Lesson 7

The purpose of this warm-up is for students to notice how numbers are alike and different, which will be useful when students connect the number of tens and ones to how two-digit numbers are read and written in a later activity. In the synthesis, students are introduced to the term two-digit number. While students may notice and wonder many things about these numbers, the differences between one-digit numbers and two-digit numbers are the important discussion points.

• Groups of 2
• Display the image.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• 1 minute: quiet think time

• “Discutan con su pareja lo que pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

• “Los números del conjunto B se llaman números de dos dígitos” // “The numbers in Set B are called two-digit numbers.”
• Display 89.
• “Este es un número, el número ochenta y nueve. Este número tiene 2 dígitos, un 8 y un 9” // “This is one number, the number eighty-nine. This number has two digits, an 8 and a 9.”
• “En el número 89, el 8 nos dice cuántas decenas hay en el número y el 9 nos dice cuántas unidades hay en el número” // “In the number 89, the 8 tells us how many tens are in the number and the 9 tells us how many ones are in the number.”
• “Hoy van a formar números de dos dígitos” // “Today you will work on making two-digit numbers.”

The purpose of this activity is for students to extend their understanding of teen numbers as a ten and some ones to an understanding of all two-digit numbers as some tens and some ones. Students choose two number cards and create a two-digit number. As they build the two-digit numbers with towers of 10 and singles, students see that each two-digit number is composed of a number of tens and a number of ones (MP8). Some students may read the two-digit number and count out towers of 10 and singles until they have made the number. For example, they may read 82 as eighty-two and count by 10 to 80 and count on by one to 82. Some students may begin to think about the meaning of each digit and take that many tens and ones to make the number. For example, they show they know the digit 8 in 82 means 8 tens and the 2 means 2 ones, so they grab 8 towers of 10 and 2 singles.

During the launch the teacher demonstrates how to make a two-digit number using number cards and explains how students record their thinking. However, the teacher should not demonstrate making the number using the connecting cubes, drawings, or _____ tens _____ ones. It is important for students to explore these representations during the activity.

• Groups of 2
• Give each group a set of number cards, connecting cubes in towers of 10 and singles, and recording sheets.
• Ask students to take out the cards with 10 on them.
• “Vamos a jugar un juego que se llama ‘Fórmalo’. Con su pareja, van a formar un número de dos dígitos y van a representar el número de diferentes maneras” // “We are going to play a game called Make It. You will work with your partner to make a two-digit number and represent the number in different ways.”
• Display two number cards and the recording sheet.
• “Primero, uno de ustedes escoge dos tarjetas de números y forma un número de dos dígitos. Yo escogí un [3] y un [5]. ¿Qué números de dos dígitos puedo formar?” // “First, one partner picks two number cards and makes a two-digit number. I picked a [3] and a [5]. What two-digit numbers can I make?” (35 or 53)
• Demonstrate writing one of the numbers on the recording sheet.
• “Ahora los dos compañeros dicen el número” // “Now both partners say the number.”
• “Después, el compañero que formó el número observa al otro compañero construir un número con cubos encajables. Asegúrense de que los dos estén de acuerdo en cómo construir el número. Después, los dos compañeros completan la hoja de registro con un dibujo y el número de decenas y unidades” // “Then, the partner who made the number watches the other partner build the number with connecting cubes. Make sure you both agree on how to build the number. Then both partners complete the recording sheet with a drawing and the number of tens and ones.”

• 10 minutes: partner work time
• As students work, consider asking:
  • “¿Cómo se dice este número de dos digitos?” // “How do you say this two-digit number?”
  • “¿Cuál es su plan para construir el número?” // “What is your plan for building the number?”
  • “¿Cuántas decenas tiene este número?” // “How many tens does this number have?”
  • “¿Cuántas unidades tiene este número?” // “How many ones does this number have?”

