Lesson 6

The purpose of this What Do You Know About _____? is to invite students to share what they know and how they can represent the number 1,000. This routine allows teachers to collect information about students' ideas about the relative magnitude of 1,000.

• Display the number.
• “¿Qué saben acerca del 1,000?” // “What do you know about 1,000?”
• 1 minute: quiet think time

• Record responses.
• “¿Cómo podríamos representar el número 1,000?” // “How could we represent the number 1,000?”

• “¿Pueden recordar alguna vez en la que hayan visto 1,000 de algo?” // “Can you think of a time you have seen 1,000 of something?”

The purpose of this activity is to generate, say, and represent multi-digit numbers. Students arrange digit cards to create multi-digit numbers, and use base-ten blocks to represent each number. Teachers should remove cards showing 1 before distributing the set of digit cards, as they will be used later in the activity.

As students build numbers to the ten-thousands place, they may struggle to name the number. As they make sense of the value of the number, they should realize a need for more base-ten blocks, but should be given space to represent the number in a way that makes sense to them. It is not critical to name the number correctly or accurately describe how to build it. The idea is to create a bit of struggle to motivate another way to make sense of the number (MP1). Students see one way to represent 10,000 in the next activity.

• Create a set of cards from the blackline master for each group of 4. Remove the cards showing 1. These cards will be redistributed during the activity.
• Each group of 4 needs a small collection of base-ten blocks (for instance: 2 thousands, 5 hundreds, 10 tens, and 20 ones).

• Groups of 4
• Give each group a small set of base-ten blocks and a set of number cards. Ask them to find all the cards that show 2, 3, 4, or 5 and put the rest of the cards aside.

• “Vamos a crear números usando tarjetas de dígitos” // “We are going to create numbers with digit cards.”
• “Presten mucha atención a las instrucciones porque no siempre van a usar todas las tarjetas” // “Pay close attention to the directions because you will not use all the cards each time.”
• “Tómense un minuto para leer las dos primeras instrucciones y piensen qué preguntas surgen luego de leer” // “Take a minute to read the first two directions and think about any questions you have after reading them.”
• 1 minute: Collect and answer questions.
• 5 minutes: group work time
• Monitor for students who:
  • rearrange digits to make a new number and representation each time
  • add a digit to each number without rearranging digits
• Provide each group with the digit “1” and say “Asegúrense de que el 1 sea el primer dígito de su número (el de más a la izquierda)” // “make sure the 1 is the first digit in your number.”
• 5 minutes: group work time

Students may recognize that it is challenging to represent numbers greater than 1,000 with a small set of base-ten blocks. Consider asking:

• “¿Tienes bloques suficientes para representar el número?” // “Do you have enough blocks to represent the number?”
• “Si tuvieras bloques suficientes, ¿cuáles usarías?” // “If you had enough blocks, which would you use?”
• “¿Qué podrías dibujar o escribir para explicarle esto a un compañero?” // “What could you draw or write to explain this to a classmate?”

• “¿Cómo construirían 9,000?” // “How would you build 9,000?” (Use 9 of the large cubes)
• “¿Qué número formaríamos si añadiéramos un 1,000 más?” // “What number would we make if we add one more 1,000?” (10,000)

The purpose of this activity is to develop a sense of the magnitude of 10,000 and to establish ten-thousand as a unit consisting of 10 units of one-thousand.

In the launch, students learn that the 10-by-10 grid that represented 1 whole in a previous section now represents 100 in this activity. (It is important to establish that in these representations, each small square in the grid represents 1.) Students begin by organizing grids of 100 into groups of 1,000. Some students may intuitively decide to group grids by ten, while others may depend on counting each grid by 100. In the synthesis, students are invited to use their grids to create a class chart to show 10,000 as 10 units of one-thousand.

• Groups of 4
• Give each student a copy of the black line master.
• Display the 10-by-10 grid
• “¿Qué cantidad está representada por esta cuadrícula?” // “What amount is represented by this grid?” (1, 100, \(\frac{100}{100}\))
• “En la sección anterior, usamos una cuadrícula como esta para representar decimales y fracciones. En esta sección, esta cuadrícula va a representar centenas, como las que hay en los bloques de valor posicional” // “In the previous section a grid like this was used to represent decimals and fractions. In this section this grid will represent hundreds like those found in place value blocks.”
• “En la siguiente actividad, vamos a practicar cómo construir números usando estas cuadrículas” // “We are going to practice building numbers using these grids during the next activity.”
• “En grupo, construyan números usando las cuadrículas de 10 por 10” // “Work together to build numbers using 10-by-10 grids.”

• 10 minutes: group work time
• Monitor for students who organize the grids in groups of 1,000.
• As students work, consider asking,
  • “¿Cómo están agrupando sus cuadrículas?” // “How are you grouping your grids?”
  • “¿Por qué decidieron agrupar sus cuadrículas de esa manera?” // “Why did you decide to group your grids that way?”

Students may be unsure how to represent larger numbers in the thousands with the grids. Encourage them to represent numbers in the hundreds and work their way up, by adding more hundreds (one at a time, if helpful).

• “Organicemos nuestras cuadrículas en grupos de 1,000 para hacer un póster de 10,000. ¿Qué tan grande creen que será el póster?” // “Let’s organize our grids into groups of 1,000 to make a chart of 10,000. How large do you think the chart is going to be?” (Sample responses: As big as the wall, the length of the whiteboard.)
• Combine groups of 10-by-10 grids to form 10 rows of 1,000 to create a class chart of 10,000.
• Choral count by 1,000 and highlight how the chart reflects the count.
• “Anotemos los grupos de 1,000 en el póster a medida que contamos” // “Let’s record the groups of 1,000 on the chart as we count.”