Lesson 3

In this number talk, students find products of a decimal number and a power of 10 and quotients of a whole number and a power of 10 whose value is a decimal. This skill will be useful throughout the next several lessons as students convert between different metric units of measurement and also specifically address how a whole or decimal number changes when it is multiplied or divided by a power of 10.

• 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

• Record answers and strategy.
• Keep expressions and work displayed.
• Repeat with each expression.

• “¿En qué se parecen los valores de las expresiones?” // “What is the same about the values of the expressions?” (There is a 1 and a 5 in each value.)
• “¿En qué son diferentes los valores de las expresiones?” // “What is different about the values of the expressions?” (Some of them are whole numbers and some are decimals.)

The goal of this activity is to convert meters to centimeters and millimeters and to convert kilometers to meters. This metric measurement context gives students an opportunity to observe several patterns (MP7).

• When students convert from meters to centimeters or multiply by 100, the digits shift 2 places to the left.
• When students convert from kilometers to meters or multiply by 1,000, the digits shift 3 places to the left.

• Groups of 2
• Give students access to meter sticks.
• Display image from student workbook.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• Display additional information about track and field events:
  • The height of a hurdle is 1 meter.
  • The approximate distance between hurdles in 110 meter races is 10 meters.
  • The shortest race in many track competitions is 100 meters.
• “Completen los problemas con su compañero” // “Work with you partner to complete the problems.”

• 1–2 minutes: quiet think time
• 8–10 minutes: partner work time
• Monitor for students who observe that:
  • the digits shift 2 places to the left when converting from meters to centimeters or multiplying by 100
  • the digits shift 3 places to the left when converting from kilometers to meters or multiplying by 1,000

If students do not fill in the tables show them a meter stick and ask, “¿Cómo puedes usar la vara de un metro para completar la primera fila de la tabla?” // “How can you use the meter stick to fill in the first row of the table?”

• Display completed tables for all to see. 
• Invite students to share patterns they observed in the tables.
• “¿En qué se parecen las tablas? ¿En qué son diferentes?” // “How are the tables the same? How are they different?” (Some of the numbers in the tables are the same. Some of the relationships are the same. Going from meters to millimeters is the same as going from kilometers to meters because they are both 1,000 times greater. The second table only has two columns but has a bigger number, 1,000,000.)
• “Después de haber hecho la conversión de kilómetros a metros, ¿qué observan acerca de la ubicación del 1 y de la cantidad de ceros?” // “What do you notice about the location of the 1 and the number of zeros after converting from kilometers to meters?” (Each number in the meters column has three more zeros than the number in the kilometers column. The one in each number in the meters column is three places to the left of the corresponding number in the kilometers column.)

The purpose of this activity is for students to convert from meters to centimeters using the context of a standing broad jump, a common test for physical fitness. Students may multiply by 100 to convert from meters to centimeters or divide by 100 to convert from centimeters to meters. Students should be encouraged to use whatever strategy makes sense to them. Future lessons will focus specifically on conversion from centimeters to meters. Give students access to meter sticks.

• Groups of 2
• Display the image from student workbook.
• Give students access to meter sticks.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?” (The girl is jumping. There are numbers on the mat. Did she start where the footprints are? How far did she jump?)

• 1–2 minutes: quiet think time
• 6–8 minutes: partner work time
• Monitor for students who:
  • use their result for Tyler’s jump in centimeters to find his jump in millimeters
  • use the result in meters to find how far Tyler jumped in millimeters

If students do not know the relationship between millimeters, centimeters, and meters, show them a meter stick and ask “¿Cómo puedes usar la vara de un metro para averiguar cuántos milímetros hay en 1 metro?” // “How can you use the meter stick to figure out how many millimeters are in 1 meter?”

• Display the expression: \(1.43 \times 100\).
• “¿Cómo representa esta expresión el salto de Tyler, en centímetros?” // “How does this expression represent Tyler’s jump in centimeters?” (There are 100 centimeters in a meter.)
• Invite students to share how they found Tyler’s jump in millimeters.
• Display the expression: \((1.43 \times 100) \times 10\).
• “¿En qué unidad de medida está representado el salto de Tyler en esta expresión? ¿Cómo lo saben?” // “In what unit of measurement does this expression represent Tyler's jump? How do you know?” (It represents Tyler’s jump in millimeters. There are 10 millimeters in a centimeter and \(1.43\times100\) represents the centimeters, so if we multiply the number of centimeters by 10, we will get the number of millimeters.)
• Display the expression: \(1.43 \times 1,\!000\).
• “¿Cómo representa esta expresión el salto de Tyler, en milímetros?” // “How does this expression represent Tyler’s jump in millimeters?” (There are 1,000 millimeters in a meter so I have to multiply by 1,000 to get millimeters from meters.)
• Display the equation: \(1.43 \times 1,\!000 = (1.43 \times 100) \times 10\).
• Invite students to share which unit they prefer to express the distances that the students jumped.
• “Es importante que escojan una unidad que tenga sentido para ustedes” // “It’s important to choose a unit that makes sense to you.”