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Year 8 Review 1 – All about Number (Four operations, place value, common indices and estimation)
Foundation Pathway
Growing Pathway
Secure Pathway
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Read Roman numerals up to 1000 and recognise years
Round any number up to 1,000
Add and subtract numbers up to 4 digits
Multiply a 4 digit number by a one digit number
Divide a 3 digit number by a one digit number
Show what an inverse operation is
• Show the use of estimation correctly
• Read, write, order and compare numbers
up to 1,000,000
• Count forwards / backwards in powers of
10 up to 1,000,000
• Round any number up to 1,000,000
• Round decimals up to two decimal places
• Multiply a 3 digit by a 2 digit number
• Divide a 4 digit number by a 1 digit
number
• Demonstrate an understanding of using
an inverse operation
• Use rounding to estimate & check an
answer
• Read, write, order and compare numbers up to
10,000,000
• Add and subtract numbers with more than 4 digits
• Multiply a 4 digit number by a two digit number
• Divide a 4 digit number by a 2 digit number using
fractions and / or decimals to show remainders.
• Recognise and use square and cube numbers up to 100
• Perform mentally calculations, including with mixed
operations and large numbers
• Use the =, ≠, <, >, ≤, ≥ symbols within simple problems.
• Solve addition and subtraction multi step problems
deciding which operations and methods to use and why
• Use estimation to check answers to calculations to
determine, in the context of a problem, and correct use
of rounding
• Use the order of operation correctly to carry out
calculations
Exceeding Pathway
• Understand and use place value (eg when working with
very large and small numbers and when calculating with
decimals)
• Round numbers and measures to a specified number of
decimal places or significant figures
• Use conventional notation for priority of operations,
including brackets (BIDMAS) and also involving indices
• Use positive integer powers and associated real roots
(square, cube and higher), recognise powers of 2,3,4,5.
• Recognise and use relationships between operations,
including inverse operations (eg cancellation to simplify
calculations and expressions)
• Use the 4 operations including formal written methods,
also decimals and simple fractions and mixed numbers
Highest Pathway
• Interpret standard form A x 10n, where 1
≤ A < 10 and n is an integer
• Apply the four operations, including
formal written methods, to integers,
decimals and simple fractions (proper and
improper), and mixed numbers – all both
positive and negative
• Use the concepts and vocabulary of
prime numbers, highest common factor,
lowest common multiple, prime
factorisation, including using product
notation and the unique factorisation
theorem (product of primes)
Mathematical language
Stage 6: Page 1
Place value
Digit
Integer
Negative number
Difference, Minus, Less
Operation
Multiply, Multiplication,
Times, Product
Estimate
Divide, Division, Divisible
Divisor, Dividend
Operation
Estimate
Approximate
Round
Decimal place
Accuracy
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Year 8 Review 2 – Working with decimals, sequences, coordinates & algebraic graph functions.
Foundation Pathway
Growing Pathway
Secure Pathway
• Multiply and divide whole numbers by 10, 100 and 1000
• Round decimals with two decimal places to the nearest whole
number
• Recognise thousandths and relate them to tenths and hundredths
and decimal equivalents
• Identify factor pairs including finding all factors of a number.
• Establish whether a number up to 100 is prime and recall all primes
up to 20
• Recognise a linear sequence
• Describe a number sequence
• Find the next term in a number sequence
• Find missing values within the sequence using the rule
• Read any points in all four quadrants
• Plot any points in all four quadrants
• Plot specific points and join sides to create a specific polygon in any
quadrant
• Read, write, order and compare numbers with up
to three decimal places
• Solve problems involving number up to three
decimal places
• Round decimals with two decimal places to one
decimal place
• Multiply and divide numbers involving decimals
by 10, 100 and 1000
• Identify common factors, common multiples and
prime numbers of numbers up to 20
• Know and use the vocabulary of prime numbers,
prime factors and composite numbers (non
prime numbers)
• Find a missing term in a linear sequence
• Generate a linear sequence from its description
• Work with points in all four quadrants
• Identify the value of each digit in numbers given to three
decimal places
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Multiply and divide numbers by 10, 100 and 1000 giving
answers up to three decimal places
• Use written division methods in cases where the answer has
up to two decimal places
• Identify common factors, common multiples and prime
numbers of numbers up to 100
Exceeding Pathway
Highest Pathway
• Work interchangeably with terminating
decimals and their corresponding fractions
(such as 3.5 and 7/2 or 0.375 or 3/8)
• Identify the nth term for simple quadratic
sequences
• Continue or find a missing term from a
quadratic sequence
• Apply the four operations, including formal written methods, to
integers and decimals.
