Topic: Addition and Subtraction
Expected Heuristics: Creating a picture to count things out, breaking down operations into
simple parts
Grade Range: First or Second Grade
The Problem: Last vacation, my cousin came over to stay at my home. We made the most of her
stay at my place, and I even earned a few chocolates. Everyday, we would play a game of chess.
Whoever lost the game owed a chocolate to the other. After the last game we played (that was the
day she was to leave), we counted the number of games each of us had won and lost. Wow! I had
won more than her. So, she handed me 18 chocolates... though she herself was the winner in 6
games. How many days did my cousin spend at my place?
Answer: 30
My solution: We first have to look at what we know. We know that the cousin won 6 games, and
that the speaker received 18 chocolates from the cousin. Those 18 chocolates mean that the
speaker won 18 more games than the cousin. This is where the trick is – at first, students might
be tempted to say that the answer is 24 days, arrived at by adding the numbers they know about
together. However, that is simply the number of games won by the speaker. The chocolates that
the speaker would owe the cousin are subtracted from the chocolates that she is owed. In other
words, the speaker won 24 games. Add the 6 games won by the cousin, and you arrive at the
answer of 30.
Syvum Technologies Inc., Initials. (n.d.). Puzzles & brain teasers : Game of chocolate:.
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Topic: Addition, Multiplication
Expected Heuristics: Drawing a picture, Creating a chart, simplifying parts of problem
Grade Range: Third Grade
The Problem: Last weekend, I went to play in the nearby park. It was real fun! I rode my new
bicycle that Mom had given me for my birthday. On reaching the park, I saw that there were a
total of 16 bicycles and tricycles. If the total number of wheels was 38, how many tricycles were
there?
Answer: 6
My solution: We are told that there are 16 different kinds of cycles parked at the park. Knowing
that there are only bicycles and tricycles (no unicycles!), we know that each cycle must have at
least two wheels. So, we multiply 16 by 2, and arrive at 32. This accounts for 32 of the 38
wheels. Those extra wheels belong to tricycles, which have three wheels. So, we subtract 32
from 38 and arrive at 6. There are 6 tricycles parked at the park.
Syvum Technologies Inc., Initials. (n.d.). Puzzles & brain teasers : Bicycles or tricyles?:.
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Topic: Adding fractions, Division, Multiplication
Expected Heuristics: Drawing a diagram or using some kind of manipulation that shows the
different fractions of the number as belonging to a larger whole.
Grade Range: Fourth or Fifth Grade
The Problem: Old Man Wrinkle spent one-fourth of his life as a boy, one-eighth as a youth, and
one-half as an active man. If Old Man Wrinkle spent 10 years as an old man, then how many
years did he spend as an active man?
Answer: 40
My solution: First, add together the given fractions. ¼+1/8+1/2 can be expressed as 2/8+1/8+4/8,
which when added together is 7/8. It can be helpful to make a diagram or use pieces of paper to
represent these different fractions that make up the whole of Old Man Wrinkle's life in order to
visualize the problem. Take the 7/8 fraction of Old Man Wrinkle's life and subtract it from 1 (the
whole) to see what fraction he spent as an old man. 1-7/8=1/8. Old Man Wrinkle has spent 1/8 of
his life as an old man. We are told that Old Man Wrinkle has spent 10 years as an old man, so 10
years is 1/8 of his life. Since it takes eight of those tens to make a whole life, Old Man Wrinkle is
80 years old. Looking at the problem again, we see that Old Man Wrinkle spent half of his life as
an active man. ½ is equal to 4/8. In other words, ½ is equal to four times as much time as Old
Man Wrinkle has spent as an old man. 4*10=40. Old Man Wrinkle spent 40 years as an active
man.
Syvum Technologies Inc., Initials. (n.d.). Puzzles & brain teasers : old man wrinkle:. Retrieved
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