# Lesson 2

Sumemos y restemos con decenas y centenas

## Warm-up: Conversación numérica: Sumemos múltiplos de 10 (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for adding multiples of 10 to two- and three-digit numbers. This activity helps students extend their fluency with adding multiples of 10 to two-digit numbers to their work in the lesson activities with adding and subtracting multiples of 10 and 100 within 1,000. As students share their thinking, consider recording on an open number line.

### 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 an open number line.
• Keep expressions and work displayed.
• Repeat with each expression.

### Student Facing

Encuentra mentalmente el valor de cada expresión.

• $$34 + 20$$
• $$34 + 60$$
• $$58 + 30$$
• $$158 + 40$$

### Activity Synthesis

• “¿Cómo encontraron el valor de estas expresiones?” // “How did you find the value of these expressions?” (We noticed we could count on by tens. We added the number of tens in each one. The number in the ones place didn’t change.)

## Activity 1: Mostrémoslo con bloques en base diez (15 minutes)

### Narrative

The purpose of this activity is to add and subtract three-digit numbers and multiples of 10 or 100 using base-ten blocks and equations. The structure of the base-ten blocks encourages students to notice that hundreds are added to or subtracted from hundreds and tens are added to or subtracted from tens (MP7). To help students focus on this structure, the numbers are chosen so that the addition and subtraction of tens can take place without needing to compose or decompose a hundred.

If you do not have enough hundred blocks for each group of 2 students, students may work in larger groups.

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• Give each group base-ten blocks and a number cube.

### Activity

• “Con su pareja, muestren cada número con bloques en base diez” // “Work with your partner to show each number with base-ten blocks.”
• “Por turnos, lancen el dado numérico para saber cuántas decenas o centenas deben sumar o restar” // “Take turns rolling the number cube to see how many tens or hundreds to add or subtract.”
• 10 minutes: partner work time
• Monitor for students to share their equations for the number of hundreds they subtract from 805.

### Student Facing

Usa tus bloques en base diez para mostrar cada número. Después, lanza un dado numérico para ver cuántas decenas o centenas debes sumar o restar.
1. Muestra 297.

1. Suma _____ centenas.
2. Completa la ecuación: $$297 + \underline{\hspace{1cm}} =\underline{\hspace{1cm}}$$
2. Muestra 432.

1. Suma _____ decenas.
2. $$432 + \underline{\hspace{1cm}} =\underline{\hspace{1cm}}$$
3. Muestra 982.

1. Resta _____ decenas.
2. $$982 - \underline{\hspace{1cm}} =\underline{\hspace{1cm}}$$
4. Muestra 351.

1. Suma _____ centenas.
2. Escribe una ecuación:
5. Muestra 805.

1. Resta ____ centenas.
2. Escribe una ecuación:

### Activity Synthesis

• Invite previously identified students to share equations or display
• $$805 - 400 = 405$$
• Display a base-ten diagram, or, if possible, allow students to demonstrate with base-ten blocks.
• “¿Cómo se relaciona la ecuación con el diagrama o con los bloques?” // “How does the equation connect to the diagram or blocks?” (You take away 4 hundreds from the blocks and you’re left with 4 hundreds and 5 ones.)
• “¿Qué observaron acerca de cómo cambió el valor de los bloques?” // “What did you notice about how the value of the blocks changed?” (There are fewer blocks. The hundreds place changed because you subtracted hundreds.)

## Activity 2: Averigüemos cuántos hay con bloques en base diez y ecuaciones (20 minutes)

### Narrative

The purpose of this activity is for students to add and subtract multiples of 10 and 100 within 1,000. Students interpret situations with base-ten blocks and base-ten diagrams and use equations to represents sums and differences. In the activity synthesis, students relate the situation, base-ten diagram, and equation and notice, through repeated reasoning, that when adding and subtracting, one can add or subtract hundreds and hundreds and tens and tens (MP7, MP8).

