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The following files are worked example animations generated using the question bank from Maths White Board (click here). The animations are a great way of modelling or providing a silent example for students to narrate. The animations could be started but paused half way to get students to think about what comes next. There are so many ways these animations could be used. For ease, all files have been built into the "Model it" tool on the site and also in the "Secure WB" board.

Design your animation:

To begin, search the question bank for a specific topic:

SELECT TOPIC

Feel free to use the FREE animation library but where possible, please provide a link to this site for others to explore. When using the animations, they are to be used to generate freely available resources. For any commercial services looking to embed these animations, please contact me first.

Shared/Live animation

In this section you can view and download any of the shared animations. These animations are also made available in the Maths White Board "Model it" tool and any on-screen practice page ("Secure WB").

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Algebra vocabulary and understanding
1★ What is it? (term, expression, equation, formula or identity?)
Algebra vocabulary and understanding
1★ What is it? (term, expression, equation, formula or identity?)
Algebra vocabulary and understanding
2★ Is it an equation or an identity?
Algebra vocabulary and understanding
2★ Is it an equation or an identity?
Algebra vocabulary and understanding
3★ Product of two brackets equating coefficients (quadratics)
Algebra vocabulary and understanding
3★ Product of two brackets equating coefficients (quadratics)
Algebra vocabulary and understanding
4★ Equating coefficients (inc. factorising)
Algebra vocabulary and understanding
5★ Equating coefficients (inc. completing the square)
Algebra vocabulary and understanding
6★ Equating coefficients (inc. completing the square) - harder
Algebraic proof
1★ Provide a counterexample to disprove a statement
Algebraic proof
2★ Show a simple identity by expanding a linear expression is true
Algebraic proof
2★ Show a simple identity by expanding a linear expression is true
Algebraic proof
3★ Show that an identity involving a product of two linear expressions is true
Algebraic proof
3★ Show that an identity involving a product of two linear expressions is true
Algebraic proof
4★ Show that an expression is even, odd, multiple of or factor of a number
Algebraic proof
5★ Show that a harder expression is a even, odd, multiple of or factor of a number
Simplify an expression
1★ Single variable addition and subtraction
Simplify an expression
2★ Addition and subtraction of multiples of a single variable
Simplify an expression
3★ Multiplying and dividing terms
Simplify an expression
3★ Multiplying and dividing terms
Simplify an expression
4★ Collecting two or more variables
Simplify an expression
4★ Collecting two or more variables
Simplify an expression
5★ Collecting two or more variables inc powers
Simplify an expression
5★ Collecting two or more variables inc powers
Simplify an expression
6★ Find the perimeter of a shape with linear expressions as the lengths of the sides
Simplify an expression
6★ Find the perimeter of a shape with linear expressions as the lengths of the sides
Algebraic fractions
1★ Simplify
Algebraic fractions
1★ Simplify
Algebraic fractions
2★ Add or subtract fractions
Algebraic fractions
2★ Add or subtract fractions
Algebraic fractions
3★ Simplify a fraction by factorising
Algebraic fractions
3★ Simplify a fraction by factorising
Algebraic fractions
4★ Multiply or divide
Algebraic fractions
4★ Multiply or divide
Algebraic fractions
5★ Add or subtract fractions with linear denominator expressions
Algebraic fractions
5★ Add or subtract fractions with linear denominator expressions
Algebraic fractions
6★ Solve algebraic fractional equations (integer solutions)
Change the subject
1★ Rearrange in 1 step
Change the subject
2★ Rearrange in 2 steps
Change the subject
3★ Rearrange a formula involving a fraction
Change the subject
4★ Rearrange a formula involving powers or roots
Change the subject
5★ Rearrange common formula
Change the subject
6★ Rearrange a formula where the subject appears more than once
Identify coordinates in all 4 quadrants
1★ First quadrant only
Identify coordinates in all 4 quadrants
2★ First and second quadrant only
Identify coordinates in all 4 quadrants
3★ Third and fourth quadrants only
Identify coordinates in all 4 quadrants
4★ All quadrants
Identify coordinates in all 4 quadrants
5★ Identify a coordinate to complete a shape
Identify coordinates in all 4 quadrants
6★ Find the midpoint of a line between 2 points
Find and use y = a, x = a and y = x
1★ State the equation from a graph
Find and use y = a, x = a and y = x
2★ Sketch the graph from the equation (integer intercepts)
Find and use y = a, x = a and y = x
3★ Sketch the graph from the equation (decimal intercepts)
Find and use y = a, x = a and y = x
4★ Where does x = a and y = b meet?
Find and use y = a, x = a and y = x
5★ Does the point lie on the line?
Find and use y = a, x = a and y = x
5★ Does the point lie on the line?
Find y = mx + c from a graph
1★ Find the y-intercept
Find y = mx + c from a graph
2★ Calculate the gradient where Δx is 1
Find y = mx + c from a graph
2★ Calculate the gradient where Δx is 1
Find y = mx + c from a graph
3★ Calculate a positive gradient where Δx is not 1
Find y = mx + c from a graph
4★ Calculate a negative gradient where Δx is not 1
Find y = mx + c from a graph
5★ Finding gradient from a graph
Find y = mx + c from a graph
6★ Finding y=mx+c from a graph
Rearranging into the form y = mx + c
1★ Interpret the gradient or y-intercept from y = mx + c
Rearranging into the form y = mx + c
1★ Interpret the gradient or y-intercept from y = mx + c
Rearranging into the form y = mx + c
1★ Interpret the gradient or y-intercept from y = mx + c
Rearranging into the form y = mx + c
2★ Rearrange ax + by = c into the form y = mx + c and interpret the gradient or y-intercept (integer values only)
Rearranging into the form y = mx + c
2★ Rearrange ax + by = c into the form y = mx + c and interpret the gradient or y-intercept (integer values only)
Rearranging into the form y = mx + c
3★ Rearrange ax + by = c into y = mx + c and interpret the gradient or y-intercept
Rearranging into the form y = mx + c
3★ Rearrange ax + by = c into y = mx + c and interpret the gradient or y-intercept
Using and exploring y = mx + c
1★ Complete a table of coordinate pairs (find y coordinates)
Using and exploring y = mx + c
2★ Complete a table of coordinate pairs (find x or y coordinates)
Using and exploring y = mx + c
2★ Complete a table of coordinate pairs (find x or y coordinates)
Using and exploring y = mx + c
3★ Find the y-intercept given the gradient and a coordinate
Using and exploring y = mx + c
3★ Find the y-intercept given the gradient and a coordinate
Using and exploring y = mx + c
4★ State the equation of a line given the gradient and a coordinate
Using and exploring y = mx + c
4★ State the equation of a line given the gradient and a coordinate
Using and exploring y = mx + c
5★ Calculate the gradient given 2 coordinates
Using and exploring y = mx + c
5★ Calculate the gradient given 2 coordinates
Using and exploring y = mx + c
6★ State the equation of a line given 2 coordinate pairs
Find the equation of a parallel line
1★ Given coordinates for two lines, determine if they are parallel
Find the equation of a parallel line
2★ Write down the equation of a line parallel to y=mx+c
Find the equation of a parallel line
3★ Given 2 linear equations, determine if they are parallel
Find the equation of a parallel line
3★ Given 2 linear equations, determine if they are parallel
Find the equation of a parallel line
4★ Write the linear equation of a line parallel to y=mx+c that passes through (a,b)
Find the equation of a parallel line
5★ Given the equation of a line and the horizontal distance between this and a parallel line, find the equation of the parallel line
Find the equation of a parallel line
5★ Given the equation of a line and the horizontal distance between this and a parallel line, find the equation of the parallel line
Find the equation of a perpendicular line
1★ Write the perpendicular gradient to a given gradient
Find the equation of a perpendicular line
1★ Write the perpendicular gradient to a given gradient
Find the equation of a perpendicular line
2★ Given two pairs of coordinates from two straight lines, determine if they are perpendicular
Find the equation of a perpendicular line
3★ Write down a linear equation that is perpendicular to y=mx+c
Find the equation of a perpendicular line
3★ Write down a linear equation that is perpendicular to y=mx+c
Find the equation of a perpendicular line
4★ Given 2 linear equations, prove they are perpendicular to eachother
