Download Year 8 - Portland Place School

Mathematics
Scheme of Work
Year 7
New Mathematics Framework
Year 7 Mathematics – Scheme of Work (22-06-2010)
1
YEAR 7: Overview of year 7 scheme of work
New Maths Frameworking
YEAR
7
Term
1
Term
2
Term
3
Assessment
Tests
Algebra 1
Sequences and functions (6 hours)
Number 2
Fractions, decimals, percentages,
ratio and proportion (5 hours)
Number 1
Place values, integers, calculations (6 hours)
Statistics 1
Geometry and Measures 1
Mensuration (perimeter and area) (4 hours)
Algebra 2
Statistics including probability (5 hours)
Equations and formulae (5 hours)
Geometry and Measures 2
Coordinates, geometrical reasoning:
lines, angles and shapes (3 hours)
Algebra 3
Integers, powers and roots.
Sequences, functions and graphs (5
hours)
Statistics 2
Statistics (4 hours)
Geometry and Measures 3
Number and Measures 3
Place value, calculations, calculator
methods, measures (7 hours)
Number 4
Geometrical reasoning: lines, angles and
shapes. Construction (3 hours)
Fractions, decimals, percentages, ratio and
proportion (4 hours)
Algebra 4
Equations and formulae (3 hours)
Number 5
Place value, calculations including
calculator methods, fractions,
decimals, percentages, ratio and
proportion, solving problems (6
hours)
Geometry and Measures 4
Transformations (5 hours)
Algebra 5
Statistics 3
Statistics, including probability (5 hours)
Geometry and Measures 5
Sequences, functions and graphs, equations
and formulae (4 hours)
Geometrical reasoning: lines, angles and
shapes; construction (3 hours)
Year 7 Mathematics – Scheme of Work (22-06-2010)
2
Test 1
Test 2
Test 3
Test 4
Test 5
End of year test
YEAR 7: AUTUMN TERM
MATHEMATICAL
TOPIC - Context
Algebra 1
(6 hours)
►OVERVIEW – Teacher Pack 2
► FRAMEWORK OBJECTIVES – Teacher Pack 2
►OVERVIEW – Teacher Pack 3
► FRAMEWORK OBJECTIVES – Teacher Pack 3
1.1 Sequences and rules
1.2 Finding missing terms
1.3 Functions and mappings
1.4 Using letter symbols to
represent functions
1.5 The general term (nth term)
1.6 An nth term investigation
1.1 Describe integer sequences.
1.2 Generate terms of a simple sequence given a
rule (for example, finding a term from the previous
term; finding a term given its position in the
sequence).
1.3 Express simple functions in words, then using
symbols; represent them in mappings.
1.4 Use letter symbols to represent unknown
numbers or variables.
1.5 Generate sequences from patterns or practical
contents and describe the general term in simple
cases.
1.6 Identify the necessary information to understand
or simplify a context or problem; represent problems,
making correct use of symbols, words, diagrams,
tables and graphs; use appropriate procedures.
Classify and visualise properties and patterns;
generalise in simple cases by working logically.
1.1 Sequences and rules
1.2 Finding missing terms
1.3 Finding the general term (nth
term)
1.4 Functional and mappings
1.5 Using letter symbols to
represent functions
1.6 A function investigation
Number 1
(6 hours)
2.1 Decimals
2.2 Ordering decimals
2.3 Directed numbers
2.4 Estimates
2.5 Column method for addition
and subtraction
2.6 Solving problems
2.1 Understand and use decimal notation and place
value. Multiply and divide integers and decimals by
10, 100, 1000, and explain the effect.
2.2 Compare and order decimals in different
contexts. Know that when comparing measurements
the units must be the same.
2.3 Understand negative numbers as positions on a
number line. Order, add and subtract integers in
context.
2.4 Make and justify estimates and approximations
of calculations.
2.5 Use efficient written methods to add and subtract
whole numbers and decimals with up to two places.
2.6 Represent problems, making correct use of
symbols, words and diagrams; use appropriate
procedures and tools.
2.1 Decimals
2.2 Ordering decimals
2.3 Directed numbers
2.4 Estimates
2.5 Column method for addition,
subtraction and multiplication
2.6 Solving problems
1.1 Describe integer sequences; generate terms of a
simple sequence.
1.2 Generate terms of a simple sequence, given a
rule (for example, finding a term from the previous
term, finding a term given its position in the
sequence).
1.3 Generate sequences from patterns or practical
contexts and describe the general term in simple
cases.
1.4 Express simple functions in words, then using
symbols; represent them in mappings.
1.5 Use letter symbols to represent unknown
numbers or variables.
1.6 Identify the necessary information to understand
or simplify a context or problem; represent problems,
making correct use of symbols, words, diagrams,
tables and graphs; use appropriate procedures.
