Lesson 16

The purpose of this True or False is to elicit strategies and understandings students have for composing or decomposing numbers in different ways. These understandings will be helpful later when students decompose tens and hundreds when they subtract. In this activity, students look for and make use of structure of base-ten units (MP7) when they explain why statements are true or false.

• Display one statement.
• “Hagan una señal cuando sepan si la afirmación es verdadera o no, y puedan explicar cómo lo saben” // “Give me a signal when you know whether the statement is true and can explain how you know.”
• 1 minute: quiet think time

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

• “¿Cómo podemos cambiar la primera afirmación para que sea verdadera?” // “How could we change the first statement to make it true?” (You could change 3 tens to 2 tens on the right side. You change the left side so it has 14 ones too. You could change the left side so it has 4 tens.)

The purpose of this activity is for students to interpret and connect different representations for methods that decompose to subtract by place. They also make sense of Jada's choice to use a number line to find the value of \(402-298\) and critique her reasoning . Students then find the value of the difference in any way that makes sense to them to explain why they agree or disagree with Jada's reasoning (MP3).

This activity uses MLR8 Discussion Supports. Advances: listening, conversing

• Groups of 2
• Give students access to base-ten blocks.
• Display Lin’s diagram.
• “Tómense un minuto para darle sentido a la resta de Lin” // “Take a minute to make sense of Lin’s subtraction.”
• 1–2 minutes: quiet think time
• “Discutan con su compañero el trabajo de Lin” // “Discuss Lin’s work with your partner.”
• 1–2 minutes: partner discussion
• Share and record responses.
• Highlight that a ten was decomposed and discuss student ideas about the numbers being subtracted.

• “Jada y Lin encontraron el valor de \(582 - 145\). Con su compañero, comparen el trabajo de Lin y el de Jada. Después, completen el trabajo de Jada para encontrar el valor de \(582 - 145\)” // “Jada and Lin both found the value of \(582 - 145\). Work with your partner to compare Lin and Jada's work. Then complete Jada's work to find the value of \(582 - 145.\)”
• 3–5 minutes: partner work time
• “Jada encontró el valor de \(402 - 298\) con un método distinto. Con su compañero, denle sentido a lo que pensó Jada. Discutan si están de acuerdo o en desacuerdo con la razón que dio Jada para escoger este método” //  “Jada found the value of \(402 - 298\) with a different method. Work with your partner to make sense of Jada's thinking. Discuss if you agree or disagree with Jada’s reason for why she chose this method.”

MLR8 Discussion Supports

• Display sentence frames to support partner discussion:
  • “Estoy de acuerdo porque . . .” // “I agree because . . .”
  • “Estoy en desacuerdo porque . . .” // “I disagree because . . . ”
• 7–8 minutes: partner work time
• Monitor for students who share why they agree with some (or all) of what Jada says and those that disagree and use a diagram to show decomposing to subtract by place.

If students say they agree with Jada’s thinking about decomposing to find the value of \(402-298\), consider asking:

• “¿Con qué partes del razonamiento de Jada estás de acuerdo y por qué?” // “What parts of Jada's reasoning do you agree with and why?”
• “¿Puedes usar bloques en base diez para mostrar cómo podría ella restar usando el valor posicional?” // “Can you use base-ten blocks to show how she could subtract by place?”

• “¿Cómo funciona el método de Jada para encontrar el valor de \(402-298\)?” // “How does Jada’s method for finding the value of \(402-298\) work?”
• Record student explanation using a series of equations. (\(298+2= 300\), \(300+100 = 400\), \(400+2 = 402\), \(2+100+2 = 104\))
• “¿Por qué piensan que Jada usó esta estrategia?” // “Why do you think Jada used this strategy?” (She thought you couldn’t decompose. She noticed 298 is close to 300 and 402 is close to 400.)
• “¿Están de acuerdo con Jada en que no pueden descomponer 402?” // “Do you agree with Jada that you can't decompose 402?” (I agree that there are no tens so it’s hard to subtract ones right away. I disagree that you can’t decompose. You can decompose a hundred first to get tens, then decompose tens to get ones.)
• Display the sentence frames to support the whole-group discussion.
• If time, select previously identified students to share how they decomposed to find \(402-298\).

The purpose of this activity is for students to choose methods flexibly for finding the value of differences. Students might subtract by place, count on, or make an easier problem. There is no right answer to which method should be used for each problem. Students should choose a method that makes sense to them and justify their choice (MP3).

• Groups of 2
• Give students access to base-ten blocks.
• “Hemos aprendido cómo descomponer unidades en base diez para restar usando el valor posicional y distintas formas de representarlo. También hemos aprendido otros métodos para restar. Los usamos cuando tienen sentido para nosotros o cuando son adecuados para los números de una expresión” // “We’ve learned how to decompose units to subtract by place and different ways to represent that. We’ve also learned other methods for subtracting. We use them when they make sense to us or when they make sense for the numbers in an expression.”

• “Encuentren el valor de cada expresión usando un método que tenga sentido para ustedes. Tendrán la oportunidad de compartir su trabajo con los demás” // “Find the value of each expression using a method that makes sense to you. You’ll have a chance to share your work with others.”
• 6 minutes: independent work time
• Monitor for expressions that most students find the same way and expressions that many students find in different ways.
• “Busquen a un compañero que haya encontrado el valor de _____ de la misma manera que ustedes” // “Find a partner who found the value of _____ the same way as you.”
• 1–2 minutes: partner discussion
• “Ahora, busquen a un compañero que haya encontrado el valor de _____ de una manera distinta a la de ustedes. Compartan cómo pensaron” // “Now find a partner that found the value of _____ in a different way than you. Share your thinking.”
• 2–3 minutes: partner discussion
• Repeat for additional expressions as desired.

If students use the same method for each problem, ask students to think about how they could use Jada’s way to find the value of \(701 - 599\). Consider asking:

• “¿Qué observaste acerca de los números de esta expresión que hace que sea más fácil usar la estrategia de Jada?” // “What do you notice about the numbers in this expression that makes it easier to use Jada’s way?”
• “¿En qué otras expresiones ves que podrías probar la estrategia de Jada?” // “What other expressions do you see where you might try Jada’s way?”

• Have 3–4 students share a method or representation that someone they talked to shared.
• “¿Qué métodos o representaciones quieren seguir probando?” // “What methods or representations do you want to try more?”