If students build the numbers with single connecting cubes, consider asking:

• “¿Cómo usaste los cubos para construir el número?” // “How did you use cubes to build the number?”
• “¿Cómo puedes usar las torres de 10 para construir este número? ¿Cuántas torres necesitarías?” // “How could you use towers of 10 to build this number? How many towers would you need?”

• Display the number 24 and a base-ten drawing of 4 tens and 2 ones.
• “Tyler hizo un dibujo de 24. ¿Están de acuerdo con la forma en la que mostró 24? ¿Por qué sí o por qué no?” // “Tyler made a drawing of 24. Do you agree with how he showed 24? Why or why not?” (No, because he drew 4 tens and 2 ones instead of 2 tens and 4 ones. He made the number 42 instead of 24.)
• “El dibujo de Tyler muestra 42, no 24. Ambos tienen los dígitos 2 y 4, pero en lugares diferentes, y esto los hace números diferentes” // “Tyler’s drawing shows 42, not 24. They both have the digits 2 and 4, but they are in different places, which makes them different numbers.”

The purpose of this activity is for students to think about the value of tens and ones and consider a representation where the tens are not presented to the left of the ones. In the previous activity, students saw that the order of the digits matters when writing a two-digit number. In this activity, students see that although the order matters when writing a number, the position of tens or ones in a drawing or diagram does not change their value. Students have access to connecting cubes in towers of 10 and singles if needed and should be encouraged to use them if they have difficulty making meaning of the base-ten diagram in their workbook.

During the activity synthesis, the teacher emphasizes the value of the units in the diagram and the digits and connects them to the commutative property.

When students decide who they agree with and explain their reasoning, they critique the reasoning of others (MP3).

• Groups of 2
• Give students access to connecting cubes in towers of 10 and singles.

• Read the task statement.
• 1 minute: quiet think time
• “Discutan con su pareja cómo pensaron” // “Share your thinking with your partner.”
• 2 minutes: partner discussion
• “Ahora muestren en su libro cómo pensaron” // “Now show your thinking in your book.”
• 3 minutes: independent work time
• Monitor for a student who explains that the order of the representation doesn’t change the value of the digits in the number and justifies that the representation shows:
  • 10, 20, 30, 40, 50, 60, 70, 80, 81, 82, 83, 84, 85, 86
  • 1, 2, 3, 4, 5, 6, 16, 26, 36, 46, 56, 66, 76, 86
  • 8 tens as 80, count on 81, 82, 83, 84, 85, 86

• Invite previously identified students to share.
• Display 68 and 86.
• “Cuándo veo estos números de dos dígitos, el orden de los dígitos importa. El orden me ayuda a decir el número. Pero, cuando mostramos dibujos de números de dos dígitos, no importa si las decenas o las unidades van primero. De todas maneras hay 8 decenas y 6 unidades” // “When I look at these two-digit numbers, the order of the digits matters. The order helps me say the number. However, when showing two-digit numbers with drawings, it doesn’t matter whether the tens or the ones come first. There are still 8 tens and 6 ones.”

The purpose of this activity is for students to choose from activities that offer practice adding and subtracting within 20, or with multiples of 10. Students choose from any stage of previously introduced centers.

• Shake and Spill
• How Close
• Check It Off

• Gather materials from previous centers:
  • Shake and Spill, Stages 3–5
  • How Close, Stages 1 and 2
  • Check It Off, Stages 1–3

• Groups of 2
• “Ahora van a escoger un centro de los que ya conocemos” // “Now you are going to choose from centers we have already learned.”
• Display the center choices in the student book.
• “Piensen qué les gustaría hacer” // “Think about what you would like to do.”
• 30 seconds: quiet think time

• Invite students to work at the center of their choice. 
• 10 minutes: center work time

• Display nine red counters and put eight yellow counters under a cup.
• “Mai juega ‘Revuelve y saca’ con 17 fichas. ¿Cuántas fichas amarillas hay debajo del vaso? ¿Cómo lo saben?” // “Mai is playing Shake and Spill with 17 counters. How many yellow counters are under the cup? How do you know?”