How important is learning the strategy? (singapore maths question)

[withgrace]

Last year I started DD on the Singapore Maths program.
 

Today we did a lesson on how to add a single digit number to another number between 11 and 20 by borrowing from the smaller number to create "10", then adding the remaining units. This is the strategy I learned at school so it feels quite important to me, however as DD has memorised these facts through her Kumon work, she found the whole process superfluous and is having trouble grasping the concept for her own calculations. Frustration for both of us ensued.
 

Writing this out has me realising I am asking her to take 3 or 4 steps to do something that she "just knows", which doesn't make a lot of sense! However, I don't think it is so known that it can be depended upon for instant recall just yet. Do you think it is worth having her learn the strategy or is it a waste of time?
 

I appreciate your thoughts!

[EndOfOrdinary]

The important part is her realizing that when you are adding things, you are taking groups and smashing them together. So 15 + 3 is the exact same as 5+10+3 or 12+3+3. It has relatively nothing to do with math facts. All adding is, is combining. In this way it does not matter how you combine, as long as everything is included in the pile at the end.

 

When the numbers are small and easy memorized, then it doesn't matter. If she is asked to add 649 + 37, you now have problem. If she can see that stealing one from the 37 will make 650 + 30 + 6, then she can easily solve and no problem.

 

Does that make sense? It is not math facts, but that adding is commutative. If she gets that adding is commutative, then she can see how hacking the numbers up and recombining them in easier to package groups is allowed. This will help later.

 

I have found manipulatives are your best friend in this instance.

 

You do not need to force her through doing long sets of practice problems if she is having trouble getting why you want her to now do something totally differently than before. (I can see her point. My son frequently will look at me and say, "Uh...Mom...I'm getting mixed messages). Just try to expose her to the idea that she can choose anyway to combine that is easiest for her. Ds does not combine the way I do. He thinks differently, and that is totally cool. Just let her know that rhe book is trying to show a way to figure out the ones she might not have memorized before. You can even give her some larger problems to illustrate.

[Tanikit]

If it really seems too simple then show her how it works more easily when the numbers are in the thousands or ten thousands or millions especially where there is multiple borrowing - if she is doing these sums mentally that is great - you could always just leave it and teach the method when for her it would be simpler to use that method than others she has learnt.

[withgrace]

Thanks for your thoughts guys. So it looks as if I have been looking at the small picture rather than the big picture.

 

This makes sense. We have been using lots of manipulatives and she loves that and she understood, or seemed to. We then reverted to solving a written problem in the work book so she just relied on her memory and was quitely confused at my insistance that we take the long route.

 

I will expand on it at our next lesson to include bigger numbers and how we "smash numbers together" :)

[pitterpatter]

As far as SM goes, I don't think there is anything more important than understanding and being able to automatically apply "making tens" forwards and backwards. It's the basis of the entire program. Seems that way to me anyway. Even with subtraction, you use your knowledge of making tens. And since multiplication and subtraction is just repeated addition or subtraction...

[letsplaymath]

 

...as DD has memorised these facts through her Kumon work, she found the whole process superfluous and is having trouble grasping the concept for her own calculations...

 

 

If the memory work is getting in the way, then you need to move on to numbers she hasn't memorized. For instance, if the page says "13+8" but she knows that one automatically, then try changing it to "43+8." Same make-a-ten concept, but without the mental interference.

 

[go_go_gadget]

If the memory work is getting in the way, then you need to move on to numbers she hasn't memorized. For instance, if the page says "13+8" but she knows that one automatically, then try changing it to "43+8." Same make-a-ten concept, but without the mental interference.

 

 

This is exactly what I was going to say.

[withgrace]

Fabulous, thanks Ladies! Of course - seems so obvious now that you have pointed it out :)

[SparklyUnicorn]

I think it's important, but this one concept isn't EVERYTHING.  KWIM?  You could try making a game out of it.  Or find a game that uses the concept. 

[IsabelC]

I think it's important that she 'gets' how this strategy works, but not essential that she habitually uses it. I often need to remind myself that even the simplest arithmetical calculation can have many ways of reaching the solution, and that my 'easy' or 'obvious' way of understanding it might be different from somebody else's.