# Lesson 17

True or False?

## Warm-up: True or False: Fraction Addition (10 minutes)

### Narrative

The purpose of this True or False is for students to demonstrate strategies and understandings they have for adding fractions with unlike denominators. These understandings help students deepen their understanding of the properties of operations and will be helpful later in this lesson when students will develop their own true or false activity.

In the synthesis it is important to discuss things the writer had to pay attention to when they designed this activity.

### Launch

• Display one equation.
• “Give me a signal when you know whether the equation is true and can explain how you know.”
• 1 minute: quiet think time

### Activity

• Share and record answers and strategy.
• Repeat with each equation.

### Student Facing

Decide if each statement is true or false. Be prepared to explain your reasoning.

• $$\frac{3}{4}+\frac{3}{8} = \frac{3}{8}+\frac{3}{8}$$
• $$\frac{7}{5}+\frac{2}{3} = \frac{21}{15}+\frac{8}{15}$$
• $$\frac{8}{9}+\frac{5}{12}=\frac{32}{36}+\frac{15}{36}$$

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• “What did the writer of this activity have to pay attention to when they designed this activity?” (Some equations are true and some are false. Some terms on both sides are equal. Pay attention to the unlike and like denominators.)
• “Where do we see those things in how the equations change during the True or False?” (The first two equations are false, but they use an appropriate common denominator.)

## Activity 1: True or False: Design 1 (15 minutes)

### Narrative

The purpose of this activity is for students to reason about subtracting fractions with unlike denominators to add one equation to a partially-completed True or False activity. If there is time, students can facilitate their True or False with another group.

MLR8 Discussion Supports. Prior to solving the problems, invite students to make sense of the situations and take turns sharing their understanding with their partner. Listen for and clarify any questions about the context.
Representation: Internalize Comprehension. Synthesis: Use multiple examples and non-examples to emphasize the importance of finding like units in order to subtract fractions.
Supports accessibility for: Conceptual Processing, Memory

### Launch

• Groups of 2 or 4
• “Now you will work with your group to complete a True or False activity. This activity has one equation missing. Decide on an equation that would complete the True or False and write it on the blank line.”

### Activity

• 10 minutes: small-group work time
• As students work, monitor for groups who discuss and design an equation based on some of the following:
• They create equations where the fractions on one side of the equation have unlike denominators and the other side consists of fractions with like denominators.
• They create an equation where the common denominator is appropriate, but the corresponding fraction used is not equivalent.
• They create an equation that is similar to a previous equation. For example: $$\frac{5}{6}-\frac{4}{9}=\frac{30}{36}-\frac{16}{36}$$
• They create an equation where a similar strategy can be used to determine if it’s true.

### Student Facing

Write an equation to complete the True and False task. Be prepared to share your reasoning for the last equation.

• $$\frac{5}{6}-\frac{4}{9}=\frac{45}{54}-\frac{24}{54}$$
• $$\frac{5}{6}-\frac{4}{9}=\frac{15}{36}$$
• _______________________

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• Choose small groups to share that had different reasons for their fourth equation.
• Ask students to share their completed True or False and ask the class to share reasons for the last equation.
• As each group shares, continually ask others in the class if they agree or disagree and the reasons why.

## Activity 2: Design 2 (15 minutes)

### Narrative

The purpose of this activity is for students to reason about adding fractions with unlike denominators to add two equations to a partially-completed True or False activity. If there is time, students can facilitate their True or False with another group.

### Launch

• Groups of 2 or 4
• “Now you will work with your group to complete a True or False activity. This activity has two equations missing. Decide on equations that would complete the True or False and write them on the blank lines.”

### Activity

• 10 minutes: small-group work time
• As students work, monitor for groups who discuss and design equations based on some of the following:
• They create equations where the fractions on one side of the equation have unlike denominators and the other side consists of fractions with like denominators.
• They create an equation where the common denominator is appropriate, but the corresponding fraction used is not equivalent.
• They create an equation that is similar to a previous equation.
• They create an equation where a similar strategy can be used to determine if it’s true.

### Student Facing

Write two equations to complete the True or False task. Be prepared to share your reasoning for the equations.

• $$\frac{8}{14}+\frac{3}{7}=\frac{4}{7}+\frac{3}{7}$$
• _______________________
• _______________________

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• Choose small groups to share that had different reasons for their equations.
• Ask students to share their completed True or False and ask the class to share reasons for the equations.
• As each group shares, continually ask others in the class if they agree or disagree and the reasons why.

## Activity 3: Design 3 (15 minutes)

### Narrative

The purpose of this activity is for students to reason about adding and subtracting fractions with unlike denominators. Students create equations to complete a True or False activity. If there is time, students can facilitate their True or False with another group.

### Launch

• Groups of 2 or 4
• “Now you will work with your group to complete a True or False activity. This activity has all three equations missing. Decide on equations that would complete the True or False and write them on the blank lines.”

### Activity

• 10 minutes: small-group work time
• As students work, monitor for groups who discuss and design equations based on some of the following:
• They create equations where the fractions on one side of the equation have unlike denominators and the other side consists of fractions with like denominators.
• They create an equation where the common denominator is appropriate, but the corresponding fraction used is not equivalent.
• They create an equation that is similar to a previous equation.
• They create an equation where a similar strategy can be used to determine if it’s true.

### Student Facing

Write three equations to complete the True or False task. Be prepared to share your reasoning for the equations.

• _______________________
• _______________________
• _______________________

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• Choose small groups to share that had different reasons for their equations.
• Ask students to share their completed True or False and ask the class to share reasons for the equations.
• As each group shares, continually ask others in the class if they agree or disagree and the reasons why.

## Lesson Synthesis

### Lesson Synthesis

“What were the most important things about your equations you had to consider as you created your True or False? Why were these things important?” (I needed to find equations where you could figure out whether or not it was true with a mental strategy. So the numbers had to be related in a nice way and there needed to be some structure to help see if the expressions were equal or not, without finding the sums or differences.)

## Cool-down: Reflection (5 minutes)

### Cool-Down

For access, consult one of our IM Certified Partners.