I cannot thank you enough for all the feedback lately about math! It's so helpful in guiding students' learning and hopefully, by taking a little extra time now and building a strong foundation students will be able to really excel as they get into more complicated math in upper grades. I will admit that upon first seeing an addition problem done this way I thought it was so unnecessary to take so many extra steps to solve such a simple math problem. However, after observing Singapore Math in an upper grade it all made sense!! By having a good understanding of 10s and 1s and how to manipulate numbers, these students were able to do extremely complex math equations mentally!! Meaning, without a pencil and paper! I was so impressed! So if it is any comfort, there actually is a great reason for all these extra steps and it will, believe it or not, serve to simplify math when your student is in higher grades.
I can also tell you that this is one of the most difficult math concepts that my first graders will be expected to master all year long... so hang in there and thank you so much for all the support you have already been giving!
Now down to business. The purpose of this post is to hopefully shed some light on the steps we are taking and why. Let me start with this example:
Of these 4 math problems, which seems the easiest/simplest to solve?
Most people (and ALL of my first graders) said the last one, 10 + 3, would be easiest.
Now, because you are not in first grade, you know that all four problems actually have the same answer, but this is a big discovery for a lot of first graders! Many students are still trying to grasp that 9 + 4, 8 + 5, and 7 + 3, are all "secret codes" for the number 13. Even as we are solving a problem I will ask students several times is the answer to the code is still the same? And of course, is should be a yes.
Here is an example of a problem that I'll walk you through:
5 + 7... are there any groups of 10s in this problem? No. Can we make a 10 by moving some of the 1s around? YES!
Now, the way we decide which number is going to become a 10 is by deciding which number is already closer to 10, which in this case is 7. I would then ask students "how many more does 7 need to make it a 10?" Because we cannot add a 3 to the problem without changing the number, we have to pull 3 out of the 5.
And if we pull 3 out of the 5, there will be an extra 2 left over.
So our math problem has now changed from 5 + 7 to 2 + 3 + 7.
Next we are ready to make a 10! I circle the 3 and 7 because they make 10, so now I have 2 + 10.
And there you have it!
Here is another example:
Again, the goal is to make a 10 and I'll use 9 because it is already closer to 10 than 4. To make 10 I have to add 1 to 9. Again, I can't just add a 1 without changing the number so I'll need to pull that 1 out of the 4. When I do that there will be an extra 3 left over from the 4.
Now my problem has changed from 9 + 4 to 9 + 1 + 3.
Because 9 and 1 make 10 I circle those and add them together. That make a 10 and 3 extra ones.
10 + 3!
. . . . . .
AND HERE IS YOUR HOMEWORK!!!
I told students today, that by completing these problems the way we've been practicing they can earn
2 BONUS POINTS on their next math test! I just need to see all the steps!
8 + 7
9 + 2
6 + 5
7 + 6
9 + 8
8 + 5
Good luck and I can't wait to see your work!!! Let me know if you have any questions or if there is anything I can clarify!
