# Lesson 14

Comparemos con sumas y restas

## Warm-up: Verdadero o falso: Signo igual (10 minutes)

### Narrative

The purpose of this True or False is to continue to develop and deepen student understanding of the equal sign. These understandings will be helpful when students work with equations with expressions on both sides of the equal sign in a later unit.
This is the second time students will do this instructional routine. The teacher should read aloud each equation. When students are more familiar with equations, they do not need to be read by the teacher.

### Launch

• Display one statement.
• “Hagan una señal cuando sepan si la afirmación es verdadera o no, y puedan explicar cómo lo saben” // “Give me a signal when you know whether the statement is true and can explain how you know.”
• 1 minute: quiet think time

### Activity

• Share and record answers and strategy.
• Repeat with each equation.

### Student Facing

Prepárate para explicar tu razonamiento.

• $$7 + 3 = 10$$
• $$10 = 7 + 3$$
• $$10 = 3 + 6$$

### Activity Synthesis

• “¿Cómo es 10 la misma cantidad que $$7 + 3$$?” // “How is 10 the same amount as $$7 + 3$$?” (When I add 7 and 3, the total is 10.)
• “Si $$7 + 3 = 10$$ y $$10 = 7 + 3$$, ¿es $$10 = 3 + 7$$?” // “If $$7 + 3 = 10$$, and $$10 = 7 + 3$$, would $$10 = 3 + 7$$?” (Yes, because 7 + 3 is the same amount as 10, and 10 is the same amount as $$3 + 7$$.)

## Activity 1: ¿Es una suma o una resta? (15 minutes)

### Narrative

The purpose of this activity is for students to explore the relationship between addition and subtraction through a Compare, Difference Unknown story problems. They analyze two equations, one addition and one subtraction, that match the same problem and discuss the relationship between the two equations and the story problem. Students should notice that both equations can be used to describe how they solve the problem. This also helps them relate addition and subtraction and see that often either operation can be used to solve a problem (MP7).

### Launch

• Groups of 2
• Display the image in the student book.
• 1 minute: quiet think time
• 2 minutes: partner discussion
• Share responses.

### Activity

• 5 minutes: partner work time
• Encourage students to use the representation to make sense of both equations.
• Monitor for a group who uses the representation to explain the addition equation and one who explains the subtraction equation.

### Student Facing

En la estación de arte hay 8 barras de pegamento y 3 tijeras.
¿Cuántas tijeras menos que barras de pegamento hay?

Mai hizo un dibujo.

Ella no está segura de cuál ecuación debe usar para encontrar la diferencia.

$$8 - 3 = \boxed{5}$$
$$3 + \boxed{5} = 8$$

Ayúdala a decidir.
Muestra cómo pensaste. Usa dibujos, números o palabras.

### Student Response

If students find the difference using only one operation, consider asking:

• “¿Puedes explicar cómo encontraste la diferencia entre el número de barras de pegamento y el número de tijeras?” // "Can you explain how you found the difference between the number of glue sticks and scissors?"
• “En tu dibujo (objetos), ¿dónde ves la diferencia? ¿Cómo puedes encontrar esa parte de la representación usando una suma (una resta)?” // "Where in your drawing (objects) do you see the difference? How could you find that part of the representation by adding (subtracting)?"

### Activity Synthesis

• “¿Qué tratamos de averiguar en este problema-historia?” // “What are we trying to find out in this story problem?” (How many fewer scissors there are than glue sticks. The difference between the number of scissors and glue sticks.)
• Invite previously identified groups to share.
• “¿Qué es lo mismo? ¿Qué es diferente?” // “What is the same? What is different?” (3, 5, and 8 are in each equation. The numbers represent the same things in both. The 5 is boxed in both. One uses addition and the other uses subtraction. The boxed number is in a different place.)

## Activity 2: ¿Cuál ecuación? (10 minutes)

### Narrative

The purpose of this activity is for students to identify addition and subtraction equations that match Compare, Difference Unknown story problems. Students may not initially choose more than one equation for each problem, so this is the emphasis of the activity synthesis. Students continue to build their language of Compare problems and solidify the relationship between addition and subtraction.

MLR2 Collect and Display. Collect the language students use to explain their thinking. Display words and phrases such as: more, fewer, equation, drawings, words. During the synthesis, invite students to suggest ways to update the display: “¿Qué otras palabras o frases deberíamos incluir?” // “What are some other words or phrases we should include?”, etc. Invite students to borrow language from the display as needed.
Engagement: Internalize Self-Regulation. Synthesis: Provide students an opportunity to self-assess and reflect on their own progress. For example, ask students to check over their work to make sure they used drawings, numbers, or words to show their thinking, and also included at least one equation to show how they solved the problem.
Supports accessibility for: Conceptual Processing, Attention

• Groups of 2

### Activity

• 3 minutes: independent work time
• 2 minutes: partner discussion
• Monitor for a student who can show and explain how they chose which equation matches.

