Download Year 8 - Portland Place School

Mathematics
Scheme of Work
Year 8
New Mathematics Framework
Year 8 Mathematics – Scheme of Work (22-06-2010)
1
YEAR 8: Overview of year 8 scheme of work
YEAR 8
Term 1
Term 2
Term 3
Number & Algebra 1
Integers, powers and roots; sequences,
functions and graphs (8 hours)
Statistics 1
Probability (6 hours)
Geometry and Measures 2
Measures and mensuration (5 hours)
Geometry and Measures 3
Transformations, Geometrical
reasoning: lines, angles and shapes (5
hours)
Number 4
Geometry and Measures 1
Geometrical reasoning: lines, angles and
shapes; constructions (5 hours)
Number 2
Fractions, decimals, percentages, ratio and
proportion (6 hours)
Algebra 3
Integers, powers and roots; sequences,
functions and graphs (6 hours)
Algebra 4
Calculations, measures (6 hours)
Geometry and Measures 4
Equations and formulae, graphs (6 hours)
Algebra 5
Sequences, functions and graphs,
equations and graphs (7 hours)
Statistics 3
Geometrical reasoning: lines, angles
and shapes; transformations,
mensuration (9 hours)
Statistics, including probability (7 hours)
Year 8 Mathematics – Scheme of Work (22-06-2010)
2
Assessment
Tests
Test 1
Algebra 2
Test 2
Equations and formulae (6 hours)
Number 3
Test 3
Place value, calculations, calculator
methods, fractions, decimals, percentages,
ratio and proportion, solving problems (7
hours)
Statistics 2
Test 4
Statistics (6 hours)
Solving problems
Including fractions, decimals, percentages,
ratio and proportion (5 hours)
Test 5
End of year test
YEAR 8: AUTUMN TERM
MATHEMATICAL
TOPIC - Context
Algebra 1
(8 hours)
►OVERVIEW – Teacher Pack 2
► FRAMEWORK OBJECTIVES – Teacher Pack 2
►OVERVIEW – Teacher Pack 3
► FRAMEWORK OBJECTIVES – Teacher Pack 3
1.1 Multiplying and dividing
negative numbers
1.2 HCF and LCM
1.3 Powers and roots
1.4 Prime factors
1.5 Sequences 1
1.6 Sequences 2
1.7 Solving problems
FM Blackpool Tower
1.1 Multiplying and dividing
negative numbers
1.2 HCF and LCM
1.3 Powers and roots
1.4 Prime factors
1.5 Sequences 1
1.6 Sequences 2
1.7 Solving problems
FM Blackpool Tower
Geometry &
Measures 1
(5 hours)
2.1 Alternate and corresponding
angles
2.2 Angles in triangles and
quadrilaterals
2.3 Geometric proof
2.4 The geometric properties of
quadrilaterals
2.5 Constructions
1.1 Add, subtract, multiply and divide integers.
1.2 Use multiples, factors, common factors, highest
common factors, lowest common multiples and
primes.
1.3 Use squares, positive and negative square roots,
cubes and cube roots, and index notation for small
positive integer powers.
1.4 Find the prime factor decomposition of a
number, for example, 8000 = 26 × 53.
1.5 Generate terms of a linear sequence using termto-term and position-to-term rules.
1.6 Use linear expressions to describe the nth term
of a simple arithmetic sequence, justifying its form by
referring to the activity or practical context from
which it was generated.
1.7 Identify the mathematical features of a context or
problem; try out and compare mathematical
representations; select appropriate procedures and
tools, including ICT.
FM Identify the mathematical features of a context or
problem; try out and compare mathematical
representations; select appropriate procedures and
tools, including ICT.
2.1 Identify alternate angles and corresponding
angles.
2.2 Understand 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.
2.3 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.
2.4 Solve geometrical problems using side and
angle properties of special quadrilaterals, explaining
reasoning with diagrams and text; classify
quadrilaterals by their geometrical properties.
2.5 Use a 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.
1.1 Multiply and divide integers.
1.2 Use multiples, factors, common factors, highest
common factors, lowest common multiples and
primes.
1.3 Use squares, positive and negative square roots,
cubes and cube roots, and index notation for small
positive integer powers.
1.4 Find the prime factor decomposition of a
number, for example, 8000 = 26 × 53.
1.5 Generate terms of a linear sequence using termto-term and position-to-term rules.
1.6 Use linear expressions to describe the nth term
of a simple arithmetic sequence, justifying its form by
referring to the activity or practical context from
which it was generated.
1.7 Identify the mathematical features of a context or
problem; try out and compare mathematical
representations; select appropriate procedures and
tools, including ICT.
FM Identify the mathematical features of a context or
problem; try out and compare mathematical
representations; select appropriate procedures and
tools, including ICT.
2.1 Identify alternate angles and corresponding
angles.
2.2 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 (Year 9 Framework
Objective).
2.3 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.
2.4 Solve geometrical problems using side and
angle properties of special quadrilaterals, explaining
reasoning with diagrams and text; classify
quadrilaterals by their geometrical properties.
2.5 Use a 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. Use ICT to explore these constructions.
Use straight edge and compasses to construct
triangles, given right angle, hypotenuse and side
(RHS) (Year 9 Framework Objective).