Classify and visualise properties and patterns;
generalise in simple cases by working logically.
Recall number facts, including positive integer
complements to 100 and multiplication facts to 10 ×
10, and quickly derive associated division facts.
2.1 Understand and use decimal notation and place
value; multiply and divide integers and decimals by
10, 100, 1000, and explain the effect.
2.2 Compare and order decimals in different
contexts; know that when comparing measurements
the units must be the same.
2.3 Understand negative numbers as positions on a
number line; order, add and subtract integers in
context.
2.4 Strengthen and extend mental methods of
calculation to include decimals, fractions and
percentages. Make and justify estimates and
approximations of calculations.
2.5 Use efficient written methods to add and subtract
whole numbers and decimals with up to two places.
Extend to multiplying decimals with one or two
places by single-digit whole numbers.
2.6 Classify and visualise properties and patterns;
generalise in simple cases by working logically; draw
simple conclusions and explain reasoning;
understand the significance of a counter-example;
take account of feedback and learn from mistakes.
Year 7 Mathematics – Scheme of Work (22-06-2010)
3
YEAR 7: AUTUMN TERM
MATHEMATICAL
TOPIC - Context
Geometry &
Measures 1
(4 hours)
►OVERVIEW – Teacher Pack 2
► FRAMEWORK OBJECTIVES – Teacher Pack 2
►OVERVIEW – Teacher Pack 3
► FRAMEWORK OBJECTIVES – Teacher Pack 3
3.1 Length, perimeter and area
3.2 Areas of some 2-D shapes
3.3 3-D shapes
3.4 Surface area and volume of
cuboids
3.1 Length, perimeter and area
3.2 Areas of some 2-D shapes
3.3 3-D shapes
3.4 Surface area and volume of
cuboids
3.1 Know and use the formula for the area of a
rectangle; calculate the perimeter and area of
shapes made from rectangles.
3.2 Derive and use formulae for the area of a
triangle, parallelogram and trapezium; calculate
areas of compound shapes (Year 8 Framework
objective).
3.3 Use 2-D representations to visualise 3-D shapes
and deduce some of their properties.
3.4 Calculate the surface area of cubes and cuboids.
Know and use the formula for the volume of a
cuboid; calculate volumes and surface areas of
cuboids and shapes made from cuboids (Year 8
Framework objective).
Number 2
(5 hours)
4.1 Fractions
4.2 Fractions and decimals
4.3 Adding and subtracting
fractions
4.4 Equivalences
4.5 Solving problems
3.1 Choose and use units of measurement to
measure, estimate, calculate and solve problems in
everyday contexts.
3.2 Choose and use units of measurement to
measure, estimate, calculate and solve problems in
everyday contexts. Know and use the formula for the
area of a rectangle; calculate the perimeter and area
of shapes made from rectangles.
3.3 Use 2-D representations to visualise 3-D shapes
and deduce some of their properties. Make accurate
mathematical diagrams, graphs and constructions
on paper and on screen.
3.4 Know and use the formula for the area of a
rectangle. Calculate the perimeter and area of
shapes made from rectangles. Calculate the surface
area of cubes and cuboids.
4.1 Express a smaller whole number as a fraction of
a larger one. Simplify fractions by cancelling all
common factors and identify equivalent fractions.
4.2 Convert terminating decimals to fractions: for
4.1 Fractions
4.2 Fractions and decimals
4.3 Adding and subtracting
fractions
4.4 Calculations and
equivalences
4.5 Solving problems
4.1 Express a smaller whole number as a fraction of
a larger one; simplify fractions by cancelling all
common factors and identify equivalent fractions.
4.2 Convert terminating decimals to fractions, for
23
example 0.23 = 100 . Use a diagram to compare two
or more simple fractions.
4.3 Add and subtract simple fractions and those with
common denominators.
4.4 Calculate simple fractions of quantities and
measurements (whole-number answers). Multiply a
fraction by an integer. Understand percentage as the
‘number of parts per 100’. Calculate simple
percentages and use percentages to compare
simple proportions. Recognise the equivalence of
percentages, fractions and decimals.
4.5 Check results by considering whether they are of
the right order of magnitude and by working the
problem backwards.
Year 7 Mathematics – Scheme of Work (22-06-2010)
4
23
example, 0.23 = 100 . Use diagrams to compare two
or more simple fractions.
4.3 Add and subtract simple fractions and those with
common denominators.
4.4 Calculate simple fractions of quantities and
measurements (whole number answers); multiply a
fraction by an integer. Calculate simple percentages.
Recognise the equivalence of percentages, fractions
and decimals. Calculate percentages and find the
outcome of a given percentage increase or decrease
(Year 8 Framework objective).
