Lesson 18

The purpose of this warm-up is to elicit the idea that diagrams can represent many operations, which will be useful when students connect diagrams to situations and equations in a later activity. While students may notice and wonder many things about these images, what operations the diagrams could represent is the important discussion point.

• 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.

• “You’ve seen the first two types of diagrams before, when you represented addition situations and multiplication situations. We are going to make sense of the last type of diagram in today's lesson.”
• “What operations do you think could be represented in the last diagram?” (It could be multiplication and addition. Like you multiply 4 times 5 and add it to 142.)
• Consider asking:
  • “Could the last diagram represent addition and multiplication?”

The purpose of this activity is for students to connect two-step word problems, diagrams, and equations with a symbol for the unknown quantity. Interpreting and relating given representations prepare students to use these as tools for reasoning when they solve two-step word problems.

As students analyze written statements and other representations and make connections among them, they reason quantitatively and abstractly (MP2).

• Create a set of cards from the blackline master for each group of 4. 

• Groups of 4
• Distribute one set of pre-cut cards to each group of students.

• “This set of cards includes situations, equations, and diagrams. Work with your partner to find the cards that belong together because they represent the same situation. Be prepared to explain your decisions.”
• 8 minutes: small-group work time

• “Were there any cards whose placement you disagreed on? How did you come to an agreement?” (We went back and read the situation carefully together.)
• Choose a set of cards that belong together, such as B, D, and L, to discuss in detail. Ask, “How do the equation and diagram represent the situation?”
• Attend to the language that students use to describe their matches and the situations, equations, and diagrams, giving them opportunities to describe them more precisely.

The purpose of this activity is for students to solve one of the problems from the card sort in the previous activity and examine their classmates' solutions to other problems. Students work in groups to create a poster of their solution. As students visit the posters, they leave comments about how they know the solution on the poster makes sense. As students make comments on the work of others, they critique the reasoning of others (MP3).

• Groups of 4
• Assign each group a situation from the previous activity.
• Give each group tools for creating a visual display and sticky notes.

• “Now you are going to solve a problem from the card sort with your group.”
• “After you’ve solved the problem together, create a poster that shows your solution strategy.”
• 8–10 minutes: small-group work time

If students try to find exact answers to determine if their peers’ solutions make sense, consider asking:

• “What are some ways that we could determine if the solution makes sense without solving the problem?”
• “How could we use estimating to determine if the solution makes sense? How could we use rounding?”

• Display posters around the room. If more than one group solved the same problem, consider grouping their posters together.
• Give each student a sticky note.
• “As you visit the posters, leave a comment on one poster that explains how you know the answer makes sense.”