Exploring the Number Line

Est. Class Sessions: 2

Developing the Lesson

Part 1: Compare the 200 Chart and the Number Line

Draw students’ attention to the classroom number line.

Ask:

How is the number line like the 200 Chart? (Possible responses: They both have numbers in order; they don’t skip numbers.)
How is the number line different from the 200 Chart? (Possible responses: The number line has the numbers all in one row; the 200 Chart has ten numbers in a row and there are 20 rows. The number line starts at 0 and goes to 130; The 200 Chart starts at 1 and goes
to 200.)

Show a display of the 200 Chart from the Student Activity Book Reference section and ask students to think back to the patterns they found on it.

After the class has discussed the patterns, display the Patterns on the 200 Chart Master. Read through the list, noting which patterns students mention and discussing others they may not have.

Begin a discussion of how to show the same patterns or moves on the number line.

Choose one particular pattern on the list, such as skip counting by twos, and ask:

How can you show skip counting by twos on the number line? (Make hops of 2.)
How is skip counting by twos on the number line different from skip counting by twos on the 200 Chart? (On the number line, you keep going in a straight line; on the 200 Chart, you move to the next row after 5 numbers. On the 200 Chart the numbers that you land on are all in the same columns.)
How is it the same? (On both, you skip every other number.)
What does it look like on the number line when we show the skip counting? (Many hops, each skipping one number.) [See Figure 1.]
What does it look like on the 200 Chart when we show the skip counting? (Every other number is shaded or marked on each row; when all the rows are done, there are five columns shaded or marked.)

Have a student demonstrate by drawing the hops on a display of the Number Lines 0–30 page from the Student Activity Book while another student shades the numbers for skip counting by twos on the 200 Chart.

Choose another one of the patterns you have listed and go through the same process. Choose a pattern other than skip counting so students see a different kind of pattern translated to the number line. Have a student show the pattern on the display of the Number Lines 0–30 page and another demonstrate on the 200 Chart.

Refer students to the Number Lines 0–30 page in the Student Activity Book and the 200 Chart in the Reference section. Assign two or three patterns or moves from the list to each student pair. The partners write the letters of their assigned patterns in the spaces provided on the Number Lines 0–30 pages. They discuss how to represent their assigned patterns or moves on a number line and mark each pattern on a separate number line. Circulate about the room as students are working to observe and answer questions.

Ask questions similar to the following:

Show me your pattern on the 200 Chart.
Tell me what numbers are in the pattern.
How can you show those numbers on the number line?
What will it look like?

When students have finished, have individual pairs report and demonstrate how their patterns translate to the number line. Use the display of the Number Lines 0–30 page and have students mark the patterns. Make sure that adding and subtracting are included in your discussion, particularly adding and subtracting 1, 5, and 10. See Sample Dialog 1 for a discussion of Pattern D. A student discusses how on both the 200 Chart and the number line, all the numbers in a row, except for the last number, begin with the same number. See Sample Dialog 2 for a discussion of Patterns G–J. Students discuss how to add and subtract on both the 200 Chart and on the number line.

In the following Sample Dialog, a student connects a row on the 200 Chart to the same interval on the number line and discusses the patterns.

Romesh: I looked at Pattern D: The numbers in a row, except the last number, begin with the same digit.

Teacher: Can you show us the same pattern on the number line?

Romesh: If you take each row, it’s like a piece of the number line. Like if I take the second row. The first number is 1 all across except for the last space. The second number is counting, 1, 2, 3, 4, 5, 6, 7, 8, 9, just like we said. In the last space, it’s a 2 and a 0, 20. On the number line it is this part. [With his hands, he frames the interval 11–20.]

Teacher: That’s interesting, Romesh. How did you draw it on your number line?

Romesh: I didn’t really know how to, so I drew a circle around it to show that it all went together.

Teacher: I think that’s a reasonable way to show it, Romesh. It shows that the whole row on the 200 Chart is also the same as that chunk of the number line. Do you remember what we called it when we had a group of numbers all together on the 200 Chart? [See Figure 2.]

Romesh: I think an interval.

Teacher: When you mark it on the number line is it still an interval?

Romesh: Yes.

Teacher: Does it show the same pattern as the interval that is the second row of the 200 Chart?

Romesh: Yes. It’s got the same numbers. The numbers all start with 1 except for the last one and the second numbers count 1, 2, 3, 4.

Teacher: Good. Romesh has shown us that an interval on the 200 Chart can also be shown on the number line and the numbers show the same pattern.

In the following Sample Dialog, students discuss adding and subtracting on the 200 Chart and on the number line.

Teacher: What do we do to show adding on the number line?

Nicholas: We go to the bigger numbers, to the right.

Teacher: And when we subtract on the number line?

Nicholas: We go the other way to the left.

Teacher: What about adding 10? How does that show up on the number line? We can’t just go to the next row, because it’s all one row. Jessie?

Jessie: You hop 10.

Teacher: Can you show us? Say you want to add
10 to 16. [See Figure 3.]

Teacher: Where would that be on the 200 Chart?

Jessie: Right under it. The next row, but the same space. The number right below 16 is 26.

Maya: I could do it a different way. I would make just one big hop on the number line, from 16 to 26. That adds ten.

Teacher: But if you didn’t do the little hops like Jessie did, how would you know where to stop?

Maya: Because I know that it ends the same when you add ten. 26 ends in a 6, just like 16, so I know I added ten. Just like on the 200 Chart.

Teacher: What if you added 10 three times? Where would you land?

Maya: I would go 16—that’s where I start—then 26, 36, 46. I’d be at 46. [See Figure 4.]

Teacher: Where would you land if you subtracted 10?

Maya: 6.

Teacher: How do you know that?

Maya: It’s the same thing. When you subtract 10, you always get a number that ends the same. And I know that when I add 6 and 10, I get 16. So that’s how I know to
subtract 10.

Adventure Book:

Student Activity Book: 145