Counting On to Add with Number Lines

Est. Class Sessions: 1

Developing the Lesson

Use a Calendar to Count On. Display the calendar you prepared prior to the lesson. (See Materials Preparation.)

Share the following story with the class:

Sam and his grandma lived in the same city, but they did not see each other every day. They decided to send letters to each other in the mail. Sometimes it took one day and sometimes it took two days for their letters to be delivered. Sometimes it took as many as three days. Sam found a calendar for the month of October and wrote down when his letters were sent from his house and when they arrived at his grandma's house.

Direct students' attention to the calendar. Tell them that Sam mailed a letter on October 7 and that it took one day for it to be delivered to his grandma's house.

Ask:

When did Sam's letter arrive at Grandma's house? (October 8)
How do you know? Share your strategy for solving this problem. (Possible response: I counted on in my head. I started at 7 and counted on one day to 8.)
Show how you can use the calendar to solve the problem. (You start at October 7 on the calendar and count on to the next day, October 8.)
Write a number sentence for this problem. (7 + 1 = 8)

After students have shared their strategies, remove the self-adhesive note from October 8.

Use a Number Line to Count On. Display and refer students to the Number Line 0–30 page in the Student Activity Book Reference section.

Ask students to think about how to use this tool to show counting-on strategies and solve the following problem:

Grandma mailed her letter on October 15. It took three days to get to Sam. When did her letter arrive at his house? (October 18)

Several ways to demonstrate counting on using a number line are shown in Figure 2. In the first example, the first addend is shown by one long jump from 0 to 15, then three little hops for each number counted on are shown. This representation most graphically shows the counting-on strategy using the number line. However, some students may be more comfortable with other representations, such as 15 short hops and then 3 more short hops, or one long jump from 0 to 15 and then a medium jump from 15 to 18. All of these representations are correct and should be accepted.

Ask:

Show how to use the number line to solve this problem. (Answers will vary. Possible response: I take one long jump to 15 and then 3 little hops, 16, 17, 18.)
Can you use another tool to solve this problem? (Possible response: I use the calendar. I start on October 15 because that is when Grandma mailed her letter. It took 3 days to get to Sam so I count on October 16, 17, 18.)
What is the number sentence for this problem? (15 + 3 = 18 or 18 = 15 + 3)
What does the 15 mean in the number sentence? The 3? The 18? (Grandma mailed the letter on October 15; The letter took 3 days to be delivered; Sam got the letter on October 18.)

Count on one more time, removing the self-adhesive notes as you count aloud together: 16, 17, 18. Restate that the letter was mailed on October 15 and it arrived at Sam's house three days later on October 18.

Choose Tools to Solve Addition Problems.

Use the calendar and the number line display to work through the next problem with the class:

Sam mailed a letter on October 20. It took two days to get to his grandma. When did it arrive? (October 22)
Show how to solve this problem using the calendar.
Check this answer using a number line.
Do you get the same answer? (yes)

After students have shared their solution strategies, remove the self-adhesive notes from the calendar as you count on aloud together: 21, 22. Give the class additional calendar problems to solve with both the calendar and number line, or ask them create some problems on their own.

Display the It's in the Mail pages. Tell students they are to solve at least two problems using the number lines and at least two using the calendar. They may use connecting cubes to check their work.

Use the display to demonstrate how they can use counters on the page's calendar in place of self-adhesive notes. If they choose, students can put a counter on the date when the letter was mailed and then cover the days that the letter was in transit with more counters. For example, on the first problem, the letter was mailed on the 10th. Cover the 10th with a counter. It took three days, so cover three more dates with counters. Uncover the last date covered with a counter to find the date on which the letter arrived.

Assign the It's in the Mail pages to student pairs. Provide small counters and connecting cubes for students who choose to use them. As students work, circulate about the room and identify a student to demonstrate later in the lesson how to use a calendar and how to use a number line.