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GPS Alignment: Instructor Page
Week 1: Number - Intergers


How Old are Three Daughters? (Printable PDF)

A census taker walks up to a house and asks the man answering the door to state the number of people in his household.

"Five," he says. "There's me, my wife, and my three daughters."

"How old are your daughters?" the census taker asks.

"The product of their ages is 72, and the sum of their ages is the number on my house."

The census taker leaves, but soon he comes back and replies, "That's not enough information."

"Oh, I forgot, the youngest one likes chocolate pudding."

How old are the three daughters? Explain how you found the result.

GPS

As seen in Problem Exploration

M6N1:  Students will understand the meaning of the four arithmetic operations as related to positive rational numbers and will use these concepts to solve problems.

a. Apply factors and multiples.

b. Decompose numbers into their prime factorization (Fundamental Theorem of Arithmetic.)
 

a. Students have to find the factorizations of 72 to solve this problem.

b. Students can decompose 72 into its prime factorization (2*2*2*3*3).  By finding the various combinations of the factors will help the students find the ages of the three daughters.

M7A1. Students will represent and evaluate quantities using algebraic expressions.

a. Translate verbal phrases to algebraic expressions.

b. Simplify and evaluate algebraic expressions, using commutative, associative, and distributive properties as appropriate.

Let a,b,c be daughters ages. Let n= house number. a*b*c=72, a+b+c=n. We know that there is a youngest, so a does not equal b. We know that we didn’t have enough information so a+b+c=n has multiple solutions.

M8A1. Students will use algebra to represent, analyze, and solve problems.

a. Represent a given situation using algebraic expressions or equations in one variable.

b. Simplify and evaluate algebraic expressions.

c. Solve algebraic equations in one variable, including equations involving absolute values.

d. Interpret solutions in problem contexts.

Let a,b,c be daughters ages. Let n= house number. a*b*c=72, a+b+c=n. We know that there is a youngest, so a does not equal b. We know that we didn’t have enough information so a+b+c=n has multiple solutions.

*same unpacking as M7A1*