Mental Addition & Subtraction

Test yourself

Mental Addition and Subtraction

You need to think about our place value rules when adding and subtracting mentally.

4,372 + 6

You look at the 'ones' column because that is the column you are adding to.
- I know that 2 + 6 = 8
- So 4,372 + 6 = 4,378

Carrying over

Sometimes you need to carry over a value to the next column.

Carrying over example

E.g. 4372 + 9
- You look at the 'ones' column because that is the column you are adding to.
I know that 2 + 9 = 11
- So I know that my 'ones' column will be 1 and I need to carry one ten to the 'tens' column.
- So 4,372 + 9 = 4,381

A different method

There are loads of different ways to do mental addition.
I'm trying to do the same calculation as the previous example (4,372 + 9).
- Instead of adding 9, I can add 10 because that's easier!
- I know 4,372 + 10 = 4,382
- But I've added 1 too many, so I need to take 1 away.
- 4,382 − 1 = 4,381
- So 4,372 + 9 = 4,381

Adding Double/Triple/Quadruple Digit Numbers in Your Head

You can also add more than one digit to a number. You can add more than one digit to a number by splitting the number into its place values.

Example

I want to work out 4,372 + 25.
I can split 25 into its place values.
- 25 = 20 + 5

First, add the 'tens'

I have split 25 into 20 + 5.
First, add 20 to 4,372
- 4,372 + 20 = 4,392

Then, add the 'ones'

Then, add 5 to 4,392
- 4,392 + 5 = 4,397
So you know that 4,372 + 25 = 4,397

Adding larger numbers

You can use the same process to add larger numbers in your head.
E.g. 4,372 + 214
- Start by splitting 214 into 200 + 10 + 4.

Adding 214

Then add 200 to 4,372.
- 4,372 + 200 = 4,572
Then add 10 to 4,572.
- 4,572 + 10 = 4,582
Then add 4 to 4,582.
- 4,582 + 4 = 4,586

1Year 5 - Number

1.1Number & Place Value

1.1.1The Value of Digits to Millions

1.1.2Smallest & Biggest Numbers to Millions

1.1.3Ordering Numbers to Millions

1.1.4Counting in Powers of 10

1.1.5Counting in Negative Numbers

1.1.6Rounding Numbers up to 1,000,000

1.1.7Reading Roman Numerals

1.2Addition & Subtraction

1.2.1Written Methods for Adding Large Numbers

1.2.2Written Methods for Subtracting Large Numbers

1.2.3Mental Addition & Subtraction

1.2.4Rounding to Check Your Answer

1.3Multiplication & Division

1.3.1Multiples

1.3.2Factors

1.3.3Prime Numbers

1.3.4Prime Factors

1.3.5Composite Numbers

1.3.6Factor Trees

1.3.7Multiplication by a 1 Digit Number

1.3.8Long Multiplication Using Column Method

1.3.9Times Tables

1.3.10Division

1.3.11Multiplying & Dividing by 10, 100 & 1,000

1.3.12Square & Cube Numbers

1.4Fractions & Decimals

1.4.1Compare & Order Fractions

1.4.2Identifying Equivalent Fractions

1.4.3Add & Subtract Fractions

1.4.4Mixed Numbers & Improper Fractions

1.4.5Multiplying Fractions by Whole Numbers

1.4.6Converting Between Decimals & Fractions

1.4.7Rounding Decimals

1.4.8Ordering Decimals

2Year 5 - Measurement

2.1Measures

2.1.1Metric Measurements

2.1.2Imperial Measurements

2.2Perimeter & Area

2.2.1Perimeter

2.2.2Area

2.3Time

2.3.1Units of Time

3Year 5 - Geometry

3.1Properties of 3D Shapes

3.1.1Types of 3D Shapes

3.1.2Faces, Edges & Vertices

3.2Properties of 2D Shapes

3.2.1Polygons

3.3Angles

3.3.1Angles in Degrees

3.3.2Types of Angle

3.3.3Finding Missing Angles

3.4Position & Direction

3.4.1Reflection & Translation

4Year 5 - Statistics

4.1Graphs

4.1.1Line Graphs

4.1.2Tables

4.1.3Timetables

5Year 6 - Number

5.1Number & Place Value

5.1.1The Value of Digits to Ten Millions

5.1.2Ordering Numbers to Millions

5.1.3Rounding

5.1.4Negative Numbers

5.2Multiplication & Division

5.2.1Multiplication by a 2 Digit Number

5.2.2Division

5.2.3Multiples

5.2.4Factors

5.2.5Primes

5.3Mental Maths

5.3.1Multiplying & Dividing by 10, 100 & 1,000

5.3.2Addition & Subtraction

5.3.3Adding & Subtracting 10, 100 & 1,000

5.3.4Multiplication & Division

5.4Order of Operations

5.4.1BIDMAS

5.5Problem Solving

5.5.1Addition & Subtraction Multi-step Problems

5.5.2Problem Solving with Proportion

5.6Fractions & Decimals

5.6.1Simplifying Fractions Using Equivalents

5.6.2Ordering Different Types of Fraction

5.6.3Adding & Subtracting Fractions

5.6.4Adding & Subtracting Mixed Numbers

5.6.5Multiplying Fractions

5.6.6Dividing Fractions by Whole Numbers

5.6.7Converting Between Decimals & Fractions

5.6.8Dividing Decimals

6Year 6 - Ratio & Proportion

6.1Ratio

6.1.1Using Ratios

6.1.2Simplifying Ratios

6.2Percentages

6.2.1Calculating Percentages

6.3Scale

6.3.1Scale of 2D Shapes

7Year 6 - Algebra

7.1Sequences

7.1.1Describing Sequences

7.1.2Finding Gaps in Sequences

7.2Missing Number Problems

7.2.1Missing Number Problems

7.3Equations

7.3.1Balancing Equations

7.3.2Combining Two Variables

8Year 6 - Measurement

8.1Problem Solving

8.1.1Problem Solving with Measures

8.2Unit Conversion

8.2.1Conversion Between Miles & Kilometres

8.3Perimeter, Area & Volume

8.3.1Area

8.3.2Volume

8.3.3Nets

8.3.4Faces, Edges & Vertices

8.4Angles

8.4.1Types of Angle

8.4.2Finding Missing Angles

8.4.3Finding Missing Angles in Triangles

8.4.4Vertically Opposite Angles

8.5Circles

8.5.1Parts of a Circle

8.6Coordinate Grids

8.6.1Positions on Coordinate Grids

8.6.2Reflection & Translation

9Year 6 - Statistics

9.1Displaying Data

9.1.1Pie Charts

9.1.2Line Graphs

9.2Averages

9.2.1Mean

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