Lesson 5

This warm-up prompts students to carefully analyze and compare ways to represent multiplicative comparison.

• 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
• Record responses.

• “How does each representation show an unknown?”
• “What is the unknown in each representation? Explain how you know.”
• Record student responses.
• Consider asking students to create a situation that can be described by these representations.

The purpose of this activity is for students to represent and solve problems in context involving multiplicative comparison. The first 2 questions only require one operation, and the last one requires 2 operations. Students must interpret what values are unknown and make a plan for how to represent these values. Students may use one or more equations to represent the situation.

Students reason abstractly and quantitatively when they make sense of the given information and use it to find the different numbers of books (MP2).

This activity uses MLR6 Three Reads. Advances: Reading, Representing.

• Groups of 2

• “We are going to read this problem 3 times.”
• 1st Read: (First paragraph) “The book fair ordered 16 science experiment books and 6 times as many picture books.”
• “What is this story about?”
• 1 minute: partner discussion
• Listen for and clarify any questions about the context.

• 2nd Read: (First and second paragraphs) “For this year’s book fair, a school ordered 16 science experiment books and 6 times as many picture books.

  Last year, the school ordered 4 times as many picture books and 4 times as many science experiment books as they did this year.”

• “Name the quantities we can count in this situation.” (The number of books of each kind.)
• 30 seconds: quiet think time
• 1 minute: partner discussion 
• Share and record all quantities.
• Reveal the questions.
• 3rd Read: Read the entire problem, including the questions, aloud.
• “What are different ways we can solve these problems?”
• 30 seconds: quiet think time
• 1 minute: partner discussion

• “Solve the problems and share your thinking with a partner.”
• 2–5 minutes: independent work time
• 1–2 minutes: partner share time
• Monitor for students who write equations, including equations that have a symbol for the unknown value to solve each problem.

• “How is this problem different from other problems we solved in this unit?” (We had to do more than one calculation to solve the problem.)
• Select 1–2 students share their solutions and equations that show multiple steps.

The purpose of this activity is for students to apply what they learned about interpreting and representing multiplicative comparison to solve multi-step problems. They also make connections between strategies for solving problems. The synthesis of this activity makes use of the 5 Practices. As students are working, identify students who clearly represent using multiple steps to solve the problem and those who do not show every step yet share the same answers (MP6). Compare students' samples that show the same solution in different ways. Make connections between samples that clearly show multiplicative comparison more discretely and those that use more abstract representations.

• Groups of 2

• 5 minutes: independent work time
• “Compare strategies with a partner. You may decide to revise your thinking after talking with a partner.”
• As students are sharing with partners, identify students who noticed that they missed a step and revised their thinking to include the step after talking with a partner.
• 5 minutes: partner discussion
• Consider asking:
  • “What did you hear or see that made you decide to revise your thinking?” ( I noticed that I missed a step when I heard or saw what my partners shared about Tuesday and Thursday.)
  • “Would you be willing to share your revision in the class discussion? That was a great revision.”

• See lesson synthesis.