### Student Facing

1. Hay 5 almohadas rojas y 3 almohadas azules sobre la alfombra de lectura.
Muestra cómo pensaste. Usa dibujos, números o palabras.

Marca la ecuación que corresponde al problema.

$$5 + 3 = \boxed{\phantom{8}}$$

$$5 - 3 = \boxed{\phantom{2}}$$

$$5 + \boxed{\phantom{2}} = 3$$

$$3 + \boxed{\phantom{2}} = 5$$

2. Hay 7 calculadoras sobre la mesa.
Hay 8 libros de matemáticas.
¿Cuántos libros de matemáticas más que calculadoras hay?
Muestra cómo pensaste. Usa dibujos, números o palabras.

Marca la ecuación que corresponde al problema.

$$7 + \boxed{\phantom{1}} = 8$$

$$8 - 7 = \boxed{\phantom{1}}$$

$$7 - 8 = \boxed{\phantom{0}}$$

$$8 + \boxed{\phantom{1}} = 7$$

3. En la clase del Sr. Green, 3 estudiantes tienen mochilas moradas y 7 estudiantes tienen mochilas negras.
¿Cuántos estudiantes más tienen mochilas negras que mochilas moradas?
Muestra cómo pensaste. Usa dibujos, números o palabras.

Marca la ecuación que corresponde al problema.

$$3 + 7 = \boxed{\phantom{10}}$$

$$3 + \boxed{\phantom{4}} = 7$$

$$7 - \boxed{\phantom{4}} = 3$$

$$7 + \boxed{\phantom{1}} = 3$$

### Activity Synthesis

• “¿Cómo supieron cuál ecuación correspondía al problema sobre las mochilas?” // “How did you know which equation matched the problem about backpacks?" (I made a tower of 3 cubes to show the purple backpacks, and a tower of 7 cubes to show the black backpacks. Then I broke off the difference, which is 4. This matches 7 - __ = 3 because the 4 shows the difference.)
• “¿Hay otras ecuaciones que representen este problema?” // “Are there any other equations that represent this problem?” (Yes, 3 + ___ = 7 also matches. I started with 3 cubes, and added cubes until I got to 7. The amount I added was 4.)
• “Hay dos ecuaciones que corresponden a este problema. Revisen los otros problemas para ver si hay otras ecuaciones que les correspondan” // "There were two equations that match this problem. Check the other problems to see if there are any other equations that match."

## Activity 3: Centros: Momento de escoger (15 minutes)

### Narrative

The purpose of this activity is for students to choose from activities that offer practice telling and solving story problems and adding and subtracting within 10. Students choose from any stage of previously introduced centers.

• Capture Squares
• Math Stories
• Shake and Spill

### Required Materials

Materials to Gather

### Required Preparation

• Gather materials from previous centers:
• Capture Squares, Stage 1
• Math Stories, Stage 4
• Shake and Spill, Stages 3 and 4

### Launch

• Groups of 2
• “Ahora van a escoger un centro de los que ya conocemos” // “Now you are going to choose from centers we have already learned.”
• Display the center choices in the student book.
• “Piensen qué les gustaría hacer” // “Think about what you would like to do.”
• 30 seconds: quiet think time

### Activity

• Invite students to work at the center of their choice.
• 10 minutes: center work time

### Student Facing

Escoge un centro.

Historias matemáticas

Revuelve y saca

### Activity Synthesis

• “Cuéntenle a su pareja una cosa que haya hecho y que les haya ayudado hoy cuando trabajaron en los centros” // “Tell your partner one thing they did that helped you during center time today.”

## Lesson Synthesis

### Lesson Synthesis

Display: In Mr. Green's class, 3 students have purple backpacks and 7 students have black backpacks. How many more students have black backpacks than purple backpacks?

​​$$3 + \boxed{4} = 7$$ y $$7 - 3 = \boxed{4}$$.

“Hoy explicamos cómo ecuaciones diferentes pueden corresponder a la misma historia. Estas son las ecuaciones que corresponden a esta historia. ¿Por qué cambia la posición de la respuesta?” // “Today we explained how different equations can match the same story. These are the equations that match this story. Why does the position of the answer change?” (Because one equation is addition and one is subtraction, because they used different methods to solve the problem, so the answer came in different places.)

“¿Qué representa cada número?” // “What does each number represent?”