Lesson 22

The purpose of this warm-up is for students to look for and make use of structure in a set of related equations each having less information specified (MP7). The specific structure they might notice is that each expression on the left is equivalent to 9. Students may notice that the first two equations will result in the same thing, but there is flexibility with the end result of the last equation. The synthesis gives students an opportunity to make a story to represent the equation which they will continue to explore in the upcoming activities.

• Groups of 2
• Display the image.
• “What do you notice? What do you wonder?”
• 1 minute: quiet think time

• “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses. 

• “What goes in the boxes to make these equations true?”
• “What story might these equations match?”

The purpose of this activity is for students to write equations to represent the data they collected in Unit 1. Students can write any equation that makes sense to them.

This activity is intended to follow the last lesson of Unit 1. If that lesson was not completed, students can use sample data from the blackline master to complete this task.

When students use real-world data that they collect and determine ways of fitting their data into an existing mathematical model—put-together problems with unknowns in various positions—they model with mathematics (MP4).

To make this activity more challenging, students can share only their equation. Then their partner looks at the data and determines what story the writer intended to represent.

• Gather survey data from the last lesson in the previous unit, Animals in the Jungle.

• Groups of 2
• Give each group the data or posters from the previous unit or the sample data from the blackline master.
• “Take a look at the work you did a few weeks ago. Review what you investigated and what you discovered.”
• 1 minute: quiet think time
• “Discuss with a partner.”
• 2 minutes: partner discussion 

• Read the task statement.
• 5 minutes: independent work time
• “Take turns telling your partner a story problem that matches the equations you wrote.”
• 5 minutes: partner discussion 

• “What did you notice about making up a story problem for your equation? Were some easier than others? Why were they easier?”

The purpose of this activity is for students to use their data to generate questions and represent the answer using an equation. Then students take turns asking and answering each other’s questions.

Students need access to the survey data used in the previous activity.

• Groups of 2
• “We’re going to use our data again. This time we will create how many more and how many fewer questions about your data that you will ask your classmates to answer.”
• Read the task statement.
• “Use the categories in your survey data to complete the questions. You do not need to answer the questions."
• 3 minutes: independent work time

• "Take turns asking and answering questions with your partner. After asking your question, let your partner show their work in your book."
• 10 minutes: partner work time 

• "Clare asked, 'How many more students like pizza than burgers?' Her partner said six more people like pizza than burgers and wrote \(10 - 4 = 6\)."
• “How could we turn this ‘more than’ question into a ‘fewer than’ question? Does this change the equation you would write? Why or why not?"