Personalised Key Stage 3 maths tutoring to close gaps before GCSE

Partitioning numbers up to 10,000,000

Knowing the value of each digit in numbers with up to 3 decimal places

Comparing and ordering numbers with up to 3 decimal places

Multiplying and dividing whole numbers and decimals by 10 and 100

Rounding numbers to 2 decimal places

Using a number line to calculate across zero

Using mental methods to add and subtract whole numbers and decimals

Adding whole numbers and decimals using the column method

Subtracting whole numbers and decimals using the column method

Finding prime numbers

Finding square numbers

Using mental strategies to multiply

Using mental strategies to divide

Multiplying using short multiplication

Dividing using short division with exchange

Finding equivalent fractions

Simplifying fractions by finding common factors

Adding and subtracting fractions including mixed numbers

Finding percentages of amounts

Comparing numbers up to 10,000

Rounding numbers to the nearest 10

Finding factors

Finding common multiples

Multiplying 2-digit numbers using the area model

Dividing using short division with exchange

Adding decimals using the column method

Subtracting decimals using the column method

Simplifying fractions

Writing simple fractions as decimals

Adding and subtracting fractions with different denominators

Using fractions to solve problems

Finding percentages of an amount

Using symbols and letters for unknown amounts

Using simple formulas

Solving one-step equations

Using ratio language and symbol

Making and describing linear sequences

Finding missing angles on a straight line

Knowing the value of each digit in numbers up to 10,000,000

Using the number line with decimal values

Rounding numbers to 2 decimal places

Multiplying and dividing whole numbers and decimals by 10, 100, 1,000

Finding the lowest common multiple using listing

Finding the highest common factor using listing

Finding equivalent fractions.

Solving problems using the order of operations.

Probability Scales

Change the subject of a formula – Simple One-step equations

Express one quantity as a fraction of another

Constructing angles with a protractor

Form algebraic expressions given information in words

Form algebraic expressions

Use 4 operations with algebra

Using the bar model to solve multi-step problems

One and two step function machines

Work out inputs and outputs of a functions machine.

Work out missing operations given a function machine.

Work with algebraic expressions as input or output of a function machine.

Derive rules for patterns and be able to work out consecutive patterns.

Find missing terms in the middle or start of a sequence.

Angles around a point add to 360

Know the different types of angles and descriptors

Label and identify parts of a circle

Perimeter of squares and rectangles

Area of squares and rectangles

Solving measure problems involving reading scales

Writing decimals as fractions and percentages

Ordering FDPs

Working out quantities using FDP

Use estimation to check answers to calculations

Find fraction of an amount (f(proper)xf(proper) or f(proper)xi)

Addition and subtraction of fractions with common denominator

Convert between mixed and improper fractions

Comparing and ordering fractions

Dividing fractions by whole numbers

Fractions of Time (1/2 hour = 30 mins)

Develop full understanding of the order of operations

Comparing and ordering numbers with up to 3 decimal places

Finding and estimating the position of decimals on a number line

Ordering numbers up to 10,000,000

List numbers that could be rounded to a given accuracy.

Represent percentages in diagrams

Increasing and decreasing by percentages by finding the amount and adding on/subtracting

Understanding Tally Charts

Understanding Pictograms

Prime Factorisation

Adding and subtracting fractions including mixed numbers.

Writing percentages as fractions and decimals.

Finding percentages of amounts without using a calculator.

Sharing in Ratio.

Multiplying using long multiplication.

Dividing a number and writing the remainder as a fraction or decimal (incl. recurrance)

Multiplying a decimal by a decimal.

Simplifying an expression by collecting like terms.

Substituting into expressions.

Finding the nth term of arithmetic sequences.

Solving two-step equations involving fractions.

Finding missing angles

Adding or subtracting a negative number

Multiplying and dividing directed numbers

Working with square numbers

Defining and finding square roots

Cubing and cube rooting numbers

Reading, writing and evaluating powers

Understanding Prime Numbers

Finding prime factors

Multiplying Fractions

Dividing fractions

Writing the equation of a line parallel to the x-axis or y-axis

Area of triangles

Change the subject of a formula – Simple Two-step equations

Solve two step equations with negative x e.g. 3 – x = 10 or 3 – x = 1

Write integer solutions to bounded inequalities

Inequalities on a number line

Angles on a straight line at a point add to 180

Vertically opposite angles are equal

Work in real life context with area and perimeter

Converting between miles and kilometres

Solving area and perimeter problems

Solving problems involving time tables

Be able to find the surface area of basic 3D shapes

Be able to work with surface area in real life context

Work with volume in real life context

Plans and elevations of cube structures

Plans and elevations of standard 3D shapes

Dividing using short division giving remainders as decimals

Multiplying decimals using powers of 10

Solving mixed multiplication and division problems

Fraction of amounts where the fraction is improper or mixed

Mixed number of an amount

Problems involving fractional increase/decrease.

Finding common factors

Be able to recognize multiples, factors, square and cube numbers, prime numbers, powers and roots.

Using a calculator

Simplify ratio

Write ratios in the form 1:n

Find limiting factors to a given recipe

Use proportion to find any given amount needed to make a quantity.

