Identify Estimation Strategies. Direct students' attention to the Addition and Subtraction: Practice and Estimation pages in the Student Guide. Read the vignette about Art's Dime Store together with the class. Look at the list of items that students can purchase with $75.00. Tell students that since they are buying items for the school they will not need to pay tax on their purchases.
- What makes a good estimate? (It should be easy to calculate and should give you an answer that is close to the actual answer so you can make a good decision.)
- The student groups in Ms. Alfonso's class have to decide which items they can buy with $75. In this case, is an estimate that is too big useful? (No) Explain your thinking. (They need to estimate to select items that cost less than the budget of $75. Students who choose to estimate the cost of each item higher than the actual cost may go over the $75 budget.)
- What are some quick and efficient strategies that the student groups could use to help them as they estimate? (Possible responses: They can use convenient numbers so they add easily in their heads. They could use the number lines to add quickly. They can round numbers to a close benchmark, like rounding the $29 for the Electronic Journal to $30, so it is easy to add.)
Use Estimation Strategies. Ask students to work in pairs to answer Question 1. Encourage them to use quick and efficient strategies to decide if the three groups made good estimates. For example, Group A chose items that cost $20, $25, and $38. If students jot down the prices and then mentally add $20 + $25 + $40, they should quickly see that the estimate is too high and that the items cannot be bought for $75.
As students work, ask pairs to explain their thinking using the following prompts:
- What did you need to write down?
- Did you round any numbers? If so, which ones? How?
- What calculations did you do in your head? What did you “see”?
- Did you use your number line? If so, how?
When students have finished Questions 1A–C, ask:
- Which group do you think made the best estimate? Why? (Possible response: Group B made the best estimate. The cost of the three items is $29, $19, and $25. They added $30 + $20 + $25 and got $75. Since two items cost a little less [$2], they would spend almost all the money without going over.)
- What do you think of the other two estimates? (Possible response: Group A picked items that cost too much. Group C chose items that cost a lot less than $75: $19 + $14 + $13 + $11 is about $20 + $15 + $15 + $10 or $60. That is too low. They could buy more.)
Ask students to work together to choose their own list of items from the website so that the $75 buys the most for the class (Question 2). As students finish their choices, ask pairs to put their lists on a display or chart paper with the exact prices, but without the totals and amounts left over. Ask the rest of the class to look over the lists.
- Which pair spent close to $75 without going over? How did you decide?
- If you were going to buy the items on the website, would you need an exact answer or an estimate? (Answers may vary. Students may say that they need an exact answer to pay the bill. Other students may point out that the website will calculate the total and they can estimate to be sure the total is reasonable.)
- When you decided whether the lists on the board were good choices, did you estimate or find exact answers? Explain. (Answers may vary. Students may say that they estimated or they have decided that they can find exact answers for some totals using mental math.)
When classes have solved problems similar to this one, some students have chosen to spend less money and save the rest or give it to charity. While these may be good choices in the real world, for this lesson push the mathematics and encourage students to spend as much of the $75 as possible.
Solve Problems at Art's Dime Store. Ask students to quickly read but not solve Questions 3–6 to prepare for a discussion about the Math Practices Expectations. In Questions 3 and 4 students are asked to find an exact answer, then check for reasonableness and accuracy. Question 5 needs only an estimate. Then students use these problems to write their own problem about sales at Art's Dime Store in Question 6.
Display the Math Practices page in the Reference section of the Student Guide.
Before students begin their work ask them to review the Math Practices page in the Reference section of the Student Guide.
Use the following discussion prompts to help students think about the Math Practices:
- What strategies can you use to solve these problems [MPE2]? (Possible responses: You can use paper-and-pencil methods to find exact answers. You can use convenient numbers or benchmark numbers to estimate answers. You can use base-ten pieces or base-ten shorthand to help you add or subtract.)
- How can you check to make sure your answers are reasonable [MPE3]? (Possible responses: You can check your work using a different method. For example, if you round to the nearest 100 the first time to estimate you can check your answer by using front end estimation to see if your answer is reasonable. You can check to see if an exact answer is reasonable using estimation.)
- How can you show or tell how you solved the problems so someone else can understand your thinking [MPE5]? (Possible response: You can show the convenient numbers or benchmark numbers you used to estimate. You can write number sentences to show how you solved each problem. You can write sentences to tell the steps you used to find your answer.)
Assign Questions 3–6. As students are working watch for strategies students are using to check the reasonableness of their answer [MPE3] and identify strategies students are using to solve each problem [MPE5]. Have students trade problems they made in Question 6, so that classmates can solve each other's problems.
