The purpose of this activity is for students to estimate the number represented by a point on a number line and to justify their reasoning. Encourage students to explain why their estimates are reasonable. For each successive number line, the given tick marks are farther apart to encourage students to use their understanding of features of the number line.

Monitor for and select students with the following approaches for their estimate on the number line with only two tick marks to share in the Synthesis:

• Estimate by explaining how close to 60 (or far away from 0) they think the point is without estimating any other numbers.
• Estimate and label the number at the middle of the number line (30) and explain how close they think the number is to the middle.
• Estimate and label multiples of 10 or 5 to help support their reasoning.

The approaches are sequenced based on how many additional numbers students estimate to support their reasoning. This helps students connect the accuracy with which they can locate the given numbers to how much extra work they do thinking about other numbers that they can locate accurately (MP1). Accept a range of estimates and accuracy with the additional numbers students add to the number line. It is important to focus on the ways students reason rather than absolute accuracy. Aim to elicit both key mathematical ideas and a variety of student voices, especially students who haven’t shared recently.

• Invite previously selected students to share in the given order. Record or display their work for all to see.
• Connect students’ approaches by asking:
  • “How are these ways of estimating the number that the point represents the same?” (They all showed thinking about some of the numbers that were close to the point.)
  • “How are they different?” (Some ways showed more numbers on the number line. Some students thought only about the number they think is in the middle, others tried to estimate all the 10s or all the numbers you say when you count by 5.)
• Connect students’ approaches to the learning goal by asking:
  • “Which estimate are you most confident in? Why?” (The first one because it showed more numbers. It was easier to estimate how big one unit would be.)
  • “Which estimates are you least confident in? Why?” (The last one because I tried to label the tens, but I wasn’t sure how long ten would be. I’m not sure if all my tens are the same size.)
  • “What would help you be more accurate with your estimates?” (If I knew more numbers that were closer to the point. If the 10s and 5s were labeled.)

The purpose of this activity is for students to locate numbers on a number line without tick marks to represent each number. Students use what they know about multiples of 10, the relative position of numbers on the number line, and comparing length to locate and label a set of numbers on the number line. Students start by organizing number cards on a number line and make adjustments to their positions after each card is placed. After they place all of their cards, students locate and label the numbers on the number line. In the Synthesis, students compare the number lines that were created and discuss, using the structure of the number line, why some numbers were placed more accurately than others (MP7). This discussion also gives students a chance to construct viable arguments for how they placed the numbers and to critique the reasoning of others (MP3).

This activity uses MLR7 Compare and Connect. Advances: representing, conversing.

• “Check to make sure all of your numbers are represented in the spots you want them on the number line.”
• 1–2 minutes: group work time
• 5–7 minutes: Gallery Walk
• “What is the same and what is different between the different number lines?”
• Consider asking:
  • “Which numbers did most groups have in the same spot on their number lines?”
  • “Which numbers look like they are in different spots?”