MLR7 Compare and Connect. Synthesis: Lead a discussion comparing, contrasting, and connecting their different ways of representing the value of Mai and Lin’s blocks together. Ask, “¿De qué manera estas representaciones diferentes muestran la misma información?” // “How do these different representations show the same information?” “¿En qué son diferentes?” // “How are they different?”
Representation: Access for Perception. Invite students to act out the scenario of giving and taking hundreds on a number line. Discuss the individual jumps of 100 if a jump of 400 is too much to begin.
Supports accessibility for: Conceptual Processing, Language, Organization

### Required Materials

Materials to Gather

• Groups of 2

### Activity

• “Estos estudiantes estaban usando bloques en base diez para encontrar el valor de sumas y diferencias” // “These students were using base-ten blocks to find the value of sums and differences.”
• “En cada problema, representen el valor de los estudiantes de una forma que tenga sentido para ustedes. Pueden usar bloques en base diez, diagramas o ecuaciones” // “For each problem, represent the student’s value in a way that makes sense to you. You can use base-ten blocks, diagrams, or equations.”
• 10 minutes: partner work time
• For Priya and Jada’s blocks, monitor for students who:
• write equations to show the sums and differences.
• use base-ten diagrams to show subtraction.

### Student Facing

1. Mai tiene 2 centenas, 2 decenas y 3 unidades. Lin tiene 4 centenas.

Representa sus valores con bloques en base diez o con diagramas.

¿Cuál es el valor total de sus bloques? Muestra cómo pensaste.

2. Andre tiene 4 centenas, 2 decenas y 8 unidades.

Representa su valor con bloques en base diez o con diagramas.

Andre le da 2 centenas a Clare.

¿Cuál es el valor de sus bloques ahora? Muestra cómo pensaste.

3. Diego tiene 6 decenas. Tyler tiene 8 centenas, 3 decenas y 6 unidades.

¿Cuál es el valor total de sus bloques? Muestra cómo pensaste.

4. Elena tiene 5 centenas, 7 decenas y 2 unidades. Ella le da 2 decenas a Kiran.

¿Cuál es el valor de sus bloques ahora? Muestra cómo pensaste.

5. Priya tiene 6 centenas, 5 decenas y 8 unidades. Han le da 3 centenas.

¿Cuál es el valor de sus bloques ahora? Muestra cómo pensaste.

6. Jada tiene 4 centenas, 8 decenas y 2 unidades. Ella le da 3 centenas a Noah.

¿Cuál es el valor de sus bloques ahora? Muestra cómo pensaste.

### Student Response

If students draw diagrams that do not match the situation or write equations that are not true, consider asking:

• “¿Puedes explicar lo que hiciste?” // “Can you explain what you did?”
• “¿Qué patrones observas cuando sumas o restas centenas y centenas? ¿Y decenas y decenas?” // “Do you notice any patterns when you add or subtract hundreds and hundreds? Tens and tens?”

### Activity Synthesis

• Invite a student to share their representation and equation for Jada’s blocks. If no students use a base-ten diagram, select a student to share how they use base-ten blocks, and use a base-ten diagram to record their steps.
• “¿Cómo se ven los bloques de Jada en el diagrama en base 10?” // “How does the base-ten diagram show Jada’s blocks?” (The blocks show how many Jada started with. The lines show the 3 hundreds that were taken away.)
• Display $$482 - 300 = 182$$
• “¿Cómo se ven los bloques de Jada en la ecuación?” // “How does the equation show Jada’s blocks?” (482 is what Jada started with and 300 is the 3 hundreds she gave away. 182 is how much she has left.)

## Lesson Synthesis

### Lesson Synthesis

“Hoy le sumaron y le restaron centenas o decenas a números de tres dígitos” // “Today you added and subtracted hundreds or tens to and from three-digit numbers.”

Invite previously identified students to share representations for Priya’s blocks.

Display $$658 + 300 = 958$$.

“¿En qué es diferente la representación de los bloques de Jada de la representación de los bloques de Priya?” // “How is the representation of Jada’s blocks different from the representation for Priya’s blocks?” (Jada’s blocks show 3 hundreds crossed out. Priya’s show 3 hundreds added.)