Year 8 Mathematics – Scheme of Work (22-06-2010)
3
2.1 Alternate and corresponding
angles
2.2 Interior and exterior angles of
polygons
2.3 Geometric proof
2.4 The geometric properties of
quadrilaterals
2.5 Constructions
YEAR 8: AUTUMN TERM
MATHEMATICAL
TOPIC - Context
Statistics 1
(6 hours)
►OVERVIEW – Teacher Pack 2
► FRAMEWORK OBJECTIVES – Teacher Pack 2
►OVERVIEW – Teacher Pack 3
► FRAMEWORK OBJECTIVES – Teacher Pack 3
3.1 Probability
3.2 Probability scales
3.3 Mutually exclusive events
3.4 Calculating probabilities
3.5 Experimental probability
FM Fun in the fairground
3.1 Interpret the results of an experiment using the
language of probability; appreciate that random
processes are unpredictable.
3.2 Know that if the probability of an event occurring
is p, then the probability of it not occurring is 1 – p.
3.3 Use diagrams and tables to record in a
systematic way all possible mutually exclusive
outcomes for single events and for two successive
events.
3.4 Use diagrams and tables to record in a
systematic way all possible mutually exclusive
outcomes for single events and for two successive
events.
3.5 Collect data using a suitable method (for
example, observation, controlled experiment, and
data logging using ICT). 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.
FM Interpret the results of an experiment using the
language of probability. 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.
3.1 Probability
3.2 Probability scales
3.3 Mutually exclusive events
3.4 Calculating probabilities
3.5 Experimental probability
FM Fun in the fairground
3.1 Interpret the results of an experiment using the
language of probability; appreciate that random
processes are unpredictable.
3.2 Know that if the probability of an event occurring
is p, then the probability of it not occurring is 1 – p.
3.3 Use diagrams and tables to record in a
systematic way all possible mutually exclusive
outcomes for single events and for two successive
events.
3.4 Use diagrams and tables to record in a
systematic way all possible mutually exclusive
outcomes for single events and for two successive
events.
3.5 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.
FM Interpret the results of an experiment using the
language of probability. 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 Mathematics – Scheme of Work (22-06-2010)
4
YEAR 8: AUTUMN TERM
MATHEMATICAL
TOPIC - Context
Number 2
(6 hours)
►OVERVIEW – Teacher Pack 2
► FRAMEWORK OBJECTIVES – Teacher Pack 2
►OVERVIEW – Teacher Pack 3
► FRAMEWORK OBJECTIVES – Teacher Pack 3
4.1 Fractions and decimals
4.2 Adding and subtracting
fractions
4.3 Multiplying and dividing
fractions
4.4 Percentages
4.5 Percentage increase and
decrease
4.6 Real-life problems
FM Going on holiday
4.1 Refine own findings and approaches on the
basis of discussions with others; recognise efficiency
in an approach; relate the current problem and
structure to previous situations. Order decimals.
Recognise that a recurring decimal is a fraction; use
division to convert a fraction to a decimal; order
fractions by writing them with a common
denominator or by converting them to decimals.
4.2 Add and subtract fractions by writing them with a
common denominator; calculate fractions of
quantities (fraction answers).
4.3 Multiply and divide an integer by a fraction.
4.4 Interpret percentage as the operator ‘so many
hundredths of’ and express one given number as a
percentage of another.
4.5 Calculate percentages and find the outcome of a
given percentage increase or decrease. Use the
equivalence of fractions, decimals and percentages
to compare proportions.
4.6 Recall equivalent fractions, decimals and
percentages; use known facts to derive unknown
facts, including products involving numbers such as
0.7 and 6, and 0.03 and 8.
FM Identify the mathematical features of a context or
problem. Calculate percentages and find the
outcome of a given percentage increase or
decrease. Carry out more difficult calculations
effectively and efficiently. Know rough metric
equivalents of imperial measures in common use.
Interpret tables and diagrams.
4.1 Fractions and decimals
4.2 Adding and subtracting
fractions
4.3 Multiplying and dividing
fractions
4.4 Percentages
4.5 Percentage increase and
decrease
4.6 Real-life problems
FM Going on holiday
Algebra 2
(6 hours)
5.1 Algebraic shorthand
5.2 Like terms
5.3 Expanding brackets
5.4 Using algebra with shapes
5.5 Use of index notation with
algebra
5.1 Recognise that letter symbols play different roles
in equations, formulae and functions.
5.2 Simplify or transform linear expressions by
collecting like terms.
5.3 Understand that algebraic operations, including
the use of brackets, follow the rules of arithmetic.
Multiply a single term over a bracket.
5.4 Understand that algebraic operations, including
the use of brackets, follow the rules of arithmetic.
Multiply a single term over a bracket.
5.5 Understand that algebraic operations, including
the use of brackets, follow the rules of arithmetic;
use index notation for small positive integer powers.
5.1 Algebraic shorthand
5.2 Like terms
5.3 Expanding brackets and
factorising
5.4 Using algebra with shapes
5.5 Index notation with algebra
4.1 Recognise that a recurring decimal is a fraction;
use division to convert a fraction to a decimal; order
fractions by writing them with a common
denominator or by converting them to decimals.