• Understand and use place value (e.g. when working with very large
or very small numbers, and when calculating with decimals)
• Approximate by rounding to any significant figure in any number
• Use the concepts and vocabulary of prime numbers, factors
(divisors), multiples, common factors, common multiples, highest
common factor and lowest common multiple.
• Identify the nth term within a numerical sequence
• Use the nth term confidently within any linear sequence problem • Plot graphs of equations that correspond to
straight-line graphs in the coordinate plane
• Generate a sequence from a position-to-term rule
• Identify and interpret gradients and
• Recognise square or cube number sequences and apply a rule
• Recognise triangular numbers within a sequence
intercepts of linear functions graphically and
• Work with coordinates confidently and fluently in all four quadrants
algebraically
• Recognise, sketch and interpret graphs of
linear functions and quadratic functions
Stage 6: Page 1
• Show an understanding of Identifying the nth term within a
numerical sequence
• Generate a sequence from a term-to-term rule
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Describe positions on the full coordinate grid (all four
quadrants)
Mathematical language
Place value
Digit
Negative number
(Common) multiple
(Common) factor
Divisible
Prime number, Composite number
Pattern
Sequence
Linear
Term
Ascending
Descending
X axes
Y axes
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Year 8 Review 3 – Expressions, equations and all about angles.
Foundation Pathway
Growing Pathway
Secure Pathway
• Know and use the basic rules of algebraic notation
(2a, not a2)
• Use a term confidently to represent a missing value
• Recognise the < and > symbols
• Collect like terms within an expression
• Express missing number problems algebraically
• Solve simple one step equations (not fractional)
• Collect like terms within a problem (eg. perimeter)
• Solve one-step linear equations including fractions
• Find a pair of numbers which satisfy an equation
with two unknowns
• List possibilities of combination of numbers with
two variables
• Estimate and compare acute and obtuse angles
• Draw angles and measure them in °
• Explain what a polygon is
Exceeding Pathway
• Use standard algebraic notation (ab instead of a x b,
use of the fraction line instead of division and
squaring of indices)
• Understand the vocabulary of expression, equation
and formulae
• Substitute numerical values into a formulae
• Solve two-step equations (Showing clear methods)
• Check the solution to an equation by substitution
• Simplify expressions by multiplying out a single
bracket
• Know the meaning of the ‘subject’ of an equation
• Use standing conventions for reading and labelling
angles and sides of triangles
• Solve complex problems using missing angles in
isosceles triangles
• Identify fluently angles at a point, angles at a point
on a line and vertically opposite angles
• Use the fact that angles in a triangle total 180° to
work out the total of the angles in any polygon
• Use properties of rectangles to find missing angles
• Recognise where angles meet at a point and in a
right angle.
• Describe the difference between a regular and
irregular polygon
• Estimate and compare reflex angles
Highest Pathway
• Use and interpret algebraic notation, including: a²b
in place of a × a × b, coefficients written as fractions
rather than as decimals
• Substitute numerical values into scientific formulae
• Understand and use the concepts and vocabulary of
inequalities and factors
• Simplify and manipulate algebraic expressions by
taking out common factors and simplifying
expressions involving sums, products and powers,
including the laws of indices
• Rearrange formulae to change the subject
• Solve linear equations with the unknown on both
sides of the equation
• Derive and use the sum of angles in a triangle (e.g.
to deduce and use the angle sum in any polygon,
and to derive properties of regular polygons)
• Understand and use alternate and corresponding
angles on parallel lines
Stage 6: Page 1
• Begin to prove why the angles in a triangle add up
to 180°
• Find missing angles on a straight line and a
triangle.
• Find angles sums of regular polygons
• Find interior angles of a regular polygon
Mathematical language
Algebra, algebraic,
algebraically
Symbol
Expression
Variable
Substitute
Equation
Unknown
Enumerate
Angle
Degrees
Right angle
Acute angle
Obtuse angle
Reflex angle
Protractor
Vertically opposite
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Year 8 Review 4 – Fractions, decimals, percentages and probability.
