Dec. 2, 2005 - Addition Strategies

Addition Strategies Summary

All of the following information comes from the Right Start Math Program which can be review on alabacus.com. These strategies start with an American abacus that has 10 rows of 10 beads (100 total beads) in two colors. First row is 5 of one color and 5 of another contrasting color and the first five rows are like that. The last five rows have the colors switched. When looking at it all together, the colors make a chekerboard pattern of four 25's.

Point 1: Show what numbers 6-10 and 60-100 look like with the contrasting colors. 6 is five and one. 7 is five and two. 8 is five and three. 9 is five and four. 10 is five and five. 60 is 5 tens and 1 ten, etc. Anything above 10 is named with a tens. Example: 65 is 6 ten 5.

Basic Strategy: Even (2-10) and odd (1-9) numbers are memorized. Anything plus 2 is the next odd or even number.

Point 2 - Adding single digits (or what some might call fact families): solve the problem without counting and memorizing forward and backward by looking at the pattern of numbers in fives or tens. All addition problems can be solved mentally or with the visualization of the abacus.

Strategy 1 - Facts to 10: Memorized by their pattern.

1+9

2+8

3+7

4+6

5+5

Play Memory game or Go Fish with facts to ten to help memorize them. Also, anything plus ten is just that number as the ones. So, 10+7 is 1 ten 7 or 17 (seventeen).

Strategy 2 - Doubles: Any single number added with the same number. Notice the pattern. When you get to 6+6 and higher, use the visualization of 6 or that number; meaning, if 6 is 5+1 and 1+1=2 then 6+6 can actually be seen as 10+2. 7+7 is 10+4, etc.

1+1=2

2+2=4

3+3=6

4+4=8

5+5=10

6+6=12

7+7=14

8+8=16

9+9=18

Notice all the answers are even.

Strategy 3 - Near Doubles and Middle Doubles: ND - 6+7: Those numbers are near each other when counting by ones. Take the lower number and double it and add one. MD - 6+8: Take the number in the middle when counting consecutively and double it. 6+8 is actually 7+7 which is 14.

Strategy 4 - Two Fives: Any number above 5 can be added using the pattern from the abacus. 5+7 is 10+2 (because 7 is 5&2), thus the two fives. 8+7 is actually seen as two fives plus 3&2 = 15.

Strategy 5 - Give and Take: Anything plus 8 is the previous odd or even number. What you do to show this is that you take 2 from the other number to make 8 a 10 and add the other number which was the previous odd or even number. When adding 9, just give and take 1 instead of 2 since 9 is 1 away from 10.

Strategy 6 - Double digit under 100 w/o trading (10 ones for 1 ten or 10 tens for 1 hundred): Add tens and ones from left to right. Different, I know but this is not a paper pencil exercise. It's mental math. Seeing patterns of numbers and in this case it's tens and ones. 34+55 is actually 80+9 or 84+5. This encourages skip counting which actually reveals patterns.

Strategy 7 - Double Digit under 100 with trading: Same concept as above. Add the 10s but increase it by 1 ten when the ones are greater than 10. When done on the abacus, it shows the purpose behind trading (carrying, as some incorrectly call it). You are not just teaching them the skill of carrying, you are teaching them how and why we do that. 57+38 is 80+15 or 87+8 which is 95.

Strategy 8 - Double Digit over 100 with trading: Add the tens and ones. Reuse the simple strategies 1-5 to add mentally. 78+63 is 7 ten and 6 ten is 13 ten (using two fives or near doubles) or 130. 8 plus 3 is 11 because 8+2 is ten and add one. So we have 130+11=141.

The double digit addition (and the others for that matter) take awhile to think and use. Practice everyday and see how fast you catch on. It is a challenge, but if you help your child do it this way, they will be faster at math than you. And they’ll have more understanding and meaning than the mere skill we learn growing up. Some of us probably still rely on counting or calculators to balance our checkbooks.

I had a student in middle school math (pre-alg) a few years ago who we as a class relied on to do our simple addition because he could do it faster coming from an Asian background and upbringing. Using an Asian abacus helped him do that but he was also better able to reason through the principles of pre-algebra.

Let me know if this helps.