Lesson 11

Distintas formas de sumar y de restar

Warm-up: Conversación numérica: Usemos decenas (10 minutes)

Narrative

This Number Talk encourages students to think about decomposing the subtrahend to get to a ten when subtracting. For example, in the first problem it is helpful to think about 6 as 2 + 4. This way you can subtract 2 to get to 30, and then subtract 4 from 30. The understandings elicited here will be helpful later in the lesson when students represent sums and differences on a number line by jumping to the nearest ten.

In reasoning together about the number line representation, and connecting the strategy of making a ten to jumping to the nearest ten, students need to be precise in their word choice and use of language (MP6).

Launch

• Display one expression.
• “Hagan una señal cuando tengan una respuesta y puedan explicar cómo la obtuvieron” // “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

Activity

• Record answers and strategy on a number line.
• Keep expressions and work displayed.
• Repeat with each expression.

Student Facing

Encuentra mentalmente el valor de cada expresión.

• $$32 - 6$$

• $$43 - 8$$

• $$51 - 5$$

• $$52 - 7$$

Activity Synthesis

• “Para encontrar el valor de $$52 - 7$$, algunos estudiantes descompusieron el 7 para que fuera más fácil llegar a una decena. ¿De qué manera esta representación de recta numérica se conecta con esa estrategia?” // “For $$52 - 7$$, some students decomposed the 7 to make it easier to get to a ten. How does this number line representation connect to that strategy?”
• Draw a number line showing 52 represented with a point, a jump of 2, and then a jump of 5.

Activity 1: Comparemos métodos (15 minutes)

Narrative

The purpose of this activity is for students to use a number line to compare different methods for getting to a ten when subtracting a two-digit number from a two-digit number. Students analyze and try a method where they add or subtract the tens first and then decompose the ones to reach a multiple of 10. Diego's method is an example of this for $$53 - 29$$.

They analyze a method that begins by decomposing the ones being added or subtracted to get to a multiple of ten. In the synthesis, students discuss each method and which one they prefer. Tyler’s method is an example of this for $$53 - 29$$.

Action and Expression: Internalize Executive Functions. Check for understanding by inviting students to explain where the parts of the problem can be found in their work with the number line. For example, “¿En qué parte del trabajo de Diego/Tyler está el 29? ¿Dónde está el 53? ¿Encontraron la diferencia? ¿Dónde está?” // “Where is the 29 in Diego/Tyler’s work? Where is the 53? Did you find the difference? Where is it?” Use different colored markers or pencils to represent the numbers and keep this visible throughout the activity.
Supports accessibility for: Memory, Organization, Conceptual Processing

Required Materials

Materials to Copy

• Number Line to 100

Launch

• Groups of 2
• Give each student a copy of the blackline master.
• “Diego y Tyler encontraron el valor de $$53 -29$$ en la recta numérica. Cada estudiante representó cómo encontró la diferencia. Expliquen el método de cada estudiante” // “Diego and Tyler found the value of $$53 -29$$ on the number line. Each student represented how they found the difference. Explain each student’s method.”
• 1 minute: quiet think time
• 2 minutes: partner discussion
• Share responses.
• “¿En qué se parecen y en qué son distintas las formas en que Diego y Tyler encontraron la diferencia?” // “What is the same and what is different about how Diego and Tyler found the difference?” (Diego started by subtracting the tens and Tyler started by subtracting the ones. They both decomposed the ones to make subtracting the ones easier. They both thought of a way they could decompose to get to a ten.)

Activity

• “Ahora tendrán la oportunidad de probar los métodos de Diego y de Tyler. Encuentren el valor de cada expresión. Usen la recta numérica para representar los métodos” // “Now, you will have the opportunity to try out Diego and Tyler’s methods. Find the value of each expression. Represent the methods on the number line.”
• 8 minutes: independent work time
• 2 minutes: partner discussion

Student Facing

Diego y Tyler encontraron el valor de $$53 - 29$$. Este es su trabajo.

