Unit 4, Lesson 21
Solve Problems Using the Four Operations
Grade 3
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The purpose of this Warm-up 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.
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.
None
The purpose of this activity is for students to think about what they need to know to solve two-step word problems. Students choose numbers that make sense together to complete the problem from the Warm-up. 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 those relationships put on which numbers can describe the situation (MP1).
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 |
|---|---|---|---|
| total number of apples | number of apples not in boxes | number of boxes | number of apples in each box |
|---|---|---|---|
| 200 | 152 | 8 |
None
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 Activity Synthesis focuses on student thinking for the first problem. Students might represent the situation with:
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.
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?
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. Now there is $125 in the cash box. How much money was in the cash box before that purchase?
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?
We divided greater numbers and solved problems that involve division.
We used base-ten 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
10 groups of 4 make 40.
3 groups of 4 make 12.
13 groups of 4 make 52.
At the end of the section, we used all 4 operations to solve problems.
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