Lesson 19

This warm-up prompts students to make sense of a problem before solving it, by familiarizing themselves with a context and the mathematics that might be involved. Students observe images that show three ways of making a T shape using sticky notes, a context they will see in the first activity.

This prompt gives students opportunities to look for structure (MP7)—specifically, the number and orientation of sticky notes of which each T shape is composed—and make use of it to solve problems later. 

• 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.

• “All three Ts are made of the same number of sticky notes. Do the Ts have the same width and height?” (No)
• “Why might that be?” (The sticky notes have a longer side and a shorter side, and are not all oriented the same way.)

This optional activity prompts students to analyze a design problem that involves fractional measurements. Students determine which of the three designs they saw in the warm-up would fit on a folder that is 9 inches wide and 12 inches tall. To do so, they find the heights and widths of each design using addition, subtraction, multiplication, or a combination of operations.

• Each group needs 12 small sticky notes measuring 1\(\frac{7}{8}\) by 1\(\frac{3}{8}\) inches.

• Groups of 2–4
• Read the task together as a class.
• “What do you think the problem is asking? What questions do you need answered before working on it?”
• 1 minute: group discussion
• Share responses. Clarify any confusion before students begin the task.

• “Work independently on the task for about 8–10 minutes. Then, discuss your thinking with your group.”
• 10 minutes: independent work time
• 5 minutes: group discussion

Students may perform correct calculations and obtain fractions greater than 1 for the results but are not sure how to compare them to 9 and 12. Consider asking them how many eighths are in 1, 2, 3, and so on, and to extend the pattern to find out how many eighths are equivalent to the width and height of the folder.

• Invite a group to share their response and reasoning on each design. Display their reasoning or record it for all to see.
• Ask others if they agree and if approached it the same way.
• Explain to students that they will now verify their responses. Assign one design for each group to verify.
• Give 12 small sticky notes (measuring \(1\frac{7}{8}\) by \(1\frac{3}{8}\)) to each group. Ask students to use the sticky notes to create the design.
• Next, give each group an inch ruler and ask them to measure if their design is less than 9 inches wide and less than 12 inches tall.

This optional activity offers students to interpret and solve problems involving fractional measurements and operations of fractions in the context of distances on a map. First, students examine the measurements on the map and use them to answer questions. Next, they interpret given expressions and consider what the expressions might represent in the situation. Finally, they write a new problem based on the given quantities and information. The work here prompts students to reason quantitatively and abstractly (MP2).

This activity uses MLR6 Three Reads. Advances: reading, listening, representing

• Groups of 2

MLR6 Three Reads

• Display only the problem stem, without revealing the question(s).
• “We are going to read this problem 3 times.”
• 1st Read: “Jada and Noah’s class are hiking at a park. Here is a map of the trails. The length of each trail is shown.”
• “What is this situation about?”
• 1 minute: partner discussion
• Listen for and clarify any questions about the context.
• 2nd Read: “Jada and Noah’s class are hiking at a park. Here is a map of the trails. The length of each trail is shown.” (Display the trail map.)
• “Name the quantities. What can we count or measure in this situation?”
• 30 seconds: quiet think time
• 2 minutes: partner discussion
• Share and record all quantities.
• Reveal the question(s).
• 3rd Read: Read the entire problem, including question(s) aloud.
• “What are some strategies we can use to solve this problem?”
• 30 seconds: quiet think time
• 1–2 minutes: partner discussion

• “Work independently on the task for 10 minutes. Then, discuss your responses and complete the last problem with your partner.”
• 10 minutes: independent work time
• 3–4 minutes: group work time

• Invite 2–3 students to share their responses to the last two problems.

In this optional activity, students hone the skills they have learned in this unit: multiplying a fraction by a whole number, adding and subtracting fractions with the same denominator (including mixed numbers), and adding tenths and hundredths. Students are each given a fractional expression. They evaluate the expression, find a classmate whose expression is different but has the same value (verifying that this is indeed the case), and write a new expression that also has the same value. (See Student Responses for the matched expressions.)

In addition to evaluating expressions, students who have cards J, K, and L will also need to think about fractions that are equivalent to the value of their expression in order to find their matches. For instance, a student may reason that the value of card K is \(\frac{8}{10}\) or \(\frac{80}{100}\), but the match—card 2—shows \(\frac{4}{5}\). Consider using these expressions to differentiate for students who could use an extra challenge.

• Create one set of Match Cards for each group of 24 students.

• Give one card from the blackline master to each student.
• Tell students that they are to find the value of the expression, and then find a classmate in the class whose expression has the same value.
• “If your expression is labeled with a letter, your match is someone whose expression is labeled with a number. And vice versa.”
• “Once you’ve found your match, complete the rest of the task as directed in the task statement.”

• 7–8 minutes: independent work time on the first problem and then matching time
• 7–8 minutes: partner work time
• Give each group tools for creating a visual display. Ask them to show that their two expressions are a match, and that their new expressions also have the same value.

Students may not find a match for their expression because they are looking only for expressions with the same denominator. Remind them that fractions with different denominators can be equivalent.

• Ask students to display their work around the room.
• “Take a few minutes to walk around and look at the work of at least 3 other groups.”
• “As you study others’ work, pay attention to how the work is like and unlike yours.”
• 6–7 minutes: gallery walk
• “What is the same about the calculations that you saw? What is different?”
• 1 minute: quiet think time
• Discuss responses.