Find the equation of a perpendicular line
4★ Given 2 linear equations, prove they are perpendicular to eachother
Find the equation of a perpendicular line
5★ Given 2 linear equations, determine if they are perpendicular
Find the equation of a perpendicular line
5★ Given 2 linear equations, determine if they are perpendicular
Find the equation of a perpendicular line
5★ Given 2 linear equations, determine if they are perpendicular
Find the equation of a perpendicular line
6★ Write the linear equation of a line perpendicular to y=mx+c that passes through (a,b)
Equation of a tangent to a circle
1★ Write the perpendicular gradient to a given gradient
Equation of a tangent to a circle
1★ Write the perpendicular gradient to a given gradient
Equation of a tangent to a circle
2★ State the gradient of a tangent given the gradient of the radius
Equation of a tangent to a circle
2★ State the gradient of a tangent given the gradient of the radius
Equation of a tangent to a circle
3★ Find the equation of the tangent given the equation of the radius and coordinates of tangent intersection with the radius on the circumference of the circle
Equation of a tangent to a circle
4★ Find the equation of the tangent given equation of circle and coordinates of the intersection with the tangent and the radius on the circumference of the circle
Equation of a tangent to a circle
5★ Find the equation of the tangent given the equation of the circle and the x-coordinate of the intersection with the tangent and the radius on the circumference of the circle
Equation of a tangent to a circle
6★ Problem solving - e.g. find the area bounded by the axes and the tangent to a circle
Graphical solutions of equations
1★ Use a graph to solve when x=a and y=b
Graphical solutions of equations
2★ Use a graph to solve when x=a/y=b and y=mx+c
Graphical solutions of equations
3★ Use a graph to solve when y=ax+b and y=cx+d
Graphical solutions of equations
4★ Use a graph to show why there no solution to two linear equations - they are parallel
Graphical solutions of equations
5★ Use a graph to solve when a quadratic and linear equation
Quadratic and cubic functions
1★ Complete a table of coordinate pairs for simple quadratics y=x^2 or cubics y=x^3
Quadratic and cubic functions
2★ Complete a table of coordinate pairs for quadratics y=x^2+bx+c or cubics y=x^3 + bx^2 + d
Quadratic and cubic functions
3★ Draw a quadratic y=ax^2+c or cubic y=ax^3 + cx function
Quadratic and cubic functions
4★ Given a quadratic and cubic, identify the equation from a given graph
Quadratic and cubic functions
5★ Given a quadratic or cubic graph, find x or y estimates from the graph
Equation of a circle
1★ State the radius or the coordinates of the centre point given the equation of a circle
Equation of a circle
2★ Given the centre and radius state the equation of the circle
Equation of a circle
3★ Draw a circle with specific equation
Equation of a circle
4★ State the equation of a circle given its graph
Equation of a circle
5★ Does a coordinate lie on the circle given the centre and radius of the circle
Equation of a circle
6★ Problem solving - e.g. given the two points on the diameter of a circles circumference, find the equation of the circle with centre (0,0)
Area under a graph
1★ Draw a speed-time graph for a given scenario
Area under a graph
2★ Calculate the area under a speed-time graph (given that the graph is trapezium or rectangular in shape)
Area under a graph
3★ Calculate the y-axis scale given a speed-time graph and the area under the graph
Area under a graph
4★ Estimate the area under a graph (quadratic)
Area under a graph
5★ Given a curve, determine if the estimate for the area under the curve is an under or over estimate
Area under a graph
6★ Given a curve, calculate the area under the curve when it includes calculating negative areas (dependent on context)
Reciprocal functions
1★ Complete a table of coordinate pairs given a domain of values
Reciprocal functions
1★ Complete a table of coordinate pairs given a domain of values
Reciprocal functions
2★ Draw an reciprocal function given the equation and domain
Reciprocal functions
3★ Given a reciprocal and exponential function, identify the equation of a given graph
Reciprocal functions
4★ Given a reciprocal graph, find x or y estimates from the graph
Reciprocal functions
5★ Identify asymptotes of a reciprocal function given its graph
Exponential functions
1★ Complete a table of coordinate pairs given a domain of values
Exponential functions
1★ Complete a table of coordinate pairs given a domain of values
Exponential functions
2★ Draw an exponential functio given the equation and domainn
Exponential functions
3★ Given a reciprocal and exponential function, identify the equation of a given graph
Exponential functions
4★ Given an exponential graph, find x or y estimates from the graph
Exponential functions
5★ Use a graph to solve exponential equations in the form a^x=b
Trigonometry graphs
1★ Given a trigonometry graph, identify whether it is the sin, cos and tan graph
Trigonometry graphs
1★ Given a trigonometry graph, identify whether it is the sin, cos and tan graph
Trigonometry graphs
1★ Given a trigonometry graph, identify whether it is the sin, cos and tan graph
Trigonometry graphs
2★ Identify specific coordinates on a sin, cos or tan graph
Trigonometry graphs
2★ Identify specific coordinates on a sin, cos or tan graph
Trigonometry graphs
3★ Sketch y=sinx, y=cosx or y=tanx for a given domain
Trigonometry graphs
3★ Sketch y=sinx, y=cosx or y=tanx for a given domain
Trigonometry graphs
4★ Using the graph of y=sinx, y=cosx or y=tanx and 1 solution to a given equation for the same function, find another solution using the graph
Trigonometry graphs
4★ Using the graph of y=sinx, y=cosx or y=tanx and 1 solution to a given equation for the same function, find another solution using the graph
Trigonometry graphs
5★ Given a solution to sinx=a, cosx=a or tanx=a, find another solution without the aid of a graph
Trigonometry graphs
5★ Given a solution to sinx=a, cosx=a or tanx=a, find another solution without the aid of a graph
Solve linear equations (unknown on 1 side, int ans)
1★ Solve a 1 step equation by reversing the addition or subtraction of a constant
Solve linear equations (unknown on 1 side, int ans)
2★ Solve a 1 step equation by reversing a multiplication or division of a constant
Solve linear equations (unknown on 1 side, int ans)
3★ Solve a 2 step equation in the form ax+b=c where x has a positive coefficient
Solve linear equations (unknown on 1 side, int ans)
4★ Solve a 2 step equation in the form ax+b=c where x has a negative coefficient
Solve linear equations (unknown on 1 side, int ans)
5★ Solve a linear equation in the form a(x+b)=c
Solve linear equations (unknown on 1 side, int ans)
5★ Solve a linear equation in the form a(x+b)=c
Solve linear equations (unknown on 1 side, int ans)
6★ Problem solving
Solve linear equations (unknown on 1 side, dec ans)
1★ Solve a 1 step equation by reversing the addition or subtraction of a constant
Solve linear equations (unknown on 1 side, dec ans)
1★ Solve a 1 step equation by reversing the addition or subtraction of a constant
Solve linear equations (unknown on 1 side, dec ans)
2★ Solve a 1 step equation by reversing a multiplication or division of a constant
Solve linear equations (unknown on 1 side, dec ans)
2★ Solve a 1 step equation by reversing a multiplication or division of a constant
Solve linear equations (unknown on 1 side, dec ans)
3★ Solve a 2 step equation in the form ax+b=c where x has a positive coefficient
Solve linear equations (unknown on 1 side, dec ans)
3★ Solve a 2 step equation in the form ax+b=c where x has a positive coefficient
Solve linear equations (unknown on 1 side, dec ans)
4★ Solve a 2 step equation in the form ax+b=c where x has a negative coefficient
Solve linear equations (unknown on 1 side, dec ans)
4★ Solve a 2 step equation in the form ax+b=c where x has a negative coefficient
Solve linear equations (unknown on 1 side, dec ans)
5★ Solve a linear equation in the form a(x+b)=c
Solve linear equations (unknown on 1 side, dec ans)
5★ Solve a linear equation in the form a(x+b)=c
Solve linear equations (unknown both sides)
1★ Solve a linear equation with the unknown on both sides in the form ax=bx+c
Solve linear equations (unknown both sides)
2★ Solve a linear equation with unknowns on both sides in the form ax+b=cx+d where x has positive coefficients
Solve linear equations (unknown both sides)
3★ Solve a linear equation with unknowns on both sides in the form ax+b=cx+d where x has negative coefficients
Solve linear equations (unknown both sides)
4★ Solve a linear equation with unknowns on both sides in the form a(x+b)=cx+d
Solve linear equations (unknown both sides)
4★ Solve a linear equation with unknowns on both sides in the form a(x+b)=cx+d
Solve linear equations (unknown both sides)
5★ Solve a 'I think of a number' problem where the unknown number appears on both sides of a linear equation
