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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.

Standards for Mathematical Practice:

3.   Construct viable arguments and critique the reasoning of others.

6.   Attend to precision.

Student Outcomes:

• I can create a number line using equal spacing. (with whole number increments)

• I can represent whole numbers on a number line.

Materials:

• Yarn or string

• One Index card for each of the following numbers: 0, 20, 50, 100, 25, 75, 10, 80, 15, 90, 70, 60, 30, 40, 5, 35, 45, 55, 65, 85, 95, 22, 64

• Clothespins or other clips

• Adding machine tape or cut bulletin board paper into long strips

Advance Preparation:

• Collect and organize the necessary materials.

Directions:

1. The task begins with the teacher asking two students to hold the yarn at each end, one student will have the card with the number 0 at one end and the other student will have the card with the number 100 at the other end.

2. The teacher passes out the rest of the numbers to the class. After all numbers have been passed out the teacher poses the question, “What number should we place next on the number line?” She will continue to ask questions such as, “Who feels confident about putting their number in the correct place on the number line? Why?” When students decide where to stand they place their number on the number line attempting to be precise both within the correct sequence and in regards to the spacing between values. When students volunteer and place themselves on the line, have them tell why they think they should be next and how they have decided where to stand. For example, “The number 50 would be a good number to begin with because it will mark the middle of the number line.” or “40 should go about here because that’s how far 30 is after 20 on the number line.” Prompt students to agree or disagree with each other to clarify their justifications for the placement of each number.

3. The teacher allows students to volunteer their number if they think it is a good time to place their number. If necessary, the teacher can call on certain students to keep the activity moving. Encourage students to question the placement of numbers and to suggest moving them as needed to adjust the sequence of and/or distance between values.

4. Continue until all numbers and students are placed on the human number line. Have students observe where they are standing and see if it is the best place for them to be. Discuss equal spacing on the number line and again ask students to move if they are not at the correct point as numbers are added. Facilitate the discussion that will arise when some students want to space each other equally and others pay more careful attention to the specific differences between numbers such as 20 and 22 or 0 and 20.

5. After all students are satisfied with their placement, have students hang the number with a clothespin and display the number line somewhere in the room.

6. Have students get a strip of paper and make their own number line with a range of at least 20 numbers between 0 and 100. For example, if a student starts at 40 they would need to go to at least 60.

7. Students share their number lines in small groups. Teacher monitors groups to see if number lines are precise and have equally spaced points and are labeled correctly. During this time teachers can take anecdotal notes regarding the understanding of the number lines.

8. Students summarize by writing what they believe is important about creating number lines.

Questions to Pose:

Before:

Why is it important for numbers on a number line to have equal spaces from each other?

During:

What number should we place on the number line next?

Why did you choose to place your number where you did?

Which numbers should we move to have better placement on our number line? Why?

If you were given a different end point would your number still be placed where you clipped it?

About how far would it be for me to “hop” by 5 or 10?

About how far would it be for me to “step” up or down 1?

After:

What other numbers could we place on the number line?

Why did you choose the range of numbers you put on your number line?

Extension

1. Bring students back to the larger shared number line and ask students how it could be used for addition and subtraction. Use facts that involve the numbers placed on the yarn such as 35 - 5 or 50 + 15. Have students direct you to the right or left and make mistakes when directions are unclear to encourage revision and precision. Attempt to make “hops” and “steps” to match students moving by 10s or 1s, etc. After a few examples, have a few students do the same then shift back to their small groups.

2. In small groups, the students take turns creating addition and subtraction problems for the different number lines they have created. For example, if the number line is from 20 to 100 a problem could be what is 52 + 8, or what 58 - 9 is. Encourage students to walk up and down their number lines with their fingers to represent the “hops” and “steps” taken in front of the larger number line.

Possible Misconceptions/Suggestions:

Special Notes:

This human number line task could be repeated with different numbers at a later date. The small number lines could be displayed in the classroom and could be used for more problem solving tasks.

Solutions: NA