Lesson 14

This warm-up prompts students to carefully analyze and compare base-ten diagrams. The activity also enables the teacher to hear the terminologies students know and how they talk about composing and decomposing numbers with hundreds, tens, and ones.

• Groups of 2
• Display the image.
• “Escojan uno 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 lo que pensaron” // “Discuss your thinking with your partner.”
• 2–3 minutes: partner discussion
• Share and record responses.

• “¿Qué tienen en común A, B y C?” // “What do A, B, and C have in common?” (They all show 125.)
• “¿Por qué querrían representar 125 con 12 decenas en lugar de 1 centena y 2 decenas?” // “Why would you want to represent 125 with 12 tens instead of 1 hundred and 2 tens?” (If you are going to subtract more than 2 tens.)

The purpose of this activity is for students to use their understanding that numbers can be decomposed in different ways to subtract within 1,000. They use what they know about place value to make sense of two different ways for finding the same difference (MP7). They describe how it is helpful to represent the number with enough tens and ones to subtract, rather than needing to redraw or exchange blocks to represent decomposing a unit. They also learn that sometimes it may be necessary to decompose a hundred and a ten to subtract within 1,000.

• Groups of 2
• Give students access to base-ten blocks.
• “Tyler y Clare usaron cada uno diagramas en base diez para encontrar el valor de \(244-67\). Tyler y Clare estuvieron de acuerdo en que debían descomponer unidades en base diez antes de restar” // “Tyler and Clare each used base-ten diagrams to find the value of \(244-67\). Tyler and Clare both agreed that they should decompose units before they subtract.”
• “Examinen los primeros pasos de Tyler y Clare. ¿Qué hicieron? ¿Qué creen que estaban pensando?” // “Look at Tyler and Clare’s first steps. What did they do? What do you believe they were they thinking?”
• 1–2 minutes: quiet think time
• 2 minutes: partner discussion
• Share responses.

• “Con su compañero, completen la forma de encontrar el valor de Tyler y de Clare. Cuando terminen, comparen los diagramas” // “Work with your partner to complete Tyler’s way and Clare’s way. When you finish, compare the diagrams.”
• 4 minutes: partner work time

If students do not see that Tyler’s first step and Clare’s first step show the same number, prompt students to use base-ten blocks or a base-ten diagram to show 244. Consider asking:

• “Si tu representación muestra 244, ¿qué unidad en base diez descompuso Tyler?” // “If your representation shows 244, what unit did Tyler decompose?”
• “Si tu representación muestra 244, ¿qué unidad en base diez descompuso Clare?” // “If your representation shows 244, what unit did Clare decompose?”

• Display student work that shows using Tyler’s way and Clare’s way to find the difference.
• “¿En qué se parecían el método de Tyler y el de Clare? ¿En qué eran diferentes?” // “How were Tyler’s way and Clare’s way the same? How were their methods different?” (They both show decomposing a ten and a hundred to subtract. They both show the same difference. Tyler decomposed a hundred first, then a ten. Clare decomposed a ten first, then a hundred.)

The purpose of this activity is for students to think about the numbers and attend to the value of the digits in subtraction expressions before beginning to subtract (MP7). Students determine whether or not they will decompose to subtract by place. They also determine whether they will decompose more than one unit. Students find the value of different expressions by using any method that makes sense to them.

• Groups of 2
• Give students access to base-ten blocks.
• Draw or display the base-ten diagram for 341.
• “Andre quiere usar un diagrama para encontrar el valor de \(341-68\). Él dice que va a descomponer una decena y una centena para restar. ¿Por qué piensan que dijo eso?” // “Andre wants to use a diagram to find the value of \(341-68\). He says he will decompose a ten and a hundred to subtract. Why do you think he said that?” (If you take tens from tens, there’s not enough to take 6 tens from 4 tens. If you take ones from ones, there are not enough ones to take 8 ones from 1 one.)
• 1 minute: quiet think time
• 1 minute: partner discussion
• “Si Andre sabe que va a descomponer una centena y una decena, ¿de qué otra forma podría haber empezado su diagrama?” // “If Andre knows he will decompose a hundred and a ten, what’s another way he could have started his diagram?” (He could have started with 3 hundreds, 3 tens, and 11 ones. He could have started with 2 hundreds, 14 tens, and 1 one. He could have started with 2 hundreds, 13 tens, and 11 ones.)
• 1 minute: quiet think time
• 1 minute: partner discussion
• Share and record responses.

• “Andre solo quiere utilizar un diagrama para restar usando el valor posicional si va a descomponer una unidad en base diez” // “Andre only wants to use a diagram to subtract by place if he will decompose a unit.”
• “Con su compañero, clasifiquen las expresiones de Andre en 3 grupos. Examinen los números de cada expresión y decidan si descompondrían 2 unidades en base diez, 1 unidad en base diez o ninguna unidad en base diez para restar usando el valor posicional. Explíquenle a su compañero cómo lo saben. Usen bloques en base diez o hagan sus propios diagramas para ayudarse. Después, escriban la expresión en la columna correspondiente” // “Work with your partner to sort Andre's expressions into 3 groups. Look at the numbers in each expression and determine if you would decompose 2 units, 1 unit, or 0 units to subtract by place. Explain to your partner how you know. Use base-ten blocks or create your own diagrams to help. Then, write the expression in the appropriate column.”

MLR8 Discussion Supports

• Display sentence frames to support students when they explain their strategy and listen to others:
  • “Observé _____, entonces pensé que . . .” // “I noticed ____ so I think that . . . ”
  • “Te escuché decir . . .” // “I heard you say . . .”
  • “Estoy de acuerdo porque . . .” // “I agree because . . .”
  • “Estoy en desacuerdo porque . . .” // “I disagree because . . .”
• 8 minutes: partner work time

• Display a completed chart from student responses.
• Ask students to choose an expression and explain how they know it belongs in that column.
• “Cuando encontraron la diferencia, ¿usaron el mismo método para las 3 expresiones? ¿Cómo escogieron su método?” // “When you were finding the difference, did you use the same method for all 3 expressions? How did you choose your method?” (I used the blocks when I needed to decompose, but I didn’t need to when I didn’t decompose so I just wrote equations. Since I knew before starting when I was going to decompose, I knew I didn’t need the blocks for one of them,)