Order decimals.
4.2 Add and subtract fractions by writing them with a
common denominator.
4.3 Calculate fractions of quantities (fraction
answers); multiply and divide an integer by a
fraction.
4.4 Interpret percentage as the operator 'so many
hundredths of' and express one given number as a
percentage of another.
4.5 Calculate percentages and find the outcome of a
given percentage increase or decrease. Use the
equivalence of fractions, decimals and percentages
to compare proportions.
4.6 Refine own findings and approaches on the
basis of discussions with others; recognise efficiency
in an approach; relate the current problem and
structure to previous situations. Recall equivalent
fractions, decimals and percentages; use known
facts to derive unknown facts, including products
involving numbers such as 0.7 and 6, and 0.03 and
8.
FM Interpret tables and diagrams. Identify the
mathematical features of a context or problem. Know
rough metric equivalents of imperial measures in
common use. Carry out calculations effectively and
efficiently when using a calculator. Calculate
percentages and find the outcome of a given
percentage increase or decrease.
5.1 Recognise that letter symbols play different roles
in equations, formulae and functions.
5.2 Simplify or transform linear expressions by
collecting like terms.
5.3 Understand that algebraic operations, including
the use of brackets, follow the rules of arithmetic.
Multiply a single term over a bracket.
5.4 Multiply a single term over a bracket.
5.5 Understand that algebraic operations, including
the use of brackets, follow the rules of arithmetic;
use index notation for small positive integer powers.
31 Hours Teaching
Year 8 Mathematics – Scheme of Work (22-06-2010)
5
YEAR 8: SPRING TERM
MATHEMATICAL
TOPIC - Context
Geometry &
Measures 2
(5 hours)
►OVERVIEW – Teacher Pack 2
► FRAMEWORK OBJECTIVES – Teacher Pack 2
►OVERVIEW – Teacher Pack 3
► FRAMEWORK OBJECTIVES – Teacher Pack 3
6.1 Area of a triangle
6.2 Area of a parallelogram
6.3 Area of a trapezium
6.4 Volume of a cuboid
6.5 Imperial units
6.1 The circle
6.2 Circumference of a circle
6.3 Area of a circle
6.4 Surface area and volume of
prisms
6.5 Imperial units
6.1 Make accurate mathematical diagrams, graphs
and constructions. Know the definition of a circle and
the names of its parts (Year 9 Framework
Objective).
6.2 Know and use the formula for the circumference
of a circle (Year 9 Framework Objective).
6.3 Know and use the formula for the area of a circle
(Year 9 Framework Objective).
6.4 Choose and use units of measurement to
measure, estimate, calculate and solve problems in
a range of contexts. Convert between area
measures (for example, mm2 to cm2, cm2 to m2,
and vice versa) and between volume measures (for
example, mm3 to cm3, cm3 to m3, and vice versa)
(Year 9 Framework Objective). Calculate the surface
area and volume of right prisms (Year 9 Framework
Objective).
6.5 Choose and use units of measurement to
measure, estimate, calculate and solve problems in
a range of contexts; know rough metric equivalents
of imperial measures in common use, such as miles,
pounds (lb) and pints.
Algebra 3
(6 hours)
7.1 Linear functions
7.2 Finding a function from its
inputs and outputs
7.3 Graphs from functions
7.4 Gradient of a straight line
(steepness)
7.5 Real-life graphs
FM M25
6.1 Choose and use units of measurement to
measure, estimate, calculate and solve problems in
a range of contexts. Derive and use formulae for the
area of a triangle; calculate areas of compound
shapes.
6.2 Choose and use units of measurement to
measure, estimate, calculate and solve problems in
a range of contexts. Derive and use formulae for the
area of a parallelogram.
6.3 Choose and use units of measurement to
measure, estimate, calculate and solve problems in
a range of contexts. Derive and use formulae for the
area of a trapezium; calculate areas of compound
shapes.
6.4 Choose and use units of measurement to
measure, estimate, calculate and solve problems in
a range of contexts. Know and use the formula for
the volume of a cuboid; calculate volumes and
surface areas of cuboids and shapes made from
cuboids.
6.5 Choose and use units of measurement to
measure, estimate, calculate and solve problems in
a range of contexts; know rough metric equivalents
of imperial measures in common use, such as miles,
pounds (lb) and pints.
7.1 Express simple functions algebraically and
represent them in mappings or on a spreadsheet.
7.2 Express simple functions algebraically and
represent them in mappings or on a spreadsheet.
7.3 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.
7.4 Recognise that equations of the form y = mx + c
correspond to straight-line graphs.
7.5 Construct linear functions arising from real-life
problems and plot their corresponding graphs;
discuss and interpret graphs arising from real
situations, for example, distance–time graphs.
FM Identify the mathematical features of a context or
problem; try out and compare mathematical
representations; select appropriate procedures and
tools, including ICT. Use logical argument to
interpret the mathematics in a given context or to
establish the truth of a statement; give accurate
solutions appropriate to the context or problem;
evaluate the efficiency of alternative strategies and
approaches.
7.1 Linear functions
7.2 Finding a function from inputs
and outputs
7.3 Graphs from functions
7.4 Gradient of a straight line
7.5 Real-life graphs
FM M25
7.1 Express simple functions algebraically and
represent them in mappings or on a spreadsheet.
