# Lesson 9

Gramos y kilogramos, litros y mililitros

## Warm-up: Cuál es diferente: Metrito, metrito, quién es el más cortito (10 minutes)

### Narrative

This warm-up prompts students to carefully analyze and compare 4 length measurements and how they are expressed. To make comparisons, students apply what they know about the relationship between meters and centimeters and the convention for writing the units.

### 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 compañero lo que pensaron” // “Discuss your thinking with your partner.”
• 2–3 minutes: partner discussion
• Share and record responses.

### Student Facing

¿Cuál es diferente?

1. 2 m
2. 2,000 metros
3. 200 centímetros

### Activity Synthesis

• “¿Cómo se relacionan estas medidas entre sí? ¿Cómo lo saben?” // “How do these measurements compare to one another? How do you know?” (Three of them are equivalent: 2 m, 200 centimeters, and the diagram showing 2 segments of 1 meter, all represent 2 meters. One of them, B, is 1,000 times as long as all the others. It is 2 kilometers.)

## Activity 1: Una gran cantidad de clips (15 minutes)

### Narrative

The purpose of this activity is to build students’ intuition for 1 gram, 1 kilogram, and the relationship between them. Students learn that 1 kilogram is 1,000 times as heavy as 1 gram. Students convert quantities from kilograms to grams and compare quantities given in different units.

As in earlier lessons, when an amount given in kilograms is a fraction ($$\frac{1}{2}$$ or $$\frac{1}{10}$$), students are not expected to find its equivalent in grams by multiplying the fraction by 1,000. Instead they are to reason about the conversion based on what they know about fractions and the number 1,000.

If possible, prepare one or more boxes of 100 or 250 paper clips and allow students to feel and compare the weight of 1 paper clip, 100 paper clips, 500 paper clips, and so on.

MLR2 Collect and Display. Circulate, listen for, and collect the language students use as they work to solve comparison problems using kilograms and grams. On a visible display, record words and phrases such as: kilograms, grams, times as much, and unit. Invite students to borrow language from the display as needed, and update it throughout the lesson.
Engagement: Provide Access by Recruiting Interest. Synthesis: Invite students to generate a short list of items they would like to weigh. For each item, discuss whether it makes more sense to measure in grams or kilograms, and invite students to make an estimate. If possible, actually weigh the items using a digital scale, and display the weight in both grams and kilograms.
Supports accessibility for: Conceptual Processing, Attention

### Required Materials

Materials to Gather

### Required Preparation

• Gather one or more boxes of 100 metal paper clips, if available.

### Launch

• Groups of 2
• Survey the class on their familiarity with the units grams and kilograms.
• “Para los que conocen estas unidades, ¿dónde las han escuchado, visto o usado?” // “For those who are familiar with it, where might you have heard, seen, or used these units?”
• Explain that while pounds and ounces are more commonly used in the U.S. for measuring weight, in other countries, grams and kilograms are standard.

### Activity

• 6–7 minutes: independent work time
• 2–3 minutes: partner discussion
• Monitor for the ways students:
• describe the relationship between kilograms and grams.
• reason about fractional amounts in kilograms and express them in grams.
• compare quantities given in different units.

### Student Facing

Un clip pesa 1 gramo.

1. ¿Cuántos gramos pesan los clips de cada imagen?

2. Los clips de esta imagen, juntos, pesan 1 kilogramo.

¿Cuál es la relación entre kilogramos y gramos?

3. Completa la tabla con las cantidades que faltan, en gramos.
kilogramos (kg) gramos (g)
2
7
15
$$\frac{1}{2}$$
$$9\frac{1}{2}$$
4. ¿Cuál pesa más? Prepárate para explicar cómo lo sabes.

1. 8 kilogramos u 8 cajas con 100 clips cada una
2. 1,250 clips o 1 kilogramo
3. 500 gramos o 2 cajas con 250 clips cada una
4. $$\frac{1}{2}$$ kilogramo o 500 clips

### Activity Synthesis

• “¿Cuál unidad es más pesada: un kilogramo o un gramo?” // “Which unit is heavier a kilogram or a gram?” (kilogram)
• “¿Creen que su mochila es más liviana o más pesada que 1 kilogramo?” // “Do you think your book bag is lighter or heavier than 1 kilogram?” (Heavier because I have a lot of books in it. Lighter because it’s empty.)
• Display the table and invite students to share their responses and reasoning.
• Discuss students’ responses to the comparison problems.

## Activity 2: Litros y mililitros (20 minutes)

### Narrative

Previously, students learned about kilograms, grams, and the relationship between the two units. In this activity, they develop their sense of 1 milliliter, 1 liter, and the relationship between them. They do so by observing the number of times a smaller container with 1, 20, or 100 milliliters of liquid needs to be filled to make a larger amount, up to 1 liter. Students see that 1 liter is 1,000 times as much as 1 milliliter and convert quantities from liters to milliliters. When they visualize the relationship between liters and milliliters and use their understanding of this relationship to make conversions, students reason abstractly and quantitatively (MP2).

