# Lesson 3

Historias con fracciones

## Warm-up: Conversación numérica: Un entero, muchos nombres (10 minutes)

### Narrative

This Number Talk encourages students to think about equivalent forms of whole numbers and decomposing fractions in order to subtract. When students consider equivalent fractions, look for ways to decompose fractions, or use the structure of mixed numbers to find the value of each difference, they look for and make use of structure (MP7).

### 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.”

### Activity

• 1 minute: quiet think time
• Keep expressions and work displayed.
• Repeat with each expression.

### Student Facing

Encuentra mentalmente el valor de cada expresión.

• $$1 - \frac{8}{10}$$
• $$1\frac{4}{10} - \frac{8}{10}$$
• $$2\frac{4}{10} - \frac{8}{10}$$
• $$10\frac{5}{10} - \frac{8}{10}$$

### Activity Synthesis

• “¿En qué se parecen estas expresiones?” // “How are these expressions alike?” (They all involve subtracting $$\frac{8}{10}$$ from a number that is at least 1. To subtract, it’s helpful or necessary to decompose a 1 or to write an equivalent fraction.)
• “¿Cómo usaron las primeras expresiones como ayuda para encontrar el valor de las últimas expresiones?” // “How did you use earlier expressions to help you find the value of later expressions?”

## Activity 1: Carrera de relevos en el recreo (20 minutes)

### Narrative

In previous lessons, students have used their understanding of fraction equivalence to compare fractions and solve problems. The purpose of this activity is to practice solving addition and subtraction problems involving decimal fractions (MP2). Students use what they know about equivalent fractions and the relationship between 10 and 100 to add tenths and hundredths.

Representation: Develop Language and Symbols. Represent the problem in multiple ways to support understanding of the situation. For example, show a picture of children working with clay and invite students to draw a comic strip or storyboard to represent the problem.
Supports accessibility for: Conceptual Processing, Language, Attention

• Groups of 2

### Activity

• 1–2 minutes: independent work time
• “Comparen sus estrategias con las de su compañero” // “Compare your strategies with your partner’s.”
• 5 minutes: partner discussion
• Monitor for expressions, strategies, and representations students use to determine connections between strategies and evidence of reasoning about equivalence.

### Student Facing

Los estudiantes de cuarto grado hicieron una carrera de relevos durante el recreo. Cada equipo tenía cuatro corredores. Cada corredor corrió a lo largo del patio de recreo de la escuela.

Estos son los tiempos de los corredores de los dos equipos.

corredor Equipo de Diego, tiempo (segundos) Equipo de Jada, tiempo (segundos)
1 $$10\frac{25}{100}$$ $$11\frac{9}{10}$$
2 $$11\frac{40}{100}$$ $$9\frac{8}{10}$$
3 $$9\frac{7}{10}$$ $$9\frac{84}{100}$$
4 $$10\frac{5}{100}$$ $$10\frac{60}{100}$$
1. ¿Cuál equipo ganó la carrera de relevos? Muestra cómo razonaste.

2. ¿Cuánto más rápido fue el equipo ganador que el otro equipo? Muestra cómo razonaste.

3. El tiempo récord de la carrera de relevos del patio de recreo era 40.27 segundos. ¿El equipo ganador mejoró este tiempo récord? Muestra cómo razonaste.

### Activity Synthesis

• Invite previously identified students to share how they solved the problems.
• “¿En qué se parecen resolver estos problemas y resolver los problemas de las lecciones anteriores? ¿En qué son diferentes?” // “How was solving these problems the same as the problems we solved in previous lessons? How was it different?” (It was the same because we were adding and subtracting mixed numbers. We still looked for ways to make a new whole number when we could. We had to add up fractions that had different denominators in these problems. We had to compare with a decimal fraction written with decimal notation.)

## Activity 2: Sean los autores (15 minutes)

### Narrative

The purpose of this activity is to create and solve addition and subtraction problems with fractions. Students first create stories to match a given value or equation and some given constraints.

MLR8 Discussion Supports. Display sentence frames to support small-group discussion: “_____ y _____ se parecen porque . . .” // “_____ and _____ are the same/alike because . . .” or “_____ y _____ son diferentes porque . . .” // “_____ and _____ are different because . . . .”

### Launch

• Groups of 2
• “Piensen en una situación que tenga un problema que se pueda resolver encontrando el valor de $$3\frac{4}{10} + \frac{2}{10} + \frac{1}{2}$$” // “Think of a situation with a problem that could be solved by finding the value of $$3\frac{4}{10} + \frac{2}{10} + \frac{1}{2}$$.”
• 1–2 minutes: partner discussion
• Share responses.

### Activity

• 56 minutes: independent work time
• 45 minutes: compare with a partner
• Monitor for students who create situations that involve different problem types. For example, for the problem that can be solved with addition, look for students who create an Add to, Result Unknown problem and a student who creates a Compare, Difference Unknown problem.

### Student Facing

Piensa en tres situaciones como estas. Después de escribir cada problema, intercambia tu hoja con la de un compañero para comparar los problemas y revisar las soluciones.

1. Un problema que se pueda resolver sumando y que su respuesta sea $$9\frac{2}{5}$$
2. Un problema que se pueda resolver restando y que su respuesta sea $$\frac{32}{100}$$
3. Un problema que se pueda resolver escribiendo la ecuación: $$9 - \underline{\hspace{1cm}} = 3\frac{3}{5}$$

### Activity Synthesis

• Invite 1–2 previously identified students to share their situations for each problem.
• “¿En qué se parecen estas situaciones? ¿En qué son diferentes? ¿De qué manera cada una corresponde a las instrucciones?” // “How are these situations the same? How are they different? How does each one match the directions?”

## Lesson Synthesis

### Lesson Synthesis

“En esta sección, resolvimos muchos problemas en los que había sumas, restas, multiplicaciones y comparaciones de fracciones” // “In this section, we have solved many problems that involved adding, subtracting, multiplying, and comparing fractions.”

“Digan dos cosas que hayan aprendido al escuchar las ideas de otros estudiantes durante estas lecciones” // “What are two things that you have learned from listening to the ideas of other students in these lessons?”

“Digan una cosa que quieran seguir practicando cuando resuelvan problemas en los que haya fracciones” // “What is one thing you want to continue to practice when solving problems with fractions?“