7.2 Express simple functions algebraically and
represent them in mappings or on a spreadsheet.
7.3 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.
7.4 Recognise that equations of the form y = mx + c
correspond to straight-line graphs.
7.5 Construct linear functions arising from real-life
problems and plot their corresponding graphs;
discuss and interpret graphs arising from real
situations, for example, distance–time graphs.
FM Identify the mathematical features of a context or
problem; try out and compare mathematical
representations; select appropriate procedures and
tools, including ICT. Use logical argument to
interpret the mathematics in a given context or to
establish the truth of a statement; give accurate
solutions appropriate to the context or problem;
evaluate the efficiency of alternative strategies and
approaches.
Year 8 Mathematics – Scheme of Work (22-06-2010)
6
YEAR 8: SPRING TERM
MATHEMATICAL
TOPIC - Context
Number 3
(7 hours)
►OVERVIEW – Teacher Pack 2
► FRAMEWORK OBJECTIVES – Teacher Pack 2
►OVERVIEW – Teacher Pack 3
► FRAMEWORK OBJECTIVES – Teacher Pack 3
8.1 Powers of 10
8.2 Large numbers
8.3 Estimations
8.4 Adding and subtracting
decimals
8.5 Efficient calculations
8.6 Multiplying and dividing
decimals
FM Taxes
8.1 Read and write positive integer powers of 10,
multiply and divide integers and decimals by 0.1,
0.01. Round decimals to the nearest whole number
or to one or two decimal places. Strengthen and
extend mental methods of calculation, working with
decimals, fractions, percentages, squares and
square roots, and cubes and cube roots; solve
problems mentally.
8.2 Round positive numbers to any given power of
10; round decimals to the nearest whole number or
to one or two decimal places.
8.3 Make and justify estimates and approximations
of calculations. Select from a range of checking
methods, including estimating in context and using
inverse operations.
8.4 Use efficient written methods to add and subtract
integers and decimals of any size, including
numbers with differing numbers of decimal places.
8.5 Carry out more difficult calculations effectively
and efficiently using the function keys for sign
change, powers, roots and fractions; use brackets
and the memory.
8.6 Use efficient written methods 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.
FM Interpret percentage as the operator ‘so many
hundredths of’ and express one given number as a
percentage of another; calculate percentages and
find the outcome of a given percentage increase or
decrease.
8.1 Powers of 10
8.2 Large numbers
8.3 Estimations
8.4 Working with decimals
8.5 Efficient calculations
8.6 Multiplying and dividing
decimals
FM Taxes
8.1 Read and write positive integer powers of 10,
multiply and divide integers and decimals by 0.1,
0.01. Round decimals to the nearest whole number
or to one or two decimal places. Strengthen and
extend mental methods of calculation, working with
decimals, fractions, percentages, squares and
square roots, and cubes and cube roots; solve
problems mentally.
8.2 Round positive numbers to any given power of
10.
8.3 Make and justify estimates and approximations
of calculations. Select from a range of checking
methods, including estimating in context and using
inverse operations.
8.4 Round decimals to the nearest whole number or
to one or two decimal places. Use efficient written
methods to add and subtract integers and decimals
of any size, including numbers with differing
numbers of decimal places. Use formulae for the
area of a triangle, parallelogram and trapezium;
calculate areas of compound shapes.
8.5 Carry out more difficult calculations effectively
and efficiently using the function keys for sign
change, powers, roots and fractions; use brackets
and the memory. Enter numbers and interpret the
display in different contexts (extend to negative
numbers, fractions, time).
8.6 Use efficient written methods 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.
FM Interpret percentage as the operator ‘so many
hundredths of’ and express one given number as a
percentage of another; calculate percentages and
find the outcome of a given percentage increase or
decrease.
Year 8 Mathematics – Scheme of Work (22-06-2010)
7
YEAR 8: SPRING TERM
MATHEMATICAL
TOPIC - Context
Geometry &
Measures 3
(5 hours)
►OVERVIEW – Teacher Pack 2
► FRAMEWORK OBJECTIVES – Teacher Pack 2
►OVERVIEW – Teacher Pack 3
► FRAMEWORK OBJECTIVES – Teacher Pack 3
9.1 Congruent shapes
9.2 Combinations of
transformations
9.3 & 9.4 Enlargements
9.5 Shape and ratio
9.1 Know that if two 2-D shapes are congruent,
corresponding sides and angles are equal. Identify
all the symmetries of 2-D shapes.
9.2 Transform 2-D shapes by rotation, reflection and
translation, on paper and using ICT. Try out
mathematical representations of simple
combinations of these transformations.
9.3 & 9.4 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; explore enlargement
using ICT.
9.5 Apply understanding of the relationship between
ratio and proportion; simplify ratios, including those
expressed in different units, recognising links with
fraction notation.
9.1 Congruent shapes
9.2 Combinations of
transformations
9.3 Enlargements
9.4 Planes of symmetry
9.5 Shape and ratio
9.1 Know that if two 2-D shapes are congruent,
corresponding sides and angles are equal. Identify
all the symmetries of 2-D shapes.
