Misconception generator

Feel free to use or add to the FREE misconception community library using the tools below. When using the misconception, they are to be used to generate freely available resources. For any commercial services looking to embed or share the misconceptions via social media, please contact me first.

Shared/Live misconceptions

In this section you can view and download any of the shared misconceptions.

Algebra vocabulary and understandingL1

1★ What is it? (term, expression, equation, formula or identity?)

Simplify an expressionL1

1★ Single variable addition and subtraction

Simplify an expressionL2

2★ Addition and subtraction of multiples of a single variable

Simplify an expressionL3

3★ Multiplying and dividing terms

Simplify an expressionL4

4★ Collecting two or more variables

Simplify an expressionL5

5★ Collecting two or more variables inc powers

Change the subjectL1

1★ Rearrange in 1 step

Change the subjectL2

2★ Rearrange in 2 steps

Identify coordinates in all 4 quadrantsL1

1★ First quadrant only

Identify coordinates in all 4 quadrantsL2

2★ First and second quadrant only

Identify coordinates in all 4 quadrantsL3

3★ Third and fourth quadrants only

Identify coordinates in all 4 quadrantsL4

4★ All quadrants

Identify coordinates in all 4 quadrantsL6

6★ Find the midpoint of a line between 2 points

Find and use y = a, x = a and y = xL1

1★ State the equation from a graph

Find y = mx + c from a graphL1

1★ Find the y-intercept

Find the equation of a perpendicular lineL1

1★ Write the perpendicular gradient to a given gradient

Area under a graphL1

1★ Draw a speed-time graph for a given scenario

Area under a graphL2

2★ Calculate the area under a speed-time graph (given that the graph is trapezium or rectangular in shape)

Solve linear equations (unknown on 1 side, int ans)L1

1★ Solve a 1 step equation by reversing the addition or subtraction of a constant

Solve linear equations (unknown on 1 side, int ans)L2

2★ Solve a 1 step equation by reversing a multiplication or division of a constant

Solve linear equations (unknown on 1 side, int ans)L3

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)L4

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)L5

5★ Solve a linear equation in the form a(x+b)=c

Solve linear equations (unknown both sides)L2

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)L4

4★ Solve a linear equation with unknowns on both sides in the form a(x+b)=cx+d

Expand over a single bracketL1

1★ Expand a(x+b)

Expand over a single bracketL3

3★ Expand x(x+a)

Expand 2 or more binomialsL1

1★ Expand (x + a)(x + b)

Expand 2 or more binomialsL2

2★ Expand (x±a)(x±b)

Factorise a simple expressionL1

1★ Factorise linear expression ax±b

Factorise a quadratic expressionL1

1★ Factorise a quadratic resulting in (x + a)(x + b)

Factorise a quadratic expressionL2

2★ Factorise a quadratic resulting in (x + a)(x - b)

Factorise a quadratic expressionL3

3★ Factorise a quadratic resulting in (x - a)(x - b)

Factorise a quadratic expressionL4

4★ Factorise a quadratic resulting in (x + a)(x - a)

Solve a quadratic by factorisingL1

1★ Solve a quadratic resulting in (x + a)(x + b)

Solve a quadratic by factorisingL2

2★ Solve a quadratic resulting in (x + a)(x - b)

Complete the squareL2

2★ Completing the square (x+a)^2+b where b<0

Solve a quadratic by using the formulaL4

4★ Use of the discriminant to show how many roots a quadratic has

Use simple function machinesL3

3★ Find the input value of a 2 operation function machine given the output

Use composite functionsL1

1★ Find gf(x) or fg(x) for a given value knowing that f(x)=ax and g(x)=x+b

Read/Represent inequalities on a number lineL1

1★ Interpreting a not equal to representation from a number line

Read/Represent inequalities on a number lineL2

2★ Interpreting an equal to representation from a number line

Solve linear inequalitiesL4

4★ Solve a 1 step inequality where x has a negative coefficient

Recognise common sequencesL1

1★ Continue an arithmetic sequence for the next two terms

Recognise common sequencesL2

2★ Continue a geometric sequence for the next two terms

Understand linear sequencesL2

2★ Given the first and last term in a small linear sequence, find the missing middle values

Understand linear sequencesL3

3★ Write the first 4 terms of a linear sequence given the nth term rule

Understand linear sequencesL4

4★ Find the nth term rule for a linear sequence

Understand geometric sequencesL2

2★ Find the next 2 terms of a geometric sequence (integer common ratio)

Solve linear simultaneous equationsL2

2★ Solve 2 simultaneous equations where a term in each equation has a common term but a different sign

Solve non linear simultaneous equationsL4

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)

Substitute into expressions/formulaL1

1★ Substitute a positive value into an expression that includes only 1 operation

Substitute into expressions/formulaL2

2★ Substitute a positive value into an expression that includes 2 operations

Capture recaptureL1

1★ Find an easy estimate of the population

Capture recaptureL2

2★ Find an estimate of a population

Capture recaptureL3

3★ Find the estimate of a population given the percentage with tags

Capture recaptureL4

4★ Critically analyse the sampling technique

Calculate averages from a listL1

1★ Calculate the mode

Calculate averages from a listL2

2★ Calculate the median (odd number of values)

Calculate averages from a listL3

3★ Calculate the median (even number of values)

Calculate the mode/mean from a frequency tableL1

1★ Calculate the mode from a frequency table

Calculate the mode/mean from a frequency tableL2

2★ Calculate the total score from a frequency table

Calculate the mode/mean from a frequency tableL3

3★ Calculate the mean from a frequency table

Draw/Interpret a histogramL3

3★ Estimate how many got greater than a score from a histogram

Construct a pictogramL4

4★ Draw a pictogram (involving frequencies that require only whole diagrams)

Place valueL3

3★ 100/10/1 more or less than a specific number

Commutative, associative and distributive lawsL1

1★ Commutative law involving only addition or multiplication

Factors and multiplesL1

1★ Write down all the factors of a number

Factors and multiplesL2

2★ Write down the first 5 multiples of a number

Factors and multiplesL3

3★ Find a common factor of 2 numbers

Prime factorsL1

1★ Write down a specific prime number

Prime factorsL2

2★ Calculate a number from a product of its prime factors

Prime factorsL3

3★ Write a number as product of its prime factors

Prime factorsL4

4★ Finish an incomplete product of prime factors

Prime factorsL5

5★ Find the LCM or HCF of 2 numbers

Order of operationsL1

1★ Evaluate a simple calculation involving a combination of addition, subtraction, multiplication or division

Order of operationsL2

2★ Evaluate a calculation involving brackets

Order of operationsL3

3★ Evaluate a calculation involving brackets and powers

Order of operationsL4

4★ Find the value of a multi-step calculation involving the application of all parts of BIDMAS

Interpret fractionsL1

1★ Identify the unit fraction from a given diagram

Equivalent fractionsL1

1★ Simplify a fraction given the denominator of the simplified fraction

Equivalent fractionsL2

2★ Simplify a fraction

Equivalent fractionsL3

3★ Compare 2 fractions using an equals or inequalities

Add or subtract fractionsL1

1★ What fraction is needed to complete a diagram?

Add or subtract fractionsL2

2★ Two fractions with common denominators

Add or subtract fractionsL3

3★ Two fractions with different denominators

Add or subtract fractionsL4

4★ Combination of adding and subtracting 3 fractions

Fraction of an amount (part i)L1

1★ Multiply a fraction by an integer

Multiply or divide fractionsL2

2★ Integer by a fraction

Multiply or divide fractionsL3

3★ 2 fractions

FDP conversionL1

1★ Convert between common FDP

Order numbersL1

1★ Order positive integers

Order numbersL2

2★ Order positives and negatives

Column multiplicationL1

1★ 2 digit integer x 1 digit integer

Column multiplicationL3

3★ 3 digit integer x 2 digit integer

Short divisionL2

2★ Division by integer with integer answer

Short divisionL4

4★ Division by integer with decimal answer

Pay slipsL6

6★ Calculate National Insurance given annual salary and personal tax free threshold

Percentage of an amountL1

1★ Percentage to find is a multiple of 10

Percentage of an amountL2

2★ Percentage to find is a multiple of 5 (exc multiples of 10)

Percentage changeL4

4★ Find a simple percentage change

Reverse percentageL3

3★ Simple reverse percentage

Basic rules of rounding (inc dp and bounds)L3

3★ Round to the nearest integer

Basic rules of rounding (inc dp and bounds)L5

5★ Round to 2dp

Upper and lower bound calculationsL1

1★ Define the bounds/error interval of a number

Squares, cubes and rootsL2

2★ Knowledge of square numbers up to 225

Squares, cubes and rootsL3

3★ Knowledge of square roots of numbers up to 225

Squares, cubes and rootsL4

4★ Combination of operations with squares and roots of numbers

Use the laws of indicesL1

1★ 1st index law - multiplying terms

Use the laws of indicesL2

2★ 2nd index law - dividing terms

Use the laws of indicesL3

3★ Mixture of 1st and 2nd index law

Use the laws of indicesL3

3★ Mixture of 1st and 2nd index law

Use the laws of indicesL4

4★ 3rd index law - power of power

Use the laws of indicesL5

5★ Harder 3rd index law involving simple algebraic expressions raised to a power

Use the laws of indicesL6

6★ Write a calculation as a single power of a number

Integers with negative/fractional indicesL2

2★ To the power of a negative number

Conversion of standard formL2

2★ Convert to standard form (numbers greater than 1)

Operate in standard formL2

2★ Add and subtract numbers written in standard form with different powers of 10

Simplify a surdL5

5★ Simplify a surd

Measuring/Drawing anglesL2

2★ Measuring acute/90°/obtuse angles using a protractor

Constructions/lociL4

4★ Construct a perpendicular bisector using loci constructions

90°, 180°, and 360° anglesL1

1★ Calculate an unknown angle on a straight line

90°, 180°, and 360° anglesL2

2★ Use the vertically opposite angles property to find an unknown angle

90°, 180°, and 360° anglesL3

3★ Calculate an angle using the fact that a right angle is 90°

90°, 180°, and 360° anglesL4

4★ Calculate an unknown angle using the fact angles around a point sum to 360°

Angles in trianglesL1

1★ Name a given triangle

Angles in trianglesL2

2★ Calculate an unknown angle in a triangle

Angles in trianglesL3

3★ Calculate an unknown angle in an equilateral triangle

Angles in trianglesL4

4★ Calculate an unknown angle in a right angle triangle

Angles in trianglesL5

5★ Calculate an unknown angle in an isosceles triangle

Angles in quadrilateralsL1

1★ Name a given quadrilateral

Angles in quadrilateralsL2

2★ Calculate an unknown angle in a quadrilateral

Angles in quadrilateralsL3

3★ Calculate an unknown angle in a quadrilateral where one angle is 90°

Angles in quadrilateralsL4

4★ Calculate an unknown exterior angle given 3 interior angles

Angles in quadrilateralsL5

5★ Calculate an unknown angle in special quadrilaterals

Angles on parallel linesL1

1★ Revision of all angle types

Angles on parallel linesL2

2★ Application of both angles on parallel lines and angles on a straight line

Angles in polygonsL1

1★ Find the interior angle sum of a polygon

BearingsL2

2★ Measure a bearing

ReflectionsL4

4★ Reflect a shape in x=a/y=a

ReflectionsL6

6★ Describe the reflection transformation

TranslationsL5

5★ Describe a vector translation

Area of 2D shapesL1

1★ Calculate the area of a shape by counting squares

Area of 2D shapesL2

2★ Calculate the area of a triangle or rectangle

Area of 2D shapesL3

3★ Calculate the area of a parallelogram

Area of 2D shapesL4

4★ Calculate the area of a trapezium

Area of composite shapesL1

1★ Calculate the area of a compound shape made from combining 2 rectangles

Area of composite shapesL2

2★ Calculate the area of a compound shape made from combining 2 triangles

Area of composite shapesL3

3★ Calculate the area of a compound shape made from combining a triangle and a rectangle