Solve linear equations (unknown both sides)
6★ Problem solving, e.g. opposite sides of a rectangle are given as linear expressions and need to solve for an unknown
Solve linear equations with brackets
1★ Solve linear equation in the form a(x+b)=c
Solve linear equations with brackets
1★ Solve linear equation in the form a(x+b)=c
Solve linear equations with brackets
2★ Solve an equation involving the collection of like terms when finding the sum or difference of two linear expressions involving brackets
Solve linear equations with brackets
2★ Solve an equation involving the collection of like terms when finding the sum or difference of two linear expressions involving brackets
Solve linear equations with brackets
3★ Solve a linear equation in the form a(bx+c)=dx+e
Solve linear equations with brackets
3★ Solve a linear equation in the form a(bx+c)=dx+e
Solve linear equations with brackets
4★ Solve a linear equation in the form a(bx+c)=dx+e where the multiplier of the bracket is a unit fraction
Solve linear equations with brackets
4★ Solve a linear equation in the form a(bx+c)=dx+e where the multiplier of the bracket is a unit fraction
Solve linear equations with brackets
5★ Solve a linear equation involving the expansion of brackets on both sides of the equals sign
Solve linear equations with brackets
5★ Solve a linear equation involving the expansion of brackets on both sides of the equals sign
Solve linear equations with brackets
6★ Solve a linear equation involving multiple expansion of brackets
Solve rational equations
1★ Solve a linear rational equation in the form ax/b=c
Solve rational equations
1★ Solve a linear rational equation in the form ax/b=c
Solve rational equations
2★ Solve a linear rational equation in the form (ax+b)/c=d
Solve rational equations
2★ Solve a linear rational equation in the form (ax+b)/c=d
Solve rational equations
3★ Solve a linear rational equation in the form (ax+b)/(cx+d)=e
Solve rational equations
3★ Solve a linear rational equation in the form (ax+b)/(cx+d)=e
Solve rational equations
4★ Solve a linear equation with fractional expressions on each side of the equals
Solve rational equations
5★ Solve a linear rational equation where you have the sum or difference of two fractional expressions
Solve rational equations
6★ Solve a rational equation involving the sum or difference of two linear equations, that leads to solving a quadratic equation
Expand over a single bracket
1★ Expand a(x+b)
Expand over a single bracket
1★ Expand a(x+b)
Expand over a single bracket
2★ Expand a(bx+c)
Expand over a single bracket
2★ Expand a(bx+c)
Expand over a single bracket
3★ Expand x(x+a)
Expand over a single bracket
3★ Expand x(x+a)
Expand over a single bracket
4★ Expand ax(bx+c)
Expand over a single bracket
4★ Expand ax(bx+c)
Expand over a single bracket
5★ Expand the sum or difference of two linear brackets and simplify
Expand over a single bracket
5★ Expand the sum or difference of two linear brackets and simplify
Expand over a single bracket
6★ Given a linear identity in the form a(bx+c)=dx+e, identify unknown values where 1 letter is not given on each side
Expand 2 or more binomials
1★ Expand (x + a)(x + b)
Expand 2 or more binomials
1★ Expand (x + a)(x + b)
Expand 2 or more binomials
1★ Expand (x + a)(x + b)
Expand 2 or more binomials
2★ Expand (x±a)(x±b)
Expand 2 or more binomials
2★ Expand (x±a)(x±b)
Expand 2 or more binomials
2★ Expand (x±a)(x±b)
Expand 2 or more binomials
3★ Expand (x+a)(x-a)
Expand 2 or more binomials
3★ Expand (x+a)(x-a)
Expand 2 or more binomials
3★ Expand (x+a)(x-a)
Expand 2 or more binomials
4★ Expand (ax±b)(cx±d)
Expand 2 or more binomials
4★ Expand (ax±b)(cx±d)
Expand 2 or more binomials
4★ Expand (ax±b)(cx±d)
Expand 2 or more binomials
5★ Expand the product of 2 quadratic or cubic expressions
Expand 2 or more binomials
5★ Expand the product of 2 quadratic or cubic expressions
Expand 2 or more binomials
6★ Expand the product of 3 linear expressions
Expand 2 or more binomials
6★ Expand the product of 3 linear expressions
Factorise a simple expression
1★ Factorise linear expression ax±b
Factorise a simple expression
1★ Factorise linear expression ax±b
Factorise a simple expression
2★ Factorise a quadratic expression ax^2±bx
Factorise a simple expression
2★ Factorise a quadratic expression ax^2±bx
Factorise a simple expression
3★ Factorise a quadratic expression ax^2±bx with a expression common factor
Factorise a simple expression
3★ Factorise a quadratic expression ax^2±bx with a expression common factor
Factorise a simple expression
4★ Can a quadratic in the form ax^2±bx be factorised?
Factorise a simple expression
5★ Problem solving, e.g. find the sides of a rectangle given a quadratic that represents the area
Factorise a simple expression
6★ Fully factorise a linear expression by combining a sum of 2 terms where 1 is partially factorised
Factorise a quadratic expression
1★ Factorise a quadratic resulting in (x + a)(x + b)
Factorise a quadratic expression
1★ Factorise a quadratic resulting in (x + a)(x + b)
Factorise a quadratic expression
2★ Factorise a quadratic resulting in (x + a)(x - b)
Factorise a quadratic expression
2★ Factorise a quadratic resulting in (x + a)(x - b)
Factorise a quadratic expression
3★ Factorise a quadratic resulting in (x - a)(x - b)
Factorise a quadratic expression
3★ Factorise a quadratic resulting in (x - a)(x - b)
Factorise a quadratic expression
4★ Factorise a quadratic resulting in (x + a)(x - a)
Factorise a quadratic expression
4★ Factorise a quadratic resulting in (x + a)(x - a)
Factorise a quadratic expression
5★ Factorise a quadratic resulting in (ax + b)(x + c)
Factorise a quadratic expression
6★ Factorise a quadratic resulting in (ax + b)(c - dx) or (ax + b)(cx + d)
Solve a quadratic by factorising
1★ Solve a quadratic resulting in (x + a)(x + b)
Solve a quadratic by factorising
1★ Solve a quadratic resulting in (x + a)(x + b)
Solve a quadratic by factorising
2★ Solve a quadratic resulting in (x + a)(x - b)
Solve a quadratic by factorising
3★ Solve a quadratic resulting in (x - a)(x - b)
Solve a quadratic by factorising
3★ Solve a quadratic resulting in (x - a)(x - b)
Solve a quadratic by factorising
4★ Solve a quadratic resulting in (x + a)(x - a)
Solve a quadratic by factorising
5★ Solve a quadratic resulting in (ax + b)(x + c)
Solve a quadratic by factorising
6★ Solve a quadratic resulting in (ax + b)(c - dx) or (ax + b)(cx + d)
Solving quadratics in disguise
1★ Solve like a quadratic x^(2n)±bx^n+c where n>1
Solving quadratics in disguise
2★ Solving like a quadatic involving a rearrangement e.g. x^(2n)=bx^n+c where n>1
Solving quadratics in disguise
3★ Solve like a quadratic involving fractional powers e.g. x^(1/n)+bx^(1/2n)=c
Solving quadratics in disguise
4★ Solve like a quadratic involving variable as a power
Solving quadratics in disguise
5★ Solve like a quadratic involving trigonometric equations
Complete the square
1★ Completing the square (x+a)^2+b where b>0
Complete the square
2★ Completing the square (x+a)^2+b where b<0
Complete the square
3★ Completing the square of x^2+bn+c where b is divisible by 2
Complete the square
4★ Completing the square x^2+bn+c where b is not divisible by 2
Complete the square
5★ Find the minimum point of a quadratic function by completing the square
Complete the square
5★ Find the minimum point of a quadratic function by completing the square
Complete the square
6★ Identify the translation of a function given it is based on f(x)=x^2
Solve a quadratic by completing the square
1★ Solve by completing the square given part of the working
Solve a quadratic by completing the square
2★ Solve by completing the square given part of the working
Solve a quadratic by completing the square
3★ Solve by completing the square of x^2+bn+c where b is divisible by 2
Solve a quadratic by completing the square
4★ Solve by completing the square of x^2+bn+c where b is not divisible by 2
Solve a quadratic by completing the square
5★ Solve by completing the square ax^2+bx+c where a>0
Solve a quadratic by completing the square
6★ Solve by completing the square ax^2+bx+c
Solve a quadratic by using the formula
1★ Substituting positive numbers into the quadratic formula
Solve a quadratic by using the formula
2★ Substituting any numbers into the quadratic formula
Solve a quadratic by using the formula
3★ Given that numbers were correctly substituted into the quadratic formula state the quadratic equation
Solve a quadratic by using the formula
4★ Use of the discriminant to show how many roots a quadratic has
Solve a quadratic by using the formula
4★ Use of the discriminant to show how many roots a quadratic has
Solve a quadratic by using the formula
5★ Solve a quadratic using the quadratic formula
Graph transformations
1★ Describe a quadratic graph transformation in words
Graph transformations
1★ Describe a quadratic graph transformation in words
Graph transformations
2★ Describe the effect of a transformation on a single point on a quadratic function
