Lesson 10

This warm-up prompts students to compare four representations. The reasoning here prepares students to connect the previous multiplication work to the division work of this lesson. It gives students an opportunity to use precise terms such as “factors,” “product,” and “quotient” in making comparisons (MP6). During the synthesis, ask students to explain the meaning of any terminology they use.

• Groups of 2
• Display images and expression.
• “Escojan una que sea diferente. Prepárense para compartir por qué es diferente” // “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
• 1 minute: quiet think time

• “Discutan con su compañero cómo pensaron” // “Discuss your thinking with your partner.”
• 2-3 minutes: partner discussion
• Share and record responses.

• “En cada caso, ¿qué ecuación puede estar representada por el diagrama?” // “What equation can each diagram represent?” (The array represents \(4\times6=24\) because there are 4 rows of 6 dots, and there are 24 dots in the array. The area diagram could represent \(4\times7=28\) or \(28\div4=7\) since the sides are 4 and 7, and the area is 28. The tape diagram could represent \(24\div3={?}\) or \(3\times{?}=24\) because we know the total is 24 and there are 3 groups, but we don’t know how many are in each group.)

The purpose of this activity is for students to relate multiplication and division using a variety of representations. Students are given a card with a base ten diagram, tape diagram, area diagram, multiplication equation with a missing factor, or division equation. Students need to find the other student who has the card that matches their card. Each pair of cards includes a division equation. After students find the student with the matching card, they work together to create another diagram and a division situation that their cards could represent (MP2).

Here are images of the cards for reference:

• The blackline master has 24 cards. Copy and cut enough cards so that each student can have one card.

• Groups of 2
• Give one card to each student.
• Display an example of each type of representation shown on the cards (division equation, multiplication equation with missing factor, area diagram, tape diagram, and base ten diagram).
• “En el calentamiento vimos que diagramas y ecuaciones distintos pueden representar la misma situación. Por ejemplo: 4 grupos de 6 o 4 veces 6” // “We saw in the warm-up that different diagrams and equations can represent the same situation such as 4 groups of 6 or 4 times 6.”
• “Piensen qué situación o qué cantidades representan sus tarjetas. Luego, piensen cuál podría ser otra representación de la situación o de las cantidades” // “Think about what situation or quantities your card represents. Then, think about what another representation of the situation or quantities might look like.”
• 1 minute: quiet think time

• “Busquen un estudiante que tenga una tarjeta que represente la misma situación o las mismas cantidades de su tarjeta. Prepárense para explicar por qué sus tarjetas van juntas” // “Find a student whose card represents the same situation or quantities as your card does. Be ready to explain why your cards belong together.”
• 2-3 minutes: partner work time
• Invite 2-3 groups to share their matches and how they knew they matched.
• “Con su compañero, hagan un póster que incluya sus tarjetas y un diagrama y una situación que le correspondan a su ecuación de división. Vamos a usarlos para hacer un recorrido por el salón, así que organicen su trabajo para que los demás puedan entenderlo” // “Work with your partner to create a poster that includes your cards and a diagram and situation that match your division equation. We’ll use these for a gallery walk, so organize your work so others can understand it.”
• Give students glue or tape and tools for creating a visual display.
• 10-15 minutes: partner work time

• Display students' posters around the room.

The purpose of this activity is to reinforce students' understanding of the relationship between multiplication and division by examining different representations of that relationship.

• Keep posters from the previous activity displayed.

• Groups of 2

• Arrange for half of the groups to stand at their poster and answer questions while the other half visit their posters.
• 8–10 minutes: gallery walk
• Ask groups to switch roles after 4–5 minutes.

• See lesson synthesis.