Videos that show liquid being poured are provided, but a live demonstration—if possible—is preferred.

### Required Materials

Materials to Gather

### Required Preparation

• If possible, gather a 1-milliliter medicine dropper, a 20-milliliter medicine dosage cup, a 100-milliliter measuring cup or cylinder, and an empty 1-liter bottle with a line at the 1-liter mark.
• Obtain 1.5 liters of water or access to a water source.

### Launch

• Groups of 2
• If available, display a 1-milliliter medicine dropper, a 20-milliliter dosage cup, a 100-milliliter cup, and a 1-liter bottle. Refer to them when asking the following questions. Or refer to the image in the student book.
• “¿Cuántas veces tenemos que llenar el gotero de 1 mililitro para llenar un vaso de 20 mililitros?” // “How many times do we need to fill the 1-milliliter medicine dropper to fill a 20-milliliter cup?” (20 times) “¿Y un cilindro de 100 mililitros?” // “A 100-milliliter cylinder?” (100 times)
• “¿Cuántas veces tenemos que llenar el vaso de 20 mililitros para obtener 100 mililitros? Supongan que cada vez el vaso se llena de líquido hasta la línea de 20 mililitros” // “How many times do we need to fill the 20-milliliter cup to get 100 milliliters? Assume that each time the liquid is filled to the 20-milliliter line.” (5 times, because $$5\times 20 = 100$$, or show the video at: vimeo.com/450153736.)
• “Ahora estimen cuántas veces tenemos que llenar el cilindro de 100 mililitros para obtener 1 litro. Supongan que cada vez el cilindro se llena de líquido hasta la línea de 100 mililitros. Escriban su estimación” // “Now estimate how many times we’d need to fill the 100-milliliter cylinder to get 1 liter. Assume that each time the liquid is filled to the 100-milliliter line. Write down your estimate.”
• 30 seconds: quiet think time
• “Compartan su estimación con un compañero” // “Share your estimate with a partner.”
• If materials are available, allow students to check their estimates.
• Add 100 milliliters of water into the 1-liter bottle repeatedly until the water reaches the 1-liter mark. Ask students to keep count. Alternatively, show the video at: vimeo.com/450147862.

### Activity

• “Completen la actividad teniendo en cuenta lo que acaban de aprender sobre 1 litro” // “Complete the activity based on what you just learned about 1 liter.”
• “Trabajen individualmente durante unos minutos. Después, discutan con su compañero cómo pensaron” //“Work independently for a few minutes. Then, discuss your thinking with your partner.”
• 7–8 minutes: independent work time
• 2–3 minutes: partner discussion
• Monitor for the ways students reason about the number of groups of 1 milliliter, 250 milliliters, and 20 milliliters in 1 liter.

### Student Facing

1. Estima: ¿Cuántas veces llenamos el vaso de 100 mililitros para obtener 1 litro de líquido? (Supón que cada vez el vaso se llena de líquido hasta la línea de 100 mililitros).
2. Escribe una oración que describa la relación entre los mililitros y los litros.
1. ¿Cuántas veces tenemos que llenar cada uno de estos recipientes para obtener 1 litro?

1. Un gotero de 1 mililitro

2. Una taza para medir de 250 mililitros

3. Una taza de 20 mililitros

2. Completa la tabla con las cantidades que faltan, en litros o mililitros.
litros (L) mililitros (mL)
1
4
7
16
$$\phantom{0000000000}$$ 500
20,000

### Activity Synthesis

• Select students to share their responses to the second and third sets of problems of the last activity.
• If no students use equations to show their reasoning for the second set of problems, consider writing them: $$1,\!000 \times 1 = 1,\!000$$, $$4 \times 250 = 1,\!000$$, and $$50 \times 20 = 1,\!000$$.
• Display and complete the table as students discuss their responses and reasoning for the last problem.

## Lesson Synthesis

### Lesson Synthesis

“Hoy aprendimos sobre una pareja de unidades para medir el peso —kilogramos y gramos— y otra para medir la cantidad de líquido —litros y mililitros—” // “Today we learned about a pair of units for measuring weight—kilograms and grams—and another for measuring the amount of liquids—liters and milliliters.”

“¿En qué se parecen las dos parejas?” // “How are the two pairs of units alike?” (In each pair, there is a larger unit and a smaller unit. One unit is 1,000 times the other.)

“¿Cuál pesa más: 5 kilogramos o 500 gramos?” // “Which weighs more: 5 kilograms or 500 grams?” (5 kilograms, because it is equivalent to 5,000 grams)

“¿Cuál contiene más: una botella de 2 litros o una botella de 20,000 mililitros?” // “Which holds more: a 2-liter bottle, or a 20,000-milliliter bottle?” (A 20,000-milliliter bottle, because 2 liters is equivalent to 2,000 milliliters)