Area of composite shapesL4

4★ Calculate the area of a compound shape made from combining a triangle and a semi circle

Perimeter of 2D shapesL2

2★ Calculate the perimeter of a given square, rectangle or triangle

Perimeter of 2D shapesL3

3★ Calculate the perimeter of a simple compound shape made from rectangles

Parts of a circleL3

3★ Name the given part of a circle

Circumference of a circleL2

2★ Calculate the circumference given the radius

Area of a circleL2

2★ Calculate the area of a circle given the diameter

Circle theoremsL1

1★ Calculate an unknown angle using the angles in a semi-circle theorem

Apply Pythagoras' TheoremL2

2★ Calculate a shorter side of a right angled triangle

Apply Pythagoras' TheoremL5

5★ Calculate the distance between 2 coordinates

Apply SOH CAH TOAL2

2★ Apply SOH CAH TOA to calculate a side in a right-angled triangle

Surface area of 3D shapesL2

2★ Surface area of a cube or cuboid

Surface area of 3D shapesL3

3★ Surface area of a cylinder or triangular prism

Volume of 3D shapesL2

2★ Calculate the volume of a cuboid

Volume of 3D shapesL4

4★ Calculate the volume of a cylinder or triangular prism

List outcomesL2

2★ List outcomes from 2 events (sample space table)

List outcomesL3

3★ Given a menu options for 3 courses, create a sample space diagram to show all possible outcomes of selecting 2 courses

Calculate simple probabilitiesL3

3★ Calculate the probability of selecting a letter from a given word

Calculate simple probabilitiesL4

4★ Calculate the probability of an event given a simple sample space diagram showing all possible outcomes from 2 events

Calculate simple probabilitiesL5

5★ Calculate the probability of an event from a sample space diagram showing all possible outcomes from 2 events

Mutually exclusive eventsL1

1★ Calculate the probability of a simple mutually exclusive event

Calculate relative/expected frequencyL1

1★ Find the relative frequency where the total is 100

Probabilities of independent eventsL1

1★ Calculate a probability given a complete tree diagram for 2 events - AND style questions

Probabilities of independent eventsL2

2★ Calculate a probability given an incomplete tree diagram for 2 events - AND style questions

Probabilities of independent eventsL3

3★ Calculate a probability of 2 events - AND style questions

Probabilities of independent eventsL4

4★ Calculate a probability of 2 events where you can only have 1 of each - OR style questions

Probabilities of independent eventsL5

5★ Calculate a probability of 2 events for AT LEAST style questions

Probabilities of dependent eventsL1

1★ Calculate a probability given a complete tree diagram for 2 events - AND style questions

Conversion of metric unitsL1

1★ Conversion between metric units of length, mass and volume

Compound measuresL1

1★ Convert between different units of time

Compound measuresL2

2★ Speed, distance and time calculations

Simplify a ratioL2

2★ Simplify a ratio into the form 1:n

Divide a quantity into a given ratioL1

1★ Divide an amount into a:b

Currency conversionL1

1★ Simple conversion involving a scale of 1:n

Currency conversionL2

2★ Given the currency conversion ratio, convert pounds into another currency (£1:...)

Direct proportionL1

1★ Simple direct proportion based on a word problem

Direct proportionL3

3★ What is the most I can make given basic ingredients and a recipe?

Awaiting development

Click on a skill to select and create your own misconception:

Algebra vocabulary and understandingL5

5★ Equating coefficients (inc. completing the square)

Algebra vocabulary and understandingL6

6★ Equating coefficients (inc. completing the square) - harder

Algebraic proofL2

2★ Show a simple identity by expanding a linear expression is true

Algebraic proofL3

3★ Show that an identity involving a product of two linear expressions is true

Algebraic proofL4

4★ Show that an expression is even, odd, multiple of or factor of a number

Algebraic proofL5

5★ Show that a harder expression is a even, odd, multiple of or factor of a number

Algebraic fractionsL1

1★ Simplify

Algebraic fractionsL4

4★ Multiply or divide

Algebraic fractionsL5

5★ Add or subtract fractions with linear denominator expressions

Algebraic fractionsL6

6★ Solve algebraic fractional equations (integer solutions)

Change the subjectL3

3★ Rearrange a formula involving a fraction

Change the subjectL4

4★ Rearrange a formula involving powers or roots

Change the subjectL5

5★ Rearrange common formula

Change the subjectL6

6★ Rearrange a formula where the subject appears more than once

Identify coordinates in all 4 quadrantsL5

5★ Identify a coordinate to complete a shape

Find and use y = a, x = a and y = xL2

2★ Sketch the graph from the equation (integer intercepts)

Find and use y = a, x = a and y = xL3

3★ Sketch the graph from the equation (decimal intercepts)

Find and use y = a, x = a and y = xL4

4★ Where does x = a and y = b meet?

Find and use y = a, x = a and y = xL5

5★ Does the point lie on the line?

Find y = mx + c from a graphL2

2★ Calculate the gradient where Δx is 1

Find y = mx + c from a graphL3

3★ Calculate a positive gradient where Δx is not 1

Find y = mx + c from a graphL4

4★ Calculate a negative gradient where Δx is not 1

Find y = mx + c from a graphL5

5★ Finding gradient from a graph

Find y = mx + c from a graphL6

6★ Finding y=mx+c from a graph

Rearranging into the form y = mx + cL1

1★ Interpret the gradient or y-intercept from y = mx + c

Rearranging into the form y = mx + cL2

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 + cL3

3★ Rearrange ax + by = c into y = mx + c and interpret the gradient or y-intercept

Using and exploring y = mx + cL1

1★ Complete a table of coordinate pairs (find y coordinates)

Using and exploring y = mx + cL2

2★ Complete a table of coordinate pairs (find x or y coordinates)

Using and exploring y = mx + cL3

3★ Find the y-intercept given the gradient and a coordinate

Using and exploring y = mx + cL4

4★ State the equation of a line given the gradient and a coordinate

Using and exploring y = mx + cL5

5★ Calculate the gradient given 2 coordinates

Using and exploring y = mx + cL6

6★ State the equation of a line given 2 coordinate pairs

Find the equation of a parallel lineL1

1★ Given coordinates for two lines, determine if they are parallel

Find the equation of a parallel lineL2

2★ Write down the equation of a line parallel to y=mx+c

Find the equation of a parallel lineL3

3★ Given 2 linear equations, determine if they are parallel

Find the equation of a parallel lineL4

4★ Write the linear equation of a line parallel to y=mx+c that passes through (a,b)

Find the equation of a parallel lineL5

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 lineL2

2★ Given two pairs of coordinates from two straight lines, determine if they are perpendicular

Find the equation of a perpendicular lineL3

3★ Write down a linear equation that is perpendicular to y=mx+c

Find the equation of a perpendicular lineL4

4★ Given 2 linear equations, prove they are perpendicular to eachother

Find the equation of a perpendicular lineL5

5★ Given 2 linear equations, determine if they are perpendicular

Find the equation of a perpendicular lineL6

6★ Write the linear equation of a line perpendicular to y=mx+c that passes through (a,b)

Find a instanteous rate of changeL1

1★ Calculate the gradient of a straight line

Find a instanteous rate of changeL2

2★ Calculate a rate of change between 2 points

Find a instanteous rate of changeL3

3★ Calculate a rate of change at a point

Find a instanteous rate of changeL4

4★ Analysing the meaning of the rate of change

Find a instanteous rate of changeL5

5★ Contextualised rates of change

Equation of a tangent to a circleL1

1★ Write the perpendicular gradient to a given gradient

Equation of a tangent to a circleL2

2★ State the gradient of a tangent given the gradient of the radius

Equation of a tangent to a circleL3

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 with the center at the origin

Equation of a tangent to a circleL4

4★ Find the equation of the tangent given equation of circle with the center at the origin and coordinates of the intersection with the tangent and the radius on the circumference of the circle

Equation of a tangent to a circleL5

5★ Find the equation of the tangent given the equation of the circle with the center at the origin 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 circleL6

6★ Problem solving - e.g. find the area bounded by the axes and the tangent to a circle with the center at the origin

Graphical solutions of equationsL1

1★ Use a graph to solve when x=a and y=b

Graphical solutions of equationsL2

2★ Use a graph to solve when x=a/y=b and y=mx+c

Graphical solutions of equationsL3

3★ Use a graph to solve when y=ax+b and y=cx+d

Graphical solutions of equationsL4

4★ Use a graph to show why there no solution to two linear equations - they are parallel

Graphical solutions of equationsL5

5★ Use a graph to solve when a quadratic and linear equation

Quadratic and cubic functionsL1

1★ Complete a table of coordinate pairs for simple quadratics y=x^2 or cubics y=x^3

Quadratic and cubic functionsL2

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 functionsL3

3★ Draw a quadratic y=ax^2+c or cubic y=ax^3 + cx function

Quadratic and cubic functionsL4

4★ Given a quadratic and cubic, identify the equation from a given graph

Quadratic and cubic functionsL5

5★ Given a quadratic or cubic graph, find x or y estimates from the graph

Equation of a circleL1

1★ State the radius or the coordinates of the centre point given the equation of a circle

Equation of a circleL2

2★ Given the centre and radius state the equation of the circle

Equation of a circleL3

3★ Draw a circle with specific equation

Equation of a circleL4

4★ State the equation of a circle given its graph

Equation of a circleL5

5★ Does a coordinate lie on the circle given the centre and radius of the circle

Equation of a circleL6

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 graphL3

3★ Calculate the y-axis scale given a speed-time graph and the area under the graph

Area under a graphL4

4★ Estimate the area under a graph (quadratic)

Area under a graphL5

5★ Given a curve, determine if the estimate for the area under the curve is an under or over estimate

Area under a graphL6

6★ Given a curve, calculate the area under the curve when it includes calculating negative areas (dependent on context)

Reciprocal functionsL1

1★ Complete a table of coordinate pairs given a domain of values

Reciprocal functionsL2

2★ Draw an reciprocal function given the equation and domain

Reciprocal functionsL3

3★ Given a reciprocal and exponential function, identify the equation of a given graph

Reciprocal functionsL4

4★ Given a reciprocal graph, find x or y estimates from the graph

Reciprocal functionsL5

5★ Identify asymptotes of a reciprocal function given its graph

Exponential functionsL1

1★ Complete a table of coordinate pairs given a domain of values

Exponential functionsL2

2★ Draw an exponential function given the equation and domain

Exponential functionsL3

3★ Given a reciprocal and exponential function, identify the equation of a given graph

Exponential functionsL4

4★ Given an exponential graph, find x or y estimates from the graph

Exponential functionsL5

5★ Use a graph to solve exponential equations in the form a^x=b

Trigonometry graphsL1

1★ Given a trigonometry graph, identify whether it is the sin, cos and tan graph

Trigonometry graphsL2

2★ Identify specific coordinates on a sin, cos or tan graph

Trigonometry graphsL3

3★ Sketch y=sinx, y=cosx or y=tanx for a given domain

Trigonometry graphsL4

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 graphsL5

5★ Given a solution to sinx=a, cosx=a or tanx=a, find another solution without the aid of a graph

