Lesson 3

Compongamos números de tres dígitos

Warm-up: Conversación numérica: Sumemos decenas y unidades (10 minutes)

Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for adding by place and composing a ten mentally. These understandings help students develop fluency and will be helpful later in this lesson when students describe base-ten representations by place and use the fewest number of base-ten blocks to represent a number.

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

• Keep expressions and work displayed.
• Repeat with each expression.

Student Facing

Encuentra mentalmente el valor de cada expresión.

• $$42+42$$
• $$21+63$$
• $$50+34$$
• $$48+36$$

Activity Synthesis

• “¿Qué observaron sobre las sumas?” // “What did you notice about the sums?” (The expressions were all different, but all had a value of 84.)
• “¿Cómo podrían explicar por qué la tercera y la cuarta expresión tienen el mismo valor?” // “How could you explain why the third and fourth expressions have the same value?” (You could take 2 ones from 36 and add it to 48 to make $$50+34$$.)

Activity 1: Clasifiquemos bloques por su valor (20 minutes)

Narrative

In this activity, students sort base-ten blocks and record the total number of blocks they have by the unit each block represents. Students work together to look for ways to compose larger units from smaller units in order to represent the same value with the fewest number of blocks (MP7). They represent composing a hundred by exchanging 10 ten blocks for a hundred block and represent composing a ten by exchanging 10 one blocks for a ten block. In the synthesis, students compare different ways that groups represent the total value which may include representing the value as a three-digit number.

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

Required Materials

Materials to Gather

Required Preparation

• Each group of 34 students will need a container with 2 hundreds, 28 tens, and 15 ones.
• Each group of 34 students will need access to additional base-ten blocks (hundred blocks and ten blocks).

Launch

• Groups of 34
• Give each group a container of blocks, access to base-ten blocks, and supplies for making a group display.

Activity

• “Su grupo tiene un recipiente con bloques en base diez” // “Your group has a container of base-ten blocks.”
• “Clasifiquen los bloques de acuerdo a la unidad que ellos representan y anoten en su hoja la cantidad de cada tipo de bloque” // “Sort the blocks by the unit they represent and record the number of each type of block on your paper.”
• “Descubran cómo pueden representar el mismo valor total usando el menor número posible de bloques” // “Work together to figure out how to represent the same total value using the fewest number of blocks possible.”
• 6 minutes: small-group work time

MLR7 Compare and Connect

• “Creen una presentación visual que muestre el valor total de los bloques. Incluyan detalles, como diagramas, marcas y números, para ayudar a los demás a entender lo que pensaron” // “Create a visual display to show the total value of the blocks. Include details such as diagrams, labels, and numbers to help others understand your thinking.”
• 25 minutes: group work time
• “A medida que miran las representaciones de otros grupos, miren las diferentes formas como los grupos muestran el valor. ¿Cuáles formas se parecen a las representaciones que hizo su grupo? ¿Cuáles son diferentes? ¿Cómo saben que representan el mismo valor?” // “As you look at other groups’ representations, look for different ways groups show the value. Which ways are the same as your group’s representation? Which ways are different? How do you know they represent the same value?”
• 5 minutes: gallery walk
• “Discutan en su grupo los ajustes que les gustaría hacerles a sus representaciones” // “Discuss any revisions you would like to make to your representations with your group.”
• 12 minutes: small-group work time
• Monitor for students who:
• create a base-ten diagram with the fewest amount of blocks represented
• write 4 hundreds, 9 tens, 5 ones
• write 495
• use an expression such as $$400 + 95$$ or $$400 + 90 + 5$$

Student Facing

1. Clasifiquen los bloques.

• Tenemos _________ centenas.

• Tenemos _________ decenas.

2. Representen el mismo valor total, pero usen el menor número posible de bloques.

• Tenemos _________ centenas.

• Tenemos _________ decenas.

3. Representen el valor de sus bloques usando diagramas en base diez, palabras o números.

Student Response

If students represent their number with 10 or more of any unit, consider asking:

• “¿Cómo sabes que has usado el menor número posible de bloques?” // “How do you know that you have used the fewest number of blocks possible?”
• “¿Cómo puedes combinar las decenas o las unidades para no tener que usar tantos bloques en base diez?” // “How can you combine the tens or ones so you don’t use as many of the base-ten blocks?”