Graph transformations
2★ Describe the effect of a transformation on a single point on a quadratic function
Graph transformations
3★ Given f(x)=x^2, state the equation of a transformation of f(x)
Graph transformations
3★ Given f(x)=x^2, state the equation of a transformation of f(x)
Graph transformations
4★ Given the transformed function of f(x)=x^2, draw it alongside f(x)
Graph transformations
5★ Describe the effect of a transformation on a single point on a trig graph
Graph transformations
5★ Describe the effect of a transformation on a single point on a trig graph
Graph transformations
6★ Draw/Identify a trig graph transformation
Graph transformations
6★ Draw/Identify a trig graph transformation
Use simple function machines
1★ Substitute an input value into a single operation function machine
Use simple function machines
2★ Substitute an input value into a 2 operation function machine
Use simple function machines
3★ Find the input value of a 2 operation function machine given the output
Use simple function machines
4★ Calculate the missing operation in a 2 operation function machine given the input and output values
Use simple function machines
5★ Write an expression to represent the output of a 2 operation function machine given the input is x
Use simple function machines
6★ Calculate the missing operation of a 2 operation function machine given the input is x and the output is in the form ax+b
Identify domain and range
1★ Identify the range of f(x)=ax given the domain
Identify domain and range
1★ Identify the range of f(x)=ax given the domain
Identify domain and range
2★ Find the corresponding domain or range values given f(x)=ax
Identify domain and range
2★ Find the corresponding domain or range values given f(x)=ax
Identify domain and range
3★ Find the range of f(x)=ax+b
Identify domain and range
3★ Find the range of f(x)=ax+b
Identify domain and range
4★ Find the corresponding domain or range values given f(x)=ax+b
Identify domain and range
4★ Find the corresponding domain or range values given f(x)=ax+b
Identify domain and range
5★ Find the domain of f(x)=ax+b given a range in set notation
Identify domain and range
6★ Find the values of f(x) for which is it is undefined
Use composite functions
1★ Find gf(x) or fg(x) for a given value knowing that f(x)=ax and g(x)=x+b
Use composite functions
2★ Find gf(x) or fg(x) for a given value knowing that f(x)=ax+b and g(x)=cx+d
Use composite functions
3★ Find gf(x) or fg(x) for a given value knowing that f(x)=ax+b and g(x)=x^2+c
Use composite functions
4★ Find fg(x) for a given value knowing that f(x)=ax^2+bx+c and g(x)=dx+e
Use composite functions
5★ Problem solving e.g. find fg(x)=gf(x) where f(x)=x^2+bx+c and g(x)=x+d
Iterations
1★ Given a1 and a(n+1)=ba(n)+c, find a2
Iterations
2★ Given a1 and a(n+1)=ba(n)+c, find a3 or a4
Iterations
3★ Real world problem where an iterative formula and a0 is given
Iterations
4★ Given x0 and an iterative formula derived from a rearranged cubic, find x3
Iterations
5★ Show that a cubic equation can be rearranged to a given iterative form
Iterations
6★ Show that a cubic equation as a solution between a given ratio
Inverse functions
1★ Rearrange a function involving only 1 operation (addition, subtraction, multiplication or division)
Inverse functions
2★ Rearrange a function involving 2 operations
Inverse functions
3★ Rearrange a function that is fractional
Inverse functions
4★ Rearrange a function involving powers
Inverse functions
5★ Rearrange a quadratic function that first involves completing the square
Read/Represent inequalities on a number line
1★ Interpreting a not equal to representation from a number line
Read/Represent inequalities on a number line
1★ Interpreting a not equal to representation from a number line
Read/Represent inequalities on a number line
2★ Interpreting an equal to representation from a number line
Read/Represent inequalities on a number line
2★ Interpreting an equal to representation from a number line
Read/Represent inequalities on a number line
3★ Interpret any inequality from a number line
Read/Represent inequalities on a number line
4★ Represent a given inequality on a number line
Read/Represent inequalities on a number line
5★ Interpret a compound inequality from a number line
Read/Represent inequalities on a number line
6★ Represent a compound inequality on a number line
Solve linear inequalities
1★ Solve a 1 step inequality by reversing the addition or subtraction of a constant
Solve linear inequalities
2★ Solve a 1 step inequality by reversing the multiplication or division of a constant
Solve linear inequalities
2★ Solve a 1 step inequality by reversing the multiplication or division of a constant
Solve linear inequalities
3★ Solve a 2 step inequality where x has a positive coefficient
Solve linear inequalities
3★ Solve a 2 step inequality where x has a positive coefficient
Solve linear inequalities
4★ Solve a 1 step inequality where x has a negative coefficient
Solve linear inequalities
4★ Solve a 1 step inequality where x has a negative coefficient
Solve linear inequalities
5★ Solve a 2 step inequality where x has a negative coefficient
Solve linear inequalities
5★ Solve a 2 step inequality where x has a negative coefficient
Solve linear inequalities
6★ Solve a compound inequality in the form of a<bx+c<d
Graphical inequalities
1★ Identify the single linear inequality from a graph in the form x<a, x>b, y<c, y>d, x≤e, x≥f, y≤g or y≥h
Graphical inequalities
1★ Identify the single linear inequality from a graph in the form x<a, x>b, y<c, y>d, x≤e, x≥f, y≤g or y≥h
Graphical inequalities
1★ Identify the single linear inequality from a graph in the form x<a, x>b, y<c, y>d, x≤e, x≥f, y≤g or y≥h
Graphical inequalities
2★ Sketch the single linear inequality on a graph in the form x<a, x>b, y<c, y>d, x≤e, x≥f, y≤g or y≥h
Graphical inequalities
2★ Sketch the single linear inequality on a graph in the form x<a, x>b, y<c, y>d, x≤e, x≥f, y≤g or y≥h
Graphical inequalities
3★ Given a graph, identify the 4 inequalities that bound a rectangular region using x<a, x>b, y<c, y>d, x≤e, x≥f, y≤g or y≥h
Graphical inequalities
4★ Identify the 3 inequalities that bound a given region including y-x>a
Graphical inequalities
5★ State the coordinates of points that satisfy a given region bounded by 3 inequalities
Solve quadratic inequalities
1★ Graphically solve a quadratic inequality in the form x^2±a<0 or x^2±a>0
Solve quadratic inequalities
2★ Graphically solve a quadratic inequality in the form x^2±a≤0 or x^2±a≥0
Solve quadratic inequalities
3★ Solve a quadratic inequality x^2±a<0, x^2±a>0, x^2±a≤0 or x^2±a≥0
Solve quadratic inequalities
4★ Solve a quadratic inequality x^2±bx±c<0, x^2±bx±c>0, x^2±bx±c≤0 or x^2±bx±c≥0
Solve quadratic inequalities
5★ Solve a quadratic inequality ax^2±bx±c<0, ax^2±bx±c>0, ax^2±bx±c≤0 or ax^2±bx±c≥0
Solve quadratic inequalities
6★ Solve a quadratic inequality (where a is not 1) that first involves a rearrangement
Recognise common sequences
1★ Continue an arithmetic sequence for the next two terms
Recognise common sequences
2★ Continue a geometric sequence for the next two terms
Recognise common sequences
3★ Continue a square or triangular sequence for the next two terms
Recognise common sequences
4★ Continue a Fibonacci sequence for the next two terms
Recognise common sequences
5★ Continue a periodic sequence for the next two terms
Recognise common sequences
6★ Continue a fractional sequence for the next two terms where the numerators and denominators each follow a linear sequence
Understand linear sequences
1★ Continue a linear sequence for the next two terms
Understand linear sequences
2★ Given the first and last term in a small linear sequence, find the missing middle values
Understand linear sequences
3★ Write the first 4 terms of a linear sequence given the nth term rule
Understand linear sequences
3★ Write the first 4 terms of a linear sequence given the nth term rule
Understand linear sequences
4★ Find the nth term rule for a linear sequence
Understand linear sequences
4★ Find the nth term rule for a linear sequence
Understand linear sequences
4★ Find the nth term rule for a linear sequence
Understand linear sequences
5★ Given a number and the first 4 terms of a linear sequence, determine if the number is part of the sequence
Understand linear sequences
6★ Given 2nd and 4th term of a linear sequence find 100th term
Understand geometric sequences
1★ Determine if a given sequence is geometric, if not, state the name of the sequence family
Understand geometric sequences
2★ Find the next 2 terms of a geometric sequence (integer common ratio)
Understand geometric sequences
3★ Find the next 2 terms of a geometric sequence (decimal common ratio)
Understand geometric sequences
3★ Find the next 2 terms of a geometric sequence (decimal common ratio)
Understand geometric sequences
4★ Given the first term and common ratio, find the first 3 terms of a geometric sequence