4.5 Interpret information from a mathematical
representation or context; relate findings to the
original context; check the accuracy of the solution;
explain and justify methods and conclusions;
compare and evaluate approaches. Check results by
considering whether they are of the right order of
magnitude and by working problems backwards.
YEAR 7: AUTUMN TERM
MATHEMATICAL
TOPIC - Context
Statistics 1
(5 hours)
►OVERVIEW – Teacher Pack 2
► FRAMEWORK OBJECTIVES – Teacher Pack 2
►OVERVIEW – Teacher Pack 3
► FRAMEWORK OBJECTIVES – Teacher Pack 3
5.1 Mode, median and range
5.2 The mean
5.3 Statistical diagrams
5.4 Probability
5.5 Experimental probability
5.1 Calculate statistics for small sets of discrete
data. Find the mode, median and range, and the
modal class for grouped data. Explain and justify
methods and conclusions; compare and evaluate
approaches.
5.2 Calculate statistics for small sets of discrete
data. Calculate the mean, including from a simple
frequency table, using a calculator for a larger
number of items.
5.3 Interpret diagrams and graphs (including pie
charts), and draw conclusions based on the shape
of graphs and simple statistics for a single
distribution. Interpret information from a
mathematical representations or context.
5.4 Use vocabulary and ideas of probability, drawing
on experience. Understand and use the probability
scale from 0 to 1. Find and justify probabilities based
on equally likely outcomes in simple contexts.
Identify all the possible mutually exclusive outcomes
of a single event.
5.5 Estimate probabilities by collecting data from a
simple experiment and recording it in a frequency
table. Compare experimental and theoretical
probabilities in simple contexts.
5.1 Mode, median and range
5.2 The mean
5.3 Statistical diagrams
5.4 Probability
5.5 Experimental probability
Algebra 2
(5 hours)
6.1 Algebraic terms and
expressions
6.2 Rules of algebra
6.3 Simplifying expressions
6.4 Formulae
6.5 Equations
6.1 Use letter symbols to represent unknown
numbers or variables. Know the meanings of the
words term, expression and equation.
6.2 Understand that algebraic operations follow the
rules of arithmetic.
6.3 Simplify linear algebraic expressions by
collecting like terms. Multiply a single term over a
bracket (integer coefficients).
6.4 Use simple formulae from mathematics and
other subjects. Substitute positive whole numbers
into linear expressions and formulae and, in simple
cases, derive a formula.
6.5 Give simple linear equations with integer
coefficients (unknown on one side only) using an
appropriate method (for example, inverse
operations).
6.1 Algebraic terms and
expressions
6.2 Rules of algebra
6.3 Expanding and simplifying
expressions
6.4 Formulae
6.5 Equations
5.1 Calculate statistics for small sets of discrete
data: find the mode, median and range, and the
modal class for grouped data.
5.2 Calculate statistics for small sets of discrete
data: calculate the mean, including from a simple
frequency table, using a calculator for a larger
number of items.
5.3 Interpret diagrams and graphs (including pie
charts), and draw simple conclusions based on the
shape of graphs and simple statistics for a single
distribution.
5.4 Use vocabulary and ideas of probability, drawing
on experience. Understand and use the probability
scale from 0 to 1; find and justify probabilities based
on equally likely outcomes in simple contexts;
identify all the possible mutually exclusive outcomes
of a single event. Know that if the probability of an
event occurring is p, then the probability of it not
occurring is 1 – p; use diagrams and tables to record
in a systematic way all possible mutually exclusive
outcomes for single events and for two successive
events (Year 8 Framework objective).
5.5 Estimate probabilities by collecting data from a
simple experiment and recording it in a frequency
table.
6.1 Use letter symbols to represent unknown
numbers or variables; know the meanings of the
words term, expression and equation.
6.2 Understand that algebraic operations follow the
rules of arithmetic.
6.3 Simplify linear algebraic expressions by
collecting like terms; multiply a single term over a
bracket (integer coefficients).
6.4 Use simple formulae from mathematics and
other subjects; substitute positive integers into linear
expressions and formulae and, in simple cases,
derive a formula.
6.5 Identify the necessary information to understand
or simplify a context or problem; represent problems,
making correct use of symbols, words, diagrams,
tables and graphs; use appropriate procedures and
tools, including ICT.
31 Hours Teaching
Year 7 Mathematics – Scheme of Work (22-06-2010)
5
YEAR 7: SPRING TERM
MATHEMATICAL
TOPIC - Context
Geometry &
Measures 2
(3 hours)
►OVERVIEW – Teacher Pack 2
► FRAMEWORK OBJECTIVES – Teacher Pack 2
►OVERVIEW – Teacher Pack 3
► FRAMEWORK OBJECTIVES – Teacher Pack 3
7.1 Lines and angles
7.2 Calculating angles
7.3 Coordinates
7.1 Lines and angles
7.2 Calculating angles
7.3 Coordinates
7.1 Use correctly the vocabulary, notation and
labelling conventions for lines, angles and shapes.