El método de Diego:

El método de Tyler:

1. Usa el método de Diego para encontrar el valor de $$82 - 35$$.

2. Usa el método de Tyler para encontrar el valor de $$66-28$$.

Activity Synthesis

• Invite students to share how they used each Tyler and Diego's methods.
• “¿Qué método encontraron más útil, el de Tyler o el de Diego? Expliquen” // “Did you find Tyler’s method or Diego’s method more helpful? Explain.”
• “¿Hay otra forma de usar la recta numérica para mostrar cómo encontrar más fácilmente el valor de $$53-29$$ completando una decena?” // “Is there another way we could use the number line to show a way to make it easier to find the value of $$53-29$$ by getting to a ten?”
• If not suggested by students, ask: “¿Cómo podemos empezar con 29 y usar un método como el de Diego o el de Tyler?” // “How could we start with 29 and use a method like Diego or Tyler’s?” (Start with 29, jump over 1 to get to 30, then it's easy to see all you need to do is jump 23 to get to 53.)
• Record the method and display throughout the lesson for students to reference.
• “¿En qué se parece este método al método de Diego o al de Tyler? ¿En qué es diferente?” // “How is this method the same as Diego or Tyler’s? How is different?”

Activity 2: Más métodos (20 minutes)

Narrative

The purpose of this activity is for students to continue to develop fluency with addition and subtraction within 100. The numbers in each expression encourage the use of the methods students analyzed in the previous activity. However, students should be encouraged to use whatever method makes the most sense to them. Partners work together to create a visual display to share their representations of 1 sum and 1 difference including number lines and do a gallery walk to compare their representations to others (MP2).

This activity uses MLR7 Compare and Connect. Advances: representing, conversing

Required Materials

Materials to Gather

Materials to Copy

• Number Line to 100

Launch

• Groups of 2
• Give each student a copy of the blackline master and access to base-ten blocks.
• Assign Partner A and Partner B.

Activity

• “Encuentren el valor de la suma y el de la diferencia. Pueden continuar probando el método de Diego o el de Tyler, o pueden usar cualquier otra forma que tenga sentido para ustedes. Si les ayuda, usen la recta numérica para mostrar cómo pensaron” // “Find the value of the sum and difference. You may continue to try Diego or Tyler's method or use any other way that makes sense to you. Use the number line if it helps to show your thinking.”
• 5 minutes: independent work time
• 3 minutes: partner discussion

Student Facing

Compañero A

1. Encuentra el valor de $$59 + 27$$.

2. Encuentra el valor de $$65 - 18$$.

Compañero B

1. Encuentra el valor de $$68 - 39$$.

2. Encuentra el valor de $$22 + 49$$.

Student Response

Students can use base-ten blocks or diagrams to find the value of each expression. Consider pairing these students with partners who use methods like those students analyze Activity 1. Consider asking:

• “¿Cómo descompusiste o compusiste una decena con los bloques? Viendo las expresiones, ¿cómo puedes saber si necesitas descomponer o componer una decena?” // ”How did you decompose or compose a ten with the blocks? How can you tell by looking at the expression that you would need to decompose or compose a ten?”
• “¿En qué se parece esto a la manera como tu compañero usó la recta numérica? ¿En qué es diferente?” // ”How is this like how your partner used the number line? How is it different?”

Activity Synthesis

MLR7 Compare and Connect
• “Con su compañero, hagan una representación visual que muestre cómo pensaron para encontrar el valor de 1 suma y de 1 diferencia” // “Create a visual display that shows your thinking for 1 sum and 1 difference with a partner.”
• “Deben incluir una recta numérica para por lo menos una expresión de su presentación. Incluyan diagramas en base diez u otros detalles para ayudarle a otros a entender cómo pensaron ustedes” // “You should include a number line for at least one expression in your display. You may want to include base-ten diagrams or other details to help others understand your thinking.”
• 5 minutes: partner work time
• 6 minutes: gallery walk
• “¿En qué se parecen y en qué son diferentes las representaciones?” // ”What is the same and what is different between the representations?”

Lesson Synthesis

Lesson Synthesis

Display students’ work from the second activity showing the same sum or difference represented with a base-ten diagram and a number line.

“Cuando sumamos o restamos hasta 100, podemos usar distintos métodos dependiendo de los números que hay en el problema que estamos resolviendo. La recta numérica puede ser útil para mostrar cómo pensamos” // “When we are adding and subtracting within 100, we may use different methods based on the numbers in the problem we’re working on. The number line can be helpful to show our thinking.”

“Para mostrar cómo pensaron, ____ usó diagramas en base diez y ____ usó una recta numérica. ¿Qué conexiones podemos hacer entre estas representaciones y la manera como ellos encontraron las sumas y las diferencias?” // “____ used base ten diagrams and ____ used a number line to show their thinking. What connections can we make between these representations and how they found sums and differences?”