9.2 Transform 2-D shapes by rotation, reflection and
translation, on paper and using ICT. Try out
mathematical representations of simple
combinations of these transformations.
9.3 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; explore enlargement using ICT.
9.4 Identify reflection symmetry in 3-D shapes (Year
9 Framework Objective).
9.5 Apply understanding of the relationship between
ratio and proportion; simplify ratios, including those
expressed in different units, recognising links with
fraction notation.
Algebra 4
(6 hours)
10.1 Solving equations
10.2 Equations involving negative
numbers
10.3 Equations with unknowns on
both sides
10.4 Substituting into expressions
10.5 Substituting into formulae
10.6 Creating your own
expressions and formulae
10.1 Construct and solve linear equations with
integer coefficients (unknown on either or both sides,
without and with brackets) using appropriate
methods (for example, inverse operations,
transforming both sides in same way).
10.2 Construct and solve linear equations with
integer coefficients (unknown on either or both sides,
without and with brackets) using appropriate
methods (for example, inverse operations,
transforming both sides in same way).
10.3 Construct and solve linear equations with
integer coefficients (unknown on either or both sides,
without and with brackets) using appropriate
methods (for example, inverse operations,
transforming both sides in same way).
10.4 Substitute integers into simple formulae,
including examples that lead to an equation to solve;
substitute positive integers into expressions
involving small powers, for example, 3x2 + 4 or 2x3.
10.5 Substitute integers into simple formulae,
including examples that lead to an equation to solve;
substitute positive integers into expressions
involving small powers, for example, 3x2 + 4 or 2x3.
10.6 Derive simple formulae.
10.1 Solving equations
10.2 Equations involving negative
numbers
10.3 Equations with unknowns on
both sides
10.4 Substituting into expressions
10.5 Substituting into formulae
10.6 Creating your own
expressions and formulae
10.1 Construct and solve linear equations with
integer coefficients (unknown on either or both sides,
without and with brackets) using appropriate
methods (for example, inverse operations,
transforming both sides in same way).
10.2 Construct and solve linear equations with
integer coefficients (unknown on either or both sides,
without and with brackets) using appropriate
methods (for example, inverse operations,
transforming both sides in same way).
10.3 Construct and solve linear equations with
integer coefficients (unknown on either or both sides,
without and with brackets) using appropriate
methods (for example, inverse operations,
transforming both sides in same way).
10.4 Substitute positive integers into expressions
involving small powers, for example, 3x2 + 4 or 2x3.
10.5 Substitute integers into simple formulae,
including examples that lead to an equation to solve.
10.6 Derive simple formulae.
Year 8 Mathematics – Scheme of Work (22-06-2010)
8
YEAR 8: SPRING TERM
MATHEMATICAL
TOPIC - Context
Statistics 2
(6 hours)
►OVERVIEW – Teacher Pack 2
► FRAMEWORK OBJECTIVES – Teacher Pack 2
►OVERVIEW – Teacher Pack 3
► FRAMEWORK OBJECTIVES – Teacher Pack 3
11.1 Stem-and-leaf diagrams
11.2 Pie charts
11.3 More about pie charts
11.4 Scatter graphs
11.5 More about scatter graphs
FM Football attendances
11.1 Calculate statistics for sets of discrete and
continuous data, including with a calculator;
recognise when it is appropriate to use the range,
mean, median and mode. Construct graphical
representations, on paper and using ICT, and
identify which are most useful in the context of the
problem. Include stem-and-leaf diagrams.
11.2 Interpret tables, graphs and diagrams for
discrete and continuous data, relating summary
statistics and findings to the questions being
explored.
11.3 Construct graphical representations, on paper
and using ICT, and identify which are most useful in
the context of the problem. Include: pie charts for
categorical data; bar charts and frequency; diagrams
for discrete and continuous data; simple scatter
graphs.
11.4 Construct graphical representations, on paper
and using ICT, and identify which are most useful in
the context of the problem. Include: pie charts for
categorical data; bar charts and frequency; diagrams
for discrete and continuous data; simple scatter
graphs. Interpret tables, graphs and diagrams for
discrete data, relating summary statistics and
findings to the questions being explored.
11.5 Construct graphical representations, on paper
and using ICT, and identify which are most useful in
the context of the problem. Include: pie charts for
categorical data; bar charts and frequency; diagrams
for discrete and continuous data; simple scatter
graphs. Interpret tables, graphs and diagrams for
discrete data, relating summary statistics and
findings to the questions being explored.
FM Calculate statistics for sets of discrete and
continuous data, including with a calculator and
spreadsheet; recognise when it is appropriate to use
the range, mean, median and mode and, for
grouped data, the modal class.
11.1 Statistical surveys
11.2 Stem-and-leaf diagrams
11.3 Interpreting graphs and
diagrams
11.4 Scatter graphs
11.5 Analysing data
FM Football attendances
11.1 Discuss a problem that can be addressed by
statistical methods and identify related questions to
explore. Decide which data to collect to answer a
question, and the degree of accuracy needed;
identify possible sources; consider appropriate
sample size. Plan how to collect the data; construct
frequency tables with equal class intervals for
gathering continuous data and two-way tables for
recording discrete data. Collect data using a suitable
method (for example, observation, controlled
experiment and data logging using ICT).
