Lesson 11

The purpose of this warm-up is to elicit student ideas for how a tape diagram could be used to represent a Take From problem involving lengths. This will be useful when students solve story problems in the context of length in a later activity. While students may notice and wonder many things about these images, the connections students make between the image, the tape diagram, and the equation are the important discussion points.

• 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 do you think the diagram and the ribbon could have in common?” (Maybe the 54 is cm or in, so 16 is how much of the ribbon is being cut off.)
• “What could the question mark represent?” (The longer part of the ribbon after it is cut. It represents the value of \(54-16\).)

The purpose of this activity is for students to solve Take From problems and make sense of tape diagrams that represent this problem type. Students use the diagram to make sense of the context and help guide their calculations as they solve the problem (MP2).

• Groups of 2
• Give students access to base-ten blocks.
• Display the image.
• “What do you notice? What do you wonder?”
• 1 minute: quiet think time
• 1 minute: partner discussion
• Share responses.
• “These girls from India are wearing saree dresses. Sarees are usually worn by women and girls and are made by wrapping 5–7 meters of fabric in a special way.”
• “Many sarees are made from brightly colored silk, which is a soft fabric.”
• “Sometimes when sarees get too small or are worn out, they are cut into strips to make saree ribbon.”

• “Priya and her friends are planning to make saree silk ribbon necklaces. They want to make sure they get their measurements correct.”
• “Read the problem. Then look at Andre’s diagram and discuss the first two questions with a partner.”
• 1 minute: independent work time
• 3–4 minutes partner discussion
• “Work independently to find the unknown value and compare your answer with your partner. Don’t forget to include the units.”
• 4–5 minutes: independent work time
• 2 minutes: partner discussion

If students add the known values instead of subtract, consider asking:

• “What is happening in this story?”
• “Should your answer be a length that is longer or shorter than 44 inches?”

• “How did the tape diagram help you think about what you needed to do to find the unknown value?” (The diagram shows that 18 was being taken away, so I decided to subtract 18 from 44.)

The purpose of this activity is for students to solve Take From problems within 100 with the unknown in all positions. Students label tape diagrams and use them to make sense of the story problems before solving them (MP2). In Difference Unknown and Change Unknown problems, students may not be able to anticipate whether the unknown length will be longer or shorter than the length of the part they know. It is okay if they do not accurately label the smaller part of the tape diagram with the smaller length as long as they are accurately making sense of the problem.

Students are encouraged to use the Three Reads routine as a strategy for making sense of and persevering in solving problems (MP1).

• Groups of 2
• Give each group access to base-ten blocks.
• “The kids in Priya’s class are all making saree silk ribbon necklaces, so they are cutting ribbons to share with each other.”

• “With your partner, you are going to read each story 3 times. First, read to understand what is happening in the story. Second, read to understand the math. Think about what is known and unknown. And third, read to make a plan by completing the diagram.”
• “Work together to label each diagram, and then find the unknown values on your own using any strategy that makes sense to you.”
• “After each problem, compare with your partner to see if you agree.”
• 10 minutes: partner work time
• Monitor for students who recognize they need to add to find the answer for the third problem.

If students subtract to find the solution for the Start Unknown problem, consider asking:

• “How long is the ribbon that Priya has left? Do you think her ribbon should have been longer or shorter than 38 inches before she cut it?”
• “Does your solution show that Priya’s ribbon was longer or shorter before she cut it?”
• “How could you find out how long the ribbon was before any length was cut off?”

• Invite selected students to share how they solved the last problem.
• “What was different about the last problem?” (Even though it was about cutting ribbon, I found the answer by adding.)