Lesson 8

The purpose of an Estimation Exploration is to practice the skill of estimating a reasonable answer based on experience and known information. When students make estimates based on the number of tens they see and mentally organize the ones into groups of 10, they look for and make use of structure (MP7).

• Groups of 2
• Display the image.
• “Este diagrama muestra una colección de cubos encajables” // “This diagram shows a collection of connecting cubes.”
• ”¿Qué estimación sería muy alta?, ¿muy baja?, ¿razonable?” // “What is an estimate that’s too high? Too low? About right?”
• 1 minute: quiet think time

• “Discutan con su pareja cómo pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Record responses.
• “Miremos otra imagen de la misma colección” // “Let’s look at another image of the same collection.”
• Display the image.
• “Teniendo en cuenta la segunda imagen, ¿quieren cambiar sus estimaciones?” // “Based on the second image, do you want to change your estimates?”

• “¿Alguien cambió su estimación ‘razonable’ original? ¿Por qué la cambiaron?” // “Did anyone change their original ‘about right’ estimate? Why did you change it?” (I changed it because I see there are at least 40 cubes because there are 4 towers.)
• “Examinemos nuestras estimaciones ajustadas. ¿Por qué nuestras estimaciones fueron más precisas la segunda vez?” // “Let’s look at our revised estimates. Why were these estimates more accurate the second time?” (Some of the cubes are organized.)

The purpose of this activity is for students to interpret different base-ten representations of a two-digit number. Students compare drawings to words (_____ tens _____ ones) and an expression showing the value of the tens and ones digits as a sum. One of the representations shows the ones to the left of the tens so that students think about the value of the units. One of the representations shows a base-ten diagram with the towers of ten labeled “10” rather than representing all ten cubes in each tower. It is important that students who use this type of drawing can explain that the unit of ten contains 10 ones.

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

• Read the task statement.
• 5 minutes: independent work time
• 3 minutes: partner discussion
• Monitor for students who:
  • draw each representation as tens and ones
  • use numbers and words to connect each representation

• Invite previously identified students to share.
• “¿Qué conexiones ven entre las representaciones?” // “What connections do you see between the representations?” (Each representation shows the same amount. Each representation shows tens and ones.)
• “¿En qué se parece la representación de Han a la de Clare? ¿En qué es diferente?” // “How is Han’s representation the same as Clare’s? How is it different?" (They both show 73. Han’s shows tens and ones, but the tens don’t show all the ones. Instead he labels it as 10 or 1.)
• “La representación de Han es una representación nueva que pueden intentar usar para mostrar cómo piensan” // “Han’s representation is a new representation that you may want to try using to show your thinking.”

The purpose of this activity is for students to match cards that show different base-ten representations. The representations are base-ten diagrams, ___ tens ___ ones, and addition expressions that show the value of the tens and ones digits. Some cards represent the ones to the left of the tens to encourage students to focus on the units and the meaning of any digits (MP2, MP7). As students work, encourage them to refine their descriptions of representations and how they match using more precise language and mathematical terms (MP6).

• Create a set of cards from the blackline master for each group of 2–4.

• Groups of 2-4
• Give each group a set of cards and access to connecting cubes in towers of 10 and
  • Groups of 2-4
  • Give each group a set of cards and access to connecting cubes in towers of 10 and singles.
  • Display the student workbook page.
  • “Hoy vamos a clasificar tarjetas en grupos que muestren el mismo número de dos dígitos. Por ejemplo, miren estas tres tarjetas. ¿Cuáles dos representaciones muestran el mismo número de dos dígitos? ¿Por qué la otra es diferente?” // “Today we are going to sort cards into groups that show the same two-digit number. For example, look at these three cards. Which two representations show the same two-digit number? Why doesn’t the other one belong?” (The first two cards both show 4 tens and 1 one or 41. The last card isn't the same because it only shows 1 ten. It has the same digits, but they mean something different.)
  • 30 seconds: quiet think time
  • 1 minute: partner discussion
  • Share responses.

• “Estas tarjetas incluyen diagramas en base diez, palabras que muestran __ decenas y __ unidades, expresiones y números de dos dígitos. Encuentren todas las tarjetas que muestren el mismo número. Cada grupo que encuentren debe tener tres tarjetas que correspondan, pero pueden ser diferentes tipos de representaciones” // “This set of cards includes base-ten diagrams, words that show ___ tens and ___ones, expressions, and two-digit numbers. Find all the cards that show the same number. Each group should have three cards that match, but they might be different kinds of representations."
• “Con su pareja, expliquen de qué manera las tarjetas corresponden o por qué algunas tarjetas no pertenecen a un grupo” // “Work with your partner to explain how the cards match or why some cards don’t belong with a group.”
• 8 minutes: partner work time
• As students work, consider asking:
  • “¿Por qué asociaron estas tarjetas? ¿Cómo están asociadas?” // “Why did you match these cards together? How do they match?”
  • “¿La tarjeta __ corresponde a este grupo de tarjetas? ¿Por qué sí o por qué no?” // “Would Card __ match with this group of cards? Why or why not?”
  • “¿Cómo podrían explicar la forma en la que sus tarjetas corresponden, usando las palabras decenas y unidades?” // “How could you explain how your cards match using the words tens and ones?”
  • “¿Qué tienen en común las tarjetas de este grupo? ¿En qué son diferentes?” // “How are the cards in this group the same? How are they different?”

• Invite students to share the matches they made and how they know those cards go together.
• Attend to the language that students use to describe their matches and the representations, giving them opportunities to describe the representations more precisely with attention to how they show amounts of tens and ones.
• Highlight the use of terms like tens, ones, and digits.

The purpose of this activity is for students to learn a new center called Grab and Count. Students grab a handful of ones cubes and put them together with their partner’s. They estimate how many cubes there are and then count the cubes. Students record their estimate and the actual number of cubes on the recording sheet. Since students have not written two-digit numbers yet, students may attempt to record the two-digit number or use other, more familiar, representations to show the amount of cubes.

• Groups of 2
• Give each group two recording sheets and access to ones cubes.
• “Hoy vamos a conocer un centro nuevo llamado ‘Agarra y cuenta’” // “We are going to learn a new center called Grab and Count.”
•  “Los dos compañeros cojan un puñado de cubos. Junten sus cubos. Estimen cuántos cubos tienen y anoten su estimación en su hoja de registro. Después, cuenten los cubos de cualquier forma que tenga sentido para ustedes. Anoten el número de cubos que contaron” // “Both partners grab a handful of cubes. Put your cubes together. Then estimate how many cubes you have and record your estimate on your recording sheet. Then count the cubes in any way that makes sense to you. Record the number of cubes you counted.”

• 10 minutes: partner work time

• “¿Cómo supieron qué cubos ya habían contado mientras contaban?” // “How did you keep track of the cubes as you counted?” (We made groups of ten. We moved the cubes as we counted them.)