11.2 Calculate statistics for sets of discrete and
continuous data, including with a calculator and
spreadsheet; recognise when it is appropriate to use
the range, mean, median and mode and, for
grouped data, the modal class. Construct graphical
representations, on paper and using ICT, and
identify which are most useful in the context of the
problem. Include stem-and-leaf diagrams.
11.3 Interpret tables, graphs and diagrams for
discrete and continuous data, relating summary
statistics and findings to the questions being
explored. Discuss how different sets of data relate to
the problem; identify possible primary or secondary
sources; determine the sample size and most
appropriate degree of accuracy (Year 9 Framework
Objective). Gather data from specified secondary
sources, including printed tables and lists, and ICTbased sources, including the internet (Year 9
Framework Objective).
11.4 Construct graphical representations, on paper
and using ICT, and identify which are most useful in
the context of the problem. Include: pie charts for
categorical data; bar charts and frequency; diagrams
for discrete and continuous data; simple scatter
graphs. Interpret tables, graphs and diagrams for
discrete data, relating summary statistics and
findings to the questions being explored.
11.5 Write about and discuss the results of a
statistical enquiry using ICT as appropriate; justify
the methods used.
FM Calculate statistics for sets of discrete and
continuous data, including with a calculator and
spreadsheet; recognise when it is appropriate to use
the range, mean, median and mode and, for
grouped data, the modal class.
35 Hours Teaching
Year 8 Mathematics – Scheme of Work (22-06-2010)
9
YEAR 8: SUMMER TERM
MATHEMATICAL
TOPIC - Context
Number 4
(6 hours)
►OVERVIEW – Teacher Pack 2
► FRAMEWORK OBJECTIVES – Teacher Pack 2
►OVERVIEW – Teacher Pack 3
► FRAMEWORK OBJECTIVES – Teacher Pack 3
12.1 Fractions
12.2 Adding and subtracting
fractions
12.3 Order of operations
12.4 Multiplying decimals
12.5 Dividing decimals
FM Shopping for bargains
12.1 Use the equivalence of fractions, decimals and
percentages to compare proportions.
12.2 Add and subtract fractions by writing them with
a common denominator. Understand and use the
rules of arithmetic and inverse operations in the
context of integers and fractions.
12.3 Use the order of operations, including brackets,
with more complex calculations.
12.4 Use efficient written methods for multiplication
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.
12.5 Use efficient written methods for 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.
FM Use logical argument to interpret the
mathematics in a given context or to establish the
truth of a statement; give accurate solutions
appropriate to the context or problem; evaluate the
efficiency of alternative strategies and approaches.
12.1 Fractions
12.2 Adding and subtracting
fractions
12.3 Order of operations
12.4 Multiplying decimals
12.5 Dividing decimals
FM Shopping for bargains
Algebra 5
(7 hours)
13.1 Expand and simplify
13.2 Solving equations
13.3 Constructing equations to
solve
13.4 Problems with graphs
13.5 Real-life graphs
13.6 Change of subject
FM Train timetable
13.1 Refine own findings and approaches on the
basis of discussions with others; recognise efficiency
in an approach; relate the current problem and
structure to previous situations. Simplify or transform
linear expressions by collecting like terms; multiply a
single term over a bracket.
13.2 Solve linear equations with integer coefficients
(unknown on either or both sides, without and with
brackets) using appropriate methods (for example,
inverse operations, transforming both sides in same
way).
13.3 Construct and solve linear equations with
integer coefficients (unknown on either or both sides,
without and with brackets) using appropriate
methods (for example, inverse operations,
transforming both sides in same way).
13.4 Plot the graphs of linear functions, where y is
given explicitly in terms of x.
13.5 Construct linear functions arising from real-life
problems and plot their corresponding graphs;
discuss and interpret graphs arising from real
situations, for example, distance–time graphs.
Simplify or transform linear expressions by collecting
like terms.
FM Identify the mathematical features of a context or
problem.
13.1 Expand and simplify
13.2 Solving equations by trial
and improvement
13.3 Constructing equations
13.4 Problems with graphs
13.5 Real-life graphs
13.6 Change of subject
FM Train timetable
12.1 Use the equivalence of fractions, decimals and
percentages to compare proportions.
12.2 Add and subtract fractions by writing them with
a common denominator. Understand and use the
rules of arithmetic and inverse operations in the
context of integers and fractions.
12.3 Use the order of operations, including brackets,
with more complex calculations.
12.4 Strengthen and extend mental methods of
calculation, working with decimals. Use efficient
written methods for multiplication 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.
12.5 Strengthen and extend mental methods of
calculation, working with decimals. Use efficient
written methods for 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.
FM Use logical argument to interpret the
mathematics in a given context or to establish the
truth of a statement; give accurate solutions
appropriate to the context or problem; evaluate the
efficiency of alternative strategies and approaches.
13.1 Refine own findings and approaches on the
basis of discussions with others; recognise efficiency
in an approach; relate the current problem and
structure to previous situations. Simplify or transform
linear expressions by collecting like terms; multiply a
single term over a bracket.
13.2 Within the appropriate range and content
manipulate numbers, algebraic expressions and
equations.
