Reasoning · Grade 2-1 Addition and Subtraction Word Problems
Problem
Stepping left from 40 and right from 32 by the same amount lands on the same point.
The equal sign means both sides land on the very same value, so the same point can be reached going down from 40 or up from 32.
1.OA.D.7Draw A DiagramThe 8 between 40 and 32 is closed from both sides, so the unknown fits twice: 8 ÷ 2 = 4.
Splitting the gap of 8 evenly between the down-step and the up-step is sharing equally, which gives 4 each.
2.OA.A.1Work BackwardsCheck: 40 − 4 and 32 + 4 both give 36.
Plugging the answer back in is the surest way to know the riddle balances.
2.OA.A.1Guess And CheckTwo points sit one unknown to each side of 65.
Adding then subtracting the same number from 65 makes two points evenly spaced on either side of 65.
1.OA.D.7Draw A DiagramThe 18 between them counts the unknown twice, so 18 ÷ 2 = 9.
When two points are the same distance on each side of a center, the whole gap between them is twice that distance.
2.OA.A.1Work BackwardsBecause the two results sit the same distance either side of 65, the 18 between them is twice that distance.
Adding the number and subtracting the same number push away from 65 by the same amount in opposite directions, so 65 sits exactly midway between the two results.
The whole gap is made of the step down and the step up laid end to end, and those two steps are equal, so the gap is one step doubled.
Check: 65 + 9 = 74 and 65 − 9 = 56, a difference of 18.
Checking the two values confirms the 18 difference, so 9 is right.
2.OA.A.1Guess And CheckFind the gap between the two amounts, then split it in half - the unknown moved each side equally, so half the gap is your number!