Lesson 3

Estimate Products

Est. Class Sessions: 3

Summarizing the Lesson

Direct students to the Frank's Weight in Gold pages in the Student Activity Book. Begin by reading the problem together with the class.

Have students work with partners to solve both parts of the problem. In Question 1, students apply strategies for multiplying numbers ending in zeros to the context of the problem. Remind students to include proper units for each quantity that appears in the problem. See the Sample Dialog.

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Teacher: How did you solve the problem?

Tanya: First we multiplied 40 times 1000 to get 40,000.

Teacher: 40 of what times 1000 of what?

Tanya: 40 kilograms times 1000 grams in a kilogram.

Teacher: Gives you how much?

Tanya: 40,000.

Teacher: 40,000 of what?

Maya: 40,000 total grams. That's what Frank is in grams.

Tanya: Then we multiplied that by 43 and then by 45 to get a range.

Teacher: By 43 and 45 of what?

Tanya: Oh, I mean 43 dollars and 45 dollars because that gives you the total amount he's worth in gold. So, Frank is worth between $1,720,000 and $1,800,000.

Question 2 may require students to invent strategies and string together several steps to solve the problem. See Figure 2 for a possible student solution.

Have pairs of students share their solutions and explanations with the class.

Students may complete Check-In: Question 3 independently. Question 3 provides an opportunity to assess students' abilities to use estimation and multiplication strategies to solve multistep problems. It also provides an opportunity to set and assess expectations for problem solving and communication. Remind students of the Math Practices page in the Student Guide Reference section.

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Use Check-In: Question 3 on the Frank's Weight in Gold pages in the Student Activity Book with the Feedback Box to assess students' abilities to estimate quantities (e.g., rounding, using benchmarks) [E3]; multiply products that are multiples of ten [E7]; estimate products [E8]; find an estimation strategy [MPE2]; and show work [MPE5].

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Breaking a multistep problem into more manageable questions is one way to help all students access a problem like Frank's Weight in Gold in the Student Activity Book.

  • What is Frank trying to figure out? (what his weight in gold is worth)
  • What information does Frank have? (his weight of 40 kilograms for 88 pounds and the price of gold per gram)
  • How much does Frank weigh? Which measurement should you use? Grams or pounds? (grams because it can easily be changed to kilograms)
  • How many kilograms does Frank weigh?
    (40 kilograms × 1000 grams per kilogram = 40,000 grams)
  • How much does one gram of gold cost? ($43 to $45 per gram)
  • What is the cost of Frank's weight in gold?
    ($43 to $45 per gram × 40,000 grams = $1,720,000 to $1,800,000)

To provide support for Question 2, ask students to generate a list of questions that would guide them through this problem. Encourage students to use their solution to Frank's problem as a model. Some questions might be:

  • How many ten-dollar bills does it take to equal Frank's weight?
    (40,000 grams × 1 gram per ten-dollar bill = 40,000 ten dollar bills)
  • How much is that worth?
    (40,000 ten dollar bills × $10 = $400,000)
  • Which is worth more; Frank's weight in $10 bills or Frank's weight in gold? (Frank's weight in gold)

Modeling guiding questions helps students observe and then learn the kinds of questions they should ask themselves when they solve problems.

Student Guide:
Student Activity Book: 131 132
Answers
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SAB_Mini
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Master:
Possible solution to Question 2 of Frank's Weight in Gold
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