Understand geometric sequences
5★ Given an algebraic term to term rule and the first term, find a specific term in a geometric sequence
Understand geometric sequences
6★ Problem solving, e.g. given the 2nd and 4th term of a geometric sequence, find the 10th term
Algebraic sequences
1★ Continue an algebraic sequence that is based on an arithmetic or Fibonacci sequence
Algebraic sequences
2★ Continue an algebraic sequence that is based on a geometric sequence
Algebraic sequences
3★ Show that the sixth term of an algebraic sequence is a given expression
Algebraic sequences
4★ Find the nth term of an arithmetic algebraic sequence
Algebraic sequences
5★ Given the value of 2 terms and the first 3 terms of an arithmetic algebraic sequence, find the unknowns in the sequence
Understand quadratic sequences
1★ Continue a quadratic sequence for the next two terms
Understand quadratic sequences
2★ Write the first 4 terms a quadratic sequence given the nth term rule in the form of n^2+bn+c
Understand quadratic sequences
3★ Find the nth term rule of a quadratic sequence based on an^2
Understand quadratic sequences
4★ Find the nth term rule of a quadratic sequence based on n^2+bn+c
Understand quadratic sequences
5★ Find the nth term rule of a quadratic sequence based on an^2+bn+c
Understand quadratic sequences
6★ Use the nth term rule of a quadratic sequence based on an^2+bn+c to find a specific term
Solve linear simultaneous equations
1★ Solve 2 simultaneous equations where a term in each equation has a common coefficient
Solve linear simultaneous equations
2★ Solve 2 simultaneous equations where a term in each equation has a common term but a different sign
Solve linear simultaneous equations
3★ Solve 2 simultaneous equations where all coefficients are different
Solve linear simultaneous equations
4★ Solve a word problem that involves the creation and solving of 2 simultaneous equations
Solve linear simultaneous equations
5★ Solve 2 simultaneous equations that first involves rearranging one or both of the 2 given equations
Solve linear simultaneous equations
6★ Form and solve 2 simultaneous equations in other Maths topics
Solve non linear simultaneous equations
1★ Simultaneously solve a quadratic in the form of y=x^2 and a linear equation in the form y=ax+b
Solve non linear simultaneous equations
2★ Simultaneously solve a quadratic in the form of y=x^2±bx±c and a linear equation in the form y=ax+b
Solve non linear simultaneous equations
3★ Simultaneously solve a reciprocal equation in the form of xy=±c and a linear equation in the form y=ax+b
Solve non linear simultaneous equations
4★ Simultaneously solve a circle equation in the form of x^2+y^2=c and a linear equation in the form x+y=c (integer answers only)
Solve non linear simultaneous equations
5★ Simultaneously solve a circle equation in the form of x^2+y^2=c and a linear equation in the form x+y=c
Substitute into expressions/formula
1★ Substitute a positive value into an expression that includes only 1 operation
Substitute into expressions/formula
2★ Substitute a positive value into an expression that includes 2 operations
Substitute into expressions/formula
3★ Substitute negative values into an expression involving 2 variables
Substitute into expressions/formula
4★ Substitute values into a simple quadratic expression
Substitute into expressions/formula
5★ Substitute values into common formulae
Substitute into expressions/formula
6★ Substitute values into a linear function f(x)
Form expressions and equations
1★ Create a simple expression in the form x±a or ax based on a word problem
Form expressions and equations
2★ Create an expression to represent a word problem based I think of a number
Form expressions and equations
3★ Create a rational expression to represent a word problem based I think of a number
Form expressions and equations
4★ Create an expression based on a word problem, e.g. find the sum of 3 algebraic ages
Form expressions and equations
5★ Form and solve an equation with unknowns on both sides
Form expressions and equations
6★ Create a formula to represent the perimeter of a shape
Data handling cycle
1★ Understanding the 4 steps of the data handling cycle
Data handling cycle
2★ Determine if a given hypothesis is testable and is not opinion based
Data handling cycle
3★ Identify the given type of data
Data handling cycle
3★ Identify the given type of data
Data handling cycle
4★ Identify qualities of a good or bad survey question
Data handling cycle
4★ Identify qualities of a good or bad survey question
Data handling cycle
5★ Identify the type of sampling being used (quota/convenience/stratified/cluster/systematic)
Data handling cycle
6★ Identify causes of bias and how a sample can be improved
Calculate a stratified sample
1★ Find a stratified sample
Calculate a stratified sample
2★ Find the total frequency given the stratified sample
Capture recapture
1★ Find an easy estimate of the population
Capture recapture
2★ Find an estimate of a population
Capture recapture
3★ Find the estimate of a population given the percentage with tags
Capture recapture
4★ Critically analyse the sampling technique
Two-way tables
1★ Create a simple two-way table from images
Two-way tables
2★ Find totals from a two-way table
Two-way tables
3★ Complete missing values in a two-way table
Two-way tables
4★ Calculate probabilities or fractions of amount from a two-way table
Two-way tables
5★ Given a word problem, create and interpret a two-way table
Two-way tables
5★ Given a word problem, create and interpret a two-way table
Two-way tables
5★ Given a word problem, create and interpret a two-way table
Two-way tables
6★ Multi-skill problem solving by creating and interpreting a two-way table, including ratios or percentages
Calculate averages from a list
1★ Calculate the mode
Calculate averages from a list
2★ Calculate the median (odd number of values)
Calculate averages from a list
3★ Calculate the median (even number of values)
Calculate averages from a list
4★ Calculate the mean
Calculate averages from a list
5★ Calculate a missing value given the mean and the other values
Calculate averages from a list
6★ Write 4 numbers with a given mean, mode, median and range
Calculate quartiles from a list
1★ Calculate IQR (easy ordered list)
Calculate quartiles from a list
1★ Calculate IQR (easy ordered list)
Calculate quartiles from a list
2★ Calculate IQR (unordered list with easy quartiles)
Calculate quartiles from a list
2★ Calculate IQR (unordered list with easy quartiles)
Calculate quartiles from a list
2★ Calculate IQR (unordered list with easy quartiles)
Calculate quartiles from a list
3★ Calculate IQR (unordered list with half position values)
Calculate quartiles from a list
3★ Calculate IQR (unordered list with half position values)
Calculate quartiles from a list
4★ Calculate IQR (unordered list of decimals)
Calculate quartiles from a list
5★ IQR from a stem and leaf diagram
Calculate quartiles from a list
6★ Given the IQR and range find unknown values in a list of data
Which average should you use?
1★ Which average gives the best or worst result?
Which average should you use?
1★ Which average gives the best or worst result?
Which average should you use?
2★ State advantages or disadvantages of a specific type of average
Which average should you use?
3★ Given a data set, decide which average is best to use to represent the data
Calculate the mode/mean from a frequency table
1★ Calculate the mode from a frequency table
Calculate the mode/mean from a frequency table
2★ Calculate the total score from a frequency table
Calculate the mode/mean from a frequency table
3★ Calculate the mean from a frequency table
Calculate the mode/mean from a frequency table
4★ Calculate an estimate of the mean from a grouped frequency table
Calculate the mode/mean from a frequency table
5★ Calculate a missing score given the mean from a frequency table
Calculate the mode/mean from a frequency table
6★ Calculate a missing frequency given the mean from a frequency table
Calculate the median/IQR from a frequency table
1★ Calculate the median from a frequency table
Calculate the median/IQR from a frequency table
2★ Identify the interval that contains the median from a grouped frequency table
Calculate the median/IQR from a frequency table
3★ Use linear interpolation to find the median (always the midpoint of the interval) from a grouped frequency table
Calculate the median/IQR from a frequency table
4★ Use linear interpolation to find the median (never the midpoint of the interval) from a grouped frequency table
Calculate the median/IQR from a frequency table
5★ Find the interquartile range from a grouped frequency table
Stem and leaf diagrams
1★ Draw a stem and leaf diagram from an unordered list of data containing integers
Stem and leaf diagrams
2★ Draw a stem and leaf diagram from an unordered list of data containing decimals
Stem and leaf diagrams
3★ Interpret a stem and leaf diagram, e.g. what fraction were under a specific score?
