Deriver +/- (Composing Numbers)

Uses flexible strategies such as Break Apart to Make Ten (BAMT) and derived combinations (e.g., “7+7 is 14, so 7+8 is 15) to solve all types of problems. Can simultaneously think of numbers within a sum, and can move part of a number to another, aware of the increase in one and the decrease in another. Solves simple cases of multidigit addition (and often subtraction) by incrementing tens and/or ones.

Activities

You may see this:

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Other Examples:

  • Asked, “What’s 7 plus 8?,” thinks: 7 + 8 -> 7 + [7 + 1] -> [7 + 7] + 1 = 14 + 1 = 15. Or, using BAMT, thinks: 8 + 2 = 10, so separate 7 into 2 and 5, add 2 and 8 to make 10, then add 5 more: 15.
  • Asked “What’s 20 + 34?”, student uses connecting cubes to count up to 20, 30, 40, 50 plus 4: 54.
  • Using BAMT—a child might think "9 + 6…I break 1 off the 6 and put it on the 9 to make 10. Then the 10 and the left-over 5 is 15.”

Help your student become a(n) Deriver +/- (Composing Numbers)

Activities challenge children to solve all types of arithmetic problems using flexible strategies such as Break Apart to Make Ten (BAMT- 9 + 6, take 1 off the 6 to make 10, then 10 and 5 is 15) and derived combinations (e.g., “7+7 is 14, so 7+8 is 15) problems. So children are encouraged to move part of a number to another, aware of the increase in one and the decrease in another. Encourage children to learn a variety of strategies, but emphasize BAMT when they are ready.

Special Thanks To

Institute of Education Sciences
The research reported here was supported by the Institute of Education Sciences, U.S. Department of Education, through grant numbers R305K050157, R305A120813, R305A110188, and R305A150243. to the University of Denver. The opinions expressed are those of the authors and do not represent views of the Institute or the U.S. Department of Education.