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Activity 1

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

None

Activity Narrative

The purpose of this activity is for students to work with number lines that only have multiples of 5 or 10 labeled and do not start with 0. Students reason about how a number line can be accurate without all the whole numbers labeled. Students use the numbers that are labeled to locate specific numbers on number lines. Students rely on the regular structure of the number line and the counting sequence in order to accurately place numbers (MP7).

MLR2 Collect and Display. Collect the language students use as they work with number lines and discuss the number patterns. Display words, phrases, and representations, such as "number line," "distance from zero," "in order," "interval," "spaces," "tick mark," "point," and "pattern." During the Synthesis, invite students to suggest ways to update the display by asking, “What are some other words or phrases we should include?” Invite students to borrow language from the display as needed.
Advances: Conversing, Reading

Launch

Groups of 2
Display the first number line (labeled 0, 5, 10, 15, 20, 25, 30).
“What do you notice about this number line?” (Not all the tick marks are labeled. Only the fives are labeled.)
30 seconds: quiet think time
Share responses.
“Are the labeled tick marks in the right spots on the number line? Explain.” (Yes, because 5 is 5 length units from 0. 10 is 10 units from 0. There are 5 length units between each labeled mark.)
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
“Today we are going to make sense of and use number lines that do not label every tick mark.”

Activity

“Locate each number on the number line and mark it with a point. Be ready to show your partner how you know you located the numbers and how you know they are in the right spots.”
4 minutes: independent work time
4 minutes: partner work time
Consider asking:
- “How did you locate this number?”
- “How did you use the labeled tick marks?”
- “How do you know your number is at the right length from 0?”
Monitor for students who show their number is at the right position by:
- Counting on from 0 or referencing the length from 0.
- Counting on or back from a labeled tick mark.
- Describing the length between each labeled tick mark.

Locate 24. Mark it with a point.
Locate 37. Mark it with a point.
Locate 48. Mark it with a point.
Locate 83. Mark it with a point.
Are the numbers you marked on the number lines in the correct locations? How do you know?

Student Response

to access Student Response.

Advancing Student Thinking

If students count every tick mark to locate numbers, consider asking:

“Tell me more about how you located the numbers.”
“How could you use the labeled tick marks to help you find a number?”

Activity Synthesis

Display the number line labeled 20, 30, 40, 50, 60.
Invite 1–2 previously identified students to share how they located 48.
“How do you know your point is the right distance from 0?” (It’s like when we measured from different spots on a ruler. The tick marks are spaced the same space apart and count by 1 length unit. We could draw the line back and find where 0 is.)
“A number line representation cannot represent all numbers with tick marks, points, or labels. We can use what we know based on the numbers that are labeled to locate other numbers.”

Activity 2

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

None

Activity Narrative

The purpose of this activity is for students to locate numbers up to 100 on a number line. They complete number lines that are labeled with multiples of 5 or 10 by using what they know about length on the number line and counting by 5 and 10. They use the labeled tick marks to locate and represent numbers within 100. When students explain to one another how they located different numbers on the number lines, they construct viable arguments and may critique each other’s reasoning (MP3).

Action and Expression: Develop Expression and Communication. Give students access to two colors of connecting cubes. Build a number line that changes color back and forth at intervals of 5. For example, 5 red cubes, 5 yellow cubes, 5 red cubes, 5 yellow cubes, and so on. The concrete visual of color representing intervals of 5 can be seen clearly.
Supports accessibility for: Conceptual Processing, Organization

Launch

Groups of 2

Activity

“On your own, complete each number line by filling in the missing labels with the number the tick mark represents. Then locate each number, mark it with a point, and label the point with the number it represents.”
“When you finish, think of how you can explain to your partner how you know your labels and points are at the right spots on the number lines.”
5 minutes: independent work time
“Share your work with a partner. Make sure you agree on your answers.”
5 minutes: partner discussion
Monitor for students who:
- Explain their labeled tick marks based on counting by 5 or 10.
- Explain their labeled tick marks based on the equal lengths between each labeled tick mark.
- Use labeled tick marks to explain how they locate numbers.

Complete each number line. Fill in the labels with the number the tick mark represents. Locate each number. Mark it with a point. Label it with the number it represents.

Locate and label 17.
Locate and label 59.
Locate and label 43.
Locate and label 35.
Share your number lines with your partner.

Caterpillar with every other body segment labeled with a number. From left to right: 5, 10, 15, 20, 25, 30, 35.

Student Response

to access Student Response.

Advancing Student Thinking

If students’ labels are numbers other than the specified numbers, consider asking:

“Can you show me how you located and labeled _____?”
“How can you use the number line to prove that is the location of that number?”

Activity Synthesis

Display the image of an incomplete number line labeled with 10 and 50.
“How could you find 35 without filling in the missing labels?” (We could count back from 50. We could count on from 10.)
Invite previously identified students to explain how they found the labels and used them to locate 35.
Complete the number line as students explain.

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Settings

Language

Audience

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Lesson 3

Unlabeled Tick Marks

Warm-up

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Activity 1

Standards Alignment

Building On

Addressing

2.MD.B.6

Building Toward

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Activity 2

Standards Alignment

Building On

Addressing

2.MD.B.6

2.NBT.A.2

Building Toward

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Lesson Synthesis

Standards Alignment

Building On

Addressing

2.NBT.A.2

Building Toward

2.MD.B.6