Lesson 9

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.

• 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

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

• “¿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.)

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.

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

• 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?”
• If possible, give students access to paper clips for reference.
• 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.

• 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.

• “¿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.

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.

• 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.

• 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.

• “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.  

• 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.