Lesson 3
Stories with Fractions
Warmup: 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
 Record answers and strategy.
 Keep expressions and work displayed.
 Repeat with each expression.
Student Facing
Find the value of each expression mentally.
 \(1  \frac{8}{10}\)
 \(1\frac{4}{10}  \frac{8}{10}\)
 \(2\frac{4}{10}  \frac{8}{10}\)
 \(10\frac{5}{10}  \frac{8}{10}\)
Student Response
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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.
Supports accessibility for: Conceptual Processing, Language, Attention
Launch
 Groups of 2
Activity
 1–2 minutes: independent work time
 “Compare your strategies with your partner’s.”
 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 fourthgrade 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  \(10\frac{5}{100}\)  \(10\frac{60}{100}\) 
 Which team won the relay race? Show your reasoning.
 How much faster is the winning team than the other team? Show your reasoning.

The record time for the playground relay race was 40.27 seconds. Did the winning team beat this record time? Show your reasoning.
Student Response
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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.
Advances: Speaking, Conversing, Representing
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
 5–6 minutes: independent work time
 4–5 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.
 A problem that can be solved by addition and has \(9\frac{2}{5}\) as an answer
 A problem that can be solved by subtraction and has \(\frac{32}{100}\) as an answer

A problem that could be solved by writing the equation: \(9  \underline{\hspace{1cm}} = 3\frac{3}{5}\)
Student Response
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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?“
Cooldown: Mai’s Milky Cereal (5 minutes)
CoolDown
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