Lesson 15
Ways to Solve Problems and Show Solutions
Warmup: 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
Materials to Gather
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.

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?

How did you start your day? (Choose one.)
You arrived at the giant pumpkin weighoff 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?

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 lifesize 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?

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.
Advances: Representing, Conversing
Supports accessibility for: Conceptual Processing
Required Materials
Materials to Gather
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:
 Look for a problem that was solved using a strategy that is different from yours. What made it different? Describe the strategy.
 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)
Cooldown: Problem Solving Reflection (5 minutes)
CoolDown
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?
A cow made of butter weighs 273 kilograms. That is 277 kilograms less that the actual cow. How much does the actual cow weigh?
A grower used 84 liters to water their pumpkin seedlings. Each seedling gets 12 liters. How many seedlings were there?