Identify parallel and perpendicular lines. Identify
alternate angles and corresponding angles (Year 8
Framework objective).
7.2 Know the sum of angles at a point, on a straight
line and in a triangle; recognise vertically opposite
angles. Understand a proof that: the angle sum of a
triangle is 180° and of a quadrilateral is 360°; the
exterior angle of a triangle is equal to the sum of the
two interior opposite angles (Year 8 Framework
objective).
7.3 Use conventions and notation for 2-D
coordinates in all four quadrants; find coordinates of
points determined by geometric information.
Statistics 2
(4 hours)
8.1 Using a tally chart
8.2 Using the correct data
8.3 Grouped frequencies
8.4 Data collection
7.1 Use correctly the vocabulary, notation and
labelling conventions for lines, angles and shapes.
Identify parallel and perpendicular lines. Identify and
use angle, side and symmetry properties of triangles
and quadrilaterals. Distinguish between and
estimate the size of acute, obtuse and reflex angles.
Represent problems, making correct use of symbols,
words and diagrams.
7.2 Use correctly the vocabulary, notation and
labelling conventions for lines, angles and shapes.
Know the sum of angles at a point, on a straight line
and in a triangle, and recognise vertically opposite
angles.
7.3 Use conventions and notation for 2-D
coordinates in all four quadrants. Find coordinates of
points determined by geometric information.
8.1 Suggest possible answers given a problem that
can be addressed by statistical methods.
8.2 Decide which data would be relevant to an
enquiry and possible sources. Plan how to collect
and organise small sets of data; design a data
collection sheet or questionnaire to use in a simple
survey.
8.3 Construct frequency tables for discrete data,
grouped where appropriate in equal class intervals.
8.4 Collect small sets of data from surveys and
experiments, as planned.
8.1 Using a tally chart
8.2 Using the correct data
8.3 Grouped frequencies
8.4 Data collection
8.1Suggest possible answers, given a question that
can be addressed by statistical methods.
8.2 Decide which data would be relevant to an
enquiry and possible sources. Plan how to collect
and organise small sets of data from surveys and
experiments: design data collection sheets or
questionnaires to use in a simple survey.
8.3 Plan how to collect and organise small sets of
data from surveys and experiments: construct
frequency tables for gathering discrete data,
grouped where appropriate in equal class intervals.
8.4 Collect small sets of data from surveys and
experiments, as planned. Decide which data to
collect to answer a question, and the degree of
accuracy needed; identify possible sources; consider
appropriate sample size (Year 8 Framework
objective).
Year 7 Mathematics – Scheme of Work (22-06-2010)
6
YEAR 7: SPRING TERM
MATHEMATICAL
TOPIC - Context
Numbers &
Measures 3
(7 hours)
►OVERVIEW – Teacher Pack 2
► FRAMEWORK OBJECTIVES – Teacher Pack 2
►OVERVIEW – Teacher Pack 3
► FRAMEWORK OBJECTIVES – Teacher Pack 3
9.1 Rounding
9.2 The four operations
9.3 BODMAS
9.4 Long multiplication and long
division
9.5 Efficient calculations
9.6 Calculating with
measurements
9.7 Solving problems
9.1 Round positive whole numbers to the nearest
10, 100 or 1000 and decimals to the nearest whole
number or one decimal place.
9.2 Understand and use the rule of arithmetic and
inverse operations in the context of positive integers
and decimals.
9.3 Use the order of operations, including brackets.
9.4 Multiply and divide three-digit by two-digit whole
numbers.
9.5 Check results by considering if they are of the
right order of magnitude and by working problems
backwards. Carry out calculations with more than
one step using brackets and the memory; use the
square root and sign change keys.
9.6 Choose and use units of measurement to
measure, estimate, calculate and solve problems in
everyday contexts. Convert one metric unit to
another (for example grams to kilograms); read and
interpret scales on a range of measuring
instruments.
9.7 Draw simple conclusions and explain reasoning,
communicate own findings effectively in writing.
9.1 Rounding
9.2 The four operations
9.3 BODMAS
9.4 Long multiplication and long
division
9.5 Efficient calculations
9.6 Calculating with
measurements
9.7 Solving problems
Algebra 3
(5 hours)
10.1 Square numbers and square
roots
10.2 Triangle numbers
10.3 From mappings to graphs
10.4 Naming graphs
10.5 Naming sloping lines
10.1 Recognise and use multiples, factors, primes
(less than 100), common factors, highest common
factors and lowest common multiples in simple
cases. Recognise the squares of numbers to at least
12 × 12, and the corresponding roots.
