# Lesson 3

Hagamos y usemos una regla

## Warm-up: Conversación numérica: Restemos dos dígitos (10 minutes)

### Narrative

This Number Talk encourages students to think about subtraction with two-digit numbers in expressions that may require decomposing a ten. Students rely on using what they know about place value and counting on or back to mentally solve problems. When they share how each expression helps them find the value of the next, they look for and express regularity in repeated reasoning (MP8). The thinking elicited here helps students develop fluency when adding and subtracting within 100 using methods based on place value and the properties of operations.

### 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.

• $$63 - 3$$
• $$63 - 20$$
• $$63 - 23$$
• $$63 - 24$$

### Activity Synthesis

• “¿Cuáles expresiones fueron más fáciles de calcular mentalmente? ¿Por qué?” // “Which expressions were easier to find mentally? Why?”
• “¿Cómo les ayudó la tercera expresión a pensar en la cuarta?” // “How did the third expression help you think about the fourth one?”

## Activity 1: Hagamos una regla (20 minutes)

### Narrative

The purpose of this activity is to create a ruler with centimeter units. Students begin their ruler at 0 and measure and label each centimeter up to 25 centimeters. It is important to include 0 on the ruler as this helps build the foundation for making sense of the number line in later lessons. Just as they will on the number line, students label each tick mark—not the space between the tick marks. They notice that the length between successive tick marks on their ruler is 1 centimeter and each tick mark represents a length in centimeters from zero, allowing them to use the ruler to measure without counting cubes (MP2).

This activity uses MLR8 Discussion Supports in the synthesis to support students in describing how their ruler shows different lengths. Advances: speaking

Representation: Internalize Comprehension. Begin by asking, “¿Hacer esta herramienta le recuerda a alguien algo que hayamos hecho antes?” // “Does making this tool remind anyone of something we have done before?” Remind students of measuring with the non-standard units. “¿A qué cosas tuvieron que prestarles mucha atención al medir?” // “What were some of the things that needed close attention when measuring?” Students should recall lining up a tool right at the edge, making sure the units are touching and without gaps between them, tick marks are made at the end of the object to measure the distance from one end to the other as one unit.
Supports accessibility for: Organization, Memory, Visual-Spatial Processing

### Required Materials

Materials to Gather

Materials to Copy

• Centimeter Ruler Template

### Launch

• Groups of 2
• Give each student the Centimeter Ruler Template and access to centimeter cubes and 10-centimeter tools.

### Activity

• “Vamos a hacer nuestra propia herramienta para medir en centímetros, así no tendremos que cargar tantos cubos y bloques” // “We are going to make our own tool to measure in centimeters so we won’t have to carry around so many cubes and blocks.”
• Display the ruler template.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?” (It’s a long line. There’s a mark with 0. I wonder why there’s a 0. I wonder if we’ll have to put more numbers on it.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share connections students make to rulers and the need to add more numbers to the ruler.
• “Vamos a hacer una regla” // “We are going to make a ruler.”
• “¿Qué necesitaremos mostrar en esta regla de manera que podamos usarla para medir en centímetros? ¿Cómo nos podrían ayudar nuestras otras herramientas?” // “What will we need to show on this ruler so we can use it to measure in centimeters? How could we use our other tools to help us?” (We will need lines to show different lengths and numbers to show how long the distance is between them.)
• Ask a student to demonstrate how to line up the edge of the centimeter cube with 0. Draw a tick mark to show the length of 1 centimeter cube.
• “¿Qué tan lejos está la marca del 0? ¿Cómo lo saben?” // “How far is the tick mark from 0? How do you know?” (It’s 1 centimeter from 0 because there’s 1 centimeter cube between the tick marks.)
• Label the tick mark and repeat with the first 2-3 centimeters.
• “Completen su propia regla de la misma manera, marcando la longitud de un centímetro y etiquetando cada nueva longitud. Deténganse y corten su regla cuando hayan llegado al final de la línea” // “Complete your own ruler in the same way by marking the length of a centimeter and labeling each new length. Stop when you reach the end of the line and cut out your ruler.”
• 10 minutes: independent work time
• “Comparen su regla con la de su compañero” // “Compare your ruler with your partner.”
• 2 minutes: partner discussion

### Student Facing

1. Usa tus herramientas para hacer una regla que muestre longitudes en centímetros.
2. Compara tu regla con la de tu compañero.

### Student Response

If students create intervals that are a measurement other than 1 cm or label spaces instead of tick marks, consider asking:

• “¿Cuál marca muestra __ cm desde el 0? ¿Cómo puedes usar tus marcas para mostrar esa longitud?” // “Which tick mark shows __ cm from 0? How can you use your labels to show that length?”
• “¿Cuál de tus herramientas debería encajar entre cada par de marcas?” // “Which of your tools should fit between each tick mark?”
• “¿Cómo puedes usar tus herramientas para asegurarte de que dibujas cada nueva marca a 1 centímetro de la última marca?” // “How can you use your tools to make sure you draw each new tick mark 1 centimeter away from the last tick mark?”

