.
Ch
Ch
Ch
 Solve more complex problems by
16
16
17
breaking them into smaller steps or
tasks, choosing and using efficient
techniques for calculation, algebraic
manipulation.
Notes (2B)
 Constructing and solving linear equations references the
same materials as ‘Algebra 4’. You will need to decide which
sections will be covered in each unit.
Solving
problems (6
CORE from the Y8 teaching
programme
 Break a complex calculation
into simpler steps, choosing and
using appropriate and efficient
operations, methods and
resources, including ICT.
SUPPORT from the Y7 teaching
programme
Ch
16
2G
Impact maths sample medium-term plans for mathematics
Page 19
Ch
16
2B
Ch
17
2R
2G
2B
2R
 Use trial and improvement
where a more efficient method is
not obvious.
(in pt)
14.10
–
–
12.7,
18.9
–
Notes (2R)
 Constructing and solving linear
equations references the same materials
as ‘Algebra 4’. You will need to decide
which sections will be covered in each unit.
EXTENSION from the Y9 teaching
programme
2R
Key Stage 3 National Strategy
Year 8: Summer term
Numbers in the LH column refer to the supplement of examples for the core teaching programme
hours)
Solving
problems
(2–35)
Ratio and
proportion
(78–81)
 Represent problems
mathematically, making correct
use of symbols, words,
diagrams, tables and graphs.
Ch
16
Ch
16
Ch
17
 Break a complex
calculation into simpler steps,
choosing and using
appropriate and efficient
methods and resources,
including ICT.
Ch
16
Ch
16
Ch
17
 Understand the significance
of a counter-example.
–
–
–
 Understand the relationship
between ratio and proportion.
 Solve simple problems about
ratio and proportion using
informal strategies.
–
–
3.11
–
–
3.11
Notes (2G)
 Ratio and proportion are covered in much more detail in 3G.
Shape, space
SUPPORT from the Y7 teaching
2G
Impact maths sample medium-term plans for mathematics
Page 20
2B
2R
 Solve more demanding problems
and investigate in a range of contexts:
number and measures.
–
9.4
 Identify the necessary
information to solve a problem.
 Represent problems and
interpret solutions in algebraic or
graphical form, using correct
notation.
 Solve more complex problems by
breaking them into smaller steps or
tasks, choosing and using efficient
techniques for calculation.
Ch
16
Ch
16
6.6–
6.8,
7.3,
17.1
Ch
17
Ch
16
Ch
16
Ch
17
 Solve increasingly demanding
problems and evaluate solutions.
 Explore connections in
mathematics across a range of
contexts.
–
Ch
Ch
Ch
 Use logical argument to
16
16
17
establish the truth of a statement.
 Give solutions to an appropriate
degree of accuracy in the context of
the problem.
Ch
Ch
Ch
 Suggest extensions to problems,
16
16
17
conjecture and generalise.
 Identify exceptional cases or
counter-examples.
see
see
3.11,
 Consolidate understanding of the
notes notes 3.13
relationship between ratio and
proportion.
3.12
 Reduce a ratio to its simplest form,
including a ratio expressed in different
units, recognising links with fraction
notation.
3.13
 Divide a quantity into two or
more parts in a given ratio.
3.13
 Use the unitary method to solve
simple word problems involving
ratio and direct proportion.
Notes (2B)
 Ratio and proportion are covered in much more detail in
3B.
 Present a concise, reasoned
argument, using symbols,
diagrams, graphs and related
explanatory text.
–
CORE from the Y8 teaching
EXTENSION from the Y9 teaching
2G
2B
2R
–
 Use proportional reasoning to –
solve a problem, choosing the
correct numbers to take as 100%,
or as a whole.
–
 Compare two ratios.
 Interpret and use ratio in a range –
of contexts, including solving word
problems.
Notes (2R)
2R
Key Stage 3 National Strategy
and measures
4 (9 hours)
Geometrical
reasoning:
lines, angles
and shapes
(198–201)
Year 8: Summer term
Numbers in the LH column refer to the supplement of examples for the core teaching programme
programme
programme
9.5
 Use 2D representations to
visualise 3D shapes and deduce
some of their properties.
9.5,
9.7
7.7,
7.9
 Use ruler and protractor to
construct simple nets of 3D
shapes, e.g. cuboid, regular
tetrahedron, square-based
pyramid, triangular prism.
9.6
7.8
Transformations
(216–217)
Coordinates
 Use conventions and notation
(218–219)
for 2-D coordinates in all four
quadrants.
 Find coordinates of points
determined by geometric
information.
Construction
 Use a ruler and protractor to:
and loci

measure and draw lines
(220–227)
to the nearest millimetre and
angles, including reflex
angles, to the nearest degree.

Construct a triangle given
two sides and the included
angle (SAS) or two angles
and the included side (ASA).
 Explore these constructions
using ICT.
9.6
11.4
11.1
–
–
12.1,
12.2,
12.5
12.9
2.4,
2.5
2.4,
2.5
2.2,
2.3
–
–
–
17.6
17.7
18.7
programme
 Know and use geometric
properties of cuboids and shapes
made from cuboids.
 Begin to use plans and elevations.
–
9.7
7.9
 Visualise and use 2D
representations of 3D objects.
–
9.7
7.9
 Make simple scale drawings.
–
–
11.4
 Analyse 3D shapes through 2D
projections, including plans and
elevations.
 Use and interpret maps and
scale drawings.
 Given the coordinates of points A
and B, find the mid-point of the line
segment AB.
–
–
–
 Use straight edge and
compasses to construct:

