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Activity 1

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

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Activity Narrative

The purpose of this activity is for students to match tape diagrams, equations, and descriptions of situations, and to explain the connection to model with mathematics (MP4). The situations share the same context and numbers. Students consider how different unknown quantities are reflected in the diagrams, depending on what's happening in the situations.

When students relate the quantities and relationships in situations to the equations and diagrams that represent them, they reason quantitatively and abstractly (MP2).

Launch

Groups of 3

Activity

Part A

“Each member of your group should pick 1 of the situations to read silently. Make sense of your situation and be ready to explain to your group what is happening in your situation.”
2 minutes: quiet think time
“Take turns sharing your understanding of the situation you chose.”
“When each person has shared, work together to match each situation to a diagram. Be prepared to explain how you know they match.”
5–7 minutes: small-group work time
Display the 3 diagrams together.
“Turn and talk with your group. How are the diagrams alike? How are they different?” (They have the same numbers. They have the same structure, with a long rectangle and 2 smaller parts. A different number is missing in each diagram. The moves around.)
2–3 minutes: small-group discussion
Share responses.
“How did you connect the diagrams to the situations?” (The location of the unknown shows what we are missing in the situation. The first diagram matches the situation in which we don’t know Mai's starting number of beads. The second diagram matches the situation in which we are missing the total number of beads. The last diagram matches the situation in which we don’t know how many beads are in the 2 packs Mai bought.)
2–3 minutes: small-group discussion
Share responses.

Part B

“Now you are going to match an equation to each situation from Part A. The letter in each equation represents the unknown quantity in the situation.”
3–5 minutes: small-group work time
Monitor for groups who can articulate connections between each equation and the corresponding situation. Identify students to share during the Activity Synthesis.

In this problem, each situation has an unknown quantity. In the diagrams and in the equations, each unknown quantity is represented by the letter n.

Part A

Match each diagram with a situation. Be ready to explain your reasoning.

Situation 1: Mai had 104 beads. She buys 2 packs of beads. Now she has 124 beads. How many beads were in each pack?
Situation 2: Mai had some beads. She buys 2 packs of beads. Each pack has 10 beads in it. Now she has 124 beads. How many beads did Mai have before she bought the packs?
Situation 3: Mai had 104 beads. She buys 2 packs of beads. Each pack has 10 beads in it. How many beads does Mai have now?

<p>Diagram. One rectangle split into 3 parts. One part labeled <em>n</em>. The other two parts labeled 10. Total length, 124.</p> — A

<p>Diagram. One rectangle split into 3 parts. One part labeled 104. The other two parts labeled 10. Total length, <em>n</em>.</p> — B

<p>Diagram. One rectangle split into 3 parts. One part labeled 104. The other two parts, labeled <em>n</em>. Total length, 124.</p> — C

Part B

Match each equation with a situation in Part A.

Student Response

to access Student Response.

Advancing Student Thinking

Activity Synthesis

For each situation, select a previously identified student to share how the matching equation makes sense.

Activity 2

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

None

Activity Narrative

Previously, students matched diagrams and equations to situations with an unknown quantity. Here they generate such equations, using a letter for the unknown quantity, solve problems, and explain how they know their answers make sense. Students should be encouraged to solve, using any strategy that feels comfortable to them. If not yet addressed, mention that any letter can be used for the unknown quantity in their equation. Make the point also that the same letter can represent different unknown quantities in different equations.

While this activity is focused on independent practice, encourage students to discuss the problem with a partner if needed. Though the task asks students to write an equation first, students may complete the task in any order that makes sense to them.

Students reason abstractly and quantitatively when they write an equation that represents the situation (MP2). They also practice making sense of a problem and its solution in terms of the context (MP1).

MLR5 Co-Craft Questions: Keep books or devices closed. Display only the problem stem, without revealing the question, and ask students to write down possible mathematical questions that could be asked about the situation. Invite students to compare their questions before revealing the task. Ask, “What do these questions have in common? How are they different?” Reveal the intended questions for this task and invite additional connections.
Advances: Reading, Writing

Engagement: Develop Effort and Persistence. Differentiate the degree of difficulty or complexity. Some students may benefit from starting with a familiar example, or an example with more accessible values, before working independently on the three parts to the activity.
Supports accessibility for: Social-Emotional Functioning, Conceptual Processing

Launch

Groups of 2
“Stones are sometimes used to play games. One of the games that can be played with stones is mancala (mahn-KAH-lah). In mancala, stones are moved from pit to pit, and each player tries to capture the other player's stones. The picture shows a game of mancala in progress.”
“Now we're going to solve a problem about the stones in a game of mancala.”
“What are some ways you will be able to determine if your answer, makes sense?” (I can estimate an answer using rounding. I can think about the size of the numbers in the problem.)
Share and record responses.

Activity

“Take some independent time to work on this problem. You can choose to solve the problem first or write the equation first.”
5–7 minutes: independent work time
Monitor for different ways students:
- Write an equation.
- Represent the problem, such as by using a tape diagram.
- Decide their answer makes sense, such as by thinking about the situation or by rounding.

Kiran is setting up a game of mancala (mahn-KAH-lah). He has a jar of 122 stones.

From the jar, he takes 3 stones to put in each of the 6 pits on his side of the board.

How many stones are in the jar now?

Write an equation to represent the situation. Use a letter for the unknown quantity.
Solve the problem. Explain or show your reasoning.
Explain how you know your answer makes sense.

Activity Synthesis

Invite students to share the equations they wrote.
Discuss differences in equations students wrote. Consider asking: “_____ wrote _____, and _____ wrote _____. How are their equations alike and different?” (I used a different letter for my unknown. I wrote instead of .)
Invite several students to share different strategies used to solve the problem. Feature a student-drawn tape diagram, if possible.
Consider asking:
- “Did anyone solve the problem in a different way?”
- “Did anyone use a tape diagram to solve the problem?”
- “How did you know if your answer made sense?”

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Lesson 19

Situations and Equations

Warm-up

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Activity 1

Standards Alignment

Building On

Addressing

3.OA.D.8

Building Toward

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Activity 2

Standards Alignment

Building On

Addressing

3.OA.D.8

Building Toward

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Activity Synthesis

Lesson Synthesis

Standards Alignment

Building On

Addressing

Building Toward

3.OA.D.8

Student Response

Advancing Student Thinking