Decomposition refers to breaking down tens into ones (or hundreds into tens) so that the required subtraction can take place. If you need to pay Rs. 7 as your share of an autorickshaw fare but you only have a Rs. 10 note then you may have to exchange the note for 10 single Rs. 1 coins in order to pay the correct fare. This is decomposition in action!
Sometimes you decompose tens into ones, but you may also need to decompose 100 into tens, or ones into tenths and so on. It will be easier for young students to learn decomposition using tens and ones, but don’t forget to show that it is something that happens for all other parts of the number system.
Use strips as in Activity 1. If you did Activity 1 with your students then ask them to bring in their own strips so that you only have to make new strips for those who forget.
Ask the students to work in groups of four or five, and make sure that each group has lots of ‘ten strips’ and a few singles.
![]() Video: Talk for learning |
I had used the strips for Activity 1 several months before and most of my class kept a few strips tucked into the back of their exercise book just in case they needed to ‘see what to do’. I had encouraged them to use the strips so that they felt confident in what they were doing. I know how feeling unsure can stop students enjoying mathematics and ultimately make them think they cannot do it.
I used the number line to show subtraction so that they had the idea of taking away and the number reducing. It was natural therefore for me to use the strips when teaching the formal subtraction algorithm, and so when I asked them to bring in lots of strips themselves they knew it would be worth doing and brought them in.
They had no trouble laying them out and when I asked, ‘What shall we do, we do not have enough ones to take away 6?’ Some of the students replied, ‘Unmake the ten, rip it up!’ So we did, but first I asked some of the children who had quickly understood what to do to explain their thinking to the rest of the class. This was because I felt that quite a few students had not fully understood at this point in the lesson.
Many students needed to use the strips a great deal before they could see immediately what to do. I encouraged them to make up their own sums and to use the strips to show what was happening until I could see that they had developed confidence in what they were doing.
Of course some of them saw it straight away. I asked these students to form a group together and to discuss how this could be written down in the same way that we wrote down our additions formally. This made them think hard and when they were ready they showed the rest of the class their way. It was almost the same as I would have taught them, which delighted me. The only difference was that they talked about taking one ten and ‘ripping it up’ so that it could go in the ones column, but if that is the way they want to talk about it, it is fine by me!
![]() Pause for thought An important part of this activity is the opportunity it provides for students’ to learn through discussion and explaining their thinking. Do you feel that there were any additional opportunities in Mrs Kapur’s lesson for the students to engage in talk for learning? You may want to have a look at the key resource ‘Talk for learning’ to help you think about this. Now reflect on how your students responded to the activity and answer the following questions:
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