Interpret and construct real-life graphsL1

1★ Read values from distance–time and speed–time graphs

Interpret and construct real-life graphsL2

2★ Describe motion from graph shapes (stationary, steady, accelerating/decelerating)

Interpret and construct real-life graphsL3

3★ Using a real life graph to convert between units

Interpret and construct real-life graphsL4

4★ Use area under speed–time graph to find distance

Interpret and construct real-life graphsL5

5★ Extrapolate from a linear relationship graph

Interpret and construct real-life graphsL6

6★ Filling up vases

Solve linear equations (unknown on 1 side, int ans)L6

6★ Problem solving

Solve linear equations (unknown on 1 side, dec ans)L1

1★ Solve a 1 step equation by reversing the addition or subtraction of a constant

Solve linear equations (unknown on 1 side, dec ans)L2

2★ Solve a 1 step equation by reversing a multiplication or division of a constant

Solve linear equations (unknown on 1 side, dec ans)L3

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)L4

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)L5

5★ Solve a linear equation in the form a(x+b)=c

Solve linear equations (unknown both sides)L1

1★ Solve a linear equation with the unknown on both sides in the form ax=bx+c

Solve linear equations (unknown both sides)L3

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)L5

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)L6

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 bracketsL1

1★ Solve linear equation in the form a(x+b)=c

Solve linear equations with bracketsL2

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 bracketsL3

3★ Solve a linear equation in the form a(bx+c)=dx+e

Solve linear equations with bracketsL4

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 bracketsL5

5★ Solve a linear equation involving the expansion of brackets on both sides of the equals sign

Solve linear equations with bracketsL6

6★ Solve a linear equation involving multiple expansion of brackets

Solve rational equationsL1

1★ Solve a linear rational equation in the form ax/b=c

Solve rational equationsL2

2★ Solve a linear rational equation in the form (ax+b)/c=d

Solve rational equationsL3

3★ Solve a linear rational equation in the form (ax+b)/(cx+d)=e

Solve rational equationsL4

4★ Solve a linear equation with fractional expressions on each side of the equals

Solve rational equationsL5

5★ Solve a linear rational equation where you have the sum or difference of two fractional expressions

Solve rational equationsL6

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 bracketL2

2★ Expand a(bx+c)

Expand over a single bracketL4

4★ Expand ax(bx+c)

Expand over a single bracketL5

5★ Expand the sum or difference of two linear brackets and simplify

Expand over a single bracketL6

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 binomialsL3

3★ Expand (x+a)(x-a)

Expand 2 or more binomialsL4

4★ Expand (ax±b)(cx±d)

Expand 2 or more binomialsL5

5★ Expand the product of 2 quadratic or cubic expressions

Expand 2 or more binomialsL6

6★ Expand the product of 3 linear expressions

Factorise a simple expressionL2

2★ Factorise a quadratic expression ax^2±bx

Factorise a simple expressionL3

3★ Factorise a quadratic expression ax^2±bx with a expression common factor

Factorise a simple expressionL4

4★ Can a quadratic in the form ax^2±bx be factorised?

Factorise a simple expressionL5

5★ Problem solving, e.g. find the sides of a rectangle given a quadratic that represents the area

Factorise a simple expressionL6

6★ Fully factorise a linear expression by combining a sum of 2 terms where 1 is partially factorised

Factorise a quadratic expressionL5

5★ Factorise a quadratic resulting in (ax + b)(x + c)

Factorise a quadratic expressionL6

6★ Factorise a quadratic resulting in (ax + b)(c - dx) or (ax + b)(cx + d)

Solve a quadratic by factorisingL3

3★ Solve a quadratic resulting in (x - a)(x - b)

Solve a quadratic by factorisingL4

4★ Solve a quadratic resulting in (x + a)(x - a)

Solve a quadratic by factorisingL5

5★ Solve a quadratic resulting in (ax + b)(x + c)

Solve a quadratic by factorisingL6

6★ Solve a quadratic resulting in (ax + b)(c - dx) or (ax + b)(cx + d)

Solving quadratics in disguiseL1

1★ Solve like a quadratic x^(2n)±bx^n+c where n>1

Solving quadratics in disguiseL2

2★ Solving like a quadatic involving a rearrangement e.g. x^(2n)=bx^n+c where n>1

Solving quadratics in disguiseL3

3★ Solve like a quadratic involving fractional powers e.g. x^(1/n)+bx^(1/2n)=c

Solving quadratics in disguiseL4

4★ Solve like a quadratic involving variable as a power

Solving quadratics in disguiseL5

5★ Solve like a quadratic involving trigonometric equations

Complete the squareL1

1★ Completing the square (x+a)^2+b where b>0

Complete the squareL3

3★ Completing the square of x^2+bn+c where b is divisible by 2

Complete the squareL4

4★ Completing the square x^2+bn+c where b is not divisible by 2

Complete the squareL5

5★ Find the minimum point of a quadratic function by completing the square

Complete the squareL6

6★ Identify the translation of a function given it is based on f(x)=x^2

Solve a quadratic by completing the squareL1

1★ Solve by completing the square given part of the working

Solve a quadratic by completing the squareL2

2★ Solve by completing the square given part of the working

Solve a quadratic by completing the squareL3

3★ Solve by completing the square of x^2+bn+c where b is divisible by 2

Solve a quadratic by completing the squareL4

4★ Solve by completing the square of x^2+bn+c where b is not divisible by 2

Solve a quadratic by completing the squareL5

5★ Solve by completing the square ax^2+bx+c where a>0

Solve a quadratic by completing the squareL6

6★ Solve by completing the square ax^2+bx+c

Solve a quadratic by using the formulaL1

1★ Substituting positive numbers into the quadratic formula

Solve a quadratic by using the formulaL2

2★ Substituting any numbers into the quadratic formula

Solve a quadratic by using the formulaL3

3★ Given that numbers were correctly substituted into the quadratic formula state the quadratic equation

Solve a quadratic by using the formulaL5

5★ Solve a quadratic using the quadratic formula

Graph transformationsL1

1★ Describe a quadratic graph transformation in words

Graph transformationsL2

2★ Describe the effect of a transformation on a single point on a quadratic function

Graph transformationsL3

3★ Given f(x)=x^2, state the equation of a transformation of f(x)

Graph transformationsL4

4★ Given the transformed function of f(x)=x^2, draw it alongside f(x)

Graph transformationsL5

5★ Describe the effect of a transformation on a single point on a trig graph

Graph transformationsL6

6★ Draw/Identify a trig graph transformation

Use simple function machinesL1

1★ Substitute an input value into a single operation function machine

Use simple function machinesL2

2★ Substitute an input value into a 2 operation function machine

Use simple function machinesL4

4★ Calculate the missing operation in a 2 operation function machine given the input and output values

Use simple function machinesL5

5★ Write an expression to represent the output of a 2 operation function machine given the input is x

Use simple function machinesL6

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 rangeL1

1★ Identify the range of f(x)=ax given the domain

Identify domain and rangeL2

2★ Find the corresponding domain or range values given f(x)=ax

Identify domain and rangeL3

3★ Find the range of f(x)=ax+b

Identify domain and rangeL4

4★ Find the corresponding domain or range values given f(x)=ax+b

Identify domain and rangeL5

5★ Find the domain of f(x)=ax+b given a range in set notation

Identify domain and rangeL6

6★ Find the values of f(x) for which is it is undefined

Use composite functionsL2

2★ Find gf(x) or fg(x) for a given value knowing that f(x)=ax+b and g(x)=cx+d

Use composite functionsL3

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 functionsL4

4★ Find fg(x) for a given value knowing that f(x)=ax^2+bx+c and g(x)=dx+e

Use composite functionsL5

5★ Problem solving e.g. find fg(x)=gf(x) where f(x)=x^2+bx+c and g(x)=x+d

IterationsL1

1★ Given a1 and a(n+1)=ba(n)+c, find a2

IterationsL2

2★ Given a1 and a(n+1)=ba(n)+c, find a3 or a4

IterationsL3

3★ Real world problem where an iterative formula and a0 is given

IterationsL4

4★ Given x0 and an iterative formula derived from a rearranged cubic, find x3

IterationsL5

5★ Show that a cubic equation can be rearranged to a given iterative form

IterationsL6

6★ Show that a cubic equation as a solution between 2 values

Inverse functionsL1

1★ Rearrange a function involving only 1 operation (addition, subtraction, multiplication or division)

Inverse functionsL2

2★ Rearrange a function involving 2 operations

Inverse functionsL3

3★ Rearrange a function that is fractional

Inverse functionsL4

4★ Rearrange a function involving powers

Inverse functionsL5

5★ Rearrange a quadratic function that first involves completing the square

Read/Represent inequalities on a number lineL3

3★ Interpret any inequality from a number line

Read/Represent inequalities on a number lineL4

4★ Represent a given inequality on a number line

Read/Represent inequalities on a number lineL5

5★ Interpret a compound inequality from a number line

Read/Represent inequalities on a number lineL6

6★ Represent a compound inequality on a number line

Solve linear inequalitiesL1

1★ Solve a 1 step inequality by reversing the addition or subtraction of a constant

Solve linear inequalitiesL2

2★ Solve a 1 step inequality by reversing the multiplication or division of a constant

Solve linear inequalitiesL3

3★ Solve a 2 step inequality where x has a positive coefficient

Solve linear inequalitiesL5

5★ Solve a 2 step inequality where x has a negative coefficient

Solve linear inequalitiesL6

6★ Solve a compound inequality in the form of a<bx+c<d

Graphical inequalitiesL1

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 inequalitiesL2

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 inequalitiesL3

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 inequalitiesL4

4★ Identify the 3 inequalities that bound a given region including y-x>a

Graphical inequalitiesL5

5★ State the coordinates of points that satisfy a given region bounded by 3 inequalities

Solve quadratic inequalitiesL1

1★ Graphically solve a quadratic inequality in the form x^2±a<0 or x^2±a>0

Solve quadratic inequalitiesL2

2★ Graphically solve a quadratic inequality in the form x^2±a≤0 or x^2±a≥0

Solve quadratic inequalitiesL3

3★ Solve a quadratic inequality x^2±a<0, x^2±a>0, x^2±a≤0 or x^2±a≥0

Solve quadratic inequalitiesL4

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 inequalitiesL5

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 inequalitiesL6

6★ Solve a quadratic inequality (where a is not 1) that first involves a rearrangement

Recognise common sequencesL3

3★ Continue a square or triangular sequence for the next two terms

Recognise common sequencesL4

4★ Continue a Fibonacci sequence for the next two terms

Recognise common sequencesL5

5★ Continue a periodic sequence for the next two terms

Recognise common sequencesL6

6★ Continue a fractional sequence for the next two terms where the numerators and denominators each follow a linear sequence

Understand linear sequencesL1

1★ Continue a linear sequence for the next two terms

Understand linear sequencesL5

5★ Given a number and the first 4 terms of a linear sequence, determine if the number is part of the sequence

Understand linear sequencesL6

6★ Given 2nd and 4th term of a linear sequence find 100th term

Understand geometric sequencesL1

1★ Determine if a given sequence is geometric, if not, state the name of the sequence family

Understand geometric sequencesL3

3★ Find the next 2 terms of a geometric sequence (decimal common ratio)

