# Lesson 3

Stories with Fractions

## Warm-up: Number Talk: One Whole, Many Names (10 minutes)

### Narrative

This Number Talk encourages students to think about equivalent forms of whole numbers and decomposing fractions in order to subtract. When students consider equivalent fractions, look for ways to decompose fractions, or use the structure of mixed numbers to find the value of each difference, they look for and make use of structure (MP7).

### Launch

• Display one expression.
• “Give me a signal when you have an answer and can explain how you got it.”

### Activity

• 1 minute: quiet think time
• Keep expressions and work displayed.
• Repeat with each expression.

### Student Facing

Find the value of each expression mentally.

• $$1 - \frac{8}{10}$$
• $$1\frac{4}{10} - \frac{8}{10}$$
• $$2\frac{4}{10} - \frac{8}{10}$$
• $$10\frac{5}{10} - \frac{8}{10}$$

### Activity Synthesis

• “How are these expressions alike?” (They all involve subtracting $$\frac{8}{10}$$ from a number that is at least 1. To subtract, it’s helpful or necessary to decompose a 1 or to write an equivalent fraction.)
• “How did you use earlier expressions to help you find the value of later expressions?”

## Activity 1: Relay Race at Recess (20 minutes)

### Narrative

In previous lessons, students have used their understanding of fraction equivalence to compare fractions and solve problems. The purpose of this activity is to practice solving addition and subtraction problems involving decimal fractions (MP2). Students use what they know about equivalent fractions and the relationship between 10 and 100 to add tenths and hundredths.

Representation: Develop Language and Symbols. Represent the problem in multiple ways to support understanding of the situation. For example, show a picture of children working with clay and invite students to draw a comic strip or storyboard to represent the problem.
Supports accessibility for: Conceptual Processing, Language, Attention

• Groups of 2

### Activity

• 1–2 minutes: independent work time
• 5 minutes: partner discussion
• Monitor for expressions, strategies, and representations students use to determine connections between strategies and evidence of reasoning about equivalence.

### Student Facing

Students in the fourth-grade class had a relay race during recess. Each team had four runners. Each runner ran the length of the school playground.

Here are the times of the runners for two teams.

runner Diego’s team, time (seconds) Jada’s team, time (seconds)
1 $$10\frac{25}{100}$$ $$11\frac{9}{10}$$
2 $$11\frac{40}{100}$$ $$9\frac{8}{10}$$
3 $$9\frac{7}{10}$$ $$9\frac{84}{100}$$
4 $$10\frac{5}{100}$$ $$10\frac{60}{100}$$
1. Which team won the relay race? Show your reasoning.
2. How much faster is the winning team than the other team? Show your reasoning.
3. The record time for the playground relay race was 40.27 seconds. Did the winning team beat this record time? Show your reasoning.

### Activity Synthesis

• Invite previously identified students to share how they solved the problems.
• “How was solving these problems the same as the problems we solved in previous lessons? How was it different?” (It was the same because we were adding and subtracting mixed numbers. We still looked for ways to make a new whole number when we could. We had to add up fractions that had different denominators in these problems. We had to compare with a decimal fraction written with decimal notation.)

## Activity 2: You Be the Author (15 minutes)

### Narrative

The purpose of this activity is to create and solve addition and subtraction problems with fractions. Students first create stories to match a given value or equation and some given constraints.

MLR8 Discussion Supports. Display sentence frames to support small-group discussion: “_____ and _____ are the same/alike because . . .” or “_____ and _____ are different because . . . .”

### Launch

• Groups of 2
• “Think of a situation with a problem that could be solved by finding the value of $$3\frac{4}{10} + \frac{2}{10} + \frac{1}{2}$$.”
• 1–2 minutes: partner discussion
• Share responses.

### Activity

• 56 minutes: independent work time
• 45 minutes: compare with a partner
• Monitor for students who create situations that involve different problem types. For example, for the problem that can be solved with addition, look for students who create an Add to, Result Unknown problem and a student who creates a Compare, Difference Unknown problem.

### Student Facing

Think of three situations as described here. After each problem is written, trade papers with a partner to compare your problems and check your solutions.

1. A problem that can be solved by addition and has $$9\frac{2}{5}$$ as an answer
2. A problem that can be solved by subtraction and has $$\frac{32}{100}$$ as an answer
3. A problem that could be solved by writing the equation: $$9 - \underline{\hspace{1cm}} = 3\frac{3}{5}$$

### Activity Synthesis

• Invite 1–2 previously identified students to share their situations for each problem.
• “How are these situations the same? How are they different? How does each one match the directions?”

## Lesson Synthesis

### Lesson Synthesis

“In this section, we have solved many problems that involved adding, subtracting, multiplying, and comparing fractions.”

“What are two things that you have learned from listening to the ideas of other students in these lessons?”

“What is one thing you want to continue to practice when solving problems with fractions?“