Addition and the Part-Whole Circle

The other day Little Bean and I worked on addition up to 10 using the Part-Whole circle and tally marks. This Right Start lesson called for Little Bean to visualize the tally sticks moving from circle to circle so that he could easily solve problems up to 10 in his head (without the abacus).

Here is one of our problems: an addend goes in each smaller circle and then Bean needs to find the sum. 4 + 3 is not hard if he uses the abacus, but to do it in his mind he must visualize changing the problem into something he can understand more easily. Remember how Right Start teaches the child to think in terms of "5 and"? (5 and 2 is 7, 5 and 3 is 8, etc). This comes in super handy for doing mental math.

Here is where Bean's mind went to right off the bat: 4 + 3 is the same as 5 + 2 and 5 and 2 is 7! Therefore, 4 + 3 = 7. He decided to take away one of the tally sticks from the right circle and add it to the one on the left, giving him 5 and 2 as his parts. From there, it was a matter of recalling what 5 and 2 is from the very beginnings of Right Start Level A. I was SO impressed that Little Bean could do this in his head by thinking in terms of "5 and". We did many problems like this last week, and he loved them all. It was a fun challenge for him to answer my question, "What could we change in this problem so that we can solve it without counting?" He figured it out every time.

Just in case Little Bean wasn't getting it, there was the option of using the abacus. This doesn't require such a high level of critical thinking, but it is another way to come up with the answer without counting (counting is extremely inefficient, not to mention inaccurate; Right Start does not encourage counting at all). To do 4 + 3 on the abacus, you first push over 4 beads, then leaving a finger width gap, push over 3 beads. To see the answer, you just push the two addends together. You do not need to count the beads because the child has been trained to know that there are 5 blue beads and 5 yellow beads on each rod. So when you push them together, you'll immediately see 5 blue beads and 2 yellow beads have been entered and you have your answer because the child memorizes all the "5 and" facts in the very beginning. Easy peasy! Little Bean does this sometimes when solving math problems on worksheets or doing story problems.

Here is the completed problem 4 +3 = 7. See how easy it is to see the sum without counting? Even if you don't purchase Right Start for your math curriculum, I highly recommend getting an AL abacus from them!