Math Drills
Working Backward Review
3Word Problems
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What this worksheet covers
Rather than following a situation forward, children run it backward from the result to find the starting amount. For situations where an amount increased and for situations where it decreased, finding the size of the change and finding the starting amount are combined so that one consistent line of reasoning takes hold.
Read more
Reading a situation such as I was given 3 more and now have 12 as an addition, and answering 12 + 3 = 15, is common. The assumption that an increase means addition pushes every answer to the high side. The same assumption works in reverse for decreases, where subtracting anyway leaves the number too small.
The assumption held so far, that turning the situation straight into an expression gives the answer, breaks down here. A new way of reading is needed, tracing back from a number after an increase or a decrease to find the original amount, and this way of reading, used all the way through Order and Position Word Problems, keeps being used in Various Word Problems in grade 3, where several calculations are combined.
- Increasing Situations · Finding the Amount Added1 question
- Increasing Situations · Finding the Starting Amount2 questions
- Decreasing Situations · Finding the Amount Removed1 question
- Decreasing Situations · Finding the Starting Amount2 questions
Questions & answers
Problems and answers on this worksheet
These are the problems in “Working Backward Word Problems”, shown with their answers.
(1)There were some oranges at Grandma's house. 29 were eaten, so 18 were left. How many were there at first? Answer □
Answer: 47oranges
(2)In the park, there were 24 dogs. Some more came, so there were 41. How many dogs came? Answer □
Answer: 17dogs
(3)Olivia had 74 origami sheets. Some were used, so 45 were left. How many origami sheets were used? Answer □
Answer: 29origami sheets
(4)There were some frogs in the rice field. 23 went away, so 16 were left. How many were there at first? Answer □
Answer: 39frogs
(5)There were how many strawberries. 29 more were given, so there were 67. How many were there at first? Answer □
Answer: 38strawberries
(6)There were how many origami sheets. 27 more were given, so there were 64. How many were there at first? Answer □
Answer: 37sheets
