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Which arithmetic operations should go with which types of word problems?
Here is my best attempt at making a diagram or picture to help sort word problems:
Do not solve the world problems below.
Merely sort them by which arithmetic operation is used to solve them: +, −, ×, or ÷.
You can circle your choice below each word problem.
Then show this playground to other people. Do they agree with you about which arithmetic operation to use? When is there more than one correct answer?
It might help to make your own diagrams or pictures that are different than what I made above.
1. After a birthday party there is ½ of a cake left over. You eat ¼ of the leftover portion. What fraction of a whole cake do you eat?
2. After a birthday party there is ½ of a cake left over. You eat ¼ of a whole cake. How much of the leftover cake did you eat?
3. After a birthday party there is ½ of a cake left over. The entire cake cost $16. What is the monetary value of the leftover portion?
4. After a birthday party there is ½ of a cake left over. You have six kids, so you cut the leftover portion into six pieces so they can each get a fair share. How much of a whole cake is each child's share?
5. After a birthday party there is ½ of a cake left over. You eat ¼ of the leftover portion. What percentage of the leftover portion do you eat?
6. After a birthday party there is ½ of a cake left over. You eat 20% of the leftover portion. What fraction of a whole cake do you eat?
7. Every morning you exercise on a treadmill for ½ hour. How much time is this per week?
8. Every morning you exercise on a treadmill for ½ hour. But this morning a phone call interrupted you. You only exercised for ⅓ of an hour. How much of your normal exercise time did you miss?
9. Every morning you exercise on a treadmill for ½ hour. Your weight and treadmill settings determine that you burn 700 calories per hour exercising. How many calories do you burn each morning?
10. Every morning you exercise on a treadmill for ½ hour. So do your three housemates. How much total time per day do the four of you spend using the treadmill?
11. Every morning you exercise on a treadmill for ½ hour. Your spouse exercises on the treadmill for ⅓ hour. Your spouse's time spent on the treadmill is what percentage of your time spent on the treadmill?
12. Every morning you exercise on a treadmill for ½ hour. Your spouse exercises on the treadmill for 80% of your time. How long do your spouse spend on the treadmill?