Guide to Possible Misconceptions for Addition and Subtraction Within 10 (Year One: Unit 2)

Guide to possible misconceptions for addition and subtraction within 10 (Year One: Unit 2)

This guide provides an introduction to some of the misconceptions pupils may have. You may want to incorporate some of these misconceptions in to your modelling in order to generate discussion about key concepts as a whole class. In addition to this, being aware of some these misconceptions in advance and allowing pupils to ‘have a go’ will enable you to stop pupils at appropriate times and use misconceptions as teaching points.

One to one correspondence

Pupils may misuse one to one correspondence by missing out objects they are counting. Manipulating toys, cubes, counters or other concrete objects will help to overcome this by encouraging pupils to physically move each item as they count, one at a time.

Vocabulary

Pupils will be exposed to a range of new vocabulary related to addition and subtraction in unit 2. Be sure to introduce this vocabulary through practical activities and discussions and continue to insist on full sentence responses to questioning.

The ‘equal to’ symbol

A common misconception is that the ‘equal to’ symbol means ‘the answer is ‘. It is important to emphasise that what is on either side of the ‘equal to’ symbol is equal in value. Pupils should be exposed to a range of equations with the answer shown on the left or right of the ‘equal to’ symbol and encouraged to use the correct vocabulary when talking about addition and subtraction.

E.g. 4 + 2 = 6 4 plus 2 is equal to 6

6 = 4 + 2 6 is equal to 4 plus 2

5 – 2 = 3 5 minus 2 is equal to 3

3 = 5 – 2 3 is equal to 5 minus 2

Linking the concepts of part-part-whole to addition and subtraction

Pupils may not see that equations and number bonds represent the same number facts. Look at each part of the equation and ensure that pupils can identify what the whole and the parts are.

E.g. 3 + 2 = 5

3 plus 2 is equal to 5

The whole is 5. The parts are 3 and 2.

Counting on and counting back

In unit 2 pupils are introduced to counting on and counting back. Pupils will need to retain a number before counting on or counting back.

E.g. There are 4 bears. I add 2 more. 4. 5,6. There are 6 bears altogether.

In this example pupils are required to retain the number 4 before counting on.

Pupils will need to remember how many they have counted on without including their starter number.

E.g. There are 4 bears. I add 2 more. 4,5. There are 5 bears altogether.

In this example, the pupil has included the 4 when counting on instead of counting on from 4.

Missing number equations

When pupils are shown a missing number equation they may see two numbers and try to add them straight away without understanding what the problem is asking them to do.

E.g. 8 - _ = 5

In this case pupils may try to add the 8and the 5 together. By representing equations on the balance pupils will have the opportunity to physically act out each part of the equation, placing the appropriate number of cubes on either side of the balance as shown by the equals symbol. This will help pupils to see that rather than add the 8 cubes and the 5 cubes together, they need to take away 3 cubes from the 8 cubes in order to find the missing number and make each side of the balance level.