# Lesson 2

Hagan su propia recta numérica

## Warm-up: Cuál es diferente: Fracciones en rectas numéricas (10 minutes)

### Narrative

This warm-up prompts students to compare four images. It gives students a reason to use language precisely. It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another. During the synthesis, ask students to explain the meaning of any terminology they use, such as tick marks, labels, unit fractions, whole numbers, and length.

### Launch

• Groups of 2
• Display the image.
• “Escojan una que sea diferente. Prepárense para compartir por qué es diferente” // “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
• 1 minute: quiet think time

### Activity

• “Discutan con su pareja cómo pensaron” // “Discuss your thinking with your partner.”
• 2–3 minutes: partner discussion
• Share and record responses.

### Student Facing

¿Cuál es diferente?

### Activity Synthesis

• “Encontremos al menos una razón por la que cada una es diferente” // “Let’s find at least one reason why each one doesn’t belong.”

## Activity 1: Hagan su propia recta numérica (25 minutes)

### Narrative

The purpose of this activity is for students to use their fraction reasoning skills to practice locating fractions on a number line. Students should be in groups, but the groups should stay small enough that every member will have a chance to share their ideas. Be sure to space groups so that each has their own area to work in. Students write the fractions on their tape. Students will use the number line they create in the next activity.

As they place the different numbers students think about the meaning of the numerator and denominator in the fractions and how whole numbers can be written as fractions (MP7).

MLR8 Discussion Supports. Synthesis: At the appropriate time, give groups 2–3 minutes to plan what they will say when they present to the class. “Practiquen lo que van a decir cuando compartan su recta numérica con toda la clase. Hablen sobre lo que es importante decir y decidan quién va a compartir cada parte” // “Practice what you will say when you share your number line with the class. Talk about what is important to say, and decide who will share each part.”
Advances: Speaking, Conversing, Representing
Action and Expression: Develop Expression and Communication. Synthesis: Identify connections between strategies that result in the same outcomes but use differing approaches.
Supports accessibility for: Memory

### Required Materials

Materials to Gather

### Required Preparation

• Each group of 3-4 students needs a roll of tape and a marker.

### Launch

• Groups of 3–4
• “Hoy van a hacer una recta numérica con su grupo y van a ubicar fracciones en ella. Prepárense para compartir sus métodos con la clase” // “Today you are going to work with your group to create a number line and place fractions on it. Be prepared to share your methods with the class.”
• Give each group a roll of tape and a marker.

### Activity

• 10–15 minutes: small-group work time
• Monitor for methods that groups use to locate the points, such as:
• starting with benchmark numbers, such as unit fractions or whole numbers
• considering whether fractions are larger or smaller than 1
• considering whether fractions are equivalent to whole numbers
• comparing fractions with the same numerator or denominator

### Student Facing

Hagan una recta numérica larga en el piso.

Ubiquen y marquen cada fracción en la recta numérica. Prepárense para explicar su razonamiento.

• 0
• 1
• 2
• $$\frac{1}{2}$$
• $$\frac{1}{3}$$
• $$\frac{6}{2}$$
• $$\frac{12}{3}$$
• $$\frac{1}{4}$$
• $$\frac{5}{4}$$
• $$\frac{6}{6}$$
• $$\frac{5}{6}$$
• $$\frac{9}{8}$$
• $$\frac{15}{8}$$
• $$\frac{5}{3}$$
• $$\frac{18}{6}$$
• $$\frac{2}{8}$$

### Activity Synthesis

• Have each group share a method they used or a fraction they placed, based on what you noticed during the activity. Encourage groups to use their number lines when demonstrating their reasoning.
• “¿Algún grupo usó una estrategia similar?” // “Did any groups use a similar strategy?”
• “¿Algún grupo ubicó esa fracción de otra forma?” // “Did any groups place that fraction in a different way?”
• “¿Cuáles fracciones fueron más fáciles de ubicar?” // “Which fractions were easier to locate?”
• “¿Cuáles fracciones fueron más complicadas de ubicar?” // “Which fractions were harder to locate?”
• Keep number lines displayed for the next activity.

## Activity 2: Hagamos una afirmación (10 minutes)

### Narrative

The purpose of this activity is for students to use the number line they created in the previous activity to make comparison statements about fractions. Students use the symbols $$>$$, $$=$$, and $$<$$ to record comparisons between pairs of fractions.

### Launch

• Groups of 3–4
• “Ahora, con su grupo, van a escribir afirmaciones de comparación basándose en su recta numérica” // “Now you are going to work with your group to write comparison statements based on your number line.”

### Activity

• 8–10 minutes: small-group work time
• Monitor for a variety of student-generated statements of each type to share during the synthesis.

### Student Facing

Escribe 6 afirmaciones de comparación de fracciones acerca de los números de tu recta numérica. Haz 2 afirmaciones con cada símbolo ($$>$$, $$=$$ y $$<$$).

1.
2.
3.
4.
5.
6.

Escoge 2 afirmaciones de las que escribiste. Usa números, imágenes o palabras para mostrar que son verdaderas.

### Activity Synthesis

• Have each group share at least one comparison statement they came up with and their reasoning. Be sure to share at least one statement that uses each symbol.

## Lesson Synthesis

### Lesson Synthesis

“¿Cómo decidieron qué tan larga debía ser su recta numérica? ¿Importa qué tan larga sea?” // “How did you decide how long your number line should be? Does it matter?” (We looked at the largest number we had and made sure it would fit on the number line. Yes, because you had to make sure all the numbers would fit on the number line.)

“La recta numérica de un grupo es evidentemente más larga que la de otro grupo. ¿Eso cambia las afirmaciones de comparación que cada grupo puede hacer?” // “The number line of one group is noticeably longer than that of another group. Does that affect the comparison statements that each group could make?” (It wouldn’t affect the comparison statements for one group working on their own number line, but if two groups tried to compare fractions with number lines with different lengths, their statements could be wrong.)