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Lesson excerpt:

Common Core Standard:

Relate addition and subtraction to length.

NC.2.MD.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points and represent whole-number sums and differences, within 100, on a number line.

Related Standards:

Measure and estimate lengths in standard units.

NC.2.MD.1 Measure the length of an object in standard units by selecting and using appropriate tools such as rulers, yardsticks, metersticks, and measuring tapes.

Standards for Mathematical Practice:

1. Make sense of problems and persevere in solving them.

3. Model with mathematics

4. Use appropriate tools strategically

5. Attend to precision

Student Outcomes:

• I can create a number line to 100.

• I can measure accurately and mark numbers on the number line.

• I can solve addition and subtraction problems using a number line.

Materials:

• Adding machine tape

• 100 Unifix cubes (or some type of connecting cubes) for each pair of students. Organize the cubes in sticks of 10, alternating colors—10 of one color, 10 of a different color, etc.

• Posted number line or meter stick or yard stick

Advance Preparation:

• There is a growing body of research to suggest the importance of the number line as a tool for helping children develop greater flexibility in mental arithmetic as they construct mathematical meaning, develop number sense, come to understand number relationships, and develop powerful strategies for addition and subtraction. The number line can do much more than simply help children count to 100. The number line can be used as a tool to help children function well with the various operations. The number line is a powerful visual tool for adding and subtracting.

• Cut strips of adding machine tape for each pair of students. The length should be a little longer than 100 Unifix cubes (or other manipulative being used to measure).

• Student pairs work together to create a number line. Pair students who will work well together.

• Students will need space to work on the adding machine number line.

• Teachers may want to divide this lesson into two parts. The first day the students make a number line to 100. The second day students continue the number line to 100.

• Have students organize the Unifix cubes into sticks of 10 of the same color.

• For day 2, Students will only have one ten stick to measure from 100 to 200. This helps students use some of the foundation measurement concepts started in 1^st grade (no gaps or overlaps, using same-size units, laying multiple copies of a shorter object end to end, iteration).

0                         10                         20                        30

Directions:

1. If there is a number line posted in the room have students look at it and ask, “What do you notice about the number line?” (If there is not a number line posted in the room students can refer to a yardstick or meter stick.) Possible observations:

·         It has numbers.

·         The numbers are in order.

·         The spaces between the numbers are all the same.

2. After discussing the number line explain that they are going to make a number line to 100 with a partner using adding machine tape and cubes. Students will have 100 cubes to measure the spaces. It may be helpful to have the Unifix cubes in sticks of 10. Students would have 10 cubes of one color and then 10 of a different color (or 5 of one color, five of a different color and then repeat the sequence.) This pattern continues to 100. Students will better be able to keep track of the numbers if the cubes are organized by 10s. Ask, “What do you need to think about before you begin the number line?” Possible comments:

·         We need to cooperate. We need to take turns. We need to work together. (You might ask what that will look like.)

·         Students may talk about measuring carefully. Have students demonstrate how to measure with the cubes. Students will not mark every number on the number line. They will mark each set of 10 or 5. So a number line will be labeled 10, 20, 30, etc. or 5, 10, 15, 20, etc.

3. As students describe marking the number line, have some students demonstrate on adding machine tape how to use the Unifix cubes (connected cubes) to mark the number line. Highlight marking the number line at the end of each 10^th or 5^th cube.

4. Help students find locations in the room to make the number line.

5. As students work on number lines the teacher monitors working pairs. Refer to “Questions to Pose.”

6. After students have completed the number line to 100 reconvene the class as a whole group. Discuss their process. Have pairs share the number line. Lay 2-3 number lines on the floor or attach to the board. The numbers on the number lines will probably not line up. Second graders do not measure accurately. Ask, “We all used Unifix cubes to measure. Why do you think the 30 is in a different spot on this number line?”

7. Lay one number line on the floor (or board). Ask questions about using the number line to solve problems. Questions to ask are listed in “Questions to Pose.”

8. Ask students how they could continue this number line or create a new number line using only groups of 10 cubes (no singles) to continue the number line.

9. Ask students how to show 35 + 17 or 62 – 11 on their number lines and compare how they move to the right and left on the number line as well as their answers. Have students challenge and support each other with similar facts on their number lines. End by selecting students to share and demonstrate this process on their number lines.

Questions to Pose:

Before:

• What do you notice about a number line?

• How will you work with your partner?

• What do you need to think about before you make the number line?

• Why do you think I had you organize your cubes in sticks of ten using different colors?

During:

• How are you and your partner sharing the work?

• How do you know where to write the numbers?

• How is your number line like the one we looked at earlier?

• How is your number line different from the one we looked at earlier?

• What will happen if we overlap or leave gaps between the cubes?

• How many groups of ten do you have to make 100?

• If we made our number line to 200 (300, 400, etc.) how many groups of ten will we need?

• Why do you think I wanted you to create this number line? How does this number line help you solve problems?

After:

• Compare number lines created by students. We all used Unifix cubes to measure. Why do you think the 30 is in a different spot on this number line?”

• How can we use this number line to solve 45 + 10? Students might say start at 45 and jump 10. Or start at 45, lay a ten stick and it will be on 10 more. Continue with several problems, adding ten from a multiple of 10 or 5.

• If students are successful with the task above, ask, “How can I use the number line to solve 23 + 10.” Students may estimate where 23 is but ask them to use the cubes to mark 23 on the number line. Then they can use a 10 stick to find 23 + 10. Continue with several problems adding ten from a “nonmultiple” of 10 or 5.

Possible Misconceptions/Suggestions:

Special Notes:

• This lesson supports the 1^st grade measurement standard.

• After students use the number line to solve problems introduce the empty number line. This website http://www.k-5mathteachingresources.com/empty-number-line.html gives background information on empty number lines.

• Talk to the students about making a number line to 1000. How could we use the number lines already created? (put together 5 number lines.) How long would our number line be if we put all our number lines together? (100 x the number of student pairs) Students can line up number lines in the hallway or another large space to see the length of their combined number lines.