Understand geometric sequencesL4

4★ Given the first term and common ratio, find the first 3 terms of a geometric sequence

Understand geometric sequencesL5

5★ Given an algebraic term to term rule and the first term, find a specific term in a geometric sequence

Understand geometric sequencesL6

6★ Problem solving, e.g. given the 2nd and 4th term of a geometric sequence, find the 10th term

Algebraic sequencesL1

1★ Continue an algebraic sequence that is based on an arithmetic or Fibonacci sequence

Algebraic sequencesL2

2★ Continue an algebraic sequence that is based on a geometric sequence

Algebraic sequencesL3

3★ Show that the sixth term of an algebraic sequence is a given expression

Algebraic sequencesL4

4★ Find the nth term of an arithmetic algebraic sequence

Algebraic sequencesL5

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 sequencesL1

1★ Continue a quadratic sequence for the next two terms

Understand quadratic sequencesL2

2★ Write the first 4 terms a quadratic sequence given the nth term rule in the form of n^2+bn+c

Understand quadratic sequencesL3

3★ Find the nth term rule of a quadratic sequence based on an^2

Understand quadratic sequencesL4

4★ Find the nth term rule of a quadratic sequence based on n^2+bn+c

Understand quadratic sequencesL5

5★ Find the nth term rule of a quadratic sequence based on an^2+bn+c

Understand quadratic sequencesL6

6★ Use the nth term rule of a quadratic sequence based on an^2+bn+c to find a specific term

Solve linear simultaneous equationsL1

1★ Solve 2 simultaneous equations where a term in each equation has a common coefficient

Solve linear simultaneous equationsL3

3★ Solve 2 simultaneous equations where all coefficients are different

Solve linear simultaneous equationsL4

4★ Solve a word problem that involves the creation and solving of 2 simultaneous equations

Solve linear simultaneous equationsL5

5★ Solve 2 simultaneous equations that first involves rearranging one or both of the 2 given equations

Solve linear simultaneous equationsL6

6★ Form and solve 2 simultaneous equations in other Maths topics

Solve non linear simultaneous equationsL1

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 equationsL2

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 equationsL3

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 equationsL5

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/formulaL3

3★ Substitute negative values into an expression involving 2 variables

Substitute into expressions/formulaL4

4★ Substitute values into a simple quadratic expression

Substitute into expressions/formulaL5

5★ Substitute values into common formulae

Substitute into expressions/formulaL6

6★ Substitute values into a linear function f(x)

Form expressions and equationsL1

1★ Create a simple expression in the form x±a or ax based on a word problem

Form expressions and equationsL2

2★ Create an expression to represent a word problem based I think of a number

Form expressions and equationsL3

3★ Create a rational expression to represent a word problem based I think of a number

Form expressions and equationsL4

4★ Create an expression based on a word problem, e.g. find the sum of 3 algebraic ages

Form expressions and equationsL5

5★ Form and solve an equation with unknowns on both sides

Form expressions and equationsL6

6★ Create a formula to represent the perimeter of a shape

Understand and evaluate logarithmsL1

1★ Convert between exponential form to logarithmic form

Understand and evaluate logarithmsL2

2★ Evaluate an logarithmic form

Understand and evaluate logarithmsL3

3★ Write logarithmic operations as a single logarithmic expression

Understand and evaluate logarithmsL4

4★ Solve logarithmic equations

Understand and evaluate logarithmsL5

5★ Given logarithmic approximations, find a related logarithmic operation calculation

Understand and evaluate logarithmsL6

6★ Change the base

Data handling cycleL1

1★ Understanding the 4 steps of the data handling cycle

Data handling cycleL2

2★ Determine if a given hypothesis is testable and is not opinion based

Data handling cycleL3

3★ Identify the given type of data

Data handling cycleL4

4★ Identify qualities of a good or bad survey question

Data handling cycleL5

5★ Identify the type of sampling being used (quota/convenience/stratified/cluster/systematic)

Data handling cycleL6

6★ Identify causes of bias and how a sample can be improved

Calculate a stratified sampleL1

1★ Find a stratified sample

Calculate a stratified sampleL2

2★ Find the total frequency given the stratified sample

Two-way tablesL1

1★ Create a simple two-way table from images

Two-way tablesL2

2★ Find totals from a two-way table

Two-way tablesL3

3★ Complete missing values in a two-way table

Two-way tablesL4

4★ Calculate probabilities or fractions of amount from a two-way table

Two-way tablesL5

5★ Given a word problem, create and interpret a two-way table

Two-way tablesL6

6★ Multi-skill problem solving by creating and interpreting a two-way table, including ratios or percentages

Calculate the range from a listL1

1★ Calculate the range for a simple list of postive integers

Calculate the range from a listL2

2★ Calculate the range for positive and negative numbers

Calculate the range from a listL3

3★ Calculate the range for fractions or decimals

Calculate the range from a listL4

4★ Calculate the range real life problems

Calculate the range from a listL5

5★ Problem solve with the range

Calculate the range from a listL6

6★ Compare 2 sets of data

Calculate averages from a listL4

4★ Calculate the mean

Calculate averages from a listL5

5★ Calculate a missing value given the mean and the other values

Calculate averages from a listL6

6★ Write 4 numbers with a given mean, mode, median and range

Calculate quartiles from a listL1

1★ Calculate IQR (easy ordered list)

Calculate quartiles from a listL2

2★ Calculate IQR (unordered list with easy quartiles)

Calculate quartiles from a listL3

3★ Calculate IQR (unordered list with half position values)

Calculate quartiles from a listL4

4★ Calculate IQR (unordered list of decimals)

Calculate quartiles from a listL5

5★ IQR from a stem and leaf diagram

Calculate quartiles from a listL6

6★ Given the IQR and range find unknown values in a list of data

Which average should you use?L1

1★ Which average gives the best or worst result?

Which average should you use?L2

2★ State advantages or disadvantages of a specific type of average

Which average should you use?L3

3★ Given a data set, decide which average is best to use to represent the data

Calculate the mode/mean from a frequency tableL4

4★ Calculate an estimate of the mean from a grouped frequency table

Calculate the mode/mean from a frequency tableL5

5★ Calculate a missing score given the mean from a frequency table

Calculate the mode/mean from a frequency tableL6

6★ Calculate a missing frequency given the mean from a frequency table

Calculate the median/IQR from a frequency tableL1

1★ Calculate the median from a frequency table

Calculate the median/IQR from a frequency tableL2

2★ Identify the interval that contains the median from a grouped frequency table

Calculate the median/IQR from a frequency tableL3

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 tableL4

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 tableL5

5★ Find the interquartile range from a grouped frequency table

Stem and leaf diagramsL1

1★ Draw a stem and leaf diagram from an unordered list of data containing integers

Stem and leaf diagramsL2

2★ Draw a stem and leaf diagram from an unordered list of data containing decimals

Stem and leaf diagramsL3

3★ Interpret a stem and leaf diagram, e.g. what fraction were under a specific score?

Stem and leaf diagramsL4

4★ Find averages and range from a stem and leaf diagram

Stem and leaf diagramsL5

5★ Adding data to a stem and leaf and analysing the effects on statistical measures

Stem and leaf diagramsL6

6★ Analysing a back to back stem and leaf diagram

Draw/Interpret a frequency polygonL1

1★ Draw a frequency polygon from a grouped frequency table

Draw/Interpret a frequency polygonL2

2★ Interpret probabilities of events from a frequency polygon

Draw/Interpret a frequency polygonL3

3★ Interpret the mean from a frequency polygon

Draw/Interpret a frequency polygonL4

4★ Draw comparisons between 2 frequency polygons drawn on the same axes

Draw/Interpret cumulative frequencyL1

1★ Construct a cumulative frequency table

Draw/Interpret cumulative frequencyL2

2★ Construct a cumulative frequency table from a graph

Draw/Interpret cumulative frequencyL3

3★ Estimate a median from a cumulative frequency graph

Draw/Interpret cumulative frequencyL4

4★ Estimate the interquartile range from a cumulative frequency graph

Draw/Interpret cumulative frequencyL5

5★ Estimate the number of people that scored more or less than an amount from a cumulative frequency graph

Draw/Interpret a box plotL1

1★ Draw a box plot given 5 point summary

Draw/Interpret a box plotL2

2★ Draw a box plot from a cumulative frequency diagram

Draw/Interpret a box plotL3

3★ Draw a box plot given some information given key statistical measures about a list of data

Draw/Interpret a box plotL4

4★ Analyze a given box plot

Draw/Interpret a box plotL5

5★ Calculate median, inter-quartile range or range from a box plot

Draw/Interpret a box plotL6

6★ Make comparisons between 2 box plots drawn on the same number line

Draw/Interpret a bar chartL1

1★ Create a tally chart from a list of data

Draw/Interpret a bar chartL2

2★ Given a tally chart, interpret key measures from the chart

Draw/Interpret a bar chartL3

3★ Draw a bar chart from a frequency table

Draw/Interpret a bar chartL4

4★ Interpret least/most common or frequency from a bar chart

Draw/Interpret a bar chartL5

5★ Draw a bar chart given a word problem that requires problem solving

Draw/Interpret a composite bar chartL1

1★ Analyse a composite bar chart

Draw/Interpret a composite bar chartL2

2★ Draw a composite bar chart given a two way table

Draw/Interpret a composite bar chartL3

3★ Interpret proportions from a composite bar chart

Draw/Interpret a histogramL1

1★ Complete a frequency density column given a grouped frequency table

Draw/Interpret a histogramL2

2★ Complete missing values in a grouped frequency table including frequency density column and frequency values

Draw/Interpret a histogramL4

4★ Estimate how many got greater than a score from a grouped frequency table

Draw/Interpret a histogramL5

5★ Construct a frequency table from a histogram

Draw/Interpret a histogramL6

6★ Given the frequency of one interval represented by a histogram, complete a frequency table to represent all other intervals

Construct a pictogramL1

1★ Given a pictogram, identify least/most common or total (involving frequencies that require only whole diagrams)

Construct a pictogramL2

2★ Given a pictogram, identify least/most common or total (involving frequencies that require half a diagram)

Construct a pictogramL3

3★ Given a pictogram, find the frequency of a category or total frequency

Construct a pictogramL5

5★ Draw a pictogram (involving frequencies that require half a diagram)

Construct a pictogramL6

6★ Given a pictogram, find the percentage who answered a category

Construct a pie chartL1

1★ Draw a pie chart (total freq 360 with categories having a frequency that is a factor of 360)

Construct a pie chartL2

2★ Draw a pie chart (total frequency is 90 or 180)

Construct a pie chartL3

3★ Draw a pie chart (total frequency is a factor of 360)

Construct a pie chartL4

4★ Calculate the angles needed to construct a pie chart (total frequency is not a factor of 360)

Construct a pie chartL5

5★ Draw a pie chart (total frequency is not a factor of 360)

Construct a pie chartL6

6★ Draw a pie chart where the total frequency is given but the category frequencies are expressions in terms of x

Interpret a pie chartL1

1★ Find the mode from a given pie chart

Interpret a pie chartL2

2★ Calculate the fraction represented by a sector on a given pie chart

Interpret a pie chartL3

3★ Given a pie chart and the frequency of a sector, calculate total frequency

Interpret a pie chartL4

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 graphL1

1★ Plot a scatter diagram from a given table

Draw/Interpret a scatter graphL2

2★ Describe the correlation represented in a scatter graph

Draw/Interpret a scatter graphL3

3★ Draw a line of best fit on a given scatter graph

Draw/Interpret a scatter graphL4

4★ Estimate from a line of best fit on a scatter graph

Draw/Interpret a scatter graphL5

5★ Identify anomalies from a given scatter graph

PMCC and regression lineL1

1★ Comment on the correlation shown in a given scatter graph

PMCC and regression lineL2

2★ Find the PMCC from table

PMCC and regression lineL3

3★ Interpret the meaning of the PMCC value in a given context

PMCC and regression lineL4

4★ Calculate the regression line equation from a given table

PMCC and regression lineL5

5★ Interpolate/extrapolate using a regression line equation formed from a given table

PMCC and regression lineL6

6★ Limitations of using a regression line given a scatter graph

Standard deviationL1

1★ Substitute given values into standard deviation formula

Standard deviationL2

2★ Find the standard deviation from a sample list of data

Standard deviationL3

3★ Find the standard deviation from population list of data

Standard deviationL4

4★ Given the standard deviation from 2 experiments, comment on the results

Standard deviationL5

5★ Calculate the percentage of data within 1 standard deviation of the mean

Standard deviationL6

6★ Find the standard deviation from a frequency table

Normal distributionL1

1★ Calculate the z-score given a value, µ and the standard deviation

Normal distributionL2

2★ Find P(X < ?) where Z > 0

Normal distributionL3

3★ Find P(X < ?) or P(X > ?) where Z < 0

Normal distributionL4

4★ Find P(a < X < b)

Normal distributionL5

5★ Find X where Y% are less than X

Normal distributionL6

6★ Find µ given P(X < x)

Confidence intervalsL1

1★ Use standard error of the mean to find the P(Z < ?)

