## Task Teacher Guide

Be sure to read the teacher guide prior to running the task. When you’re ready to run the task, use the tabs at the top of the page to navigate through the lesson.

### In This Task…

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

## Spark

### Notice and Wonder

Show students the **following image:**

Then, ask students:

What do you notice?

What do you wonder?

Have students do a Think-Pair-Share routine:

- Students have individual think time to jot down ideas on paper or whiteboard.
- Students share their initial ideas with a partner.
- 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?

## Sense Making

### Crafting a Productive Struggle

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## During Moves

### 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

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

## Next Moves

### Making Connections

### Reveal

### Reflect

Consider asking students to complete the following consolidation prompt independently.

**Consolidation Prompt #1:**

**Consolidation Prompt #2:**

We suggest collecting this reflection as an additional opportunity to engage in the formative assessment process to inform next steps for individual students as well as how the whole class will proceed.

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## Resources and Downloads

## Lesson Tip Sheet

Download the lesson plan in PDF format so you can keep it handy and share with colleagues.

## Videos & Images

Download the videos, images, and related media files to your computer to avoid streaming.

## Keynote Slides

Download in Apple Keynote format to avoid streaming video and run the lesson smoothly.

## PowerPoint Slides

Download in Microsoft PowerPoint format to avoid streaming video and run the lesson smoothly.

## Printable Handout

Download/edit the handout so you can keep it handy and share with colleagues.

## Explore The Entire Unit of Study

This Make Math Moments Task was designed to spark curiosity for a multi-day unit of study with built in purposeful practice, and extensions to elicit and emerge mathematical models and strategies.

Click the links at the top of this task to head to the other related lessons created for this unit of study.

### Struggle Prompt

### Reveal Image

### Consolidation Prompt #1

### Consolidation Prompt #2

**Download Editable/Printable Handout**

Become a member to access purposeful practice to display via your projector/TV, download the PDF to upload to your LMS and/or print for students to have a physical copy