Lesson 3
Decimals on Number Lines
Warmup: Which One Doesn’t Belong: Decimals and Fractions (10 minutes)
Narrative
Launch
 Groups of 2
 Display the image.
 “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
 1 minute: quiet think time
Activity
 “Discuss your thinking with your partner.”
 2–3 minutes: partner discussion
 Share and record responses.
Student Facing
Which one doesn’t belong?
Student Response
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Activity Synthesis
 “How might we revise one or more of the options so that they all represent the same value?” (Sample responses:
 Change the \(\frac{80}{10}\) to \(\frac{8}{10}\) or \(\frac{80}{100}\).
 Change option A to say “eight,” option C to say “8” or “8.0,” and the label for the first tick mark in option D to say “1.”)
Activity 1: Points on Number Lines (20 minutes)
Narrative
In this activity, students reason about the relative size of decimals by locating them on a number line. As in a previous activity, they rely on their experience of locating fractions on a number line and the relationship of the decimal values relative to 0 and 1.
If desired and logistically feasible, consider carrying out the activity on a giant number line rather than on paper.
 Stretch a long strip of tape across a wall, at least 8 or 10 feet long. Partition the tape into 12 equal intervals, using shorter pieces of tape as tick marks. Label the locations of 0 and 1.
 Give each group of students 2–3 dot stickers, 4–5 sticky notes, and a thick marker.
 Ask each group to write (on sticky notes) labels for two of the tick marks, with one sticky note for each label.
 Assign each group one or two of the eight decimals in the second problem. Ask them to locate their assigned decimals on the number line, using dot stickers to mark the location and sticky notes to label them.
Supports accessibility for: Organization, SocialEmotional Functioning
Launch
 Groups of 3–4
Activity
 If creating a giant number line, lead the activity as outlined in the Activity Narrative. Otherwise, ask students to work with their group on the first two problems.
 Pause and discuss:
 how students knew where to put each decimal
 how the number line could help us see the least and greatest
 “Take a few quiet minutes to complete the rest of the activity.”
 5–6 minutes: independent work time
Student Facing

Label each tick mark on the number line with the number it represents.

Here are eight numbers.

0.10

0.40

0.80

1.10

0.15

0.45

0.75

1.05
 Locate and label each number on the number line.
 Which number is greatest? Which is least? Explain how the number line can help determine the greatest and least numbers.


Locate and label these numbers on the number line.

0.24

0.96

0.61

1.12

0.08


Use two numbers from the previous questions to complete each comparison statement so that it is true.

________ is greater than _______.

________ is less than _______.

________ is the greatest number.

Student Response
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Advancing Student Thinking
Activity Synthesis
 Select students to display their completed number lines (showing the locations of five additional decimals).
 Invite the class to agree or disagree with the locations of the point and discuss any disagreements.
 Select other students to share their comparison statements and how they know each statement is true.
Activity 2: Decimals Compared (15 minutes)
Narrative
In this activity, students continue to compare decimals to hundredths. They begin by reasoning with a number line and work toward generalizing their observations. Some students may compare two numbers by analyzing the value of the digits in the same place (for example, the tenths in one number and the tenths in the other), but comparing decimals by place value is a standard for grade 5 and thus not expected at this point.
Advances: Conversing, Representing
Launch
 Groups of 2
Activity
 “Take a few quiet minutes to work on the activity. Then, share your thinking with your partner.”
 7–8 minutes: independent work time
 3–4 minutes: partner discussion
 For the comparisons in the second problem, monitor for students who:
 name the decimal in words and compare the number of hundredths (for instance, 62 hundredths and 26 hundredths)
 relate the decimals to benchmarks such as 0, 0.5, and 1
Student Facing

Here is a number line with two points on it.
 Name the decimal located at point A.

Is the decimal at point A less than or greater than 0.50? Explain or show your reasoning.
 Is the decimal at point B greater or less than 0.06? Explain your reasoning.

Estimate the decimal at point B.

Compare the numbers using \(<\), \(>\), or \(=\). Can you think of a way to make comparisons without using a number line? Be prepared to explain your reasoning.

\(0.51 \underline{\hspace{0.5in}} 0.09\)

\(0.19 \underline{\hspace{0.5in}} 0.91\)

\(0.45 \underline{\hspace{0.5in}} 0.54\)

\(0.62 \underline{\hspace{0.5in}} 0.26\)

\(1.02 \underline{\hspace{0.5in}} 0.95\)

\(0.3 \underline{\hspace{0.5in}} 0.30\)

\(4.01 \underline{\hspace{0.5in}} 4.10\)

Student Response
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Activity Synthesis
 See lesson synthesis.
Lesson Synthesis
Lesson Synthesis
“Today we compared decimals in tenths and hundredths.”
“How can we use a number line to help us make comparisons?” (We can plot the decimals on the number line. The one farther to the right is the greater decimal.)
“How might we compare decimals without using a number line? What strategies did you use when completing the comparison statements in the last activity?”
If not mentioned in students’ explanations, highlight the following reasoning strategies:
 Name the decimals in words and compare the number of hundredths. (For instance, 51 hundredths is more than 9 hundredths.)
 Compare each decimal to benchmarks like 0, 0.5, 1, or other decimals. (For instance, 0.51 is close to 0.50, while 0.09 is close to 0.10 or close to 0.)
Cooldown: More to Compare (5 minutes)
CoolDown
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