Stem and leaf diagrams
4★ Find averages and range from a stem and leaf diagram
Stem and leaf diagrams
5★ Adding data to a stem and leaf and analysing the effects on statistical measures
Stem and leaf diagrams
6★ Analysing a back to back stem and leaf diagram
Draw/Interpret a frequency polygon
1★ Draw a frequency polygon from a grouped frequency table
Draw/Interpret a frequency polygon
2★ Interpret probabilities of events from a frequency polygon
Draw/Interpret a frequency polygon
3★ Interpret the mean from a frequency polygon
Draw/Interpret a frequency polygon
4★ Draw comparisons between 2 frequency polygons drawn on the same axes
Draw/Interpret cumulative frequency
1★ Construct a cumulative frequency table
Draw/Interpret cumulative frequency
1★ Construct a cumulative frequency table
Draw/Interpret cumulative frequency
2★ Construct a cumulative frequency table from a graph
Draw/Interpret cumulative frequency
2★ Construct a cumulative frequency table from a graph
Draw/Interpret cumulative frequency
3★ Estimate a median from a cumulative frequency graph
Draw/Interpret cumulative frequency
3★ Estimate a median from a cumulative frequency graph
Draw/Interpret cumulative frequency
3★ Estimate a median from a cumulative frequency graph
Draw/Interpret cumulative frequency
4★ Estimate the interquartile range from a cumulative frequency graph
Draw/Interpret cumulative frequency
4★ Estimate the interquartile range from a cumulative frequency graph
Draw/Interpret cumulative frequency
4★ Estimate the interquartile range from a cumulative frequency graph
Draw/Interpret cumulative frequency
5★ Estimate the number of people that scored more or less than an amount from a cumulative frequency graph
Draw/Interpret cumulative frequency
5★ Estimate the number of people that scored more or less than an amount from a cumulative frequency graph
Draw/Interpret cumulative frequency
5★ Estimate the number of people that scored more or less than an amount from a cumulative frequency graph
Draw/Interpret a box plot
1★ Draw a box plot given 5 point summary
Draw/Interpret a box plot
2★ Draw a box plot from a cumulative frequency diagram
Draw/Interpret a box plot
3★ Draw a box plot given some information given key statistical measures about a list of data
Draw/Interpret a box plot
4★ Analyze a given box plots
Draw/Interpret a box plot
4★ Analyze a given box plots
Draw/Interpret a box plot
5★ Calculate median, inter-quartile range or range from a box plot
Draw/Interpret a box plot
5★ Calculate median, inter-quartile range or range from a box plot
Draw/Interpret a box plot
5★ Calculate median, inter-quartile range or range from a box plot
Draw/Interpret a box plot
6★ Make comparisons between 2 box plots drawn on the same number line
Draw/Interpret a box plot
6★ Make comparisons between 2 box plots drawn on the same number line
Draw/Interpret a bar chart
1★ Create a tally chart from a list of data
Draw/Interpret a bar chart
2★ Given a tally chart, interpret key measures from the chart
Draw/Interpret a bar chart
3★ Draw a bar chart from a frequency table
Draw/Interpret a bar chart
4★ Interpret least/most common or frequency from a bar chart
Draw/Interpret a bar chart
5★ Draw a bar chart given a word problem that requires problem solving
Draw/Interpret a composite bar chart
1★ Analyse a composite bar chart
Draw/Interpret a composite bar chart
2★ Draw a composite bar chart given a two way table
Draw/Interpret a composite bar chart
3★ Interpret proportions from a composite bar chart
Draw/Interpret a histogram
1★ Complete a frequency density column given a grouped frequency table
Draw/Interpret a histogram
2★ Complete missing values in a grouped frequency table including frequency density column and frequency values
Draw/Interpret a histogram
3★ Estimate how many got greater than a score from a histogram
Draw/Interpret a histogram
4★ Estimate how many got greater than a score from a grouped frequency table
Draw/Interpret a histogram
5★ Construct a frequency table from a histogram
Draw/Interpret a histogram
6★ Given the frequency of one interval represented by a histogram, complete a frequency table to represent all other intervals
Construct a pictograph
1★ Given a pictogram, identify least/most common or total (involving frequencies that require only whole diagrams)
Construct a pictograph
2★ Given a pictogram, identify least/most common or total (involving frequencies that require half a diagram)
Construct a pictograph
3★ Given a pictogram, find the frequency of a category or total frequency
Construct a pictograph
4★ Draw a pictograph (involving frequencies that require only whole diagrams)
Construct a pictograph
5★ Draw a pictograph (involving frequencies that require half a diagram)
Construct a pictograph
6★ Given a pictogram, find the percentage who answered a category
Construct a pie chart
1★ Draw a pie chart (total freq 360 with categories having a frequency that is a factor of 360)
Construct a pie chart
2★ Draw a pie chart (total frequency is 90 or 180)
Construct a pie chart
3★ Draw a pie chart (total frequency is a factor of 360)
Construct a pie chart
4★ Calculate the angles needed to construct a pie chart (total frequency is not a factor of 360)
Construct a pie chart
5★ Draw a pie chart (total frequency is not a factor of 360)
Construct a pie chart
6★ Draw a pie chart where the total frequency is given but the category frequencies are expressions in terms of x
Interpret a pie chart
1★ Find the mode from a given pie chart
Interpret a pie chart
2★ Calculate the fraction represented by a sector on a given pie chart
Interpret a pie chart
3★ Given a pie chart and the frequency of a sector, calculate total frequency
Interpret a pie chart
4★ Given a pie chart and the percentage represented by 2 sectors and the total, calculate the frequency of a third sector
Draw/Interpret a scatter graph
1★ Plot a scatter diagram from a given table
Draw/Interpret a scatter graph
2★ Describe the correlation represented in a scatter graph
Draw/Interpret a scatter graph
3★ Draw a line of best fit on a given scatter graph
Draw/Interpret a scatter graph
4★ Estimate from a line of best fit on a scatter graph
Draw/Interpret a scatter graph
5★ Identify anomalies from a given scatter graph
PMCC and regression line
1★ Comment on the correlation shown in a given scatter graph
PMCC and regression line
2★ Find the PMCC from table
PMCC and regression line
3★ Interpret the meaning of the PMCC value in a given context
PMCC and regression line
4★ Calculate the regression line equation from a given table
PMCC and regression line
5★ Interpolate/extrapolate using a regression line equation formed from a given table
PMCC and regression line
6★ Limitations of using a regression line given a scatter graph
Standard deviation
1★ Substitute given values into standard deviation formula
Standard deviation
2★ Find the standard deviation from a sample list of data
Standard deviation
3★ Find the standard deviation from population list of data
Standard deviation
4★ Given the standard deviation from 2 experiments, comment on the results
Standard deviation
5★ Calculate the percentage of data within 1 standard deviation of the mean
Standard deviation
6★ Find the standard deviation from a frequency table
Normal distribution
1★ Calculate the z-score given a value, µ and the standard deviation
Normal distribution
2★ Find P(X < ?) where Z > 0
Normal distribution
3★ Find P(X < ?) or P(X > ?) where Z < 0
Normal distribution
3★ Find P(X < ?) or P(X > ?) where Z < 0
Normal distribution
4★ Find P(a < X < b)
Normal distribution
5★ Find X where Y% are less than X
Normal distribution
6★ Find µ given P(X < x)
Confidence intervals
1★ Use standard error of the mean to find the P(Z < ?)
Confidence intervals
2★ Find a z-score given a percentage confidence interval
Confidence intervals
3★ Construct a confidence interval given a sample
Confidence intervals
4★ Construct a confidence interval given a different confidence interval of the same sample
Facebook maths
1★ A look repetitive question involving the same number but different operations that focuses on the use of BIDMAS
Facebook maths
2★ Solving simultaneous equations but depicted as fruit
Facebook maths
3★ Order of operation circles
Place value
1★ Interpret the blocks
Place value
2★ Read the place value of a digit in a given integer
Place value
3★ 100/10/1 more or less than a specific number
Place value
4★ Read the place value of a digit within a given decimal
Place value
5★ Convert a number described in words into a numerical form
Place value
6★ Convert numbers into words
Times tables
1★ 2, 5 and 10 times tables
Times tables
2★ First half of 3 and 4 times tables
Times tables
3★ Second half of 3 and 4 times tables
Times tables
3★ Second half of 3 and 4 times tables
Times tables
4★ 6 and first half of 8 times tables
Times tables
5★ Second half of 8 times tables
Times tables
6★ 7, 9, 11 and 12 times tables
Commutative, associative and distributive laws
1★ Commutative law involving only addition or multiplication
Commutative, associative and distributive laws
2★ Commutative law involving a combination of addition and multiplication
Commutative, associative and distributive laws
3★ Associative law
Commutative, associative and distributive laws
4★ Distributive law
Commutative, associative and distributive laws
5★ Identify which number law is being shown
Commutative, associative and distributive laws
6★ Evaluate calculations based on the use of the number laws
Related calculations
1★ Given a calculation, evaluate a simple rearrangement of the same calculation
Related calculations
2★ Given a calculation, evaluate a rearrangement of the same calculation with the numbers having been changed by multiplying or dividing by positive powers of 10
Related calculations
3★ Given a calculation, evaluate a rearrangement of the same calculation with a number having been multiplied or divided by a negative power of 10
Related calculations
4★ Given a calculation, evaluate a rearrangement of the same calculation with both numbers having been multiplied or divided by a negative power of 10
Factors and multiples
1★ Write down all the factors of a number
Factors and multiples
2★ Write down the first 5 multiples of a number
Factors and multiples
3★ Find a common factor of 2 numbers
Factors and multiples
4★ Find the HCF or LCM of 2 numbers
Factors and multiples
5★ Find the HCF or LCM of 3 numbers
Factors and multiples
6★ Find a second number given 1 number and their LCM
Prime factors
1★ Write down a specific prime number
Prime factors
2★ Calculate a number from a product of its prime factors
Prime factors
3★ Write a number as product of its prime factors
Prime factors
4★ Finish an incomplete product of prime factors
Prime factors
5★ Find the LCM or HCF of 2 numbers
Prime factors
5★ Find the LCM or HCF of 2 numbers
Prime factors
6★ Problem solving, e.g. given a number written as a product of its prime factors, find a multiple of this number written as prime factors
Order of operations
1★ Evaluate a simple calculation involving a combination of addition, subtraction, multiplication or division
Order of operations
2★ Evaluate a calculation involving brackets
Order of operations
3★ Evaluate a calculation involving brackets and powers
Order of operations
4★ Find the value of a multi-step calculation involving the application of all parts of BIDMAS
Order of operations
5★ Find the value of a fractional calculation with steps to evaluate in both the numerator and denominator
Order of operations
6★ Insert brackets into a calculation to make it true
Interpret fractions
1★ Identify the unit fraction from a given diagram
Interpret fractions
2★ Shade a unit fraction of a diagram
Interpret fractions
3★ Read simple fractions from a diagram
Interpret fractions
4★ Represent simple fractions on a diagram
Interpret fractions
5★ Understanding equivalences from shaded rows or columns of a diagram
Interpret fractions
5★ Understanding equivalences from shaded rows or columns of a diagram
Interpret fractions
6★ Read a given diagram as a mixed number
Equivalent fractions
1★ Simplify a fraction given the denominator of the simplified fraction
Equivalent fractions
2★ Simplify a fraction
Equivalent fractions
3★ Compare 2 fractions using an equals or inequalities
Equivalent fractions
4★ Would you rather have this ... or this ...?
