KA-0007Working backwards
4 points, difficulty 2 of 3Level 3–4about 75sNadia gave half her stickers to her brother, then 6 more to a friend. She has 9 left. How many stickers did she start with?
Hints
Take them one at a time. The first gives nothing away.
1A nudge
Run the story backwards from the 9.
2The strategy
Undo the last thing first. Getting the 6 back comes before undoing the halving, because the halving happened earlier in the story.
3The full solution
Before giving 6 away she had 9 + 6 = 15. That 15 was the half she kept, so before giving half away she had 15 times 2 = 30.
Solution— no shortcut on this one
Work backwards, undoing the last step first. She ends with 9, and before giving 6 to a friend she had 9 + 6 = 15. That 15 is what was left after giving half away, so it is half of the original, and the original was 15 times 2 = 30. Check forwards: half of 30 is 15, minus 6 is 9. The transferable idea: reverse the operations and the order.
Why this is on the test: Working backwards is the fastest route through a whole family of Kangaroo word problems, and the order of the undoing is where students slip.