Understanding Bar Charts (single, dual and composite)

Understanding Line graphs

Use a set of instructions to complete a sample space diagram

Interpret sample space diagrams given some parameters

Applying the order of operations to multi-step calculations

Simplify a more complex expression by collecting like terms

Expanding a single bracket

Factorise an algebraic expression by taking out common factors

Rounding to significant figures

Working with metric units of length

Area of parallelograms

Working with metric units of mass and capacity

Calculating the volume of cubes and cuboids

Averages and range – Finding the Mode

Averages and range – Finding the Median

Averages and range – Finding the Mean

Averages and range – Finding the Range

Substitute positive and negative numbers into formulae

Calculating with ratios and fractions

Using multipliers to solve direct proportion problems

Solving equations with negative solutions

Solving equations with the unknown on both sides

Constructing Triangles SSS

Constructing Triangles ASA

Constructing Triangles SAS

Understand and use a frequency tree

Use frequency trees to state probabilities

Using a frequency tree to work with a wider problem

Solve fractional equations involving one variable on one side

Solve simultaneous equations graphically

Find missing lengths given the area of quadrilaterals

Find missing lengths given the perimeter of quadrilaterals

Find lengths given the surface area or volume

Fractions to Recurring Decimals

Comparing fractions of amounts (best buy, area etc)

Finding percentages of amounts

Convert ratio to fraction and percentage.

Work with ratio given a difference

Work with ratio given a part

Best Buy

Use listing strategies to find total number of combinations for a given problem

Write a probability given the listed outcomes

Using prime factorisation to find the Highest Common Factor

Using prime factorisation to find the Lowest Common Multiple

Hard Function machines including roots

Form expressions and equations from both worded and geometric problems including angle problems, perimeter, area etc.

Expand a single bracket – a(bx+-c) where a>0 and a<0

Expand a single bracket – ax^d(bx+-c) where a>0 and a<0

Expand a single bracket – a(bx+-c)+-d(ex+f)

Expanding double brackets

Substituting into tables

Substituting into geometric representations and tables

Substitution to find an expression given another expression. EG: x + y = 6 find 3x + 3y

solving basic linear inequalities

Describing inequality solutions sets using a number line – bounded

Describing inequality solutions sets using a number line – unbounded

Solving Simultaneous Equations by elimination (positive and negative coefficients)

Types of Sequence: Arithmetic, Geometric and Fibonacci sequences

Using the nth term to identify if a number is in a sequence

Solving problems in pattern sequences

Finding the nth term of arithmetic sequences – Increasing

Finding the nth term of arithmetic sequences – decreasing (including a-bn)

Finding the nth term of arithmetic sequences – fractional and decimal

Geometric sequences

Use Fibonacci rule with numbers and algebra

Understanding and applying the Index Laws for multiplication

Understanding and applying the Index Laws for division

Understanding and applying the Index Laws for Powers

Changing the subject of a formula – Area, Perimeter, Surface Area and Volume

Changing the subject of a formula – SUVAT

Change the subject of a formula – multi-step formulae involving powers and roots

Changing the subject of a formula – Other formulae: Pythagoras’ Theorem, y=mx+c

Using coordinates to solve problems

Combining properties of quadrilaterals with coordinates and symmetry with y=a or x=b

Finding the midpoint between two coordinates

Evaluating if a given point is on a line

Given an equation not in the form y = mx+c, be able to rearrange and find the gradient and y-intercept

Sketching Graphs and recognising characteristics – linear

Working with y=x+a and y=-x+a

Parallel lines

Conversion graphs – plot identify values, extrapolate, comparisons

Write error intervals given an accuracy of rounding including lengths and area

Estimating the answer to a calculation by rounding to 1 significant figure

Estimation with money

Using Standard Form to write Large Numbers

Using Standard Form to write Small Numbers

Calculating with Mixed Numbers

Dividing an integer by a decimal

Writing a value as a percentage of another

Increasing and decreasing by percentages using multipliers

Calculating a percentage change

Work with ratio given a part or a difference

Calculate speed from a distance time graph

Calculating the area of a trapezium

Calculating the Circumference

Finding the area of circles

Finding the area of compound shapes – L-shapes

Finding the area of compound shapes – Including Pythagoras

Finding the area of compound shapes – Regular Polygons and Nets

Finding the area of compound shapes – Cut outs and shaded regions

Solving Area and Perimeter Problems – Reverse Area and Perimeter

Solving Area and Perimeter Problems – Patterns and compound

Finding a longest side of a right-angled triangle using Pythagoras’ theorem

Finding a short side of a right-angled triangle using Pythagoras’ theorem

Reflecting on a coordinate grid

Describing reflections on a coordinate grid

Rotating on a coordinate grid

Describing rotations on a coordinate grid

Translating on a coordinate grid

Describing translations on a coordinate grid

Enlarging on a coordinate grid – Enlarge shapes given a positive scale factor

Describing enlargements on a coordinate grid

Invariant points

Use ratio, fraction of amount and algebra to find missing angle values.

Interior angles of polygons – Irregular

Interior angles of polygons – Regular

Exterior angles of polygons

Calculating the number of sides of a regular polygon from an angle

Angle sum of polygons

Know the correct terminology and types of angles in parallel lines

Finding angles in parallel lines

Identify bearings from a given point

Use bearings to draw on maps and find missing locations.

Finding missing lengths of similar shapes (basic)

Finding missing lengths of similar triangles

SOHCAHTOA – missing angles

SOHCAHTOA – missing sides

Draw simple vector resultants

Writing a resultant to two or more vector movements e.g. Given A and B, Find 2A + 3B

Probability of mutually exclusive events, P(not A)

Completing two-way tables

Interpreting two-way tables

Mode from a frequency table

Median from a frequency table

Mean from a frequency table

Range from a frequency table

Find missing numbers based on information given

Find missing values given the MMMR

Estimating the mean from a frequency table

Modal class from a grouped frequency table

Estimating the range from a grouped frequency table

Median class from a grouped frequency table

Given information find missing areas of a Venn diagram.

Scatter Graphs – Accurately draw and use a line of best fit for interpolation

Scatter Graphs – Know the three correlations and how to determine the strength of the correlation

Scatter Graphs – Plot values and identify outliers

Expand a single bracket – a(bx+-c) where a<0

Write answers for area and perimeter of circles and sectors in terms of π