Lesson 23

Números de dos dígitos en nuestro mundo (optional)

Warm-up: Exploración de estimación: Frijoles (10 minutes)

Narrative

The purpose of an Estimation Exploration is to practice the skill of estimating a reasonable answer based on experience and known information.

Launch

• Groups of 2
• Display the image.
• “El grupo encerrado en un círculo muestra 10 frijoles” // “The circled group shows 10 beans.”
• “¿Qué estimación sería muy alta?, ¿muy baja?, ¿razonable?” // “What is an estimate that’s too high?” “Too low?” “About right?”
• 1 minute: quiet think time

Activity

• “Discutan con su pareja lo que pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Record responses.

Student Facing

¿Cuántos frijoles hay?

Escribe una estimación que sea:

muy baja razonable muy alta
$$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$ $$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$ $$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$

Activity Synthesis

• Select one “about right” estimate.
• “Usando decenas y unidades, ¿de qué formas podemos pensar en este número?” // “What are some ways we can think about this number using 10s and 1s?”

Activity 1: Contemos los objetos (15 minutes)

Narrative

The purpose of this activity is for students to have an opportunity to apply their place value understanding to estimate quantities of objects and accurately count familiar objects.

Required Materials

Materials to Gather

Required Preparation

• Each group of 2 needs a bag of a collection of small objects.

Launch

• Groups of 2
• Display for all to see approximately 15–25 beans or other small objects.
• “¿Cuántos objetos piensan que hay en este montón?” // “How many objects do you think are in this pile?”
• 1 minute: partner discussion
• Share responses.
• “¿Cómo podemos encontrar cuántos hay exactamente?” // “How could we find out exactly?” (Count them.)

Activity

• “¿Cuántos objetos hay en 2 puñados? Hagamos un experimento” // “How many objects are in 2 handfuls? Let's do an experiment.”
• Give each group a bag of objects.
• “Cada uno agarre un puñado. Estimen cuántos objetos agarraron ambos en total. Después, encuentren exactamente cuántos objetos tienen” // “Take turns and grab a handful. Estimate how many objects you both grabbed altogether. Then find out how many you have exactly.”
• “Van a hacer este experimento tres veces” // “You will do this experiment three times.”
• 5 minutes: partner work time
• Monitor for students who:
• count by ones
• group the objects into groups of 10 and then count the tens and ones

Student Facing

Experimento 1: ¿cuántos objetos hay en 2 puñados?
Escribe una estimación que sea:
muy baja razonable muy alta
$$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$ $$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$ $$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$

Ahora, encuentra el número exacto. ____________

Experimento 2: ¿cuántos objetos hay en 2 puñados?
Escribe una estimación que sea:

muy baja razonable muy alta
$$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$ $$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$ $$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$

Ahora, encuentra el número exacto. ____________

Experimento 3: ¿cuántos objetos hay en 2 puñados?
Escribe una estimación que sea:

muy baja razonable muy alta
$$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$ $$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$ $$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$
Ahora, encuentra el número exacto. ____________

Activity Synthesis

• Invite previously identified students to share.
• “¿Sus estimaciones mejoraron con la práctica?” // “Did your estimates get better with practice?”
• “¿Cómo les ayudó organizar sus objetos a contar?” // “How did organizing your objects help you to count?”
• “Imaginen que tengo 72 objetos. ¿Cuántos tendrían si tienen 10 menos que yo? ¿Y si tuvieran 10 más?” //  “Imagine I have 72 objects. How many would you have if you have 10 fewer than I do? What if you had 10 more?”
• “Si tuvieran 72 objetos, ¿cómo se pueden organizar en montones de 10 y unidades? ¿Hay otras formas?” // “If you had 72 objects, how could they be arranged in piles of 10 and ones? Are there any other ways?" (7 tens and 2 ones, 6 tens and 12 ones)

Activity 2: Clasificación de tarjetas por cantidades (20 minutes)

Narrative

The purpose of this activity is for students to consider the number of objects in a group and represent numbers in as many ways as possible. Students should be encouraged to think about the number in terms of tens and ones. Students sort pictures based on the number of objects they estimate to be in each group.

Students should be encouraged to estimate quantities rather than try to count them. Some students may not have a reasonable estimate, but can be successful in this activity if they categorize the photograph based on whatever estimate they consider is “about right.”

MLR8 Discussion Supports. Students should take turns sorting cards into the different categories and explaining their reasoning to their partner. Display the following sentence frames for all to see: “Observé _____, entonces asocié . . .” // “I noticed _____, so I matched . . . .” Encourage students to challenge each other when they disagree.
Engagement: Develop Effort and Persistence. Chunk this task into more manageable parts. Give students a subset of the cards to start with and introduce the remaining cards once students have completed their initial set of matches.
Supports accessibility for: Attention, Organization

Required Materials

Materials to Copy

• Estimating Quantities Card Sort, Spanish

Required Preparation

• Create a set of cards from the blackline master for each group of 2.

Launch

• Groups of 2
• Give each group a set of cards.

Activity

• “Hay una imagen diferente en cada tarjeta. Clasifiquen las tarjetas según el número de objetos que piensan que hay en cada imagen” // “There is a different picture on each card. Sort the cards based on the number of objects you think are in each picture.”
• 8 minutes: partner work time
• As students work, consider asking:
• “¿Qué estimación sería muy baja?, ¿razonable?, ¿muy alta?” // “What is an estimate that is too low, about right, and too high?”

Student Facing

1. Estima cuántas cosas hay en las imágenes y clasifícalas según la cantidad que ves.
Clasifícalas en estos grupos.
1. Menos de 20
2. De 20 a 50
3. Más de 50
2. Selecciona 1 imagen de cada grupo.
Muestra de todas las formas que puedas el número de elementos que piensas que hay en la imagen.

Menos de 20

De 20 a 50

Más de 50

Activity Synthesis

• Invite students to share what object they selected and its representation.
• Record responses.
• Select two estimates that have the same digit in the ones place.
• “¿Cómo sabemos cuál estimación es más grande?” // “How do we know which estimate is bigger?”
• Highlight the use of ones and tens.

Lesson Synthesis

Lesson Synthesis

“Hoy hicimos estimaciones y contamos grupos de objetos. ¿Cómo les ayudó su comprensión de las decenas y las unidades de los números de dos dígitos en su trabajo?” // “Today we made estimates and counted groups of objects. How did you use your understanding of tens and ones in two-digit numbers to help you with your work?”