Lesson 2

The purpose of this warm-up is for students to compare solid objects. Students may use informal language to describe the structure and orientation of the objects. Later in the lesson, students will have an opportunity to connect their informal language to more formal math vocabulary. During the synthesis, connect student's descriptions of the objects to the strategies they would use to count the number of cubes in each object. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology when describing the structure and orientation of three dimensional objects. During the synthesis, ask students to explain the meaning of any terminology they use, such as volume.

• Groups of  2
• Display image.
• “Escojan uno que sea diferente. Prepárense para compartir por qué es diferente” // “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”

• 1 minute: quiet think time
• 2–3 minutes: partner discussion
• Share and record responses.

• “Podemos contar el número de cubos unitarios que hay en un objeto para medir su volumen” // “We can count the number of unit cubes in an object to measure its volume.”
• “¿Cuántos cubos unitarios hay en el objeto D? ¿Cómo los contaron?” // “How many cubes are in object D? How did you count them?” (12, there are 6 on bottom and 6 on top)
• “¿Qué estrategia usarían para contar los cubos de los demás objetos?” // “What strategy would you use to count the cubes in the other objects?” (In object A, I can also see 2 groups of 6. In object B, I can see 2 groups of 6 minus 1. In object C, there is only one group of 6 and then there are 4 cubes and 2 cubes.)

The purpose of this activity is for students to build any object they want to. In the next activity, students focus only ;on rectangular prisms. As students count, they will need to make sure to count each cube once and only once. Monitor for these strategies:

• Touch each cube as it is counted
• Count the cubes by layer (including when there are different numbers of cubes in each layer)
• Use addition or multiplication when the cubes are organized in layers

• Each group of 2 needs 24 connecting cubes.

• Groups of  2
• Give 24 connecting cubes to each group.
• “En esta actividad, van a usar cubos unitarios para construir objetos y describir cómo medirían su volumen” // “In this activity, you will use unit cubes to build objects and describe how you would measure the volume.”
• 10 minutes: partner work time

• As students work, monitor for students who build rectangular prisms to share during the synthesis.

If students are counting all of the cubes one at a time, ask, “¿Dónde ves cubos que se puedan contar en grupo?” // “where do you see cubes that could be counted as a group?”

• Discuss responses to the last problem.
• “¿Cuáles objetos fueron los más difíciles de contar?” // “Which objects were most challenging to count?” (Objects where I had to count each individual cube because it was a weird shape.)
• “¿Cuáles objetos fueron los más fáciles de contar?” // “Which objects were the simplest to count?” (Organized shapes like towers, rectangles, cubes, or boxes.)
• Invite selected students to share the rectangular prisms they built and how they counted the number of cubes.
• “¿Cómo contaron los cubos?” // “How did you count the cubes?” (I knew that there were 4 cubes in each layer and 2 layers so that’s 8 cubes.)
• “A estos objetos los llamamos prismas rectangulares. ¿De qué maneras contaron los cubos de los prismas rectangulares?” // “We call these objects rectangular prisms. What were some ways you used to count the cubes in rectangular prisms?” (I counted the cubes in groups and then skip counted. I used multiplication to find the total.)

In the previous activity, students described how to count the number of unit cubes in an object and observed that for a special shape called a rectangular prism, the cubes are organized in a structure that makes counting them more systematic. The purpose of this activity is for students to continue to explore rectangular prisms, in particular their structure. As students describe the prisms, they communicate their ideas clearly and precisely (MP6). To describe an object requires students to identify key features of the object and communicate them in an unambiguous way to their partner.

This activity uses MLR2 Collect and Display. Advances: reading, writing

• Each group of 2 needs 16-24 connecting cubes.

• Groups of  2
• Display images.
• “¿En qué se parecen? ¿En qué son diferentes?” // “What is the same? What is different?” (There are 6 cubes in each shape. Each object is 2 cubes wide and 3 cubes long. One object is standing up on a side of 2 cubes and the other one is laying down on a side of 6 cubes.)
• “En esta actividad, van a construir y describir prismas rectangulares” // “In this activity, you will build and describe rectangular prisms.”
• Give each student 16-24 connecting cubes.
• Consider having students seated back to back or with an object between them that obstructs the view such as a folder.

MLR2 Collect and Display

• Circulate, listen for and collect the language students use to compare quantities. Listen for: layers, rows, columns, length, width, height, top, bottom, or side.
• Record students’ words and phrases on a visual display and update it throughout the remainder of the lesson.

If students do not see two prisms as the same when they are oriented differently, ask them to describe a prism, change the orientation of the prism, and ask them to describe it again. Emphasize that the total number of cubes stays the same, but the prism looks different.

• Invite partners who built different prisms to share their prisms and descriptions.
• “Del lenguaje que usó su compañero, ¿qué fue lo que más les ayudó a entender cuál prisma quería que construyeran?” // “What language did your partner use that was most helpful for you to understand the prism they wanted you to build?” (My partner said there were 6 cubes on the bottom and 6 more on top. So I made a row of 6 cubes and put another row on top. But my partner had two rows of 3 instead of one row of 6.)
• Use this discussion to update the display, by adding (or removing) language, diagrams, or annotations.
• Invite groups who built the same prisms to share.
• “¿Cómo le describieron su prisma a su compañero?” // “How did you describe your prism to your partner?” (I said how many cubes were on the bottom and how tall the prism was.)
• Use this discussion to update the display, by adding (or removing) language, diagrams, or annotations.
• Display any prism made by a student.
• “¿Cómo podemos describir este prisma usando el lenguaje de nuestra presentación?” // “How can we describe this prism using language from our display?” (Highlight the use of language about layers or stacks.)