Activity Synthesis

• Display previously identified students’ representations.
• “¿En qué se parecen y en qué son diferentes las formas en las que los grupos representaron el valor total de los bloques?” // “What is the same and what is different between the ways groups represented the total value of the blocks?” (They each show 4 hundreds, 9 tens, and 5 ones. Some just use diagrams, some use only digits, some use diagrams, numbers, and expressions.)

Activity 2: Lo mismo pero diferente (15 minutes)

Narrative

In this activity, students build on their work with base-ten blocks in previous activities to use base-ten diagrams to represent a value using the fewest number of each unit possible. They first interpret images of students’ representations of a number using base-ten blocks. When representing the same value, students may choose to draw the original representation and show composing units by circling groups of 10 tens or 10 ones. Others may choose other methods, such as circling or labeling the images to show ways to compose a larger unit or by using what they have learned about patterns in units from previous lessons. In the synthesis, students connect the 3 digits in a three-digit numeral to their representations (MP7).

Engagement: Develop Effort and Persistence. Chunk this task into more manageable parts. Check in with students to provide feedback and encouragement after each chunk. Consider asking specifically about the ones first to decide whether a group of ten can be made. Then move into the tens and make connections to the work done with the ones.
Supports accessibility for: Organization

Required Materials

Materials to Gather

• Groups of 2

Activity

• “Mai y Diego usaron bloques en base diez para representar números” // “Mai and Diego each used base-ten blocks to represent numbers.”
• “Anoten el número de centenas, decenas y unidades que usó cada estudiante” // “Record the number of hundreds, tens, and ones each student used.”
• “Encuentren una forma de representar el mismo valor usando el menor número posible de cada unidad en base diez. Usen un diagrama en base diez para representar el valor” // “Find a way to represent the same value with the fewest number of each unit possible and represent it using a base-ten diagram.”
• “Usen bloques si les ayuda” // “Use blocks if it helps.”
• “Con su compañero, descubran el valor total de los bloques” // “Together with your partner, figure out the total value of the blocks.”
• 8 minutes: partner work time
• Monitor for students who write the total as a three-digit number.

Student Facing

Los bloques de Mai

1. Mai tiene ______ centenas _____ decenas _____ unidades.

2. Dibuja un diagrama en base diez para representar el mismo valor total, pero usa el menor número posible de cada unidad en base diez.
3. ¿Cuál es el valor de los bloques de Mai?

Los bloques de Diego

4. Diego tiene ______ centenas _____ decenas _____ unidades.

5. Dibuja un diagrama en base diez para representar el mismo valor total, pero usa el menor número posible de cada unidad en base diez.
6. ¿Cuál es el valor de los bloques de Diego?

Activity Synthesis

• “¿Cuánto tenía Diego en total? Expliquen cómo lo supieron” // “How many did Diego have in all? Explain how you knew.”
• Select previously identified students to share.
• Write 283 while saying “2 centenas, 8 decenas y 3 unidades” // “2 hundreds, 8 tens, and 3 ones.”
• “Este es un número de tres dígitos. Los dígitos representan cantidades de centenas, decenas y unidades” // “This is a three-digit number. The digits represent amounts of hundreds, tens, and ones.”
• As needed, demonstrate reading the number left to right and gesture to emphasize the value of each digit.

Lesson Synthesis

Lesson Synthesis

“Hoy representaron números mayores que 100 usando bloques en base diez, diagramas en base diez, números y palabras” // “Today you represented numbers that were greater than 100 using base-ten blocks, base-ten diagrams, numbers, and words.”

“También vieron cómo pueden escribir un número de tres dígitos para representar la cantidad de centenas, decenas y unidades” // “You also saw how you can write a three-digit number to represent the amount of hundreds, tens, and ones.”

Display 324.

“¿De qué manera representarían este número usando bloques en base diez o un diagrama en base diez? Expliquen cómo lo saben” // “How would you represent this number with base-ten blocks or a base-ten diagram? Explain how you know.” (I’d draw 3 hundreds, 2 tens, and 4 ones. The first digit shows how many hundreds, the second digit shows how many tens, and the last digit shows how many ones.)