10.2 Recognise the first few triangle numbers.
10.3 Generate terms of a simple sequence, given a
rule. (For example, find a term from the previous
term; find a term given its position in the sequence).
10.4 Generate coordinate pairs that satisfy a simple
linear rule. Recognise straight-line graphs parallel to
the x-axis or y-axis.
10.5 Plot the graphs of simple linear functions,
where y is given explicitly in terms of x, on paper and
using ICT.
10.1 Square numbers and square
roots
10.2 Triangle numbers
10.3 From mappings to graphs
10.4 More about graphs
10.5 Questions about graphs
9.1 Round positive whole numbers to the nearest
10, 100 or 1000, and decimals to the nearest whole
number or one decimal place.
9.2 Understand and use the rules of arithmetic and
inverse operations in the context of positive integers
and decimals.
9.3 Use the order of operations, including brackets.
9.4 Multiply and divide three-digit by two-digit whole
numbers.
9.5 Carry out calculations with more than one step
using brackets and the memory; use the square root
and sign change keys. Check results by considering
whether they are of the right order of magnitude and
by working problems backwards.
9.6 Choose and use units of measurement to
measure, estimate, calculate and solve problems in
everyday contexts; convert one metric unit to
another, for example, grams to kilograms; read and
interpret scales on a range of measuring
instruments.
9.7 Identify the necessary information to understand
or simplify a context or problem; represent problems,
making correct use of symbols, words, diagrams,
tables and graphs; use appropriate procedures and
tools, including ICT. Interpret information from a
mathematical representation or context; relate
findings to the original context; explain and justify
methods and conclusions. Communicate own
findings effectively, orally and in writing.
10.1 Recognise and use multiples, factors and
primes (less than 100). Recognise the squares of
numbers to at least 12 × 12 and the corresponding
roots. Use positive and negative square roots for
small positive integer powers (Year 8 Framework
objective).
10.2 Recognise the first few triangular numbers.
10.3 Generate coordinate pairs that satisfy a simple
linear rule; plot the graphs of simple linear functions,
where y is given explicitly in terms of x. Recognise
that equations of the form y = mx + c correspond to
straight-line graphs (Year 8 Framework objective).
10.4 Generate coordinate pairs that satisfy a simple
linear rule; plot the graphs of simple linear functions,
where y is given explicitly in terms of x, on paper and
using ICT; recognise straight-line graphs parallel to
the x-axis or y-axis.
10.5 Identify the necessary information to
understand or simplify a context or problem;
represent problems, making correct use of symbols,
words, diagrams, tables and graphs; use appropriate
procedures and tools, including ICT.
Year 7 Mathematics – Scheme of Work (22-06-2010)
7
YEAR 7: SPRING TERM
MATHEMATICAL
TOPIC - Context
Geometry &
Measures 3
(3 hours)
►OVERVIEW – Teacher Pack 2
► FRAMEWORK OBJECTIVES – Teacher Pack 2
►OVERVIEW – Teacher Pack 3
► FRAMEWORK OBJECTIVES – Teacher Pack 3
11.1 Measuring and drawing
angles
11.2 Constructions
11.3 Solving geometrical
problems
11.1 Use a ruler and protractor to: measure and
draw lines to the nearest millimetre and angles,
including reflex angles, to the nearest degree.
11.2 Use a ruler and protractor to: measure and
draw lines to the nearest millimetre and 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. Make accurate mathematical diagrams
and constructions on paper and screen.
11.3 Identify and use angle, side and symmetry
properties of triangles and quadrilaterals. Explore
geometrical problems involving these properties,
using step-by-step deduction supported by
diagrams. Make accurate mathematical diagrams
and constructions on paper. Classify and visualize in
patterns.
11.1 Measuring and drawing
angles
11.2 Constructions
11.3 Solving geometrical
problems
Number 4
(4 hours)
12.1 Percentages
12.2 Ratio and proportion
12.3 Calculating ratios and
proportions
12.4 Solving problems
12.1 Recognise the equivalence of percentages,
fractions and decimals. Calculate simple
percentages and use percentages to compare
simple proportions.
12.2 Recognise the equivalence of percentages,
fractions and decimals. Calculate simple
percentages and use percentages to compare
simple proportions.
12.3 Understand the relationship between ratio and
proportion; use ratio notation, simplify ratios and
divide a quantity into two parts in a given ratio.
12.4 Solve simple problems about ratio and
proportion using informal strategies.
12.1 Percentages
12.2 Ratio and proportion
12.3 Calculating ratios and
proportions
12.4 Solving problems
11.1 Use a ruler and protractor to measure and draw
lines to the nearest millimetre and angles, including
reflex angles, to the nearest degree.