13.3 Construct and solve linear equations with
integer coefficients (unknown on either or both sides,
without and with brackets) using appropriate
methods (for example, inverse operations,
transforming both sides in same way).
13.4 Plot the graphs of linear functions, where y is
given explicitly in terms of x.
13.5 Construct linear functions arising from real-life
problems and plot their corresponding graphs;
discuss and interpret graphs arising from real
situations, for example, distance–time graphs.
Simplify or transform linear expressions by collecting
like terms.
FM Identify the mathematical features of a context or
problem.
Year 8 Mathematics – Scheme of Work (22-06-2010)
10
YEAR 8: SUMMER TERM
MATHEMATICAL
TOPIC - Context
Solving
Problems
(5 hours)
►OVERVIEW – Teacher Pack 2
► FRAMEWORK OBJECTIVES – Teacher Pack 2
►OVERVIEW – Teacher Pack 3
► FRAMEWORK OBJECTIVES – Teacher Pack 3
14.1 Number and measures
14.2 Using algebra, graphs and
diagrams to solve problems
14.3 Logic and proof
14.4 Proportion
14.5 Ratio
14.1 Within the appropriate range and content: make
accurate mathematical diagrams, graphs and
constructions on paper and on screen; calculate
accurately, selecting mental methods or calculating
devices as appropriate; manipulate numbers,
algebraic expressions and equations, and apply
routine algorithms; use accurate notation, including
correct syntax when using ICT; record methods,
solutions and conclusions; estimate, approximate
and check working.
14.2 Identify the mathematical features of a context
or problem; try out and compare mathematical
representations; select appropriate procedures and
tools, including ICT. Use graphs and set up
equations to solve simple problems involving direct
proportion.
14.3 Use logical argument to interpret the
mathematics in a given context or to establish the
truth of a statement; give accurate solutions
appropriate to the context or problem; evaluate the
efficiency of alternative strategies and approaches.
Conjecture and generalise; move between the
general and the particular to test the logic of an
argument; identify exceptional cases or counterexamples; make connections with related contexts.
14.4 Apply understanding of the relationship
between ratio and proportion. Enter numbers and
interpret the display in different contexts (extend to
negative numbers, fractions, time).
14.5 Simplify ratios, including those expressed in
different units, recognising links with fraction
notation; divide a quantity into two or more parts in a
given ratio; use the unitary method to solve simple
problems involving ratio and direct proportion.
14.1 Number and measures
14.2 Using algebra, graphs and
diagrams to solve problems
14.3 Logic and proof
14.4 Proportion
14.5 Ratio
14.1 Identify the mathematical features of a context
or problem; try out and compare mathematical
representations; select appropriate procedures and
tools, including ICT. Move between the general and
the particular to test the logic of an argument.
14.2 Identify the mathematical features of a context
or problem; try out and compare mathematical
representations; select appropriate procedures and
tools, including ICT. Use graphs and set up
equations to solve simple problems involving direct
proportion.
14.3 Conjecture and generalise; move between the
general and the particular to test the logic of an
argument; identify exceptional cases or counterexamples; make connections with related contexts.
Use logical argument to interpret the mathematics in
a given context or to establish the truth of a
statement; give accurate solutions appropriate to the
context or problem; evaluate the efficiency of
alternative strategies and approaches.
14.4 Apply understanding of the relationship
between ratio and proportion. Enter numbers and
interpret the display in different contexts (extend to
negative numbers, fractions, time). Use proportional
reasoning to solve problems, choosing the correct
numbers to take as 100%, or as a whole (Year 9
Framework Objective).
14.5 Simplify ratios, including those expressed in
different units, recognising links with fraction
notation; divide a quantity into two or more parts in a
given ratio; use the unitary method to solve simple
problems involving ratio and direct proportion.
Year 8 Mathematics – Scheme of Work (22-06-2010)
11
YEAR 8: SUMMER TERM
MATHEMATICAL
TOPIC - Context
Geometry &
Measures 4
(9 hours)
►OVERVIEW – Teacher Pack 2
► FRAMEWORK OBJECTIVES – Teacher Pack 2
►OVERVIEW – Teacher Pack 3
► FRAMEWORK OBJECTIVES – Teacher Pack 3
15.1 & 15.2 Plans and elevations
15.3 Scale drawings
15.4 Finding the mid-point of a
line segment
15.5 To construct a triangle given
three sides
15.6 Circumference and area of a
circle
15.7 Bearings
15.8 A cube investigation
FM Photographs
15.1 & 15.2 Use geometric properties of cuboids and
shapes made from cuboids; use simple plans and
elevations.
15.3 Make scale drawings.
15.4 Find the midpoint of the line segment AB, given
the coordinates of points A and B.
15.5 Use straight edge and compasses to construct
a triangle, given three sides (SSS). Use ICT to
explore this construction.
15.6 Use formulae from mathematics and other
subjects; substitute integers into simple formulae.
15.7 Use bearings to specify direction.
15.8 Calculate surface areas of cuboids and shapes
made from cuboids.
FM Identify the mathematical features of a context or
problem. Calculate percentages and find the
outcome of a given percentage increase or
decrease. Use the unitary method to solve simple
problems involving ratio. Understand and use the
language and notation associated with enlargement.
