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Year 9 Review 1 – All about Number (Four operations, place value, common indices and estimation)
Foundation Pathway
Growing Pathway
Secure Pathway
• 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
• 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
Exceeding 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)
Highest Pathway
• Identify and interpret limits of accuracy
(bounds)
• Estimate using truncating
• Use inequality notation to specify simple error
intervals due to truncation or rounding
• Calculate with roots, and with integer indices
• Calculate exactly with multiples of π
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 9 Review 2 – Working with decimals, sequences, coordinates & algebraic graph functions.
Foundation Pathway
Growing Pathway
• 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
• Apply the four operations, including formal written
decimal places
methods, to integers and decimals.
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Multiply and divide numbers by 10, 100 and 1000 giving
• Understand and use place value (e.g. when working
answers up to three decimal places
with very large or very small numbers, and when
• Use written division methods in cases where the answer has
calculating with decimals)
up to two decimal places
•
Approximate by rounding to any significant figure in
• Identify common factors, common multiples and prime
any number
numbers of numbers up to 100
• Show an understanding of Identifying the nth term within a
numerical sequence
• Generate a sequence from a term-to-term rule
•
Describe positions on the full coordinate grid (all four
quadrants)
Exceeding 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 simple quadratic
sequence
Highest Pathway
• Change recurring decimals into their
corresponding fractions and vice versa
• Find the nth term for more complex quadratic
sequences
• Recognise and use Fibonacci type sequences
• Recognise and use quadratic sequences
• Use the form y = mx + c to identify parallel lines
• Plot graphs of equations that correspond to straight-line • Find the equation of the line through two given
graphs in the coordinate plane
points, or through one point with a given gradient
• Identify and interpret gradients and intercepts of linear
• Identify and interpret roots, intercepts, turning
functions graphically and algebraically
points of quadratic functions graphically
• Recognise, sketch and interpret graphs of linear functions • Recognise, sketch and interpret graphs of simple
and quadratic functions
cubic functions and the reciprocal function y =
1/x with x ≠ 0
Stage 6: Page 1
Secure Pathway
• 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
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 9 Review 3 – Expressions, equations and all about angles.
Foundation Pathway
Growing Pathway
• 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
• 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
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Exceeding 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
Secure 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
Begin to prove why the angles in a
• Use standing conventions for reading and labelling angles
triangle add up to 180°
and sides of triangles
Find missing angles on a straight line and • Solve complex problems using missing angles in isosceles
a triangle.
triangles
Find angles sums of regular polygons
• Identify fluently angles at a point, angles at a point on a
Find interior angles of a regular polygon
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
Highest Pathway
• Know the difference between an
equation and an identity
• Simplify and manipulate an expression by
expanding double brackets
• Simplify and manipulate algebraic
expressions (including those involving
surds) by factorising quadratic
expressions of the form x² + bx + c,
including the difference of two squares
• Solve two linear simultaneous equations
• Solve quadratic equations by factorising
• Solve linear inequalities with one variable
• Represent the solution to an inequality
on a number line
• Translate simple situations or procedures
into algebraic expressions or formulae
• Derive an equation (or two simultaneous
equations)
Stage 6: Page 1
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Highest Pathway
Construct a perpendicular
bisector
Bisect an angle
Use similarity within a
problem
Use the basic congruence
criteria for triangles (SSS,
SAS, ASA, RHS)
Mathematical language
Algebra, algebraic,
algebraically
Symbol Expression
Variable
Substitute
Equation Unknown
Enumerate
Right angle Acute
angle Obtuse angle
Reflex angle
Protractor
Vertically opposite
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Year 9 Review 4 – Fractions, decimals, percentages and probability.
Foundation Pathway
Growing Pathway
Secure Pathway
• 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.
• 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
Exceeding Pathway
Highest Pathway
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• Solve problems using compound interest and within
the context of finances.
• Work with fractions, decimals and percentages in
any context – showing an exceptional understanding
and working processes to support their knowledge
• Calculate the probability of independent and
dependent combined events, using
representations, and know the underlying
assumptions
• Show an understanding that unbiased samples tend
towards theoretical probability distributions, with
increasing sample size
• Use relative frequency to predict future events
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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
Mathematical language
Stage 6: Page 1
Fraction
Mixed number
Improper
Equivalent
Proper fraction
Simplify
Top-heavy
Cancel
fraction
Numerator,
Proportion
denominator
Proportion
Lowest terms
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Year 9 Review 5 – Ratio & proportion, space in shapes & circles.
Foundation Pathway
Growing Pathway
Secure Pathway
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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 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
• 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
• 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
Exceeding 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)
• Understand and use proportion as equality of ratios (strong
link to the parts of the ratio)
• Use scale factors, scale diagrams and maps
• Compare lengths, areas and volumes using ratio notation
• Solve problems involving direct and inverse proportion,
including graphical and algebraic representations
• Calculate the circumference of a circle
• Calculate the area of a circle showing in units²
• Find the area of composite shapes (some using circles)
• Know and apply formulae to calculate volume of right
prisms (including cylinders)
Highest Pathway
• Change freely between compound units (e.g. speed,
rates of pay, prices) in numerical contexts
• Use compound units such as density and pressure
• Change freely between compound units (e.g. density,
pressure) in numerical and algebraic contexts
• Interpret the gradient of a straight line graph as a
rate of change;
• Identify and apply circle definitions and properties,
including: tangent, arc, sector and segment
• Calculate arc lengths, angles and areas of sectors of
circles
• Calculate surface area and volume of spheres,
pyramids, cones
• Know the formulae for: Pythagoras’ theorem, a² + b²
= c², and apply it to find lengths in right-angled
triangles in two dimensional figures
• Apply the concepts of congruence and similarity
within a problem (similar shapes)
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Stage 6: Page 1
• Calculate perimeters of 2D shapes
• Know and apply formulae to calculate the
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area of 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
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 9 Review 6 – Present, measure and interpret data (including averages).
Foundation Pathway
Growing Pathway
• 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
• Solve comparison, sum and difference
problems using information presented in a
line graph
• Complete, read and interpret information in
tables, including timetables
Exceeding 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
• Use and interpret scatter graphs
• Recognise and describe reasonable
explanations of the correlation of the data
• Show an understanding of a histogram and
its differences from bar charts
Secure 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
• Interpret and construct pie charts and use these to solve
•
Construct
a stem and lead diagram to compare sets
problems
of data using appropriate averages
• Interpret and construct line graphs and use these to solve
problems
• Graph grouped data
• Interpret and construct tables, charts and
diagrams, including frequency tables, bar charts,
pie charts and pictograms for categorical data,
vertical line charts for ungrouped discrete
numerical data and know their appropriate use
Highest Pathway
• Interpret and construct tables, charts and diagrams,
including tables and line graphs for time series data and
know their appropriate use
(time/distance and real life graphs)
• Draw an accurate line of best fit on a scatter graph
• Use the line of best fit to make predictions or solve
problems
• Describe an understanding that correlation does not
indicate causation
• Showing an understanding of that Interpolate and
extrapolating apparent trends and know the dangers of
doing so
Stage 6: Page 1
Mathematical language
Data, Categorical data,
Discrete data
Pictogram, Symbol, Key
Frequency
Table, Frequency table
Tally
Bar chart
Time graph, Time
series
Scale, Graph
Axis, axes
Line graph
Pie chart
Sector
Angle
Maximum, minimum
Average
Spread
Consistency
Mean
Median
Mode
Range
Measure
Data
Statistic
Statistics
Approximate
Round