11.2 Within the appropriate range and content make
accurate mathematical constructions. Use a ruler
and protractor to construct a triangle, given two
sides and the included angle (SAS) or two angles
and the included side (ASA). Use ICT to explore
constructions. Use straight edge and compasses to
construct: the midpoint and perpendicular bisector of
a line segment; the bisector of an angle (Year 8
Framework objective).
11.3 Identify and use angle, side and symmetry
properties of triangles and quadrilaterals; explore
geometrical problems involving these properties,
explaining reasoning orally, using step-by-step
deduction supported by diagrams. Classify
quadrilaterals by their geometrical properties (Year 8
Framework objective).
12.1 Calculate simple percentages and use
percentages to compare simple proportions.
Recognise the equivalence of percentages, fractions
and decimals.
12.2 Understand the relationship between ratio and
proportion; use direct proportion in simple contexts;
use ratio notation.
12.3 Simplify ratios and divide a quantity into two
parts in a given ratio.
12.4 Solve simple problems involving ratio and
proportion using informal strategies.
26 Hours Teaching
Year 7 Mathematics – Scheme of Work (22-06-2010)
8
YEAR 7: SUMMER TERM
MATHEMATICAL
TOPIC - Context
Algebra 4
(3 hours)
►OVERVIEW – Teacher Pack 2
► FRAMEWORK OBJECTIVES – Teacher Pack 2
►OVERVIEW – Teacher Pack 3
► FRAMEWORK OBJECTIVES – Teacher Pack 3
13.1 Solving ‘brick wall’ problems
13.2 Solving square-and-circle
problems
13.3 Triangle-and-circle problems
13.1 Use letter symbols to represent unknown
numbers or variables. Simplify linear algebraic
expressions by collecting like terms. Construct and
solve linear equations with integer coefficients
(unknown on one side only) using an appropriate
method (for example, inverse operations).
13.2 Use letter symbols to represent unknown
numbers or variables. Construct and solve simple
linear equations with integer coefficients (unknown
on one side only) using an appropriate method (for
example, inverse operations).
13.3 Use letter symbols to represent unknown
numbers. Understand the significance of a counterexample.
13.1 Solving ‘brick wall’ problems
13.2 Square-and-circle problems
13.3 Triangle-and-circle problems
Geometry &
Measures 4
(5 hours)
14.1 Line symmetry
14.2 Rotational symmetry
14.3 Reflections
14.4 Rotations
14.5 Translations
14.1 Understand and use the language and notation
associated with reflections, translations and
rotations. Recognise and visualise the symmetries of
a 2-D shape.
14.2 Understand and use the language and notation
associated with rotations. Recognise and visualise
the symmetries of a 2-D shape. Transform 2-D
shapes by rotating about a given point.
14.3 Understand and use the language and notation
associated with reflections. Recognise and visualise
the symmetries of a 2-D shape. Transform 2-D
shapes by reflecting in given mirror lines. Explore
these transformations and symmetries using ICT.
14.4 Understand and use the language and notation
associated with rotations. Recognise and visualise
the transformation and symmetry of a 2-D shape.
Transform 2-D shapes by rotating about a given
point. Explore these transformations and symmetries
using ICT.
14.5 Understand and use the language and notation
associated with translations. Recognise and
visualise the transformation and symmetry of a 2-D
shape. Transform 2-D shapes by translating. Explore
the transformations and symmetries using ICT.
14.1 Line symmetry and
rotational symmetry
14.2 Reflections
14.3 Rotations
14.4 Translations
14.5 Enlargements
13.1 Use letter symbols to represent unknown
numbers or variables. Simplify linear algebraic
expressions by collecting like terms; multiply a single
term over a bracket (integer coefficients). Construct
and solve simple linear equations with integer
coefficients (unknown on one side only) using an
appropriate method (for example, inverse
operations).
13.2 Use letter symbols to represent unknown
numbers or variables. Construct and solve simple
linear equations with integer coefficients (unknown
on one side only) using an appropriate method (for
example, inverse operations).
13.3 Use letter symbols to represent unknown
numbers or variables. Understand the significance of
a counter-example.
14.1 Understand and use the language and notation
associated with reflections and rotations. Recognise
and visualise the symmetries of a 2-D shape.
14.2 Understand and use the language and notation
associated with reflections. Recognise and visualise
the symmetries of a 2-D shape. Transform 2-D
shapes by reflecting in given mirror lines. Explore
these transformations and symmetries using ICT.
14.3 Understand and use the language and notation
associated with rotations. Recognise and visualise
the symmetries of a 2-D shape. Transform 2-D
shapes by rotating about a given point. Explore
these transformations and symmetries using ICT.
14.4 Understand and use the language and notation
associated with translations. Recognise and
visualise the symmetries of a 2-D shape. Transform
2-D shapes by translating. Explore these
transformations and symmetries using ICT. Try out
mathematical representations of simple
combinations of rotation, reflection and translation
(Year 8 Framework objective).
