## 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…

In today’s lesson, students will revisit the data management concepts introduced on day 2. They will have an opportunity to engage in discourse around the big idea that intervals can be unitized and that the choice of unit will affect the representation of the data. A new concept that will be introduced is mean, the measure of central tendency. Students will be asked to redistribute the candy collected by all 6 participants and to redistribute it in a way that is more equitable.

### Intentionality…

The following big ideas will be reinforced and emerged through today’s lesson:

- There are different categories of data (i.e. categorical, numerical, continuous). The category should help determine how the data is represented.
- Value bars and other graphical representations can be used to show relations.
- There are different types of scales used in graphical representations and two different scale types can be used in a single graph (i.e. nominal and interval).
- A second axis can be used to show a precise quantity.
- Intervals on a scale can be unitized to represent larger quantities.
- Calculating the mean is a way to determine a single value to represent all of the quantities in a data set.
- Mean re-balances all of the quantities within a data set to create equilibrium.

## Math Talk

### Prompts

Ask students to consider the data represented in the stem and leaf plot below.

**Prompt #1***: *

If this data was represented on the y-axis of a bar graph, what unit would you use on your interval scale? Justify your choice.

**Prompt #2***:*

If Lorena suggests that the scale will increase by units of five, and Miguel suggests the scale should increase by units of 20, how will their graphs be the same? How will they be different?

### Walk Through Video

Here’s a quick math talk walk through video to help you build your comfort prior to delivering this math talk.

## Spark

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

You might recall the results of Lucia’s scavenger hunt.

Given what we already know about the distribution of candy from Lucia’s party, what do you notice and wonder now?

Allow students to share with their elbow partners and/or in their groups.

As usual, allow them to share their thinking with the whole class.

## Sense Making

### Crafting A Productive Struggle: Prompt

Do your best to facilitate the conversation students will start during the Spark portion of the lesson to listen for students who head down the path of whether the resulting distribution was fair or not.

A possible storyline or script you might leverage could include something like the following:

Wow, you all noticed some fantastic details and had some wonderful questions to share!

I found it interesting that many of you noticed that some participants received less candies than others. For example, mentioned that Savannah received about one-fourth as much candy as Chin.

Why do you think that may have happened?

Give students some time to turn and talk with each other first, before sharing out to the group.

Interestingly enough, at Lucia’s party, James suggested that it doesn’t really seem fair that he and some of the other participants received less candy than the others and proposed that all six friends should leave with the same amount of candy.

All six friends agree!

At this point, you can share the formal prompt for students which will craft the next productive struggle in this problem based unit:

If they should all receive the same amount, how much candy will each person be taking home?

## During Moves

### While Students Are Productively Struggling…

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### Student Approach #1: Redistributing Using Concrete/Visual Model

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### Student Approach #2: Redistributing Values Symbolically

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### Student Approach #3: Standard Algorithm Using Mental Math

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## Next Moves

### Consolidate

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### Walk Through Video

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### Reflect

Provide students an opportunity to reflect on their learning by offering these consolidation prompts to be completed independently.

**Consolidation Prompt #1:**

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**Consolidation Prompt #2:**

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**Download Editable/Printable Handout**

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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

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## Keynote Slides

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## 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.

### Consolidation Prompt #1

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### Consolidation Prompt #2

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**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