Lesson 14

This warm-up prompts students to carefully analyze and compare equations. In addition to calculating the value of each expression, students also think about the structure of each equation, including both the operations and the numbers (MP7).

• 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

• “Discuss your thinking with your partner.”
• 2–3 minutes: partner discussion
• Share and record responses.

• “Let’s find at least one reason why each one doesn’t belong.”

The purpose of this activity is to sort story problems with unknowns in all positions. Students sort the story problems by whether they are addition or subtraction problems. Some stories include actions that would be represented by one operation, but may be solved using the opposite operation. Students may sort these problems into either category as long they can explain how they sort.

For example, consider this Take From, Start Unknown story problem:

Clare has some stickers.

She gives 9 of them to her friends.

She has 5 stickers left.

How many stickers did Clare have to start with?

In the last lesson, students related this type of problem to a subtraction equation (\( ? - 9 = 5\)). This equation shows a way to use equations to represent the actions in the story. However, students may also think of an equation that shows how they would solve the problem (\(5 + 9 = ?\)). This is discussed in the activity synthesis to prepare students to identify more than one equation to match these story problems in the next activity.

• Create a set of cards from the blackline master for each group of 2.

• Groups of 2
• Give each group a set of cards and access to connecting cubes in towers of 10 and singles.
• “We have been solving stories about people doing different arts and crafts. Making collages is another popular craft.”
• Display the word “collage” for all to see and invite students to share what they know about making a collage.
• If needed ask, “What materials can you use to make a collage?” (stickers, pictures, stamps, markers, glitter, glue)

• “Today we are going to look at lots of stories about students who made collages. Sort the story problems by whether they are addition or subtraction. Be ready to explain how you know so that others can understand.”
• 10 minutes: partner work time
• Monitor for two groups who put the same story problem in different categories.

• Display the problems that students sorted into different groups (for example, A1, A5 or A6).
• “How is this an addition story problem? How is this a subtraction story problem?” (To solve card A1, I can think about how many pictures to add to 8 to get to 11, or I can think \(11 - 8\) to find how many pictures there are.)
• Repeat with other problems as time permits.

The purpose of this activity is to match equations to the story problems from the previous activity. Each story has several equations listed, two of which match the story. Students are encouraged to find both equations; however, it is more important that students can explain how an equation represents what is happening in the story, or how it is used to solve the story. In the launch, students make sense of a familiar diagram to encourage them to use objects or drawings to represent the story if it will help them find the matching equations.

In order to match stories with equations, students reason abstractly and quantitatively (MP2) as they interpret both the numbers and the operations in the equations in terms of a context.

• Groups of 2
• Give students access to connecting cubes in towers of 10 and singles.
• Display the diagram and read the first story problem. Do not display the equations.
• “How does the diagram represent the story problem?” (The eight white cubes show the pictures of people. The three blue cubes were added to get to a total of 11. So the three blue cubes show the pictures of animals.)
• 1 minute: quiet think time
• 1 minute: partner discussion
• “Which equations match the story?”
• Display the equations.
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Monitor for students who chose the second and third equations.
• Invite students to share.
• If needed: “How does the diagram match the equation?”
• “There is an addition and subtraction equation that can match this problem.”

• Read the task statement.
• 10 minutes: partner work time

• Display the problem about Noah and Tyler and a tower of 6 cubes and a tower of 16 cubes.
• “Use the cubes to explain how we can use addition to solve this problem.”

• Repeat for subtraction.