Know rough metric equivalents of imperial measures
in common use. Calculate areas of compound
shapes. Interpret tables and diagrams.
15.1 & 15.2 Plans and elevations
15.3 Scale drawings
15.4 Finding the mid-point of a
line segment
15.5 Map scales
15.6 Loci
15.7 Bearings
15.8 A cube investigation
FM Photographs
15.1 & 15.2 Use geometric properties of cuboids and
shapes made from cuboids; use simple plans and
elevations. Visualise and use 2-D representations of
3-D objects (Year 9 Framework Objective).
15.3 Make scale drawings.
15.4 Find the mid-point of the line segment AB,
given the coordinates of points A and B.
15.5 Use and interpret maps and scale drawings in
the context of mathematics and other subjects (Year
9 Framework Objective).
15.6 Find simple loci, both by reasoning and by
using ICT, to produce shapes and paths, for
example, an equilateral triangle.
15.7 Use bearings to specify direction.
15.8 Calculate surface areas of cuboids and shapes
made from cuboids.
FM Interpret tables and diagrams. Identify the
mathematical features of a contextual problem.
Know rough metric equivalents of imperial measures
in common use. Calculate areas of compound
shapes. Understand and use the language
associated with enlargement. Calculate percentages
and find the outcome of a given percentage increase
or decrease. Use the unitary method to solve simple
problems involving ratio
Year 8 Mathematics – Scheme of Work (22-06-2010)
12
YEAR 8: SUMMER TERM
MATHEMATICAL
TOPIC - Context
Statistics 3
(7 hours)
►OVERVIEW – Teacher Pack 2
► FRAMEWORK OBJECTIVES – Teacher Pack 2
►OVERVIEW – Teacher Pack 3
► FRAMEWORK OBJECTIVES – Teacher Pack 3
16.1 Frequency tables
16.2 Assumed mean and working
with statistics
16.3 Drawing frequency diagrams
16.4 Comparing data
16.5 Which average to use?
16.6 Experimental and theoretical
probability
FM Questionnaire
16.1 Discuss a problem that can be addressed by
statistical methods and identify related questions to
explore. Decide which data to collect to answer a
question, and the degree of accuracy needed;
identify possible sources. Plan how to collect the
data; construct frequency tables with equal class
intervals for gathering continuous data. Collect data
using a suitable method (for example, observation,
controlled experiment, data logging using ICT).
16.2 Calculate statistics for sets of discrete and
continuous data, including with a calculator and
spreadsheet; recognise when it is appropriate to use
the range, mean, median and mode and, for
grouped data, the modal class.
16.3 Construct graphical representations, on paper
and using ICT, and identify which are most useful in
the context of the problem. Include: bar charts and
frequency; diagrams for discrete and continuous
data; simple line graphs for time series.
16.4 Interpret tables, graphs and diagrams for
discrete and continuous data, relating summary
statistics and findings to the questions being
explored. Compare two distributions using the range
and one or more of the mode, median and mean.
16.5 Recognise when it is appropriate to use the
range, mean, median and mode and, for grouped
data, the modal class.
16.6 Write about and discuss the results of a
statistical enquiry using ICT as appropriate; justify
the methods used. Compare estimated experimental
probabilities with theoretical probabilities.
FM Calculate statistics for sets of discrete and
continuous data, including with a calculator and
spreadsheet. Interpret the results of an experiment
using the language of probability.
16.1 Collecting data for frequency
tables
16.2 Assumed mean and working
with statistics
16.3 Drawing frequency diagrams
16.4 Comparing data
16.5 Comparing sets of data
16.6 Experimental and theoretical
probability
FM Questionnaire
16.1 Decide which data to collect to answer a
question, and the degree of accuracy needed;
identify possible sources. Plan how to collect the
data; construct frequency tables with equal class
intervals for gathering continuous data. Discuss how
different sets of data relate to the problem; identify
possible primary or secondary sources; determine
the sample size and most appropriate degree of
accuracy (Year 9 Framework Objective). Design a
survey or experiment to capture the necessary data
from one or more sources; design, trial and if
necessary refine data collection sheets (Year 9
Framework Objective).
16.2 Calculate statistics for sets of discrete and
continuous data, including with a calculator and
spreadsheet; recognise when it is appropriate to use
the range, mean, median and mode and, for
grouped data, the modal class.
16.3 Construct graphical representations, on paper
and using ICT, and identify which are most useful in
the context of the problem. Include: bar charts and
frequency; diagrams for discrete and continuous
data; simple line graphs for time series.
16.4 Interpret tables, graphs and diagrams for
discrete and continuous data, relating summary
statistics and findings to the questions being
explored. Compare two distributions using the range
and one or more of the mode, median and mean.
16.5 Compare two or more distributions and make
inferences, using the shape of the distributions and
appropriate statistics (Year 9 Framework Objective).
16.6 Write about and discuss the results of a
statistical enquiry using ICT as appropriate; justify
the methods used. Compare estimated experimental
probabilities with theoretical probabilities.
FM Calculate statistics for sets of discrete and
continuous data, including with a calculator and
spreadsheet. Interpret the results of an experiment
using the language of probability.
34 Hours Teaching
Year 8 Mathematics – Scheme of Work (22-06-2010)
13