Discuss Strategies. Direct students' attention to the Katie's Job page in the Student Guide. Read the opening paragraph. The graph entitled Paper Route Earnings helps her keep track of the money she earns while delivering newspapers. Discuss Questions 1–3 and the short vignette on the page. Natasha uses a graph to determine how much money Katie earns in three weeks while Peter uses a data table. Students should conclude that both students' solution strategies solve the problem correctly.
- What other problems have we solved using a line graph or a data table? (Possible response: We used line graphs and data tables to find the side length or perimeter of regular shapes in Walking Around Shapes. We used a line graph and data table to solve problems in Lemonade Stand.)
- What other strategies can you use to solve problems? (Possible response: guess and check, using patterns in number sentences, diagrams, mental math strategies such as reasoning from known facts, repeated addition or subtraction)
Remind students that when they solve a problem a second way, they are able to check to see if their answer is reasonable. Ask students to discuss Question 4 with a partner. Then have student volunteers share how they solved the problem in Question 2 another way.
- Show another way to find out how much money Katie will have in 3 weeks. (Possible response: I see that she will have $12 after 1 week and $24 after 2 weeks. I see that you add $12 as each week passes. I added $24 + $12 = $36.)
Set Expectations and Solve Problems. Direct students' attention to the Delivering Newspapers pages in the Student Activity Book. Review the directions at the top of the page. Students solve Questions 1–4 two ways. They use the graph and a second strategy to check their answers. Encourage and expect students to use a variety of solution strategies. See Figure 1. Students show or tell what they did by writing number sentences and using labels so that others can understand their thinking. For Question 5, students look for patterns in a data table to solve problems. Remind them to not only look down the columns for patterns but to look across the rows for patterns.
Display and direct students' attention to the Math Practices page in the Student Guide Reference section. Before students begin working, use this page to review and set expectations for their solutions. Remind students of what is expected in their best work. Focus on Math Practices Expectations 2, 3, 5, and 6.
- How are you going to show how you used the graph? (Possible response: We will draw dotted lines on the graph that show where we start, how we go up to the solid line and turn, and where we stop and find the answer.)
- There are several problems. How are you going to show which dotted lines go to which problem? (Possible response: Use a different color to draw the dotted lines for each problem or label the dotted lines with the question number.)
- How will you check for reasonableness? (Possible response: Use a second strategy to check the answer, and then compare the answer to my solution from the graph.)
- What are some other possible strategies? (Possible response: make a table, use mental math strategies like reasoning from known facts, repeated addition, repeated subtraction, multiplication, division)
- How are you going to show another strategy in a way that others can understand your thinking? (Possible response: show all my steps clearly and label the numbers, draw a picture, leave a trail for trial and error, show how I solved a computation, describe the steps in words)
- What labels might you use in this problem to show what the numbers mean? ($ and weeks)
Assign Questions 1–5 on the Delivering Newspapers pages.
Delivering Newspapers offers students the opportunity to use Math Practices Expectations 2, 3, 5, and 6 in their work. If needed, provide support by focusing on only one of these Expectations.
Use Delivering Newspapers with Feedback Box in the Student Activity Book to assess students' progress toward the following Content Expectations:
- Identify and extend multiplicative patterns in graphs [E1].
- Represent multiplicative patterns [E2].
- Use mental math strategies to multiply and divide [E3].
- Represent solution strategies for multiplication problems [E4].
- Represent solution strategies for division problems including interpreting remainders [E5].
- Read a point graph [E7].
Use Delivering Newspapers to assess students' abilities to meet the following Math Practices Expectations:
- MPE2.
- Find a strategy.
- MPE3.
- Check for reasonableness.
- MPE5.
- Show my work.
- MPE6.
- Use labels.