Foundation Pathway
Growing Pathway
Secure Pathway
• Identify, name and write equivalent fractions of a given fraction,
represented visually, including tenths and hundredths
• Show common equivalent fractions
• Read and write decimal numbers as fractions [for example, 0.71 =
71
/100]
• Write percentages as a fraction with denominator 100, and as a
decimal
• Compare and order fractions whose denominators are all multiples
of the same number
• Multiply simple proper fractions by a whole number, supported by
materials and diagrams
• Solve problems which require knowing percentage and decimal
equivalents of 1/2 and 1/4
• Show an understanding that probability represents the chance of
something happening
• Use the appropriate words to describe the chance of common
events
• Place common events correctly on the probability scale (from 0-1)
• Add and subtract fractions with the same
denominator and denominators that are
multiples of the same number
• Recognise and convert mixed numbers to
improper fractions and vice versa
• Multiply improper fractions by a whole
number, supported by materials and
diagrams
• Recognise and use thousandths and relate
them to tenths, hundredths and decimal
equivalents
• Solve problems which require knowing
percentage and decimal equivalents of 1/5,
2
/5, 4/5 and those with a denominator of a
multiple of 10 or 25.
• Find percentages which are multiples of 10
• Show the outcomes of a single event.
• Show the probability of these outcomes.
• Show some understanding of fairness in (P)
• Compare and order fractions, including
fractions > 1
• Use common factors to simplify fractions; use
common multiples to express fractions in the
same denomination
• Add and subtract fractions with different
denominators, using the concept of equivalent
fractions
• Multiply fractions by a whole number
• Recall and use equivalences between simple
fractions, decimals and percentages, including
in different context
• Associate a fraction with division and calculate
decimal fraction equivalents [for example,
0.375] for a simple fraction [for example, 3/8 ]
• Find any whole number percentage of an
amount
• Show all the outcomes of two events.
• Find the probability of events using a fraction.
Exceeding Pathway
Highest Pathway
• Order positive & negative integers, decimals and fractions
• Express one quantity as a fraction of another, where the fraction is less
than 1 or greater than 1
• Interpret percentages and percentage changes as a fraction or a decimal
• Express one quantity as a percentage of another
• Compare two quantities using percentages
• Increase and decrease a quantity by a percentage
• Solve problems involving percentage change, including percentage
increase/decrease
• Add and subtract mixed numbers
• Multiply simple pairs of proper fractions, writing the answer in its simplest
form [for example, 1/4 × 1/2 = 1/8]
• Divide proper fractions by whole numbers [for example, 1/3 ÷ 2 = 1/6]
• Record, describe and analyse frequency of outcomes of probability
experiments using tables and frequency trees
• Use simple relative frequency of probability to predict outcomes for
future experiments
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Calculate exactly with fractions
Multiply and divide improper fractions
Work with percentages greater than 100%
Solve problems involving percentage
change, including original value problems,
and simple interest including in financial
mathematics
Find the original amount following a %
change
Apply the property that all events sum to 1
Show all combinations of outcomes using
tables, grids and venn diagrams
Construct theoretical possibility spaces
for combined experiments with equally
likely outcomes and use these to
calculate theoretical probabilities
Stage 6: Page 1
Mathematical language
Fraction
Improper
Proper
fraction
Top-heavy
fraction
Proportion
Proportion
Mixed number
Equivalent
Simplify
Cancel
Numerator,
denominator
Lowest terms
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Year 8 Review 5 – Ratio & proportion, space in shapes & circles.