14.5 Understand and use the language and notation
associated with enlargement; enlarge 2-D shapes,
given a centre of enlargement and a positive integer
scale factor (Year 8 Framework objective).
Year 7 Mathematics – Scheme of Work (22-06-2010)
9
YEAR 7: SUMMER TERM
MATHEMATICAL
TOPIC - Context
Statistics 3
(5 hours)
►OVERVIEW – Teacher Pack 2
► FRAMEWORK OBJECTIVES – Teacher Pack 2
►OVERVIEW – Teacher Pack 3
► FRAMEWORK OBJECTIVES – Teacher Pack 3
15.1 Pie charts
15.2 Comparing data
15.3 and 15.4 Statistical surveys
15.5 Probabilities from two way
tables
15.1 Construct, on paper and using ICT, graphs and
diagrams to represent data, including simple pie
charts. Use ICT to generate pie charts. Interpret
diagrams and graphs (including pie charts).
15.2 Compare two simple distributions using the
range and one of the modes, median or mean.
Interpret information from a mathematical
representation or context; relate findings to the
original context; check the accuracy of the solution;
explain and justify methods and conclusions;
compare and evaluate approaches.
15.3 & 15.4 Decide which data would be relevant to
an enquiry and possible sources. Plan how to
collect and organise small sets of data from surveys
and experiments. Design data collection sheets or
questionnaires to use in a simple survey. Write a
short report of a statistical enquiry and illustrate with
appropriate diagrams, graphs and charts, using ICT
as appropriate; justify the choice of presentation.
15.5 Understand and use the probability scale from
0 to1; find and justify probabilities based on equally
likely outcomes in simple contexts; identify all the
possible mutually exclusive outcomes of a single
event.
15.1 Pie charts
15.2 Comparing data
15.3 and 15.4 Statistical surveys
15.5 Comparing experimental
and theoretical probabilities
15.1 Construct, on paper and using ICT, graphs and
diagrams to represent data, including simple pie
charts. Interpret diagrams and graphs (including pie
charts). Compare two simple distributions using the
range and one of the mode, median or mean.
Recognise when it is appropriate to use the range,
mean, median and mode (Year 8 Framework
objective).
15.3 & 15.4 Within the appropriate range and
content make accurate mathematical diagrams,
graphs and constructions on paper and on screen.
Decide which data would be relevant to an enquiry
and possible sources. Plan how to collect and
organise small sets of data from surveys and
experiments: design data collection sheets or
questionnaires to use in a simple survey. Write a
short report of a statistical enquiry, including
appropriate diagrams, graphs and charts, using ICT
as appropriate; justify the choice of presentation.
15.5 Understand and use the probability scale from
0 to 1; find and justify probabilities based on equally
likely outcomes in simple contexts; identify all the
possible mutually exclusive outcomes of a single
event. Estimate probabilities by collecting data from
a simple experiment and recording it in a frequency
table; compare experimental and theoretical
probabilities in simple contexts. Compare estimated
experimental probabilities with theoretical
probabilities, recognising that: if an experiment is
repeated the outcome may, and usually will, be
different; increasing the number of times an
experiment is repeated generally leads to better
estimates of probability (Year 8 Framework
objective).
Year 7 Mathematics – Scheme of Work (22-06-2010)
10
YEAR 7: SUMMER TERM
MATHEMATICAL
TOPIC - Context
Number 5
(6 hours)
►OVERVIEW – Teacher Pack 2
► FRAMEWORK OBJECTIVES – Teacher Pack 2
►OVERVIEW – Teacher Pack 3
► FRAMEWORK OBJECTIVES – Teacher Pack 3
16.1 Adding and subtracting
decimals
16.2 Multiplying and dividing
decimals
16.3 Using a calculator
16.4 Fractions of quantities
16.5 Percentages of quantities
16.6 Solving problems
16.1 Use efficient written methods to add and
subtract whole numbers and decimals with up to two
places.
16.2 Multiply and divide three-digit by two-digit whole
numbers; extend to multiplying and dividing decimals
with one or two places by single-digit whole
numbers.
16.3 Carry out calculations with more than one step
using brackets and the memory; use the square root
and sign change keys.
16.4 Calculate simple fractions of quantities and
measurements (whole-number answers); multiply a
fraction by an integer.
16.5 Calculate simple percentages and use
percentages to compare simple proportions.
Recognise the equivalence of percentages, fractions
and decimals.
16.6 Draw simple conclusions and explain
reasoning. Communicate own findings effectively,
orally and in writing.