a triangle, given three sides
(SSS).
 Use ICT to explore this
construction.
7.9
(in pt)
7.9
(in pt)
–
 Use straight edge and
compasses to construct a triangle,
given right angle, hypotenuse and
side (RHS).
–
14.6 14.10 15.5  Calculate the surface area and
14.7
volume of right prisms.
see
see
see
notes notes notes
–
–
–
7.4
–
–
18.7,
18.8
see
18.8
 Find simple loci, both by reasoning see
and by using ICT, to produce shapes notes notes
and paths, e.g. an equilateral triangle.
 Use bearings to specify direction.
Mensuration
(232-233, 238241)
 Calculate the surface area of
cubes and cuboids.
see
see
see
 Know and use the formula for
notes notes notes the volume of a cuboid.
 Calculate volumes and surface
areas of cuboids and shapes made
Impact maths sample medium-term plans for mathematics
Page 21
see
see
see
notes notes notes
Key Stage 3 National Strategy
Year 8: Summer term
Numbers in the LH column refer to the supplement of examples for the core teaching programme
from cuboids.
Notes (2B)
 Simple loci are covered in 3B.
 Bearings are covered in 3B
 Surface area of a cuboid is covered in 1G and 1R.
Notes (2G)
 Simple loci are covered in 3G.
 Bearings are covered in 3G.
 Surface area of a cuboid is covered in 1G.
Handling data
3 (7 hours)
Handling Data
(248–275)
SUPPORT from the Y7 teaching
programme
 Given a problem that can be
addressed by statistical
methods, suggest possible
answers.
2G
2B
2R
–
–
–
 Design a data collection sheet –
or questionnaire to use in a
simple survey.
 Construct frequency tables for 12.1
discrete data, grouped where
appropriate in equal class
intervals.
 Calculate statistics for small
sets of discrete data:

find the mode, median
and range, and the modal
class for grouped data.

calculate the mean,
including from a simple
frequency table, using a
calculator for a larger number
of items.
–
13.1
12.2
13.4
2B
CORE from the Y8 teaching
programme
 Discuss a problem that can be
addressed by statistical methods and
identify related questions to explore.
2G
2R
 Decide which data to collect to
answer a question, and the degree of
accuracy needed.
 Identify possible sources.
see
see
13.1
notes notes
 Plan how to collect the data,
including sample size.
 Construct frequency tables with
given equal class intervals for sets of
continuous data.
–
EXTENSION from the Y9 teaching
programme
2R
 Discuss how data relate to a
problem.
 Identify possible sources,
including primary and secondary
sources.
 Design a survey or experiment
to capture the necessary data
from one 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.
–
see
see
13.1
notes notes see
notes
13.1
12.1
13.1
12.2
–
–
 Collect data using a suitable
method, such as observation,
controlled experiment, including data
logging using ICT, or questionnaire.
12.1, 15.1– 16.1–  Calculate statistics, including with a 15.1– 15.1–
15.1– 15.5 16.6 calculator.
15.5 15.5
15.5
15.1, 15.1, 16.1,  Calculate a mean using an
–
15.6
15.3, 15.3, 16.2, assumed mean.
15.5 15.5 16.4
 Know when it is appropriate to use
15.4 15.4, 16.3, the modal class for grouped data.
15.2 15.2
(in pt) 15.6 16.5
Impact maths sample medium-term plans for mathematics
Page 22
Notes (2R)
 Bearings are covered in 3R.
 Surface area of a cuboid is covered in
1R.
13.4
13.1
16.1–
16.7,
18.6
16.3,
16.5
16.1
–
13.1
(in pt)
13.1
(in pt)
13.1
(in pt)
16.5,
16.6
(in pt)
Key Stage 3 National Strategy
 Construct, on paper and
using ICT, graphs and diagrams
to represent data, including:

frequency diagrams for
grouped discrete data.
 Use ICT to generate pie
charts.
 Write a short report of a
statistical enquiry and illustrate
with appropriate diagrams,
graphs and charts, using ICT as
appropriate.
 Justify the choice of what is
presented.
Year 8: Summer term
Numbers in the LH column refer to the supplement of examples for the core teaching programme
12.3– 12.2,
12.6 12.3
13.2
12.6
12.2
13.2
17.5
–
18.6
–
–
–
–
–
–
Notes (2G)
 Data collection is covered in more detail in 3G.
 Comparison of experimental and theoretical probabilities is covered in
3G.
Impact maths sample medium-term plans for mathematics
Page 23
 Construct, on paper and using
ICT:

bar charts and frequency
diagrams for continuous data.
18.6
–
–

simple line graphs for time
series.
 Identify which are most useful in
the context of the problem.
 Interpret tables, graphs and
diagrams for continuous data, and
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.
12.5
12.7
13.2,
13.4,
13.5
13.2
–
–
–
–
12.7,
12.8
13.2,
13.4
–
–
12.7,
12.8
–
13.1,
13.2
16.7
 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.
–
–
–
–
–
–
see
7.6
 Compare experimental and
notes
theoretical probabilities in different
contexts.
Ch
Ch
 Solve more complex problems by
16
16
breaking them into smaller steps or
tasks, choosing and using graphical
representation, and also resources,
including ICT.
Notes (2B)
 Data collection is covered in more detail in 3G.
4.5
16.7
 Compare two or more
distributions and make inferences,
using the shape of the distributions,
the range of data and appropriate
statistics.
 Appreciate the difference
between mathematical explanation
and experimental evidence.
Ch
17
Notes (2R)
–
Notes
Impact maths sample medium-term plans for mathematics
Page 24
Key Stage 3
Sample medium term plans for maths using Impact Maths
Year 8
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