## INTEGRATING ADDITION AND SUBTRACTION, AND PLACE VALUE

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Posted by , May 20, 2017 | 0 comments

When children first learn about addition and subtraction, it is informal. They focus their learning on the meaning of the concept. Adding means ‘joining groups together’ and subtraction means ‘taking away from a group’.

When adding, children will select 2 or more number cards, make the groups counting by ones, join the groups together, then count the number in the joined group by ones.

When subtracting, children will select 2 number cards, ask themselves ‘which number could I make a group of that will give me enough to take away a group of the other number?’, make 1 group counting by ones, take away a group of the other number counting the number in that group they took away, then count the number in the group they have left.

Once children understand addition and subtraction, they begin to record their understanding using number lines, initially counting by ones, then using place value to bridge to tens numbers.

In a Year 1 classroom recently, we had children with all of these levels of understanding!
The board contain all of the levels, built up during the 10 minutes of Explicit Teaching with the children:

Students then selected the level that challenged them, then use playing card to generate numbers to investigate adding and subtracting.

Walking around the class, stopping to observe and question children, I noticed that some children had chosen the ‘black’ level, but were finding it very challenging. These children had demonstrated their understanding of adding and subtracting counting by ones on a number line, but were not yet ready to add and subtract using place value to bridge 10. What to do?

There was obviously a step in between that the children did not have deep enough understanding of, that was holding them back.

Of course, the step involved Place Value.

We had been investigating Friends of 10, Partitioning and Place Value of Teen Numbers, and I knew these were the concepts that the children now needed to apply to addition and subtraction.

I asked one child, who was adding 8 and 5, if he knew 8’s Friend of 10. He hesitated, thought hard, then said, ‘5?’ Aha! I knew that until he was more fluent in his Friends of 10, he would not be able to add and subtract bridging 10. ‘Ok,’ I said to the child, ‘You’re not going to add today. You’re going to investigate Friends of 10, then you’ll be able to add again.’ I gave the child a 10 frame and some counters. Because we had previously investigated Friends of 10, he quickly learnt to select a number, place the corresponding number of counters on the 10 frame, and record the number and its Friend of 10. The child remained sitting where he was, amongst other children who were still investigating adding and subtracting at just beyond their current level of understanding.