# Lesson 3

Decimals on Number Lines

### Lesson Purpose

The purpose of this lesson is for students to reason about and compare the size of decimals using a number line.

### Lesson Narrative

Prior to this lesson, students made sense of tenths and hundredths in decimal notation. They also analyzed and wrote equivalent decimals. In this lesson, they use number lines to reason about the relative size of two or more decimals. The reasoning here is similar to that in an earlier unit, when students used number lines to compare fractions. Students see that, just as before, they can learn about the relative size of decimals by considering their positions on a number line and their relationship to benchmarks such as 0, 0.5, and 1. They will use these insights to compare and order fractions in the next lesson.

Students attend to precision and use the structure of the number line (MP6, MP7) when they locate and label decimals between two tick marks representing tenths. For example, halfway between 0.4 and 0.5 will be the decimal 0.45 whereas 0.48 will be much closer to 0.5 than to 0.4.

• Action and Expression
• MLR8

Activity 1: Points on Number Lines

### Learning Goals

Teacher Facing

• Reason about and compare the size of decimals to hundredths using a number line.

### Student Facing

• Let’s compare some decimals.

### Lesson Timeline

 Warm-up 10 min Activity 1 20 min Activity 2 15 min Lesson Synthesis 10 min Cool-down 5 min

### Teacher Reflection Questions

In earlier units, students compared fractions using many different strategies, including comparing fractions to benchmarks and creating equivalent fractions. Where did you see evidence of students making connections to those reasoning strategies in this lesson?

### Suggested Centers

• Rolling for Fractions (3–5), Stage 1: Equivalent Fractions (Supporting)
• Get Your Numbers in Order (1–5), Stage 4: Denominators 2, 3, 4, 5, 6, 8, 10, 12, or 100 (Supporting)