Equivalent fractions
5★ Find half way between 2 fractions
Equivalent fractions
6★ Convert to and from a mixed number
Equivalent fractions
6★ Convert to and from a mixed number
Reciprocals of numbers
1★ Given an integer, provide the reciprocal so the product equals 1
Reciprocals of numbers
2★ Reciprocal of integers
Reciprocals of numbers
3★ Reciprocal of fractions
Reciprocals of numbers
4★ Reciprocal of decimals < 1
Reciprocals of numbers
5★ Reciprocal of fractions or decimals > 1
Reciprocals of numbers
6★ Equivalent fraction fill in the blank reciprocals
Add or subtract fractions
1★ What fraction is needed to complete a diagram?
Add or subtract fractions
2★ Two fractions with common denominators
Add or subtract fractions
3★ Two fractions with different denominators
Add or subtract fractions
4★ Combination of adding and subtracting 3 fractions
Add or subtract fractions
5★ Mixed numbers
Add or subtract fractions
6★ Simple algebraic fractions
Write one number as a fraction of another
1★ Write the amount shaded as a fraction of the total
Write one number as a fraction of another
1★ Write the amount shaded as a fraction of the total
Write one number as a fraction of another
2★ Write one number as a fraction of another
Write one number as a fraction of another
2★ Write one number as a fraction of another
Write one number as a fraction of another
3★ Understanding complements when finding a fraction of an amount
Write one number as a fraction of another
3★ Understanding complements when finding a fraction of an amount
Write one number as a fraction of another
4★ Write one measurement as a fraction of another when they are given with different units
Write one number as a fraction of another
4★ Write one measurement as a fraction of another when they are given with different units
Write one number as a fraction of another
5★ Given a total and the quantities of two of the three items in the total, write the third as fraction of the total
Write one number as a fraction of another
5★ Given a total and the quantities of two of the three items in the total, write the third as fraction of the total
Write one number as a fraction of another
6★ Equivalent fraction problem
Fraction of an amount (part i)
1★ Multiply a fraction by an integer
Fraction of an amount (part i)
2★ Multiply a fraction by a fraction
Fraction of an amount (part i)
3★ Find a fraction of an amount
Fraction of an amount (part i)
3★ Find a fraction of an amount
Fraction of an amount (part i)
4★ Which of two fraction of amounts statements is larger?
Fraction of an amount (part i)
5★ Word problem involving expenditure
Fraction of an amount (part i)
6★ Fraction of one amount is equal to fraction of unknown, find the unknown
Fraction of an amount (part ii)
1★ Unit fraction of an amount
Fraction of an amount (part ii)
2★ Non-unit fraction of an amount
Fraction of an amount (part ii)
3★ Mixed number of an amount
Fraction of an amount (part ii)
3★ Mixed number of an amount
Fraction of an amount (part ii)
4★ Increase or decrease by a fraction
Fraction of an amount (part ii)
5★ Word problems
Fraction of an amount (part ii)
6★ Fraction between 2 numbers
Multiply or divide fractions
1★ Given an integer, provide the reciprocal so the product equals 1
Multiply or divide fractions
2★ Integer by a fraction
Multiply or divide fractions
3★ 2 fractions
Multiply or divide fractions
3★ 2 fractions
Multiply or divide fractions
4★ 3 fractions
Multiply or divide fractions
5★ Mixed numbers
Multiply or divide fractions
6★ Simple algebraic fractions
Multiply or divide fractions
6★ Simple algebraic fractions
FDP conversion
1★ Convert between common FDP
FDP conversion
2★ Convert between FDP
FDP conversion
2★ Convert between FDP
FDP conversion
2★ Convert between FDP
FDP conversion
3★ Are 2 numbers written in different number formats (FDP) equal?
FDP conversion
4★ Order FDP
FDP conversion
5★ Convert a recurring decimal to a fraction where the recurring digit is the first decimal place
FDP conversion
6★ Convert a recurring decimal to a fraction (harder)
Order numbers
1★ Order positive integers
Order numbers
2★ Order positives and negatives
Order numbers
3★ Order decimals
Order numbers
4★ Order FDP
Order numbers
5★ Order fractions
Order numbers
6★ Order numbers written in standard form
Order numbers
6★ Order numbers written in standard form
Efficient use of a calculator
1★ Calculator familiarisation - identify what function a button has on a calculator
Efficient use of a calculator
1★ Calculator familiarisation - identify what function a button has on a calculator
Efficient use of a calculator
2★ Enter BIDMAS related calculations on a calculator
Efficient use of a calculator
2★ Enter BIDMAS related calculations on a calculator
Efficient use of a calculator
3★ Identify whether a number is prime on a calculator
Efficient use of a calculator
3★ Identify whether a number is prime on a calculator
Efficient use of a calculator
4★ Evaluate a given expression by substituting in both positive and negative values
Efficient use of a calculator
5★ Evaluate a calculation invovling standard form on a calculator
Efficient use of a calculator
6★ Perform fraction calculations on a calculator
Operate with integers (+ and -)
1★ Numbers bonds to 10 or 100
Operate with integers (+ and -)
2★ Alternative vocabulary for addition or subtraction
Operate with integers (+ and -)
2★ Alternative vocabulary for addition or subtraction
Operate with integers (+ and -)
3★ 1 digit integer ± 1 digit integer
Operate with integers (+ and -)
4★ 2 digit integer ± 2 digit integer
Operate with integers (+ and -)
4★ 2 digit integer ± 2 digit integer
Operate with integers (+ and -)
4★ 2 digit integer ± 2 digit integer
Operate with integers (+ and -)
4★ 2 digit integer ± 2 digit integer
Operate with integers (+ and -)
5★ 3 digit integer ± 2 digit integer
Operate with integers (+ and -)
5★ 3 digit integer ± 2 digit integer
Operate with integers (+ and -)
5★ 3 digit integer ± 2 digit integer
Operate with integers (+ and -)
6★ Directed number calculations
Operate with integers (+ and -)
6★ Directed number calculations
Operate with integers (+ and -)
6★ Directed number calculations
Operate with integers (x and ÷)
1★ Times tables
Operate with integers (x and ÷)
1★ Times tables
Operate with integers (x and ÷)
2★ Alternate vocabulary to multiplication or division
Operate with integers (x and ÷)
3★ 2 digit integer x÷ 1 digit integer
Operate with integers (x and ÷)
3★ 2 digit integer x÷ 1 digit integer
Operate with integers (x and ÷)
3★ 2 digit integer x÷ 1 digit integer
Operate with integers (x and ÷)
4★ 3 digit integer x÷ 2 digit integer
Operate with integers (x and ÷)
4★ 3 digit integer x÷ 2 digit integer
Operate with integers (x and ÷)
4★ 3 digit integer x÷ 2 digit integer
Operate with integers (x and ÷)
5★ Directed numbers calculations
Operate with integers (x and ÷)
5★ Directed numbers calculations
Operate with integers (x and ÷)
5★ Directed numbers calculations
Column multiplication
1★ 2 digit integer x 1 digit integer
Column multiplication
1★ 2 digit integer x 1 digit integer
Column multiplication
2★ 2 digit integer x 2 digit integer
Column multiplication
2★ 2 digit integer x 2 digit integer
Column multiplication
3★ 3 digit integer x 2 digit integer
Column multiplication
3★ 3 digit integer x 2 digit integer
Column multiplication
4★ Identify the last digit of a multiplication answer
Column multiplication
4★ Identify the last digit of a multiplication answer
Column multiplication
4★ Identify the last digit of a multiplication answer
Column multiplication
5★ Fill in the missing number of 3 digit integer x 2 digit integer calculation given all the working
Column multiplication
5★ Fill in the missing number of 3 digit integer x 2 digit integer calculation given all the working
Column multiplication
6★ 3 digit integer x 3 digit integer
Short division
1★ Inverse times tables
Short division
1★ Inverse times tables
Short division
2★ Division by integer with integer answer
Short division
3★ Complete the short division calculation using the bus stop method
Short division
3★ Complete the short division calculation using the bus stop method
Short division
4★ Division by integer with decimal answer
Short division
5★ Dividing decimal by integer
Short division
6★ Dividing an integer by a decimal
Product rule for counting
1★ Product of 3 or 4 numbers
Product rule for counting
2★ Simple product rule for counting
Product rule for counting
3★ Given the final product, find how many of one type there are
Product rule for counting
4★ Pin related problems
Operate with decimals (+ and -)
1★ Decimal (1dp) ± integer
Operate with decimals (+ and -)
2★ Integer ± decimal (1dp)
Operate with decimals (+ and -)
3★ Decimal (1dp) ± decimal (1dp) both less than 1
Operate with decimals (+ and -)
4★ Decimal (1dp) ± decimal (1dp) both more than 1
Operate with decimals (+ and -)
5★ Decimal ± Decimal (2 or more dp)
Operate with decimals (+ and -)
5★ Decimal ± Decimal (2 or more dp)
Operate with decimals (+ and -)
6★ Recurring decimal ± decimal
Operate with decimals (x and ÷)
1★ Decimal (1dp) multiplied by a power of 10
Operate with decimals (x and ÷)
2★ Decimal (1dp) divided by a power of 10
Operate with decimals (x and ÷)
3★ Decimal (1dp) x÷ integer
Operate with decimals (x and ÷)
3★ Decimal (1dp) x÷ integer
Operate with decimals (x and ÷)
4★ Decimal x÷ decimal (both 1 or 2 dp)
Operate with decimals (x and ÷)
4★ Decimal x÷ decimal (both 1 or 2 dp)
Operate with decimals (x and ÷)
4★ Decimal x÷ decimal (both 1 or 2 dp)
Operate with decimals (x and ÷)
5★ Decimal x÷ decimal (2 or more dp)
Operate with decimals (x and ÷)
6★ Contextualised use of x÷ with decimals
Money problems
1★ Given a shopping list of prices, calculate the cost of buying 1 each of two items
Money problems
2★ Given a shopping list of prices, calculate the cost of buying multiple items
Money problems
3★ Given a shopping list of prices, calculate the cost of buying multiple items with different units of money, e.g. £ and p
Money problems
4★ Given a shopping list, calculate the change due from making a multi item purchase
Money problems
5★ Given a shopping list, calculate how many can I buy of 1 item?
