Adding by making 10s, 20s...., 100s, 200s....and so on.

When I asked the class to process 7 + 8 they all flagged in and after a few seconds proclaimed that the sum was 15. Now the fun began. I asked them how they arrived at the seemingly simple result. Their answers were startlingly different. A newer Mathlete proudly proclaimed I counted on my fingers from 7 to get 15; many said that they doubled 7 and added 1; some said that they doubled 8 and subtracted 1; and then it happened, a small number said that they borrowed 3 from 8 to make 10 (7 + 3) and then looked at what remained after they borrowed the 3 from 8 which was 5. In other words, 7 + 8 was the same as 10 + 5. A few reported that they did the same thing by borrowing 2 from 7 to make 10 with 8 and then added the remainder of 5 to 10 to get 15. The latter two methods are not “better” than the doubling method, but it is more sustainable.

To those advanced students that doubled the 7 and added 1 I then asked them to do 357 + 8 and they could not make the connection because their strategy only worked for single digits. The students who borrowed 3 from 8 to make 10 were able to easily see 360 + 5 to sum to 365.

 We then proceeded to do dozens of problems by making 10, then 20 (19 + 8 = 20 + 7 = 27), then other 10s (34 + 9 = 40 + 3 = 43), then 100 (60 + 90 = 100 + 50 = 150) and so on to higher hundreds.

 Please have the K and 1^st graders do the first pdf as much as possible encouraging them to put an upside down V below the second number so they could split it up as discussed above (see the examples on the pdf); for 2^nd graders and above, please do as many problems as possible on the second pdf for 100s, 200s and other 100s as well as partial sums (examples are provided).  NOW FOR THE FUN PART.

Parents: please practice this with your children at every opportunity while driving or …. First, you just throw them numbers like 8 (they say 2), 4 (they say 6), 0 (they say 10), 10 (they say 0), 70 (they say 30), 460 (they say 40), then harder ones like 4,567 (they say 3).

Then if you and they feel comfortable, give them mental math to do (first on paper and then in their head) using the strategies from this lesson.

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Enjoy.