What do you do when one of your students decides that adding and subtracting on his fingers is easier than using the mental math strategies you’ve been teaching him or her?
I’ve been tutoring a lovely young boy in math who has a learning difficulty. Last year we had worked really hard on understanding and applying mental math strategies. While he hadn’t yet achieved number fact fluency for all facts (which to me is the ability to recall the answer to the number facts in 3 seconds) he was doing extremely well.
I had used all my number fact strategy games with him. We had played fact fluency games. He loved tutoring sessions and felt confident in his math ability.
Then we had an eight week break over Christmas and when I came back he was adding on his fingers. WHAT! No! No! No!
In that eight week period he’d decided that adding on his fingers was much easier. The problem with this is that he gets lost in his counting and now often gets the wrong answer. If he’s answering 3 + 11 he’s also ignoring the commutative property of addition and is counting on from 3 rather than 11.
How do we fix this?
We’ve been focusing on number facts for quite a while now and we need to move on so I don’t have a great deal of time to spend going back over the strategies. He knows them or knew them so I’m hoping that just a little work in this area will bring them back to the forefront of his mind when he’s needing to add or subtract.
The Commutative Property
The first thing we need to do is go back over the commutative property. We can do that by using concrete materials to show that the order of the numbers we add does not matter.
Counting on from the largest number
If he is going to insist on counting on his fingers for addition he needs to be able to count on from the largest number regardless of where it is in the number sentence. He is able to visualise a number line and telling him to start at the largest number and jump up has been successful when teaching the count on facts.
Count up from the subtrahend
We need to do the same with subtraction. It is so much slower to answer 6 – 5 if you start with 6 and count back 5. Here we need to focus on the strategy of counting up.
The next strategy we will revisit is using a double to help with both addition and subtraction. He knows his doubles, or rather did, so it’s just a matter of reminding him. He’s a visual learner so posters will help a lot with this. For him I’ve reduced the poster size to print six to a page and put them on a ring.
When revising the near doubles he needs to see that in the number sentence 6 + 7 the numbers sit side by side on the number line so he can double the smallest number and count on 1. Likewise with 6 + 8 the numbers are close by on the number line so he can double the smallest number and add 2. He has struggled constantly with making a ten which seems like the logical strategy so I won’t go there.
When it comes to subtraction, looking at making a double will help as well. So, for 13 – 6, he knows that 6 + 6 is 12 … 13 is 1 more so he needs 1 more than 6.
Practice makes perfect
Then of course I will suggest to his parents that they consolidate the number facts at home using homework games, particularly over holiday periods!
If holidays are coming up for your class check out my homework game range. You don’t want to spend the first few weeks reteaching the facts. You can find them HERE.
Well it’s two weeks later and he’s doing well. Like I thought, if the foundations are there it wouldn’t take long to convince this little guy that adding and subtracting on his fingers might look easy but it’s not helping him get the right answer. Using his strategies are the way to go!