Confidence intervalsL2

2★ Find a z-score given a percentage confidence interval

Confidence intervalsL3

3★ Construct a confidence interval given a sample

Confidence intervalsL4

4★ Construct a confidence interval given a different confidence interval of the same sample

Facebook mathsL1

1★ A look repetitive question involving the same number but different operations that focuses on the use of BIDMAS

Facebook mathsL2

2★ Solving simultaneous equations but depicted as fruit

Facebook mathsL3

3★ Order of operation circles

Place valueL1

1★ Interpret the blocks

Place valueL2

2★ Read the place value of a digit in a given integer

Place valueL4

4★ Read the place value of a digit within a given decimal

Place valueL5

5★ Convert a number described in words into a numerical form

Place valueL6

6★ Convert numbers into words

Roman numeralsL1

1★ Convert to roman numerals

Roman numeralsL2

2★ Convert from roman numerals

Roman numeralsL3

3★ Operate with roman numerals

Roman numeralsL4

4★ Interpret a clock face

Times tablesL1

1★ 2, 5 and 10 times tables

Times tablesL2

2★ First half of 3 and 4 times tables

Times tablesL3

3★ Second half of 3 and 4 times tables

Times tablesL4

4★ 6 and first half of 8 times tables

Times tablesL5

5★ Second half of 8 times tables

Times tablesL6

6★ 7, 9, 11 and 12 times tables

Commutative, associative and distributive lawsL2

2★ Commutative law involving a combination of addition and multiplication

Commutative, associative and distributive lawsL3

3★ Associative law

Commutative, associative and distributive lawsL4

4★ Distributive law

Commutative, associative and distributive lawsL5

5★ Identify which number law is being shown

Commutative, associative and distributive lawsL6

6★ Evaluate calculations based on the use of the number laws

Related calculationsL1

1★ Given a calculation, evaluate a simple rearrangement of the same calculation

Related calculationsL2

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 calculationsL3

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 calculationsL4

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 multiplesL4

4★ Find the HCF or LCM of 2 numbers

Factors and multiplesL5

5★ Find the HCF or LCM of 3 numbers

Factors and multiplesL6

6★ Find a second number given 1 number and their LCM

Prime factorsL6

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 operationsL5

5★ Find the value of a fractional calculation with steps to evaluate in both the numerator and denominator

Order of operationsL6

6★ Insert brackets into a calculation to make it true

Interpret fractionsL2

2★ Shade a unit fraction of a diagram

Interpret fractionsL3

3★ Read simple fractions from a diagram

Interpret fractionsL4

4★ Represent simple fractions on a diagram

Interpret fractionsL5

5★ Understanding equivalences from shaded rows or columns of a diagram

Interpret fractionsL6

6★ Read a given diagram as a mixed number

Equivalent fractionsL4

4★ Would you rather have this ... or this ...?

Equivalent fractionsL5

5★ Find half way between 2 fractions

Equivalent fractionsL6

6★ Convert to and from a mixed number

Reciprocals of numbersL1

1★ Given an integer, provide the reciprocal so the product equals 1

Reciprocals of numbersL2

2★ Reciprocal of integers

Reciprocals of numbersL3

3★ Reciprocal of fractions

Reciprocals of numbersL4

4★ Reciprocal of decimals < 1

Reciprocals of numbersL5

5★ Reciprocal of fractions or decimals > 1

Reciprocals of numbersL6

6★ Equivalent fraction fill in the blank reciprocals

Add or subtract fractionsL5

5★ Mixed numbers

Add or subtract fractionsL6

6★ Simple algebraic fractions

Write one number as a fraction of anotherL1

1★ Write the amount shaded as a fraction of the total

Write one number as a fraction of anotherL2

2★ Write one number as a fraction of another

Write one number as a fraction of anotherL3

3★ Understanding complements when finding a fraction of an amount

Write one number as a fraction of anotherL4

4★ Write one measurement as a fraction of another when they are given with different units

Write one number as a fraction of anotherL5

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 anotherL6

6★ Equivalent fraction problem

Fraction of an amount (part i)L2

2★ Multiply a fraction by a fraction

Fraction of an amount (part i)L3

3★ Find a fraction of an amount

Fraction of an amount (part i)L4

4★ Which of two fraction of amounts statements is larger?

Fraction of an amount (part i)L5

5★ Word problem involving expenditure

Fraction of an amount (part i)L6

6★ Fraction of one amount is equal to fraction of unknown, find the unknown

Fraction of an amount (part ii)L1

1★ Unit fraction of an amount

Fraction of an amount (part ii)L2

2★ Non-unit fraction of an amount

Fraction of an amount (part ii)L3

3★ Mixed number of an amount

Fraction of an amount (part ii)L4

4★ Increase or decrease by a fraction

Fraction of an amount (part ii)L5

5★ Word problems

Fraction of an amount (part ii)L6

6★ Fraction between 2 numbers

Multiply or divide fractionsL1

1★ Given an integer, provide the reciprocal so the product equals 1

Multiply or divide fractionsL4

4★ 3 fractions

Multiply or divide fractionsL5

5★ Mixed numbers

Multiply or divide fractionsL6

6★ Simple algebraic fractions

FDP conversionL2

2★ Convert between FDP

FDP conversionL3

3★ Are 2 numbers written in different number formats (FDP) equal?

FDP conversionL4

4★ Order FDP

FDP conversionL5

5★ Convert a recurring decimal to a fraction where the recurring digit is the first decimal place

FDP conversionL6

6★ Convert a recurring decimal to a fraction (harder)

Order numbersL3

3★ Order decimals

Order numbersL4

4★ Order FDP

Order numbersL5

5★ Order fractions

Order numbersL6

6★ Order numbers written in standard form

Understand and correctly use symbolsL1

1★ Order integers

Understand and correctly use symbolsL2

2★ Compare 2 calculations

Understand and correctly use symbolsL3

3★ Write an inequality in words

Understand and correctly use symbolsL4

4★ Identify the correct inequality for a given set

Understand and correctly use symbolsL5

5★ Write the set of values that satisfy a given inequality

Understand and correctly use symbolsL6

6★ Find approximations or changes in

Efficient use of a calculatorL1

1★ Calculator familiarisation - identify what function a button has on a calculator

Efficient use of a calculatorL2

2★ Enter BIDMAS related calculations on a calculator

Efficient use of a calculatorL3

3★ Identify whether a number is prime on a calculator

Efficient use of a calculatorL4

4★ Evaluate a given expression by substituting in both positive and negative values

Efficient use of a calculatorL5

5★ Evaluate a calculation invovling standard form on a calculator

Efficient use of a calculatorL6

6★ Perform fraction calculations on a calculator

Operate with integers (+ and -)L1

1★ Numbers bonds to 10 or 100

Operate with integers (+ and -)L2

2★ Alternative vocabulary for addition or subtraction

Operate with integers (+ and -)L3

3★ 1 digit integer ± 1 digit integer

Operate with integers (+ and -)L4

4★ 2 digit integer ± 2 digit integer

Operate with integers (+ and -)L5

5★ 3 digit integer ± 2 digit integer

Operate with integers (+ and -)L6

6★ Directed number calculations

Operate with integers (x and ÷)L1

1★ Times tables

Operate with integers (x and ÷)L2

2★ Alternate vocabulary to multiplication or division

Operate with integers (x and ÷)L3

3★ 2 digit integer x÷ 1 digit integer

Operate with integers (x and ÷)L4

4★ 3 digit integer x÷ 2 digit integer

Operate with integers (x and ÷)L5

5★ Directed numbers calculations

Column multiplicationL2

2★ 2 digit integer x 2 digit integer

Column multiplicationL4

4★ Identify the last digit of a multiplication answer

Column multiplicationL5

5★ Fill in the missing number of 3 digit integer x 2 digit integer calculation given all the working

Column multiplicationL6

6★ 3 digit integer x 3 digit integer

Short divisionL1

1★ Inverse times tables

Short divisionL3

3★ Complete the short division calculation using the bus stop method

Short divisionL5

5★ Dividing decimal by integer

Short divisionL6

6★ Dividing an integer by a decimal

Product rule for countingL1

1★ Product of 3 or 4 numbers

Product rule for countingL2

2★ Simple product rule for counting

Product rule for countingL3

3★ Given the final product, find how many of one type there are

Product rule for countingL4

4★ Pin related problems

Operate with decimals (+ and -)L1

1★ Decimal (1dp) ± integer

Operate with decimals (+ and -)L2

2★ Integer ± decimal (1dp)

Operate with decimals (+ and -)L3

3★ Decimal (1dp) ± decimal (1dp) both less than 1

Operate with decimals (+ and -)L4

4★ Decimal (1dp) ± decimal (1dp) both more than 1

Operate with decimals (+ and -)L5

5★ Decimal ± Decimal (2 or more dp)

Operate with decimals (+ and -)L6

6★ Recurring decimal ± decimal

Operate with decimals (x and ÷)L1

1★ Decimal (1dp) multiplied by a power of 10

Operate with decimals (x and ÷)L2

2★ Decimal (1dp) divided by a power of 10

Operate with decimals (x and ÷)L3

3★ Decimal (1dp) x÷ integer

Operate with decimals (x and ÷)L4

4★ Decimal x÷ decimal (both 1 or 2 dp)

Operate with decimals (x and ÷)L5

5★ Decimal x÷ decimal (2 or more dp)

Operate with decimals (x and ÷)L6

6★ Contextualised use of x÷ with decimals

Money problemsL1

1★ Given a shopping list of prices, calculate the cost of buying 1 each of two items

Money problemsL2

2★ Given a shopping list of prices, calculate the cost of buying multiple items

Money problemsL3

3★ Given a shopping list of prices, calculate the cost of buying multiple items with different units of money, e.g. £ and p

Money problemsL4

4★ Given a shopping list, calculate the change due from making a multi item purchase

Money problemsL5

5★ Given a shopping list, calculate how many can I buy of 1 item?

