Lesson 8
Compongamos decenas y centenas para sumar
Warm-up: Cuántos ves: Muchas decenas (10 minutes)
Narrative
The purpose of this How Many Do You See is to allow students to use grouping strategies to describe amounts represented with base-ten diagrams. Students look for and make use of structure (MP7) when they describe how many they see in terms of place value and how they mentally compose new units to name how many they see.
Launch
- Groups of 2
- “¿Cuántos ven? ¿Cómo lo saben?, ¿qué ven?” // “How many do you see? How do you see them?”
- Flash the image.
- 30 seconds: quiet think time
Activity
- Display the image.
- “Discutan con su pareja lo que pensaron” // “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Record responses.
- Repeat for each image.
Student Facing
¿Cuántos ves? ¿Cómo lo sabes?, ¿qué ves?
Student Response
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Activity Synthesis
- “¿En qué se parecieron las imágenes? ¿En qué fueron diferentes?” // “How were the images the same? How were they different?” (The first two had the same number of tens. I saw a group of three ones in each image. They each showed different values. The last image had more than 10 tens.)
- “¿Qué necesitarían hacer para mostrar el valor de la tercera imagen con la menor cantidad de bloques?” // “What would you need to do to show the value of the third image with the least amount of blocks?” (If you were using blocks, you could exchange 10 tens for 1 hundred. Use one hundred instead of 10 tens.)
Activity 1: Comparemos las sumas (20 minutes)
Narrative
The purpose of this activity is for students to find the sum of a two-digit and a three-digit number when both a ten and a hundred are composed when adding by place. They find the value of each sum in a string of expressions, where the first addend remains the same, but the second addend changes. These variations result in composing a ten, composing a hundred, and composing both a ten and a hundred.
Although the number choices encourage students to consider adding by place, they may use any method that makes sense to them when finding the value of each sum. Students share their thinking with a partner and explain why their method works (MP3). The lesson synthesis focuses on students sharing and making sense of strategies based on place value and using place value language to describe what they noticed about the sums and composing larger units (MP7).
This activity uses MLR8 Discussion Supports. Advances: conversing
Supports accessibility for: Language, Organization, Social-Emotional Functioning
Required Materials
Materials to Gather
Launch
- Groups of 2
- Give students access to base-ten blocks.
Activity
- “Encuentren el valor de cada suma. Muestren cómo pensaron. Usen diagramas, símbolos u otras representaciones. Si les ayuda, usen bloques en base diez. Después de que encuentren cada suma, comparen su método con el de su pareja” // “Find the value of each sum. Show your thinking using diagrams, symbols, or other representations. Use base-ten blocks if it helps. After you find each sum, compare your method to your partner’s.”
- Display sentence frames to support students when they compare methods:
- “Tenemos la misma suma, pero...” // “We have the same sum, but ...”
- “Tenemos diferentes sumas porque...” // “We have different sums because …”
- “Lo que pensamos se parece porque...” // “Our thinking is the same because …”
- “Lo que pensamos es diferente porque...” // “Our thinking is different because …”
- 12 minutes: partner work time
- Monitor for students who find the sum of \(273 + 88\) by grouping by place value using base-ten blocks or a base-ten diagram.
Student Facing
Encuentra el valor de cada suma. Muestra cómo pensaste. Si te ayuda, usa bloques en base diez.
- \(273 + 18\)
- \(273 + 81\)
- \(273 + 88\)
- ¿En qué se parecieron y en qué fueron diferentes las sumas?
Student Response
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Activity Synthesis
- Invite previously identified students to share their work for \(273 + 88\).
- “¿Cómo encontró _____ la suma?” // “How did _____ find the sum?”
- “¿En qué se pareció y en qué fue diferente lo que hicieron para encontrar el valor de cada suma?” // “What was the same and different about what you did to find the value of each sum?” (We had to make a ten and a hundred for the last one. For the first 2, we just had to make a ten or a hundred.)
Activity 2: Diferentes formas de mostrar cómo pensaste (15 minutes)
Narrative
Required Materials
Materials to Gather
Launch
- Groups of 2
- Give students access to base-ten blocks.
Activity
- “A Priya y a Lin les pidieron que encontraran el valor de \(358 + 67\). Ellas representaron cómo pensaron de diferentes formas. ¿En qué se parecen y en que son diferentes sus representaciones?” // “Priya and Lin were asked to find the value of \(358 + 67\). They represented their thinking in different ways. What is the same and different about their representations?” (Priya used the diagrams and wrote equations. Priya circled the new units she made in her diagram. Lin wrote the units and added them first. They found the same value.)
- 5 minutes: partner discussion
- “¿En qué parte ven que cada estudiante compone nuevas unidades?” // “Where do you see each student composing new units?” (Priya circled 10 tens to show a new hundred and circled 10 ones to show a new ten. Lin added the units and has 11 tens and 11 ones. 11 tens is the same as 1 hundred and 1 ten and 11 ones is the same as 1 ten and 1 one.)
- 30 seconds: quiet think time
- 1 minute: partner discussion
- Share and record responses.
- “Ahora van a encontrar el valor de \(546 + 86\) y a representar cómo pensaron” // “Now you are going to find the value of \(546 + 86\) and represent your thinking.”
- 5 minutes: independent work time
- Monitor for students who represent place value strategies using:
- base-ten blocks or base-ten diagrams
- equations in unit form
- equations with only numbers
Student Facing
-
A Priya y a Lin les pidieron que encontraran el valor de \(358 + 67\).
El trabajo de Priya
El trabajo de Lin
¿Qué observas sobre su trabajo? ¿En qué se parecen y en qué son diferentes sus representaciones? Prepárate para explicar lo que pensaste.
- Encuentra el valor de \(546 + 86\).
Muestra cómo pensaste. Si te ayuda, usa bloques en base diez.
Student Response
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Advancing Student Thinking
Activity Synthesis
- Invite previously identified students to share their work.
- “¿En qué se parecen estas representaciones? ¿En qué son diferentes?” // “What’s the same across these representations? What is different?” (They all got the same answer. They all made a ten and a hundred. Some used words, some used diagrams, and some used only numbers.)
Lesson Synthesis
Lesson Synthesis
“Hoy aprendieron que algunas veces tienen que formar una decena y una centena cuando suman. También vimos que hay diferentes formas de representar cómo pensamos” // “Today you learned that sometimes you need to make a ten and a hundred when adding. We also saw that there are different ways to represent our thinking.”
“¿Cuáles representaciones les parecieron más útiles para mostrar cómo pensaron? ¿Por qué?” // “Which representations do you find most helpful to show your thinking? Why?”
Cool-down: Forma decenas y centenas (5 minutes)
Cool-Down
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