Foundation Pathway
Growing Pathway
Secure Pathway
• Use division to share a quantity into parts
from a simple given ratio
• To represent some understanding of what a
proportion is using a value
• Correctly share out a quantity into a ratio
• Simplify simple ratios
• Use proportion within a problem using its simplest value
• Make comparisons using an understanding of ratio
• Show an understanding of proportion given as
times bigger or smaller
• Show proportion as a comparison to the original
amount
• Measure and calculate the perimeter of composite
• Measure and calculate the perimeter of
rectangular shapes in cm and m
rectangular shapes in centimetres and metres • Calculate and compare the area of rectangles (including
• Calculate the area of rectangles (including
squares), and including using standard units, square
squares), and including using standard units,
centimetres (cm²) and square metres(m²)
square centimetres (cm²) and square
• Estimate the area of irregular shapes
metres(m²)
• Estimate volume [for example, using
• Identify the radius & diameter of a circle
1 cm³ blocks to build cuboids (including cubes)]
• Identify the circumference of a circle
• Show an understanding that the circumference links to
the perimeter of a circle
Exceeding Pathway
• Divide a given quantity into two parts in a
given part:part or part:whole ratio
• Use ratio freely within other contexts
• Use proportion freely within other contexts
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Highest Pathway
• Identify and work with fractions in ratio problems
• Relate ratios to fractions and to linear functions
• Express the division of a quantity into two parts as a ratio;
apply ratio to real contexts and problems (such as those
involving conversion, comparison, scaling, mixing,
concentrations)
Calculate perimeters of 2D shapes
• Understand and use proportion as equality of ratios (strong
Know and apply formulae to calculate the
link to the parts of the ratio)
area of parallelograms & trapezia
• Use scale factors, scale diagrams and maps
Know and apply formulae to calculate
• Compare lengths, areas and volumes using ratio notation
volume of cuboids
Measure line segments in geometric figures • Solve problems involving direct and inverse proportion,
including graphical and algebraic representations
Know the formulae: circumference of a circle
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Calculate the circumference of a circle
= 2πr = πd
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Calculate the area of a circle showing in units²
Know the formulae: area of a circle = πr²
• Find the area of composite shapes (some using circles)
• Know and apply formulae to calculate volume of right
prisms (including cylinders)
Stage 6: Page 1
• Recognise that shapes with the same areas can
have different perimeters and vice versa
• Calculate the area of a triangle
• Calculate the area of a parallelogram
• Calculate and compare volume of cubes and
cuboids using standard units, including cubic
centimetres (cm³) and cubic metres (m³)
• Show an understanding that the diameter is twice
the radius and the reverse of this
Mathematical language
Proportion
Quantity
Integer
Share
Multiples
Ratio
Compare, comparison
Part
Simplify
Common factor
Cancel
Lowest terms
Unit
Length, breadth,
depth, height, width
Volume
Capacity
Perimeter, area,
Square, rectangle,
parallelogram, triangle
Composite rectilinear
Polygon
Cube, cuboid
Square centimetre,
square metre,
Cubic centimetre,
Formula, formulae
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Year 8 Review 6 – Present, measure and interpret data (including averages).
Foundation Pathway
Growing Pathway
Secure Pathway
• Know that the median represents the middle
value of a set of data
• Order a set of data to find the median value.
• Show the range of a set of data
• Use the correct method to find the mean of a set of data
• Begin to describe an understanding that averages are a
value/s that represent a group of data
• Begin to show the importance of the range for when
finding an average
• Calculate and interpret the mean as an average
• Use an understanding of mean, median and mode
to find missing values in average problems
• Interpret and present discrete and
continuous data using appropriate graphical • Solve comparison, sum and difference problems using
methods, including bar charts and time
information presented in a line graph
graphs
• Complete, read and interpret information in tables,
• Solve comparison, sum and difference
including timetables
problems using information presented in bar
charts, pictograms, tables and other graphs
Exceeding Pathway
• Interpret, analyse and compare the
distributions of data sets from cumulative
frequency graphs, identifying the median and
range of the data.
• Find the averages of grouped data sets using
midpoints within a table
• Construct a stem and lead diagram to
compare sets of data using appropriate
averages
Highest Pathway
• Have a basic understanding of data sets from cumulative
frequency graphs, using the median and range of the data
to make reasonable comments about the findings.
• Find the central tendency (average) of frequency polygons
• Interpret and construct pie charts and use these
to solve problems
• Interpret and construct line graphs and use these
to solve problems
• Graph grouped data
Mathematical language
Data, Categorical data,
Discrete data
Pictogram, Symbol, Key
Frequency
Table, Frequency table
Tally
• Use and interpret scatter graphs
Bar chart
• Recognise and describe reasonable explanations of the
Time graph, Time
correlation of the data
series
• Show an understanding of a histogram and its differences
Scale, Graph
from bar charts
• Interpret and construct tables, charts and
Axis, axes
diagrams, including frequency tables, bar
Line graph
charts, pie charts and pictograms for
Pie chart
categorical data, vertical line charts for
ungrouped discrete numerical data and know
Sector
their appropriate use
Angle
Maximum, minimum
Stage 6: Page 1
Average
Spread
Consistency
Mean
Median
Mode
Range
Measure
Data
Statistic
Statistics
Approximate
Round