Money problemsL6

6★ What proportion of the total cost of purchasing multiple items does 1 item represent?

Money problems - payment plansL1

1★ How much do I pay each month? (No deposit)

Money problems - payment plansL2

2★ How much do I pay each month? (With deposit)

Money problems - payment plansL3

3★ Given 2 offers from different shops, is it better value to buy now or spread the payments?

Money problems - payment plansL4

4★ Deposit with equal payments and one-off interest

Pay slipsL1

1★ Calculating gross pay

Pay slipsL2

2★ Calculating gross pay inc overtime

Pay slipsL3

3★ Calculating the total deductions or net pay

Pay slipsL4

4★ Calculate the monthly tax for a basic rate tax earner given the 20% and personal tax free allowance thresholds

Pay slipsL5

5★ Calculate the monthly tax for a high income earner given the tax free personal allowance, 20% tax and 40% tax thresholds

Percentage of an amountL3

3★ Percentage to find is a multiple of 1

Percentage of an amountL4

4★ Calculator use

Percentage of an amountL5

5★ Percentage to find is a multiple of 0.5

Percentage of an amountL6

6★ Populate and interpret a two-way table based on percentages of a population

Percentage changeL1

1★ Recognise that percentage is out of 100

Percentage changeL2

2★ Write one number as a percentage of another (out of 100)

Percentage changeL3

3★ Write one number as a percentage of another (not out of 100)

Percentage changeL5

5★ Contextualised percentage change

Percentage changeL6

6★ Percentage change from a compound interest problem

Increase/decrease by a percentageL1

1★ Increase/decrease by a percentage where the percentage is a multiple of 10

Increase/decrease by a percentageL3

3★ Increase/decrease by a percentage where the percentage is a multiple of 1

Increase/decrease by a percentageL4

4★ Increase/decrease by a percentage where the percentage is a multiple of 0.5

Increase/decrease by a percentageL5

5★ Effect of using a decimal multiplier on a number

Increase/decrease by a percentageL6

6★ Explain why a x% increase followed by an x% decrease does not give the original number

Reverse percentageL1

1★ What percentage is left after increasing or decreasing a number by a percentage

Reverse percentageL2

2★ Effect of using a decimal multiplier on a number

Reverse percentageL4

4★ Reverse percentage based on compound interest/decay

Simple interestL1

1★ Interest earned after 1 year

Simple interestL2

2★ Total after n years (where % is an integer)

Simple interestL3

3★ Total after n years (where % is not integer)

Simple interestL4

4★ Total after n years (where % is less than 1)

Simple interestL5

5★ Calculate the interest rate given the total and the number of years

Simple interestL6

6★ Problem solving

Calculate growth/decayL1

1★ Effect of using a decimal multiplier on a number

Calculate growth/decayL2

2★ Growth/decay percentage is an integer

Calculate growth/decayL3

3★ Growth/decay percentage is a decimal (1dp)

Calculate growth/decayL4

4★ Find the number of years to exceed a given amount

Calculate growth/decayL5

5★ Find the percentage growth/decay

Student loansL1

1★ Calculate 9% of a annual salary

Student loansL2

2★ Calculate the amount deducted from an annual salary or monthly repayment

Student loansL3

3★ Calculate how many months it will take to repay the student loan

Student loansL4

4★ Calculate the amount of student loan is left to repay after n years

Annual equivalent rateL1

1★ Compound interest

Annual equivalent rateL2

2★ Calculate AER

Annual equivalent rateL3

3★ Calculate how much would be in an account

Annual equivalent rateL4

4★ Which is better value?

Annual equivalent rateL5

5★ Backwards AER questions

Annual percentage rateL1

1★ Calculate the amount to be repaid for a 1 year loan

Annual percentage rateL2

2★ Calculate the APR for a 1 year loan

Annual percentage rateL3

3★ Calculate the amount borrowed for a 1 year loan

Annual percentage rateL4

4★ Calculate a missing payment

Annual percentage rateL5

5★ Calculate amount repaid after equal instalments

EstimationL1

1★ Estimate the product of a decimal and integer

EstimationL2

2★ Estimate money total

EstimationL3

3★ Estimate a decimal divided by a decimal (greater than 1)

EstimationL4

4★ Estimate a decimal divided by a decimal (less than 1)

EstimationL5

5★ Estimate square roots/cube roots

EstimationL6

6★ Estimate the value of longer BIDMAS related calculations

FermiL1

1★ Estimate key facts that relate to general knowledge fermi questions

FermiL2

2★ Key conversion questions e.g. time units, measures of length, speed/distance/time

FermiL3

3★ Short Fermi questions

TruncationL1

1★ Truncate to 10, 100 or 1000

TruncationL2

2★ Truncate to dp or sf

TruncationL3

3★ Error interval when truncated to 10, 100 or 1000

TruncationL4

4★ Error interval when truncated to dp or sf

TruncationL5

5★ Calculate the error interval relating to a contextualised word problem

Basic rules of rounding (inc dp and bounds)L1

1★ Round to the nearest 100

Basic rules of rounding (inc dp and bounds)L2

2★ Round to the nearest 10

Basic rules of rounding (inc dp and bounds)L4

4★ Round to 1dp

Basic rules of rounding (inc dp and bounds)L6

6★ Calculate the bounds/error interval

Round to specific sf (inc bounds)L1

1★ Integer rounding to 1 significant figure

Round to specific sf (inc bounds)L2

2★ Integer rounding to 2 significant figures

Round to specific sf (inc bounds)L3

3★ Decimal rounding to the nearest 1 significant figure

Round to specific sf (inc bounds)L4

4★ Decimal rounding to the nearest 2 significant figures

Round to specific sf (inc bounds)L5

5★ Decimal rounding to the nearest 2 significant figures (where 2nd significant figure is 0)

Round to specific sf (inc bounds)L6

6★ Calculate the bounds/error interval

Upper and lower bound calculationsL2

2★ Bounds of addition and multiplication

Upper and lower bound calculationsL3

3★ Bounds of subtraction and division

Upper and lower bound calculationsL4

4★ Mixture of operations

Upper and lower bound calculationsL5

5★ Compound measure calculations with bounds

Upper and lower bound calculationsL6

6★ Use of bounds in other Mathematical topics

Squares, cubes and rootsL1

1★ Given a square grid, count the squares to determine the square number

Squares, cubes and rootsL5

5★ Knowledge of cube numbers up to below 200

Squares, cubes and rootsL6

6★ Combination of operations with squares, cubes and roots of numbers

Equating basesL1

1★ Mixed index laws

Equating basesL2

2★ Write one number as a power of another

Equating basesL3

3★ Simplify index laws and write as a single power of a number

Equating basesL4

4★ Simplify a complex problem and write the answer as a power of a number

Equating basesL5

5★ Solving equations by equating bases

Equating basesL6

6★ Solving harder equations by equating bases

Integers with negative/fractional indicesL1

1★ To the power of -1

Integers with negative/fractional indicesL3

3★ To the power of a half or a third

Integers with negative/fractional indicesL4

4★ To the power of negative half or third

Integers with negative/fractional indicesL5

5★ To the power of a fraction (inc top heavy)

Integers with negative/fractional indicesL6

6★ To the power of a negative fraction (inc top heavy)

Decimals/fractions with negative/fractional indicesL1

1★ Decimal or fraction raised to the power of -1

Decimals/fractions with negative/fractional indicesL2

2★ Decimal or fraction raised to the power of a negative 2

Decimals/fractions with negative/fractional indicesL3

3★ To the power of a half or a third

Decimals/fractions with negative/fractional indicesL4

4★ To the power of negative half or third

Decimals/fractions with negative/fractional indicesL5

5★ To the power of a fraction (inc top heavy)

Decimals/fractions with negative/fractional indicesL6

6★ To the power of a negative fraction (inc top heavy)

Conversion of standard formL1

1★ Multiplying and dividing by powers of 10

Conversion of standard formL3

3★ Convert to standard form (numbers less than 1)

Conversion of standard formL4

4★ Convert from standard form

Conversion of standard formL5

5★ Convert ax10^b where is a<1 or a>10 into standard form

Operate in standard formL1

1★ Add and subtract numbers written in standard form with common powers of 10

Operate in standard formL3

3★ Add and subtract numbers written in standard form

Operate in standard formL4

4★ Multiplying numbers written in standard form

Operate in standard formL5

5★ Dividing numbers written in standard form

Operate in standard formL6

6★ Combination of operations with numbers written in standard form

Simplify a surdL1

1★ Write a surd as the square root of the product of 2 numbers where 1 number is missing

Simplify a surdL2

2★ Write a surd as the square root of the product of 2 numbers

Simplify a surdL3

3★ Write a surd as a product of two square roots where 1 square root is missing

Simplify a surdL4

4★ Write a surd as a product of two square roots

Operate with surdsL1

1★ Add and subtract common surds

Operate with surdsL2

2★ Simplify one surd before adding or subtracting it to another

Operate with surdsL3

3★ Multiplication of surds

Operate with surdsL4

4★ Division of surds

Operate with surdsL5

5★ Combination of operations involving surds

Operate with surdsL6

6★ Combination of operations involving the expansion of surds in brackets

Rationalise the denominatorL1

1★ Given the root of a number, how would you rationalise it?

Rationalise the denominatorL2

2★ Rationalise a unit fraction

Rationalise the denominatorL3

3★ Rationalise a simple denominator

Rationalise the denominatorL4

4★ Rationalise a denominator where the same surd appears in both the numerator and denominator

Rationalise the denominatorL5

5★ Rationalise the denominator using the difference of two squares

Rationalise the denominatorL6

6★ Rationalise the denominator using the difference of two squares and a surd in the numerator

Reading time and tablesL1

1★ Reading a clock face (12hr format) (15mins, 30mins or 45mins past)

Reading time and tablesL2

2★ Reading a clock face (12hr format)

Reading time and tablesL3

3★ Converting a pm time into 24hr format

Reading time and tablesL4

4★ Interpret a bus time table

Reading time and tablesL5

5★ Calculating a journey time from a bus time table

Reading time and tablesL6

6★ Given a departure time and length of journey, will I be late for an appointment?

