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.

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.

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?

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

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.

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?

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Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

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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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