Money problems
6★ What proportion of the total cost of purchasing multiple items doe 1 item represent?
Money problems - payment plans
1★ How much do I pay each month? (No deposit)
Money problems - payment plans
1★ How much do I pay each month? (No deposit)
Money problems - payment plans
2★ How much do I pay each month? (With deposit)
Money problems - payment plans
2★ How much do I pay each month? (With deposit)
Money problems - payment plans
3★ Given 2 offers from different shops, is it better value to buy now or spread the payments?
Money problems - payment plans
3★ Given 2 offers from different shops, is it better value to buy now or spread the payments?
Money problems - payment plans
4★ Deposit with equal payments and one-off interest
Pay slips
1★ Calculating gross pay
Pay slips
1★ Calculating gross pay
Pay slips
2★ Calculating gross pay inc overtime
Pay slips
2★ Calculating gross pay inc overtime
Pay slips
3★ Calculating the total deductions or net pay
Pay slips
3★ Calculating the total deductions or net pay
Pay slips
3★ Calculating the total deductions or net pay
Pay slips
3★ Calculating the total deductions or net pay
Pay slips
4★ Calculate the monthly tax for a basic rate tax earner given the 20% and personal tax free allowance thresholds
Pay slips
5★ Calculate the monthly tax for a high income earner given the tax free personal allowance, 20% tax and 40% tax thresholds
Pay slips
6★ Calculate National Insurance given annual salary and personal tax free threshold
Percentage of an amount
1★ Percentage to find is a multiple of 10
Percentage of an amount
1★ Percentage to find is a multiple of 10
Percentage of an amount
2★ Percentage to find is a multiple of 5 (exc multiples of 10)
Percentage of an amount
2★ Percentage to find is a multiple of 5 (exc multiples of 10)
Percentage of an amount
3★ Percentage to find is a multiple of 1
Percentage of an amount
3★ Percentage to find is a multiple of 1
Percentage of an amount
4★ Calculator use
Percentage of an amount
5★ Percentage to find is a multiple of 0.5
Percentage of an amount
5★ Percentage to find is a multiple of 0.5
Percentage of an amount
6★ Populate and interpret a two-way table based on percentages of a population
Percentage change
1★ Recognise that percentage is out of 100
Percentage change
2★ Write one number as a percentage of another (out of 100)
Percentage change
3★ Write one number as a percentage of another (not out of 100)
Percentage change
4★ Find a simple percentage change
Percentage change
5★ Contextualised percentage change
Percentage change
6★ Percentage change from a compound interest problem
Increase/decrease by a percentage
1★ Increase/decrease by a percentage where the percentage is a multiple of 10
Increase/decrease by a percentage
1★ Increase/decrease by a percentage where the percentage is a multiple of 10
Increase/decrease by a percentage
2★ Increase/decrease by a percentage where the percentage is a multiple of 5 (exc multiples of 10)
Increase/decrease by a percentage
2★ Increase/decrease by a percentage where the percentage is a multiple of 5 (exc multiples of 10)
Increase/decrease by a percentage
3★ Increase/decrease by a percentage where the percentage is a multiple of 1
Increase/decrease by a percentage
3★ Increase/decrease by a percentage where the percentage is a multiple of 1
Increase/decrease by a percentage
4★ Increase/decrease by a percentage where the percentage is a multiple of 0.5
Increase/decrease by a percentage
5★ Effect of using a decimal multiplier on a number
Increase/decrease by a percentage
6★ Explain why a x% increase followed by an x% decrease does not give the original number
Reverse percentage
1★ What percentage is left after increasing or decreasing a number by a percentage
Reverse percentage
2★ Effect of using a decimal multiplier on a number
Reverse percentage
2★ Effect of using a decimal multiplier on a number
Reverse percentage
3★ Simple reverse percentage
Reverse percentage
3★ Simple reverse percentage
Reverse percentage
4★ Reverse percentage based on compound interest/decay
Simple interest
1★ Interest earned after 1 year
Simple interest
1★ Interest earned after 1 year
Simple interest
2★ Total after n years (where % is an integer)
Simple interest
3★ Total after n years (where % is not integer)
Simple interest
4★ Total after n years (where % is less than 1)
Simple interest
5★ Calculate the interest rate given the total and the number of years
Simple interest
6★ Problem solving
Calculate growth/decay
1★ Effect of using a decimal multiplier on a number
Calculate growth/decay
1★ Effect of using a decimal multiplier on a number
Calculate growth/decay
2★ Growth/decay percentage is an integer
Calculate growth/decay
2★ Growth/decay percentage is an integer
Calculate growth/decay
3★ Growth/decay percentage is a decimal (1dp)
Calculate growth/decay
3★ Growth/decay percentage is a decimal (1dp)
Calculate growth/decay
4★ Find the number of years to exceed a given amount
Calculate growth/decay
5★ Find the percentage growth/decay
Annual equivalent rate
1★ Compound interest
Annual equivalent rate
2★ Calculate AER
Annual equivalent rate
3★ Calculate how much would be in an account
Annual equivalent rate
4★ Which is better value?
Annual equivalent rate
5★ Backwards AER questions
Estimation
1★ Estimate the product of a decimal and integer
Estimation
2★ Estimate money total
Estimation
3★ Estimate a decimal divided by a decimal (greater than 1)
Estimation
4★ Estimate a decimal divided by a decimal (less than 1)
Estimation
5★ Estimate square roots/cube roots
Estimation
6★ Estimate the value of longer BIDMAS related calculations
Fermi
1★ Estimate key facts that relate to general knowledge fermi questions
Fermi
2★ Key conversion questions e.g. time units, measures of length, speed/distance/time
Fermi
3★ Short Fermi questions
Truncation
1★ Truncate to 10, 100 or 1000
Truncation
1★ Truncate to 10, 100 or 1000
Truncation
2★ Truncate to dp or sf
Truncation
2★ Truncate to dp or sf
Truncation
3★ Error interval when truncated to 10, 100 or 1000
Truncation
4★ Error interval when truncated to dp or sf
Truncation
5★ Caculate the error interval relating to a contextualised word problem
Basic rules of rounding (inc dp and bounds)
1★ Round to the nearest 100
Basic rules of rounding (inc dp and bounds)
1★ Round to the nearest 100
Basic rules of rounding (inc dp and bounds)
1★ Round to the nearest 100
Basic rules of rounding (inc dp and bounds)
2★ Round to the nearest 10
Basic rules of rounding (inc dp and bounds)
2★ Round to the nearest 10
Basic rules of rounding (inc dp and bounds)
2★ Round to the nearest 10
Basic rules of rounding (inc dp and bounds)
3★ Round to the nearest integer
Basic rules of rounding (inc dp and bounds)
3★ Round to the nearest integer
Basic rules of rounding (inc dp and bounds)
4★ Round to 1dp
Basic rules of rounding (inc dp and bounds)
5★ Round to 2dp