Lesson 15

Ways to Solve Problems and Show Solutions

Warm-up: Number Talk: Divide by 8 (10 minutes)

Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for dividing by 8. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to divide when solving problems.

When students use multiplication facts they know to divide and then add or remove groups of 8 for facts they are less familiar with, they look for and make use of structure (MP7).

Launch

  • Display one expression.
  • “Give me a signal when you have an answer and can explain how you got it.”
  • 1 minute: quiet think time

Activity

  • Record answers and strategy.
  • Keep expressions and work displayed.
  • Repeat with each expression.

Student Facing

Find the value of each expression mentally.

  • \(80 \div 8\)
  • \(72 \div 8\)
  • \(96 \div 8\)
  • \(96 \div 4\)

Student Response

For access, consult one of our IM Certified Partners.

Activity Synthesis

  • “How did knowing \(80 \div 8\) help you find the other values?”
  • Consider asking:
    • “Who can restate _____’s reasoning in a different way?”
    • “Did anyone have the same strategy but would explain it differently?”
    • “Did anyone approach the problem in a different way?”
    • “Does anyone want to add on to _____’s strategy?”

Activity 1: A Day at the Fair (25 minutes)

Narrative

The purpose of this activity is for students to put together their knowledge of problem solving, measurement topics (time, weight, and liquid volume), and equal groups to solve a variety of problems about a day at the fair. After solving problems, students create a poster about the day.

Students should feel free to display their work in creative ways while making sure that the mathematical thinking on each problem is made clear. If they want, students could create individual posters rather than working with a partner.

Throughout the activity, students reason abstractly and quantitatively as they interpret the different problems and situations, represent them, and find solutions (MP2).

Required Materials

Launch

  • Groups of 2
  • “We’re going to solve some problems about a day at the fair. What are some things you could do during a day at the fair?” (go on rides, walk around, eat fair food, look at some of the animals)
  • 30 seconds: quiet think time
  • Share responses.
  • Give each group tools for creating a visual display.

Activity

  • “Work with your partner to solve four problems about a day at the fair. You’ll get to choose some of the activities at the fair.”
  • “Then, create a poster that shows your mathematical reasoning and solutions for each problem.” 
  • “Feel free to be creative in how you put your ideas on your poster, but make sure to organize them so that they are easy for others to understand.”
  • 25 minutes: partner work time

Student Facing

You spent a day at the fair. Solve four problems about your day and create a poster to show your reasoning and solutions.

  1. You arrived at the fair!

    Entry to the fair is $9 a person. You went there with 6 other people. How much did it cost your group to enter the fair?

  2. How did you start your day? (Choose one.)

    A giant pumpkin being weighed.

    You arrived at the giant pumpkin weigh-off at 11:12 a.m. and left at 12:25 p.m. How long were you there?
     

    You spent 48 minutes at the carnival and left at 12:10 p.m. What time did you get to the carnival?

    Ferris wheel.
  3. What was next? (Choose one.)

    You visited a barn with 7 sheep. The sheep drink 91 liters of water a day, each sheep drinking about the same amount. How much does each sheep drink a day?
     

    You visited a life-size sculpture of a cow made of butter. The butter cow weighs 273 kilograms, which is 277 kilograms less that the actual cow. How much does the actual cow weigh?

    Cow made of butter.
  4. Before you went home . . .

    You stopped for some grilled corn on the cob. On the grill, there were 54 ears of corn arranged in 9 equal rows. How many ears of corn were in each row?

Student Response

For access, consult one of our IM Certified Partners.

Activity Synthesis

  • Display the student posters around the room.

Activity 2: A Day at the Fair Gallery Walk (10 minutes)

Narrative

The purpose of this activity is for students to consider strategies different from their own (MP3) and aspects of student work that make mathematical ideas clear as they visit the posters created in the previous activity.

MLR7 Compare and Connect. Synthesis: After the Gallery Walk, lead a discussion comparing, contrasting, and connecting the different approaches. Ask, “What did the approaches have in common?”, “How were they different?”, “Why did the different approaches lead to the same outcome?” To amplify student language and illustrate connections follow along and point to the relevant parts of the displays as students speak.
Advances: Representing, Conversing
Action and Expression: Develop Expression and Communication. Synthesis: Identify connections between strategies that result in the same outcomes but use differing approaches.
Supports accessibility for: Conceptual Processing

Required Materials

Required Preparation

  • Display posters from the previous activity.

Launch

  • Groups of 2

Activity

  • Have half the students stand at their poster with their partner to share their ideas or answer questions as the other students visit their posters.
  • Have the other half of the class visit their classmates’ posters with their partner.
  • 5 minutes: partner work time
  • Switch student roles and repeat.

Student Facing

As you visit the posters with your partner:

  1. Look for a problem that was solved using a strategy that is different from yours. What made it different? Describe the strategy.
  2. Look for ways that your classmates made their thinking and the math work clear to you. Describe at least three things they did or showed on the posters.

Student Response

For access, consult one of our IM Certified Partners.

Activity Synthesis

  • “Today we created posters that put together a lot of the problem solving skills we have been learning all year.”

Lesson Synthesis

Lesson Synthesis

“What are some strategies or representations you saw that you might use in your own problem solving in the future?”

“What were some aspects of the posters you saw that helped make the math your classmates used clear for you?” (clear labels on diagrams that help me understand their thinking, organization of the algorithms they used, units on their answers)

Cool-down: Problem Solving Reflection (5 minutes)

Cool-Down

For access, consult one of our IM Certified Partners.

Student Section Summary

Student Facing

In this section, we solved all kinds of problems about time, weight, and liquid volume. We did so using addition, subtraction, multiplication, and division, as well as different reasoning strategies.

Clare spent 48 minutes at the carnival. She left the carnival at 12:10 p.m. What time did she get to the carnival?

Subtraction problem for figuring out how long Clare spent at the carnival.

A cow made of butter weighs 273 kilograms. That is 277 kilograms less that the actual cow. How much does the actual cow weigh?

Addition. Two-hundred seventy-three plus two-hundred seventy-seven equals five-hundred fifty.

A grower used 84 liters to water their pumpkin seedlings. Each seedling gets 12 liters. How many seedlings were there?

Diagram. Rectangle partitioned into 2 parts. Total length, 84. First part labeled 12. Second part has dashed outline, not labeled.