Home

Maths

Addition and subtraction

Adding numbers using mental maths

Select Lesson

Algebra

Simple formulae

Linear number sequences

Missing number problems

Solving equations with two unknowns

Ratio and proportion

Solving ratio problems

Calculating percentages of amounts

Scale factor problems

Unequal sharing

Statistics

Pie charts

Line graphs

Discrete and continuous data

Mean, median, mode and range

Geometry - position and direction

Coordinate polygons

Drawing and reflecting shapes on the coordinate grid

Drawing and translating shapes on the coordinate grid

Describing positions in the four quadrants

Geometry - properties of shapes

2D shapes: Types and properties

3D shapes: Types and properties

Comparing and classifying shapes

3D shape nets

Geometric shapes: Types and properties

Parts of a circle

Drawing and measuring angles with a protractor

Angles around a point and on a straight line

Finding missing angles

Measurement

Calculate and convert between units of measure

Perimeter of composite rectilinear shapes

Area of irregular shapes

Area of parallelograms and triangles

Formulae for the area and volume of shapes

Calculating the volume of cubes and cuboids

Fractions

Finding fractions of amounts

Mixed numbers and improper fractions

Comparing and ordering fractions greater than 1

Simplifying fractions

Add and subtract fractions: Different denominators

Multiplying pairs of proper fractions

Dividing fractions by whole numbers

Equivalent fractions, decimals and percentages

Multiplying decimals by whole numbers

Dividing and expressing the answer as a decimal

Multiplication and division

Times tables up to 12 x 12

Multiplying a 4-digit number by a 1 or 2-digit number

Dividing numbers up to 4 digits by a 2-digit number

Mental maths strategies

Common factors and multiples

Order of operations: BIDMAS

Using estimation to check answers

Addition and subtraction

Adding numbers using mental maths

Using column addition to add numbers

Subtracting numbers using mental maths

Using column subtraction to subtract numbers

Multi-step problems with addition and subtraction

Inverse operations to check calculations

Number and place value

Numbers to 10,000,000

Place value: Four-digit numbers

Representing numbers in different ways

Rounding any number up to 1,000,000

Counting using positive and negative numbers

Counting in powers of 10

Negative numbers

Explainer Video

Tutor: Toby

Summary

Adding numbers using mental maths

In a nutshell

By keeping track of your units, tens, hundreds, or other place values with many digits, you can add numbers using mental maths.

Adding a small number

Adding is just counting up. So $4+2$ is just counting up two from four. If you know how to count, you know how to add.

Example 1

Calculate

$10+8$ 

You can do this by starting at ten and counting up eight places:

So,

$10+8=\underline{18}$

Adding a bigger number

For bigger numbers however, it is harder to simply count in steps of one and would take too long. Instead, a number should be broken down into its units, tens, hundreds etc, and counted up.

Example 2

Calculate

$43+25$ 

Start by counting up the units, then move on to the tens. So initially you can add the five units and then you add the two tens.

So,

$43+25=\underline{68}$ 

Changing tens and hundreds

When using this method to add mentally there will be times when by adding units, you will end up changing the tens. Similarly, when adding tens you sometimes have to change the hundreds. As you add bigger and bigger numbers, the same thing will happen with thousands, tens of thousands, and so on.

Example 3

Calculate

$89+43$ 

Start with the units. Notice that though you are adding units, the tens value has also changed. This is because units value has exceeded ten. Next add the tens to what you have so far.

This means that:

$89+43=\underline{132}$ 

Notice that here you were adding tens but the hundreds value also changed from zero to one. This is because the tens value exceeded one hundred.

Learn with Basics

Length:

Unit 1

Place value: Four-digit numbers

Unit 2

Numbers to 1000

Jump Ahead

Optional

Unit 3