Lesson 21
Solve Problems Using the Four Operations
Warmup: Notice and Wonder: Apples Again (10 minutes)
Narrative
The purpose of this warmup is to elicit the idea that many different questions could be asked about this situation, which will be useful when students solve problems in a later activity. While students may notice and wonder many things about this situation, the various questions that could be asked about the situation are the important discussion points.
Launch
 Groups of 2
 Display the situation.
 “What do you notice? What do you wonder?”
 1 minute: quiet think time
Activity
 “Discuss your thinking with your partner.”
 1 minute: partner discussion
 Share and record responses.
Student Facing
What do you notice? What do you wonder?
A farmer picked some apples.
Some of the apples are packed into boxes and some are not.
Student Response
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Activity Synthesis
 “What does it mean that some apples are packed into boxes and some are not?” (Some apples are in groups and some apples are just loose in one big group.)
 “What questions could we ask about this situation?” (How many apples did the farmer pick? How many boxes had apples in them? How many apples were in each box?)
Activity 1: Apple Adventure (20 minutes)
Narrative
The purpose of this activity is for students to think about what they need to know to solve twostep word problems. Students choose numbers that make sense together to complete the problem from the warmup. They articulate relationships between the quantities in the problem to justify their number choices. If students quickly find a combination of numbers that work, encourage them to see if there are other possibilities or to write a completed situation with the numbers they have chosen.
Students who do not choose a matching set of numbers quickly make sense of and persevere in solving the problem as they consider the relationship between the different quantities and the restrictions that puts on which numbers can describe the situation (MP1).
Supports accessibility for: Conceptual Processing, Organization
Launch
 Groups of 2 and 4
 Keep the situation from the warmup displayed.
 “Suppose the boxes the farmer packs are all the same size.”
Activity
 “A list of numbers is shown in the activity. Work with your partner to choose 4 numbers that would make sense together in this situation. If you find one combination of numbers that works, you can look for other combinations.”
 8–10 minutes: partner work time
 Groups of 4
 “Share with another group of students how your number choices make sense.”
 2–3 minutes: smallgroup discussion
Student Facing
A farmer picked some apples. Some of the apples are packed into boxes and some are not.
From the list, choose 4 numbers that would make sense together in this situation. Write your choices in the table. Be ready to explain how your numbers make sense together.
total number of apples  number of apples not in boxes  number of boxes  number of apples in each box 

Student Response
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Activity Synthesis
 Display this partially completed row in the table, such as:
total number of apples number of apples not in boxes number of boxes number of apples in each box 200 152 8  “If you were given this information, how would you find the number of apples in each box?” (I could subtract 152 from the total of 200 and divide the answer by 8.)
 “What equation can we write to represent the situation in this example? Let’s use a letter for the quantity that we don’t know.”
 1 minute: quiet think time
 Record equations that students wrote, for instance:
 \((200  152) \div 8 = n\)
 \(8 \times n + 152 = 200\)
 \(152 + 8 \times n = 200\)
Activity 2: Apple Days (15 minutes)
Narrative
The purpose of this activity is for students to represent a problem with an equation using a letter for the unknown quantity and solve the problem. Students should be encouraged to use whatever strategy or representation makes sense to them.
The synthesis focuses on student thinking for the first problem. Students might represent the situation with:
 a tape diagram or an area diagram
 an equation that uses multiplication
 an equation that uses division
If students struggle to get started on a problem, encourage them to create a drawing or diagram. Students may also represent the situation or solve the problem before writing an equation if that makes more sense to them. While this activity is focused on independent practice, students can discuss with a partner if needed.
Advances: Reading, Representing
Launch
 “Now we’re going to solve some problems about an event at the apple orchard.”
 Survey the class on their familiarity with events or activities at farms or orchards.
 If students are familiar, ask: “What are some things you might see or do at a farm or an orchard?”
 If students are unfamiliar, share some activities that might take place at an orchard. Consider showing some images of a market or an event at an orchard.
 1–2 minutes: partner discussion
 Share responses.
Activity
 8–10 minutes: independent work time
 Monitor for:
 a variety of strategies students use to solve or represent each problem
 lingering questions or common misconceptions and how students overcome them
 Consider asking:
 “How could you represent that?”
 “What information do you know that might help you?”
Student Facing
Tyler and Clare are helping with a festival at an apple orchard.

Tyler is stacking apples to sell at the event. There are 85 apples for his display. He has already made 5 rows of 10 apples. How many apples are left?
 Write an equation with a letter for the unknown quantity to represent this situation.
 Solve the problem. Explain or show your reasoning.

Clare is helping sell baked goods at the event. A customer buys 8 brownies that cost \$3 each. Clare adds that money to the cash box and now there is \$125 in the cash box. How much money was in the cash box before that purchase?
 Write an equation with a letter for the unknown quantity to represent this situation.
 Solve the problem. Explain or show your reasoning.

The market at the orchard had 200 jars of applesauce for sale. At the end of the event, 184 jars had been sold. The rest of the jars were shared equally among 4 people who work there. How many jars of applesauce did each person get?
 Write an equation with a letter for the unknown quantity to represent this situation.
 Solve the problem. Explain or show your reasoning.
Student Response
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Advancing Student Thinking
If students say they aren’t sure how to get started on the problem, consider asking: “What is the problem about?” and “How could you represent the problem?”
Activity Synthesis
 Select students who used different strategies to share their responses and reasoning for each problem.
Lesson Synthesis
Lesson Synthesis
“What did you find most challenging about solving these problems?” (There’s a lot of information to keep track of. I have a hard time understanding how all the numbers are related to each other.)
“What ideas do you have for overcoming those challenges?” (drawing a diagram and labeling it with the numbers that we know, reading the problem carefully and acting it out, organizing what we know and don't know in a table)
“How did you know if your answer made sense?” (I put the number back into the problem and did the math to check if it makes sense. I made an estimate first so that I had an idea of about how large the answer should be.)
Cooldown: Apples at the Farm Stand (5 minutes)
CoolDown
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Student Section Summary
Student Facing
In this section, we divided larger numbers and solved problems that involve division.
We used baseten blocks, diagrams, and equations to represent the numbers we divided. To help us divide, we used what we know about place value, equal groups, and the relationship between multiplication and division.
For example, here are some ways we could find the value of \(52 \div 4\):
 Put 5 tens and 2 ones into 4 equal groups.
 Think about how many groups of 4 are in 52.
10 groups of 4 make 40.
3 groups of 4 make 12.
13 groups of 4 make 52.
 Use multiplication facts and write equations.
\(4 \times 10 = 40\)
\(4 \times 3 = 12\)
\(10 + 3 = 13\)
\(4 \times 13 = 52\)
At the end of the section, we used all four operations to solve problems.