Lesson 3

Estimate Products

Est. Class Sessions: 3

Developing the Lesson

Part 3: Choosing Efficient Estimation Strategies

Discuss the necessity of choosing convenient numbers that are close enough to give a good estimate but are also easy to use in mental computations.

Point out to students that the rounding of factors is sometimes a good strategy for estimating products. Students must decide whether rounding procedures should be used to make specific estimates.

Read the vignette in the Choosing Efficient Estimation Strategies section of the Student Guide. In this vignette, Tanya and Nick each identify a convenient number to decide if they have enough money to purchase two posters.

Use these or similar prompts to discuss the choices each student made:

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  • Explain why Nick decided to round $17.65 up to $18.00 rather than rounding it down to $17.00. (Possible response: $17.65 is closer to $18.00 than it is to $17.00 because 65 cents is more than halfway between $17.00 and $18.00.)
  • Tanya rounded $17.65 up to $20.00. What rounding strategy did she use to choose her convenient number? (Possible response: Tanya rounded to the nearest $10.00. $17.65 is between $10.00 and $20.00 but it is closer to $20.00.)

Explain that while rounding to the nearest dollar or nearest $10.00 provided a reasonable estimate for Tanya and Nick, it may not always provide the most accurate estimate.

Pose the following problem:

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  • Maya wants to purchase a science kit for $12.39 and a book of science experiments for $8.20. She has $20.00 to spend. If Maya rounds these costs to the nearest dollar will her estimate help her accurately decide if she has enough money? (Possible response: If Maya rounds to the nearest dollar, her estimate will be too low. She will think she has exactly the right amount of money, but she really doesn't.)
  • What might be a better way for Maya to estimate her total cost? (Possible response: Maya could look at the costs and see that $12.00 + $8.00 = $20.00, but since the price for both items is a little more than the dollar amount, the total cost will be more than $20.00. Maya could also round both of the amounts up to the next highest dollar and then add $13.00 + $9.00 = $21.00.)
  • Can you think of other situations where it is better to round quantities up? (Possible responses: When you are estimating the cost of a cart of groceries, the number of yards of yarn you will need for a project, and the time it will take you to walk to school.)

Assign Questions 11–14. As students work, encourage them to share their estimation strategies. Circulate and listen for specific strategies such as: choosing convenient numbers that they can easily multiply in their heads, finding the closest benchmark number by rounding to multiples of ten, doubling, using “money numbers” like 25 or 50, or other “kid friendly” numbers. Pay attention to the students who used different strategies and have them share a whole class discussion. For example, to estimate the answer for Question 11, students can think about money since they know that 4 quarters is equal to $1.00 and three quarters is equal to $.75. They can estimate that the students in Mr. Moreno's class will produce 175 liters of spit in one week.

Questions 12–13 provide students with an opportunity to use estimation to check the reasonableness of an answer. In Question 12, students should see that Tanya used benchmarks that were multiples of ten, rounded 23 to 20 and 105 to 100, and then multiplied 20 × 100 to find that the students in the library would burp about 2000 times during the week. For Question 13, one possible strategy students can use to decide if Nicholas's answer is reasonable is to think 3500 × 400 = 1,400,000. Since 1,400,000 is much more than 147,190 they can see that his answer is not reasonable.

In Question 14, students should see that when Peter rounded each price to the nearest dollar his estimate was low because of the extra cents on each dollar.

Assign Check-In: Questions 15–17 to students to complete independently.

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Use Check-In: Questions 15–17 on the Estimate Products pages of the Student Guide to assess students' abilities to use strategies to estimate quantities (e.g., rounding, using benchmarks) [E3]; multiply products that are multiples of ten [E7]; and estimate products [E8].

Student Guide: 141
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