Lesson 11

The purpose of this How Many Do You See is for students to group common decimal values and compose new units when they describe the images they see. This helps prepare students to add decimals given in numerical form in the lesson. Students may use words, fractions, or decimals to describe how many they see. 

• Groups of 2
• “¿Cuántos ven? ¿Cómo lo saben?, ¿qué ven?” // “How many do you see? How do you see them?”  
• Display the image.
• 1 minute: quiet think time

• Display the image. 
• “Discutan con su compañero cómo pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Record responses.
• Repeat for each image.

• Display the third image.
• “¿Cuántos ven? ¿Cómo lo saben?, ¿qué ven? // “How many do you see? How do you see them?” (I see 95 hundredths and 7 hundredths more. I can move 5 hundredths from the second square to the first and then I have 1 full square and 2 more hundredths.)

The purpose of this activity is for students to add decimals in a way that makes sense to them. Students may use a variety of strategies including

• drawing a diagram using hundredths grids (MP5)
• adding by place value
• adding on to the larger number

Students should be encouraged to use whatever strategies make sense to them.

This activity uses MLR7 Compare and Connect. Advances: Representing, Conversing.

• Each group of 2 needs a piece of chart paper and colored pencils, markers, or crayons.

• Groups of 2
• Give each group of students a piece of chart paper, colored pencils, crayons or markers, and access to hundredths grids.

• 5 minutes independent work time

• “Creen una presentación visual que muestre cómo pensaron en el primer problema. Incluyan detalles, como notas, diagramas o dibujos, para ayudar a los demás a entender cómo pensaron” // “Create a visual display that shows your thinking about the first problem. You may want to include details such as notes, diagrams or drawings to help others understand your thinking.”
• 2–5 minutes: partner work time
• 5–7 minutes: gallery walk

If students do not have a strategy for getting started, refer to the grids and ask, “¿Cómo podemos representar la suma en las cuadrículas?” // “How can we represent the sum on the grids?”

• Refer to the visual displays that students created or use the student solutions.
• “¿En qué se parecen y en qué son diferentes las estrategias?” // “What is the same and what is different between the strategies?” (Some of them use diagrams to show the numbers and add them and some of them use equations. They both have to think about making a new whole out of the decimals.)
• Display equation: \(0.8 + 0.2 = 1\)
• “¿Cómo se ve esta ecuación en el diagrama?” // “How does the diagram show this equation?” (I can move two shaded rows from 2.26 to complete the partly shaded square in 1.87.)
• Display equation: \(0.06 + 0.07 = 0.13\)
• “¿Cómo se ve esta ecuación en el diagrama?” // “How does the diagram show this equation?” (I can put together all of the single shaded squares that don't fill a full row from the two diagrams and I get 1 tenth and 3 hundredths.)

In the previous activity, students added decimals in a way that made sense to them. The purpose of this activity is for students to play a game that requires them to consider place value while adding decimals (MP7). This is Stage 8 of the center Target Numbers. Students played previous stages of this game with whole numbers in earlier grades.

• Each group of 2 needs 1 number cube.

• Groups of 2
• Give each group one number cube and a copy of the blackline master.
• “Vamos a jugar un juego llamado ‘Números objetivo’. Leamos las instrucciones y juguemos una ronda juntos” // “We’re going to play a game called Target Numbers. Let’s read through the directions and play one round together.”
• Read through the directions with the class and play a round with the class:
  • Display each roll of the number cube.
  • Think through your choices aloud.
  • Record your move and score for all to see.
• “Ahora jueguen el juego con su compañero” // “Now, play the game with your partner.”

• 8–10 minutes: partner work time
• Monitor for students who:
  • go over 1 and describe how they could have changed the placement of a number from the tenths place to the hundredths place to impact the game
  • don't come close to 1 and describe how they could have changed the placement of a number from the hundredths place to tenths place to impact the game

If students are not being strategic about their placement of the number rolled, ask, “¿Cómo decidiste si el número que obtuviste al lanzar el dado iba a valer décimas o centésimas?” // “How did you decide whether to make the number you rolled worth tenths or hundredths?”

• “¿Qué podrían haber hecho de otra forma para cambiar el resultado del juego?” // “What could you have done differently to change the outcome of the game?”
  • I picked too many tenths and went over.
  • I did not get close to 1 because I was worried about going over. I picked too many hundredths.
• Give students a chance to write their reflection.
• “Revisen las preguntas que escribieron en la última actividad sobre la suma de números decimales. Discutan con su compañero para ver si pueden responder algunas de sus preguntas” // “Look back at the questions you wrote in the last activity about adding decimals. Discuss with your partner whether you are able to answer any of your questions.”