16.1 Multiplying decimals
16.2 Dividing decimals
16.3 Using a calculator
16.4 Fractions of quantities
16.5 Percentages of quantities
16.6 Solving problems
Algebra 5
(4 hours)
17.1 Solving equations
17.2 Formulae
17.3 Dotty investigations
17.4 Graphs from the real world
17.1 Construct and solve simple linear equations
with integer coefficients (unknown on one side only)
using an appropriate method (for example, inverse
operations).
17.2 Use simple formulae from mathematics and
other subjects; substitute positive integers into linear
expressions and formulae and, in simple cases,
derive a formula.
17.3 Generate sequences from patterns or practical
contexts and describe the general term in simple
cases.
17.4 Generate coordinate pairs that satisfy a simple
linear rule; plot the graphs of simple linear functions,
where y is given explicitly in terms of x.
17.1 Solving equations
17.2 Formulae
17.3 Dotty investigations
17.4 Graphs from the real world
17.5 Other types of problem
16.1 Multiply three-digit by two-digit whole numbers;
extend to multiplying decimals with one or two
places by single-digit whole numbers. Understand
where to position the decimal point by considering
equivalent calculations (Year 8 Framework
objective).
16.2 Divide three-digit by two-digit whole numbers;
extend to dividing decimals with one or two places
by single-digit whole numbers. Understand where to
position the decimal point by considering equivalent
calculations (Year 8 Framework objective).
16.3 Carry out calculations with more than one step
using brackets and the memory; use the square root
and sign change keys.
16.4 Calculate simple fractions of quantities and
measurements (whole number answers); multiply a
fraction by an integer.
16.5 Calculate simple percentages and use
percentages to compare simple proportions.
Recognise the equivalence of percentages, fractions
and decimals.
16.6 Identify the necessary information to
understand or simplify a context or problem;
represent problems, making correct use of symbols,
words, diagrams, tables and graphs; use appropriate
procedures and tools, including ICT. Enter numbers
and interpret display in different contexts
(documents, percentages, money, metric measures).
17.1 Construct and solve simple linear equations
with integer coefficients (unknown on one side only)
using an appropriate method (for example,
inverse operations).
17.2 Use simple formulae from mathematics and
other subjects; substitute positive integers into linear
expressions and formulae and, in simple cases,
derive a formula.
17.3 Generate sequences from patterns or practical
contexts and describe the general term in simple
cases.
17.4 Generate coordinate pairs that satisfy a simple
linear rule. Plot and interpret the graphs of simple
linear functions arising from real-life situations, for
example, conversion graphs.
17.5 Use letter symbols to represent unknown
numbers or variables. Simplify linear algebraic
expressions by collecting like terms. Construct and
solve simple linear equations with integer
coefficients (unknown on one side only) using an
appropriate method (for example, inverse
operations).
Year 7 Mathematics – Scheme of Work (22-06-2010)
11
YEAR 7: SUMMER TERM
MATHEMATICAL
TOPIC - Context
Geometry &
Measures 5
(3 hours)
►OVERVIEW – Teacher Pack 2
► FRAMEWORK OBJECTIVES – Teacher Pack 2
►OVERVIEW – Teacher Pack 3
► FRAMEWORK OBJECTIVES – Teacher Pack 3
18.1 Polygons
18.2 and 18.3 Tessellations
18.4 and 18.5 Constructing 3-D
shapes
18.1 Identify and use angle, side and symmetry
properties of triangles and quadrilaterals; explore
geometrical problems involving these properties,
explaining reasoning orally, using step-by-step
deduction supported by diagrams. Explore these
transformations and symmetries using ICT.
18.2 and 18.3 Identify and use angle, side and
symmetry properties of triangles and quadrilaterals;
explore geometrical problems involving these
properties explaining reasoning orally, using step-bystep deduction supported by diagrams.
18.4 and 18.5 Make accurate mathematical
diagrams and constructions on paper. Use a ruler
and protractor to construct simple nets of 3-D
shapes; for example, cuboid, regular tetrahedron,
square-based pyramid, triangular prism.
18.1 Polygons
18.2 and 18.3 Tessellations
18.4 and 18.5 Constructing 3-D
shapes
18.1 Identify and use angle, side and symmetry
properties of triangles and quadrilaterals; explore
geometrical problems involving these properties,
explaining reasoning orally, using step-by-step
deduction supported by diagrams. Explore these
transformations and symmetries using ICT.
18.2 and 18.3 Identify and use angle, side and
symmetry properties of triangles and quadrilaterals;
explore geometrical problems involving these
properties, explaining reasoning orally, using stepby-step deduction supported by diagrams.
18.4 and 18.5 Use ruler and protractor to construct
simple nets of 3-D shapes, for example, cuboid,
regular tetrahedron, square-based pyramid,
triangular prism.
26 Hours Teaching
Year 7 Mathematics – Scheme of Work (22-06-2010)
12