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Year 7 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 100
Count in multiples of 6,7,9, 25 and 1000
Add and subtract numbers up to 3 digits
Multiply two and three digits numbers by a one digit number
Know what the inverse operation is used for
Round to the nearest 10, 100 or 1000
• 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
Exceeding Pathway
• 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
Highest 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
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 7 Review 2 – Working with decimals, sequences and coordinates.
Foundation Pathway
Growing Pathway
Secure Pathway
• Recognise the value of a digit up to a four digit number
(Ones, tens, hundreds and thousands)
• Round decimals with one decimal place to the nearest whole
number
• Recognise the effects of multiplying and dividing a one or two digit
number by 10 or 100
• Compare numbers with the same number of decimal places up to 2
decimal places
• Recognise and use factor pairs to show commutative operations
• Identify and communicate the pattern within a simple linear
sequence
• Continue simple number patterns using the rule
• Show an understanding of reading coordinates in the first quadrant
• Show an understanding of plotting points in the first quadrant
• 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
Exceeding Pathway
Highest Pathway
Mathematical language
• 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
• 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
• Generate a sequence from a position-to-term rule
• Recognise square or cube number sequences and apply a rule
• Recognise triangular numbers within a sequence
• Work with coordinates confidently and fluently in all four
quadrants
Place value
Digit
Negative number
(Common) multiple
(Common) factor
Divisible
Prime number, Composite number
Pattern
Sequence
Linear
Term
Ascending
Descending
X axes
Y axes
• 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)
Stage 6: Page 1
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Year 7 Review 3 – Expressions, equations and all about angles.
Foundation Pathway
Growing Pathway
Secure Pathway
• Solve missing number problems
• Begin to use a term to represent a missing
value
• 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)
• Identify acute, obtuse and reflex angles
• Compare and order angles up to two right
angles by size
Exceeding Pathway
• 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
• 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
• Estimate and compare acute and obtuse angles
• Draw angles and measure them in °
• Explain what a polygon is.
Highest 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
Stage 6: Page 1
• 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
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 7 Review 4 – Fractions, decimals and percentages.
Foundation Pathway
Growing Pathway
Secure Pathway
• Count up and down in tenths and hundredths
• Show an understanding that hundredths and tenths
arise from dividing by 100 and 10
• Add and subtract fractions with the same
denominator
• Find fractions of quantities using a unit fraction
showing a clear use of division
• Recognise and write decimal equivalents to 1/4,1/2, ¾
• Recognise and write decimal equivalents of any
number of tenths or hundredths
• Solve simple measure and money problems involving
fractions and decimals to two decimal places
• 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
• 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
Exceeding Pathway
• 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
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]
Mathematical language
Stage 6: Page 1
Fraction
Mixed number
Improper
Equivalent
fraction
fraction
Proper fraction
Cancel
Top-heavy
Numerator,
fraction
denominator
Proportion
Percent,
Decimal
percentage
Proportion
Lowest terms
Simplify
Equivalent
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Year 7 Review 5 – Ratio & proportion, space in shapes & circles.
Foundation Pathway
Growing Pathway
Secure Pathway
• Show an understanding that ratio involves
parts
• 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
• Measure and calculate the perimeter of rectangular
shapes in centimetres and metres
• Calculate the area of rectangles (including squares), and
including using standard units, square centimetres (cm²)
and square metres(m²)
• Identify the radius & diameter of a circle
• Measure and calculate the perimeter of
composite rectangular shapes in cm and m
• Calculate and compare the area of rectangles
(including squares), and including using standard
units, square centimetres (cm²) and square
metres(m²)
• Estimate the area of irregular shapes
• Estimate volume [for example, using
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
• Measure and calculate the perimeter of a
simple shape
• Find the area of a rectangle (including
squares) by counting squares
• Recognise a circle
• Identify the centre of the circle
Exceeding Pathway
• 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
• 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
Highest 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
• Calculate perimeters of 2D shapes
• Know and apply formulae to calculate the area of
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parallelograms & trapezia
Know and apply formulae to calculate volume of cuboids
Measure line segments in geometric figures
Know the formulae: circumference of a circle = 2πr = πd
Know the formulae: area of a circle = πr²
Stage 6: Page 1
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 millimetre,
square centimetre,
square metre,
Cubic centimetre,
Formula, formulae
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Year 7 Review 6 – Present, measure and interpret data (including averages).
Foundation Pathway
Growing Pathway
Secure Pathway
• Find the mode from a set of numerical data
• Know that the median represents the middle value of a set • Use the correct method to find the mean of a set
of data
of data
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Order
a
set
of
data
to
find
the
median
value.
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Begin to describe an understanding that averages
• Solve comparison, sum and difference
are a value/s that represent a group of data
problems using information presented in bar • Show the range of a set of data
• Begin to show the importance of the range for
charts and pictograms
• Interpret and present discrete and continuous data using
when finding an average
• Present discrete and continuous data using
appropriate graphical methods, including bar charts and
appropriate graphical methods, including bar
time graphs
• Solve comparison, sum and difference problems
charts and time graphs
• Solve comparison, sum and difference problems using
using information presented in a line graph
information presented in bar charts, pictograms, tables
• Complete, read and interpret information in
and other graphs
tables, including timetables
Exceeding Pathway
• 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 construct pie charts and use
these to solve problems
• Interpret and construct line graphs and use
these to solve problems
• Graph grouped data
Highest Pathway
Mathematical language
• Interpret, analyse and compare the distributions of data
Data, Categorical data,
Average
sets from cumulative frequency diagrams through
Discrete data
Spread
appropriate measures of central tendency (median, mean, Pictogram, Symbol, Key
Consistency
mode and modal class) and spread (range)
Mean
Frequency
• Find the averages of grouped data sets using midpoints
Median
Table, Frequency table
within a table
Mode
Tally
• Construct a stem and lead diagram to compare sets of data
Range
Bar chart
using appropriate averages
Measure
Time graph, Time
Data
series
• Interpret and construct tables, charts and diagrams,
Statistic
Scale, Graph
including frequency tables, bar charts, pie charts and
Statistics
Axis, axes
pictograms for categorical data, vertical line charts for
Approximate
Line graph
ungrouped discrete numerical data and know their
Round
Pie chart
appropriate use
Sector
Angle
Maximum, minimum
Stage 6: Page 1