# 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.

Note: The goal for this level goes beyond simply memorizing math facts. The goal is knowing the “breakaparts,” which means the paired values that compose a target number. For example, the breakaparts for the target 4 are: 0 and 4, 1 and 3, 2 and 2. Knowing breakaparts means knowing the component parts in any order. In other words, knowing that 2 and 3 or 3 and 2 are breakaparts for the target 5. The developing combinations at this level include 5 and 7 for the target 12 and those for targets 13 or greater that are not developed earlier, such as 4 and 9 or 6 and 7 for the target 13.

## 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.”