Math Drills
Working Backward Review
1Word 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)In the parking lot, how many cars were parked. 16 more came, so there were 38. How many were parked at first? Answer □
Answer: 22cars
(2)In the box, there were how many cookies. 22 more were given, so there were 50. How many were in it at first? Answer □
Answer: 28cookies
(3)In the pond, there were 43 fish. Some more came, so there were 71. How many fish came? Answer □
Answer: 28fish
(4)In the meadow, there were 65 rabbits. Some ran away, so 46 were left. How many rabbits ran away? Answer □
Answer: 19rabbits
(5)There were some birds perched on the roof. 22 flew away, so 19 were left. How many were there at first? Answer □
Answer: 41birds
(6)There were some books in the library. 34 were lent out, so 22 were left. How many were there at first? Answer □
Answer: 56books
