A.3.
Tony and I were comparing our baseball card collections. I have three times as many cards as Tony has. Tony has 9 cards. How many do I have?
A.4.
Tony and I were comparing our baseball card collections. I have three times as many cards as Tony. I have 27 cards. How many cards does Tony have?
First Step: Identify the givens and the question
A.3. Givens:
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- I have 3 times as many cards that Tony has
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- Tony has 9 cards.
Question:
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- How many cards do I have?
A.4.
Givens:
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- I have three times as many cards that Tony has.
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- I have 27 cards
Question:
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- How many cards does Tony have?
Second Step: Problem Analysis
A.3.
The problem clearly says that I have 3 times as many cards as Tony and Tony has 9. If I have 3 times the amount, then multiplication must be used to find my total number of cards.
A.4.
The problem states the number of cards that I have and that I have 3 times the amount of Tony. He must then have only a third of the amount of my cards. My amount of cards should be divided by 3 to find Tony’s number of cards.
Third Step: Identify the operation(s) needed to find the answer and then solve
A.3.
Multiplication
3 x 9 = 27 cards
A.4.
Division
27 / 3 = 9 cards
Fourth Step: Identify the connection between both problems and reasoning.
The problems are connected because they utilize the same numbers within both equations. They are from the same “multiplication/division family.” The equations use the inverse operations of multiplication and division to solve. It can be see that when there are 3 groups of 9 cards that there are 27 cards in all, and when those 27 cards are split back, or divided, into 3 groups there are 9 cards in each group.
The function that is expressed in the problem A.3. is multiplication (by three). A.4. gives the result of the multiplication fact and then asks for the multiple which requires performing the inverse operation of division.
