# Lesson 17

Use the Four Operations to Solve Problems

## Warm-up: True or False: Multiply by 10 (10 minutes)

### Narrative

The purpose of this True or False is to elicit strategies and understandings students have for multiplying one-digit whole numbers by multiples of 10. The reasoning students do here helps to deepen their understanding of the associative property as they decompose multiples of ten to make multiplying easier.

### Launch

• Display one statement.
• “Give me a signal when you know whether the statement is true and can explain how you know.”
• 1 minute: quiet think time

### Activity

• Share and record answers and strategy.
• Repeat with each statement.

### Student Facing

Decide if each statement is true or false. Be prepared to explain your reasoning.

• $$2 \times 40 = 2 \times 4 \times 10$$
• $$2 \times 40 = 8 \times 10$$
• $$3 \times 50 = 15 \times 10$$
• $$3 \times 40 = 7 \times 10$$

### Activity Synthesis

• “How can you justify your answer without finding the value of both sides?”
• “Who can restate _____’s reasoning in a different way?”
• “Does anyone want to add on to _____’s reasoning?”
• “Can we make any generalizations based on the statements?”

## Activity 1: Questions about a Situation (15 minutes)

### Narrative

The purpose of this activity is for students to consider a situation and think about all the mathematical questions they could ask about it. This gives students a chance to make sense of the situation before they are asked to solve problems. Students might choose to write a multiplication equation like $$(g \times 6) + 94 = 142$$. Acknowledge that this represents this situation, but focus the discussion in the synthesis on division to connect to the work in the next section.

### Launch

• Groups of 2
• “This situation is about planning for a party. What are some things that you have to think of when you plan for a party?” (Making enough food. Places for people to sit or hang out. Activities for people to do.)
• 1 minute: quiet think time
• Share responses.

### Activity

• 3–5 minutes: partner work time
• Share and record responses.
• Display: “How many guests fit at each table in Room B?” or circle the question if mentioned by a student.
• “Now work with your partner to answer this question.” (I found $$142 - 94$$ to find out how many guests were in Room B. There were 48 guests and 6 tables, I put the same amount of guests at each table and there were 8 guests at each table.)
• 3–5 minutes: partner work time

### Student Facing

There are 142 guests at a party. All the guests are in 2 rooms. Room A has 94 guests. Room B has 6 tables that each have the same number of guests. There are 4 pieces of silverware and 1 plate for each guest.

### Activity Synthesis

• “What information did we use in the problem?” (The number of guests at the party. The number of guests in Room A. The number of tables in Room B.)
• “How could we record an equation with a letter for the unknown quantity that would represent the problem? Explain your reasoning.” ($$(142 - 94) \div 6 = g$$. We had to find $$142 - 94$$ to find out how many people were in Room B. We had to divide the number of people in room B by 6 to find out how many guests were at each table. The g represents how many guests fit at each table in Room B.)
• Display: $$(142 - 94) \div 6 = g$$
• If students don’t use parentheses, say: “In this equation, we can use parentheses to show that we subtracted first.”
• “The parentheses show us that the subtraction is done first in the equation to represent the problem. Keep this in mind as you work on the next activity.”

## Activity 2: Party Problems (20 minutes)

### Narrative

The purpose of this activity is for students to solve two-step word problems using all four operations. Students should be encouraged to solve the problem first or write the equation first, depending on their preference. Encourage students to use parentheses if needed to show what is being done first in their equations.

When students make sense of situations to solve two-step problems they reason abstractly and quantitatively (MP2).

MLR5 Co-Craft Questions. Keep books or devices closed. Display only the problem stem, without revealing the question. Give students 2–3 minutes to write a list of mathematical questions that could be asked about this situation, before comparing their questions with a partner. Invite each group to contribute one written question to a whole-class display. Ask the class to make comparisons among the shared questions and their own. Reveal the intended questions for this task and invite additional connections.
Engagement: Develop Effort and Persistence. Some students may benefit from feedback that emphasizes effort and time on task. For example, check in and give feedback after each party planning problem.
Supports accessibility for: Attention

### Required Materials

Materials to Gather

Materials to Copy

• Centimeter Grid Paper - Standard

• Groups of 2

### Activity

• “Work independently to solve these problems and write an equation with a letter for the unknown quantity to represent each situation. You can choose to solve the problem first or write the equation first.”
• 5–7 minutes: independent work time
• “Share your solutions and your equations with your partner. Also, tell your partner if you think their solutions and equations make sense or why not.”
• 5–7 minutes: partner discussion

### Student Facing

For each problem:

a. Write an equation to represent the situation. Use a letter for the unknown quantity.

b. Solve the problem. Explain or show your reasoning.

1. Kiran is making paper rings each day to decorate for a party. From Monday to Thursday he was able to complete 156 rings. Friday, Kiran and 2 friends worked on making more rings. Each of them made 9 more rings. How many rings did they make over the week?
2. Mai has 168 muffins. She put 104 of the muffins in a basket. She packed the rest of the muffins into 8 boxes with the same number of muffins. How many muffins were in each box?
3. There are 184 cups on a table. Three tables with 8 people at each table come up to get drinks and each use a cup. How many cups are on the table now?

### Student Response

If students don't write a single equation to represent both steps of the problem, consider asking:
• “What equations did you write for each part of the problem?”
• “How could you combine your equations into one equation that would represent the problem?”

### Activity Synthesis

• For each problem have a student share their equation and discuss how it represents the problem.
• “Where do we see ______ from the problem in the equation?”
• “What information from the situation did we need to solve and write our equation?”
• “How are parentheses used in the equation?”

## Lesson Synthesis

### Lesson Synthesis

“Today we used multiplication, division, addition, and subtraction to solve two-step problems. What were some strategies that were helpful as you solved these types of problems?” (It was helpful to represent the situation with a drawing to help me think about what was happening in the situation. It helped to think about the information that I needed. It helped to think about how to represent each part of the problem before I put it all together into an equation.)

## Student Section Summary

### Student Facing

In this section, we learned how to multiply single-digit numbers by multiples of ten. We used strategies to multiply teen numbers and numbers greater than 20.

$$4 \times 30$$
$$7 \times 13$$
$$3 \times 28$$