## CAN'T GET ENOUGH CEREAL [DAY 2]

### VOLUME AND SURFACE AREA OF RECTANGULAR PRISMS

Explore concepts relating to volume and surface area of right prisms.

## Intentionality & Unit Overview

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Students will further explore the context from Day 1 to compare the surface area of right rectangular prisms with fractional side lengths as they decide which cereal box uses the least amount of packaging.

## Intentionality…

In this task, students will compare the surface area of rectangular prisms. This task serves to illustrate the relationship between multiplication, addition and surface area.

Some of the big ideas that will likely emerge in this task include:

• Surface area is an attribute of a three-dimensional space
• Rectangular prisms can be decomposed into measurable parts
• Area is the amount of surface or space inside a two-dimensional region
• Surface area is additive – area of parts can be combined to find the area of the whole
• The area of a rectangle can be found by tiling unit squares of the appropriate unit
• The area of a rectangle having fractional side lengths can be found by tiling unit squares of the appropriate unit fraction

## What You’ll Need…

A variety of tools for students to use to think through the problems, including, but not limited to:

• Grid paper
• Whiteboards & markers
• Connecting cubes

## What Do You Notice? What Do You Wonder?

Show students the following image:

What do you notice?

What do you wonder?

Have students do a Think-Pair-Share routine:

1. Students have individual think time to jot down ideas on paper or whiteboard.
2. Students share their initial ideas with a partner.
3. Students share as a whole group, either their own preference, or a meaningful observation they heard from their partner during the share (while giving credit to their partner). All contributions are acknowledged and recorded on an anchor chart on the board.

Possible points that may come up include:

• I notice that it’s the same cereal boxes as yesterday
• I notice that the boxes are unfolded
• I wonder which box uses the least amount of cardboard

Spending time to acknowledge and address specific thoughts that students shared, whether a notice or a wonder, is crucial to building a culture in your classroom where students know that their voice is being valued and thus encourages them to continue sharing their thoughts and opinions later in this lesson and in future lessons.

## Estimation: Prompt

Once students’ initial ideas have been acknowledged and noted, the class can settle on a question to explore:

Which option uses the least amount of packaging?
Make an estimate.
.

Consider sharing this image as well so students can spatially estimate based on the net of each box. Be sure to remind students that each option has a different number of boxes of cereal included (i.e.: Option A has 2 boxes whereas Option C has only 1):

Students begin by making an estimate before they are provided with all the information they need to answer the question, thus providing students who may be reluctant to share with a safe entry point.

Students should be given an opportunity to share their estimates at this point, but refrain from sharing their rationale just yet in order to give everyone a chance to develop their own thinking.

Have students turn to a partner and generate questions they could ask that would provide them with information they could use to answer the question. Ask students how they would use the information to answer the question.

Prompt:

What information would you need to answer the question?

How would you use that information?

## Crafting A Productive Struggle: Prompt

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## While Students Are Productively Struggling…

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## Student Approach #1: Representational Model & Partitioning Strategy

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## Student Approach #2: Decomposing Strategies

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## Student Approach #3: Fraction/Decimal Equivalencies and Use of an Algorithm

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## Reveal

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## Consolidation

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## Reflect and Consolidation Prompts

Consider asking students to complete the following consolidation prompt independently.

### Consolidation Prompt #1:

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### Consolidation Prompt #2:

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## Educator Discussion Area

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