Reading scalesL1

1★ Reading a scale with integer increments

Reading scalesL2

2★ Reading a scale with integer increments with labels for every other marker on the scale

Reading scalesL3

3★ Reading a scale with 0.5 increments and labels on the integer markers

Reading scalesL4

4★ Reading a scale with a large gaps between labelled markers

Reading scalesL5

5★ Reading a scale with only 2 values given on the scale

Reading scalesL6

6★ Reading a scale with decimal increments

Measuring/Drawing anglesL1

1★ Identify the angle type (e.g. acute, obtuse, right-angle or reflex)

Measuring/Drawing anglesL3

3★ Given that a student has incorrectly interpretted their protractor, identify the number bond to 180°

Measuring/Drawing anglesL4

4★ Draw acute/90°/obtuse angles

Measuring/Drawing anglesL5

5★ Measure a reflex angle

Measuring/Drawing anglesL6

6★ Draw a reflex angle

Convert between degrees and radiansL1

1★ Convert from degrees to radians

Convert between degrees and radiansL2

2★ Convert from radians to degrees

Convert between degrees and radiansL3

3★ Comparison between radians and degrees

Convert between degrees and radiansL4

4★ Use of a calculator with trigonometry functions

Convert between degrees and radiansL5

5★ Calculating arc and area of sectors

Constructions/lociL1

1★ Construct a scalene triangle using loci constructions

Constructions/lociL2

2★ Construct an equilateral/isosceles triangle using loci constructions

Constructions/lociL3

3★ Construct an angle bisector using loci constructions

Constructions/lociL5

5★ Construct a perpendicular line from a point using loci constructions

Constructions/lociL6

6★ Real life loci problem solving

Plans and elevationsL1

1★ Identify the number of cubes needed to make a solid shape

Plans and elevationsL2

2★ Draw the plan, front and side elevations for a solid shape

Plans and elevationsL3

3★ Sketch a solid shape on isometric paper given the plan, front and side elevation

Plans and elevationsL4

4★ Draw the plan, front and side elevations for trickier 3D solids

Plans and elevationsL5

5★ Sketch a tricky 3D solid given the plan, front and side elevation

Plans and elevationsL6

6★ Identify a solid shape from a word description of the plan, front and side elevations

90°, 180°, and 360° anglesL5

5★ Given 3 algebraic expressions to represent angles, solve the equation formed using appropriate angle facts

Angles in trianglesL6

6★ Calculate an unknown angle in 2 adjoining triangles

Angles in quadrilateralsL6

6★ Given algebraic expressions to represent the angles in a quadrilateral, form an equation and solve it

Angles on parallel linesL3

3★ Form and solve an equation given two expressions that represent 2 angles on parallel lines

Angles on parallel linesL4

4★ Solve unknown angles in geometrical shapes using angles on parallel lines

Angles in polygonsL2

2★ Find a missing angle in a n-sided polygon given all but 1 angle

Angles in polygonsL3

3★ Will it regular n-sided polygon tesselate?

Angles in polygonsL4

4★ Use an exterior angle of a regular n-sided polygon to calculate the number of sides

Angles in polygonsL5

5★ Use an interior angle of a regular n-sided polygon to calculate the number of sides

Angles in polygonsL6

6★ Problem solving

BearingsL1

1★ Measure an angle

BearingsL3

3★ Calculate a return bearing from a diagram

BearingsL4

4★ Solve a word problem involving the calculation of a return bearing

BearingsL5

5★ Given a bearing that has been read incorrectly, calculate the correct bearing

BearingsL6

6★ Real life scaled drawings involving the construction of multiple bearings

RotationsL1

1★ State the order of rotational symmetry

RotationsL2

2★ Rotate a shape about the origin

RotationsL3

3★ Describe the transformation about the origin

RotationsL4

4★ Rotate a shape about a point

RotationsL5

5★ Describe the transformation about a point

ReflectionsL1

1★ State the number of lines of symmetry

ReflectionsL2

2★ Draw the mirror line x=a/y=a mirror for a given reflection

ReflectionsL3

3★ Reflect a given shape in x=a/y=a

ReflectionsL5

5★ Reflect a shape in given y=x/y=-x

TranslationsL1

1★ Describe a translation in words

TranslationsL2

2★ Draw a horizontal/vertical translation

TranslationsL3

3★ Describe a horizontal/vertical translation

TranslationsL4

4★ Drawing any vector translation

TranslationsL6

6★ Given the vectors of A to B and B to C, state the vector C to A

EnlargementsL1

1★ Enlarge a shape (without centre of enlargement)

EnlargementsL2

2★ Finding a scale factor given 2 similar shapes (positive or fractional)

EnlargementsL3

3★ Enlarge a shape from a centre of enlargement

EnlargementsL4

4★ Describe an enlargement given 2 similar shapes on a set of axes

EnlargementsL5

5★ Enlarge a shape by a fractional scale factor

EnlargementsL6

6★ Enlarge a shape by a negative scale factor

Area/Volume scale factorsL1

1★ Find the area of an enlarged 2D shape

Area/Volume scale factorsL2

2★ Find the volume of an enlarged 3D shape

Area/Volume scale factorsL3

3★ Find the area of the original 2D shape

Area/Volume scale factorsL4

4★ Find the volume of the original 3D shape

Area/Volume scale factorsL5

5★ Find a side length given the areas of the original and enlarged shape

Area/Volume scale factorsL6

6★ Find a side length given the volumes of the original and enlarged 3D shapes

CongruenceL1

1★ Are two given shapes congruent?

CongruenceL2

2★ Knowing two shapes are congruent, find an unknown side or angle

CongruenceL3

3★ State the condition of congruence shown by 2 shapes

CongruenceL4

4★ Prove two shapes are congruent

Similar shapesL1

1★ Are two given shapes similar?

Similar shapesL2

2★ Knowing two shapes are similar, find an unknown side length (orientation exercise)

Similar shapesL3

3★ Use a scale factor to find an unknown side

Similar shapesL4

4★ Use a scale factor to find an unknown side (harder)

Similar shapesL5

5★ Use Pythagoras theorem to find an unknown side given 2 similar shapes

Names and properties of polygonsL1

1★ Given a 2D shape, identify the polygon family

Names and properties of polygonsL2

2★ Name a regular shape given its geometrical properties

Names and properties of polygonsL3

3★ Given a basic 4 sided shape, name the quadrilateral

Names and properties of polygonsL4

4★ Name a quadrilateral given its geometrical properties

Area of 2D shapesL5

5★ Calculate the area of a regular hexagon

Area of 2D shapesL6

6★ Given 2 shapes and the fact their areas are equal, calculate a missing length in 1 of the shapes

Reverse area of 2D shapesL1

1★ Given the area of a rectangle, calculate an unknown side length

Reverse area of 2D shapesL2

2★ Given the area of a triangle, calculate an unknown side length

Reverse area of 2D shapesL3

3★ Given the area of a parallelogram, calculate an unknown side length

Reverse area of 2D shapesL4

4★ Given the area of a trapezium, calculate an unknown side length

Reverse area of 2D shapesL5

5★ Given 2 shapes and the fact their areas are equal, calculate a missing length in 1 of the shapes

Reverse area of 2D shapesL6

6★ Given that a length is a multiple of another in a basic 2D shape and the area, calculate the unknown length

Algebraic area of 2D shapesL1

1★ Calculate the area of a rectangle with simple terms to represent the sides

Algebraic area of 2D shapesL2

2★ Calculate the area of a rectangle where the sides are expressions

Algebraic area of 2D shapesL3

3★ Given an expression to represent the area of a rectangle and 1 integer side, write the expression for the other side

Algebraic area of 2D shapesL4

4★ Find the area of a rectangle with expressions for both sides

Algebraic area of 2D shapesL5

5★ Find the area of shaded region with a cut out made from rectangles

Algebraic area of 2D shapesL6

6★ Calculate the area of simple compound shape with algebraic sides

Area of composite shapesL5

5★ Calculate the shaded area of a compound shape made from removing a rectangle from another rectangle

Area of composite shapesL6

6★ Calculate the shaded area of a compound shape made from removing a circle from a square

Perimeter of 2D shapesL1

1★ Calculate the perimeter of a rectangle by counting squares

Perimeter of 2D shapesL4

4★ Calculate the perimeter of a rhombus

Perimeter of 2D shapesL5

5★ Form an expression to represent the perimeter of a rectangle with algebraic side lengths

Perimeter of 2D shapesL6

6★ Calculate the perimeter of a half or quarter of a circle

Parts of a circleL1

1★ Identify which line within a circle is the diameter

Parts of a circleL2

2★ Find the radius or diameter given the other

Parts of a circleL4

4★ Draw the named part of a circle

Circumference of a circleL1

1★ Calculate the circumference given the diameter

Circumference of a circleL3

3★ Calculate the diameter given the circumference

Circumference of a circleL4

4★ Calculate the perimeter of a quarter or half circle

Circumference of a circleL5

5★ Calculate the perimeter of a sector or the arc length

Circumference of a circleL6

6★ Calculate the angle of a sector given the perimeter

Area of a circleL1

1★ Calculate the area of a circle given the radius

Area of a circleL3

3★ Calculate the radius of a circle given its area

Area of a circleL4

4★ Calculate the area of a quarter or semi circle

Area of a circleL5

5★ Calculate the area of a sector

Area of a circleL6

6★ Calculate the angle of a sector given its area

Circle theoremsL2

2★ Calculate an unknown angle using the angles in the cyclic quadrilateral property

Circle theoremsL3

3★ Calculate an unknown angle using the angle at the center is twice the angle on the circumference theorem or angles in the same segment theorem

Circle theoremsL4

4★ Calculate an unknown angle using the alternate segment theorem

Circle theoremsL5

5★ Calculate an unknown angle using circle theorems that are tricky to spot

Circle theoremsL6

6★ Form and solve an equation based on algebraic angles linked by circle theorems

Apply Pythagoras' TheoremL1

1★ Calculate the hypotenuse of a right angled triangle

Apply Pythagoras' TheoremL3

3★ Use Pythagoras theorem for right angled triangles

Apply Pythagoras' TheoremL4

4★ Apply Pythagoras theorem in non-right angle triangles

Apply Pythagoras' TheoremL6

6★ Apply Pythagoras theorem in 3D

Apply SOH CAH TOAL1

1★ Finding a length given an approximate trig value in a right-angled triangle

Apply SOH CAH TOAL3

3★ Apply SOH CAH TOA to calculate an angle in a right-angled triangle

Apply SOH CAH TOAL4

4★ Apply SOH CAH TOA in an isosceles or equilateral triangle or quadrilateral

Apply SOH CAH TOAL5

5★ Apply SOH CAH TOA multiple times in a multi-step problem

Apply SOH CAH TOAL6

6★ Apply SOH CAH TOA in a 3D problem

Sine and cosine rulesL1

1★ Label the angles and sides of triangle ABC ready to apply the sine or cosine rule

Sine and cosine rulesL2

2★ Using the sine rule to find a side or angle

Sine and cosine rulesL3

3★ Using the cosine rule to find a side

Sine and cosine rulesL4

4★ Using the cosine rule to find an angle

Sine and cosine rulesL5

5★ Apply either the sine or cosine rule in a problem

Sine and cosine rulesL6

6★ Apply both the sine and cosine rule in a multi-step problem

Area of a triangle (trigonometry)L1

1★ Label the angles and sides of triangle ABC ready to apply the sine or cosine rule

Area of a triangle (trigonometry)L2

2★ Evaluate the correct use of the formula on a calculator

Area of a triangle (trigonometry)L3

3★ Calculate the area of a non-right angled triangle using 0.5absinC

Area of a triangle (trigonometry)L4

4★ Find a side of a non-right angled triangle given the area, the angle and the length of the adjacent side

Area of a triangle (trigonometry)L5

5★ Find an angle of a non-right angled triangle given the area and two adjacent sides

Area of a triangle (trigonometry)L6

6★ Apply the area formula to find an unknown value that assists with then using the cosine rule in a multi-step problem

Trigonometry exact valuesL1

1★ Reading exact values from either a right-angled triangle or a right-angled isosceles triangle

Trigonometry exact valuesL2

2★ Recalling exact values of sin, cos or tan

Trigonometry exact valuesL3

3★ Find the sum of exact sin, cos or tan values

Trigonometry exact valuesL4

4★ SOH CAH TOA application of exact values

Trigonometry exact valuesL5

5★ Identify alternate exact values of angles greater than 90

Trigonometry exact valuesL6

6★ Apply exact values within a cosine rule problem

Surface area of 3D shapesL1

1★ Give the name of a common 3D shape given a diagram or description

Surface area of 3D shapesL5

5★ Calculate a missing length given the surface area of a sphere, cylinder or cuboid