### Activity Synthesis

• “¿Cómo pueden usar su regla para mostrarle a alguien qué tan largo es 1 centímetro?” // “How can you use your ruler to show someone how long 1 centimeter is?” (It’s the length from 0 to 1. It’s the length between any two numbers.)

MLR8 Discussion Supports

• If needed, invite students to repeat their reasoning using  mathematical language: “¿Pueden decir eso otra vez, usando la frase ‘podría mostrarles la longitud desde __ hasta __’?” // “Can you say that again, using the phrase I could show them the length from __ to __?”
• “¿Cómo pueden usar la regla para mostrarle a alguien qué tan largo es 10 centímetros?” // “How can you use the ruler to show someone how long 10 centimeters is?” (It’s the length from 0 and 10.)
• “¿Qué otras longitudes podrían mostrar con su regla?” // “What other lengths could you use your ruler to show?” (Answers vary between 0 and 25 centimeters)
• “Ahora tenemos una herramienta para medir que podemos usar en vez de muchos cubos de un centímetro. En la siguiente actividad, van a usar las reglas que hicieron” // “Now we have a measuring tool we can use instead of using lots of centimeter cubes. You’re going to use the rulers you've made in the next activity.”

## Activity 2: Midamos y comparemos longitudes (15 minutes)

### Narrative

The purpose of this activity is to measure the length of rectangles with the rulers created in a previous activity. If students’ rulers are not accurate, they should work with a partner who made an accurate ruler and encourage them to check their measurements with 10-centimeter tools and centimeter cubes. Students notice that each labeled tick mark on the ruler represents a length in centimeters from zero (MP8). The lesson synthesis allows students to share their measurements for each rectangle. They discuss any different measurements that were made and what the source of the different measurements might be (MP6).

### Required Materials

Materials to Gather

• Groups of 2

### Activity

• “Midan la longitud de cada rectángulo con su regla. Si les ayuda, pueden usar los cubos de un centímetro y los bloques de 10 centímetros para revisar sus medidas” // “Measure the length of each rectangle with your ruler. You can use the centimeter cubes and 10-centimeter blocks to check your measurement if it helps you.”
• “Cuando terminen, comprueben sus medidas con su compañero y respondan juntos las preguntas” // “When you finish, check your measurements with your partner and work together to answer the questions.”
• 3 minutes: independent work time
• 5–7 minutes: partner work time
• Monitor for students who find the difference between the longest and shortest length by:
• directly measuring the length from the end of shortest rectangle to the end of the longest rectangle
• measuring both rectangles and finding the difference

### Student Facing

1. Usa tu regla para medir la longitud de cada rectángulo. No olvides marcar las medidas.

2. ¿Cuántos centímetros más largo es el rectángulo A que el rectángulo B?
3. ¿Cuántos centímetros más largo es el rectángulo F que el rectángulo D?
4. ¿Cuáles son los dos rectángulos más largos? ¿Qué tan largo sería el rectángulo que obtendrías al juntarlos?

### Student Response

If students have measurements other than the precise measure of each rectangle, consider asking:

• “¿Cómo decidiste qué tan largo es el rectángulo?” // “How did you decide how long the rectangle is?”
• “¿En qué parte de la regla lo ves?” // “Where do you see this on the ruler?”

### Activity Synthesis

• Share measurements for each rectangle.
• Discuss any differences in measurement.
• “¿Cómo les ayudó el número 0 cuando midieron cada rectángulo?” // “How was the number 0 helpful when you measured each rectangle?” (It showed us where to put the tool. If you start with 0 then the length is the closest number to the end of the rectangle.)
• Invite previously identified students to share how they found the difference between the shortest and longest rectangles.
• “¿Cómo podemos usar nuestra regla para demostrar que el rectángulo más largo mide 10 cm más que el rectángulo más corto?” // “How can we use our ruler to prove that the longest rectangle is 10 cm longer than the shortest rectangle?”

## Lesson Synthesis

### Lesson Synthesis

“Hoy hicimos una regla para no tener que alinear cubos de un centímetro o herramientas de 10 centímetros al medir. Aprendimos lo que representan los números y las marcas de una regla” // “Today, we created a ruler so we didn’t have to line up centimeter cubes or 10-centimeter tools to measure. We learned what the numbers and tick-marks on a ruler represent.”

“¿En qué se parecen medir con una regla y medir con cubos de un centímetro o con una herramienta de 10 centímetros? ¿En qué son diferentes?” // “How is measuring with a ruler the same as measuring with centimeter cubes or a 10-centimeter tool? How is it different?” (They both measure in centimeters. The ruler just uses a line and tick-marks to show centimeter lengths and the other tools use the edges of the blocks. The ruler is easier to carry around and use to measure longer lengths. You don’t have to count on the ruler if you line up what you are measuring with 0.)

“¿Cómo usaron una regla para saber cuántos centímetros más larga era una línea que la otra?” // “How did you use a ruler to find how many more centimeters longer one line was than another?” (You can measure from the end of the shorter line to the end of the longer line. You could find the length of both lines on the ruler and count up from the shorter line. You could find both lengths and subtract the smaller length from the larger length).