The purpose of this activity is for students to apply what they know about tenths and hundredths and decimal notation to arrange two sets of numbers in order, from least to greatest, and then greatest to least. A number line is given, but students are likely to start seeing its limits as a tool for comparing and ordering decimals. It takes time to plot each value on the number line, the scale of the number line accommodates only a small range of numbers (numbers like 1.25 and 12.05 would go beyond the line), and there are other ways to compare two decimals.

Monitor for and select students with the following approaches for ordering the numbers in the second problem to share in the Activity Synthesis:

• Plot the decimals on the number line.
• Relate each decimal to benchmarks such as 0, 0.5, and 1 with or without using a number line.
• Write each number as a decimal fraction with a like denominator (for example, hundredths).
• Use and compare the word names of the decimals (for example, 95 hundredths is greater than 9 hundredths).

The approaches are sequenced from more concrete to more abstract to prompt students to compare decimals using different strategies and make connections to reasoning with place value, which will be helpful in the next activity. Aim to elicit both key mathematical ideas and a variety of student voices, especially students who haven’t shared recently. For an example of each approach, look at the Student Responses.

• Invite previously selected students to share responses to the second problem in the given order. Record or display their work for the second problem for all to see.
• Connect students’ approaches by asking:
  • “Why does ______’s way work for comparing decimals? Would it always work?” (A number line approach would work but could take a long time for some numbers.)
  • “After seeing these strategies, which one(s) do you prefer to use for ordering decimals? Why?” (I first used a number line but 12.05 didn’t fit. Benchmarks can help sort a list of numbers into groups. I like reasoning with place value.)
• Connect students’ approaches to the learning goal by asking:
  • “How does each way help you think about the size of each number?” (The number line helps us see larger numbers because they are further to the right. Thinking about benchmark numbers like 0, 0.5, 1, or other whole numbers is like thinking about the number line but just in your head. Thinking about the number of hundredths is like comparing fractions with the same denominator.)

In this activity, students compare and order decimals in the context of running times. Students compare and order two-digit whole numbers, prompting students to be more attentive to the place value of the digits. The context of track and field may be unfamiliar, so time is built into the Launch to support students in making sense of the problem.

When students look carefully at the meaning of each digit in the numbers and interpret them in terms of the running context, they are reasoning abstractly and quantitatively and observing place value structure (MP2, MP7).

This activity uses MLR6 Three Reads. Advances: reading, listening, representing

• Display the table from the activity.
• Invite students to share their ordered list and discuss how they went about arranging the numbers.
• Highlight explanations that are based on the meaning of tenths and hundredths, understanding word names of the decimals, or reasoning with place value.