Volume of 3D shapesL1

1★ Give the name of a common 3D shape given a diagram or description

Volume of 3D shapesL3

3★ Calculate the length of an edge of a cube or of a cuboid given its volume

Volume of 3D shapesL5

5★ Calculate a missing length in a cylinder or triangular prism given the volume

Volume of 3D shapesL6

6★ Calculate the most items you can fit in a container

Volume of complex 3D shapesL1

1★ Give the name of a common 3D shape given a diagram or description

Volume of complex 3D shapesL2

2★ Calculate the volume of a cone or sphere or square based pyramid

Volume of complex 3D shapesL3

3★ Calculate a missing length given the volume of a cone or sphere or square based pyramid

Volume of complex 3D shapesL4

4★ Calculate the volume of a hemi sphere or frustum

Volume of complex 3D shapesL5

5★ Calculate a missing length given the volume of a frustum

Leave your answer in exact formL1

1★ Calculate the area or circumference of a circle in terms of pi

Leave your answer in exact formL2

2★ Calculate the area or arc length of a sector in terms of pi

Leave your answer in exact formL3

3★ Calculate the longest or shortest side using Pythagoras leaving the answer in surd form

Leave your answer in exact formL4

4★ Calculate the volume of a cone, sphere or cylinder in terms of pi

Leave your answer in exact formL5

5★ Find the sum of exact sin, cos or tan values

Leave your answer in exact formL6

6★ Evaluate a value raised to a fractional power leaving the answer in surd form

VectorsL1

1★ Interpret a vector

VectorsL2

2★ Draw a vector

VectorsL3

3★ Perform vector arithmetic

VectorsL4

4★ Determine the resultant vector given 2 vectors in a geometry problem

VectorsL5

5★ Determine the resultant vector given 2 vectors in a geometry problem involving midpoints of a vector

VectorsL6

6★ Determine the resultant vector given 2 vectors in a geometry problem involving ratio of a vector

Probability scaleL1

1★ Probability vocabluary - impossible, unlikely, even chance, likely, certain

Probability scaleL2

2★ Place likelihood of an event on a number line (0 to 1)

Probability scaleL3

3★ Place the likelihood of events on a number line (0 to 1) that are mutually exclusive events

List outcomesL1

1★ List outcomes from a single event

List outcomesL4

4★ Calculate probabilities given a sample space diagram

List outcomesL5

5★ Draw and interpret a sample space diagram for the outcomes of 2 events

Calculate simple probabilitiesL1

1★ Calculate the probability for a simple single event

Calculate simple probabilitiesL2

2★ Calculate the probability of selecting an item given a list of all outcomes

Frequency treesL1

1★ Create a frequency tree for a single event

Frequency treesL2

2★ Create a frequency tree for 2 events

Frequency treesL3

3★ Create a frequency tree for 2 events involving some arithmetic to complete the tree

Frequency treesL4

4★ Create a frequency tree for 2 events involving problem solving to complete the tree

Frequency treesL5

5★ Calculate the probability of an event by first drawing a frequency tree

Mutually exclusive eventsL2

2★ Complete a table of the likelihood of outcomes of a mutually exlusive event with 3 outcomes

Mutually exclusive eventsL3

3★ Complete a table of the likelihood of outcomes of a mutually exlusive event where 2 of the outcomes are equally likely

Mutually exclusive eventsL4

4★ Complete a probability tree diagram for a single event

Mutually exclusive eventsL5

5★ Given the probabilities of a mutually exclusive event as algebraic expressions, form and solve the equation

Calculate relative/expected frequencyL2

2★ Find the relative frequency where the total is not 100

Calculate relative/expected frequencyL3

3★ Find the relative frequency where the total is not given

Calculate relative/expected frequencyL4

4★ Use relative frequency to calculate the expected frequency

Calculate relative/expected frequencyL5

5★ Complete a table of relative frequencies and expected frequencies of a single event

Calculate relative/expected frequencyL6

6★ Use relative frequency from an experiment to estimate the population

Probabilities of independent eventsL6

6★ Calculate a probability of more than 2 events

Probabilities of dependent eventsL2

2★ Calculate a probability given an incomplete tree diagram for 2 events - AND style questions

Probabilities of dependent eventsL3

3★ Calculate a probability of 2 events - AND style questions

Probabilities of dependent eventsL4

4★ Calculate a probability of 2 events where you can only have 1 of each - OR style questions

Probabilities of dependent eventsL5

5★ Calculate a probability of 2 events for AT LEAST style questions

Complete and interpret a venn diagramL1

1★ Construct a venn diagram

Complete and interpret a venn diagramL2

2★ Calculate simple probabilities from a venn diagram

Complete and interpret a venn diagramL3

3★ Calculate union or intersection probabilities from a venn diagram

Complete and interpret a venn diagramL4

4★ Calculate union or intersection probabilities from a venn diagram including NOT

Complete and interpret a venn diagramL5

5★ Calculate union or intersection probabilities given domains outlined by set notation

Complete and interpret a venn diagramL6

6★ Calculate union or intersection probabilities where an equation needs to be formed and solved

Calculate conditional probabilitiesL1

1★ Conditional probability from a venn diagram

Calculate conditional probabilitiesL2

2★ Conditional probability without a venn diagram but given domains outlined by set notation

Calculate conditional probabilitiesL3

3★ Conditional probability of selecting letters from a given word

Calculate conditional probabilitiesL4

4★ Calculating a conditional probability given percentages of specific outcomes

Conversion of metric unitsL2

2★ Conversion between cm^3 and l

Conversion of metric unitsL3

3★ Simple problem solving given measures of different metric units

Conversion of metric unitsL4

4★ Conversion between metric units of area

Conversion of metric unitsL5

5★ Conversion between metric units of volume

Conversion of metric unitsL6

6★ Problem solving with metric units of measure

Conversion of metric and imperialL1

1★ Convert between miles and kilometres

Conversion of metric and imperialL3

3★ Given a conversion ratio, change between metric and imperial units

Conversion of metric and imperialL4

4★ Problem solving with measures given in metric and imperial units

Conversion of metric and imperialL5

5★ Multiple conversions of units

Conversion of metric and imperialL6

6★ Convert between units of area/volume

Map scalesL1

1★ Given a conversion ratio, convert a map distance into a real life distance

Map scalesL2

2★ Conversion between metric units of length

Map scalesL3

3★ Given a conversion ratio, convert a real life distance into a map distance

Map scalesL4

4★ Given a scale written in different metric units, write the ratio in its simplest form

Map scalesL5

5★ Given a distance represented as a measureable line on map and a scale, convert into a real life distance

Compound measuresL3

3★ Density, mass and volume calculations/Pressure, mass and area calculations

Compound measuresL4

4★ Problem solve with compound measures

Compound measuresL5

5★ Problem solve with compound measures involving volume calculation

Compound measuresL6

6★ Convert between different units of compound measure

Simplify a ratioL1

1★ Simplify a:b

Simplify a ratioL3

3★ Simplify a:b:c

Simplify a ratioL4

4★ Simplify a simple algebraic ratio

Simplify a ratioL5

5★ Simplify an algebraic ratio that includes powers

Simplify a ratioL6

6★ Combine 2 separate ratios comparing different quantities and problem solve when interpreting the resulting ratio

Interpret ratio as a fractionL1

1★ What fraction of a bar model divided into the ratio a:b is shaded

Interpret ratio as a fractionL2

2★ What fraction of a bar model divided into the ratio a:b:c is shaded)

Interpret ratio as a fractionL3

3★ Given a ratio a:b, what fraction is represented

Interpret ratio as a fractionL4

4★ Given a ratio a:b:c, what fraction is represented

Interpret ratio as a fractionL5

5★ Given a fraction/percentage of a bar model that is shaded, represent this as a ratio

Interpret ratio as a fractionL6

6★ Represent a part of a contextualised ratio problem as fraction

Divide a quantity into a given ratioL2

2★ Divide an amount into a:b:c

Divide a quantity into a given ratioL3

3★ Divide a contextualised amount into the ratio a:b

Divide a quantity into a given ratioL4

4★ With an amount of money shared in the ratio a:b, if someone gets this, what does the other get?

Divide a quantity into a given ratioL5

5★ With an amount of money shared in the ratio a:b, if the difference is this, how much did they share?

Divide a quantity into a given ratioL6

6★ Divide an amount into a given ratio when the problem is linked with other topics in Maths, e.g. angles

Multiplicative operations with ratiosL1

1★ Given an equation of A in terms of B, write the fraction A/B

Multiplicative operations with ratiosL2

2★ Given an equation of A in terms of B, write the ratio A:B

Multiplicative operations with ratiosL3

3★ Given A:B=C:D, write the equation of A in terms of B, where C and D are positive integers

Multiplicative operations with ratiosL4

4★ Given the ratio of 2 pairs of points on a straight line give ratio between each point

Multiplicative operations with ratiosL5

5★ Given an equation of A in terms of B, problem solve with multiplicative ratios

Multiplicative operations with ratiosL6

6★ Problem solve when multiplicative operations with ratios are applied in other Mathematical topics

Best buysL1

1★ Compare 2 offers (same quantities but different prices £)

Best buysL2

2★ Compare 2 offers (different quantities and different prices £)

Best buysL3

3★ Compare 2 offers (different quantities and different prices £pp)

Best buysL4

4★ Compare 2 offers (different units, quantities and prices)

Best buysL5

5★ Compare 2 offers (special offer deals)

Currency conversionL3

3★ Given the currency conversion ratio, convert to pounds from another currency

Currency conversionL4

4★ Given the cost of an item in two countries, which is better value/what is the difference in price?

Currency conversionL5

5★ Given the cost of 2 items in different countries and the currency conversion into pounds, convert them into a comparable amount to determine which is better value

Direct proportionL2

2★ Scale ingredients using direct proportion for a different number of portions

Direct proportionL4

4★ Word direct proportion

Direct proportionL5

5★ Direct proportion linear model

Direct proportionL6

6★ Direct proportion non linear model

Inverse proportionL1

1★ Simple inverse proportion based on a word problem

Inverse proportionL2

2★ Word related inverse proportion

Inverse proportionL3

3★ Inverse proportion linear model

Inverse proportionL4

4★ Inverse proportion non linear model

Awaiting approval

Once a misconception has been created it will land here. After a short review process, the misconception will go live and be made available to the rest of the misconception community.

Algebra vocabulary and understandingL2

2★ Is it an equation or an identity?

Pending review

Algebra vocabulary and understandingL3

3★ Product of two brackets equating coefficients (quadratics)

Pending review

Algebra vocabulary and understandingL4

4★ Equating coefficients (inc. factorising)

Pending review

Algebraic proofL1

1★ Provide a counterexample to disprove a statement

Pending review

Simplify an expressionL6

6★ Find the perimeter of a shape with linear expressions as the lengths of the sides

Pending review

Algebraic fractionsL2

2★ Add or subtract fractions

Pending review

Algebraic fractionsL3

3★ Simplify a fraction by factorising

Pending review

Increase/decrease by a percentageL2

2★ Increase/decrease by a percentage where the percentage is a multiple of 5 (exc multiples of 10)

Pending review

Surface area of 3D shapesL4

4★ Surface area of a cone or sphere

Pending review

Conversion of metric and imperialL2

2★ Speed/distance/time calculations

Pending review