# Cup Stacking

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## Objective

SWBAT gather data and create a function to represent a relationship among the data.

#### Big Idea

In this task, students are given a stack of 6 cups and are challenged to find the height of 50 cups by using a table, graph or equation.

## Warm Up

5 minutes

For today's Warm Up, I have again provided students a graph that has no axes labels.  This time, however, the slope is negative. I want students to create a story that matches this graph. This may pose a challenge as we have mostly seen and worked with positive slope line previously.

Once the timer sounds, I ask some "pre-selected" volunteers (ones I have picked out and asked beforehand while taking roll) to share their stories.  After each story is shared, I ask students to respond with thumbs-up (agree), thumbs-down (disagree) or thumbs-sideways (not sure). My hope is that by practicing these graphing stories, students will continue to gain a stronger conceptual understanding of the meaning embedded in graphs.

## Box of Cups Challenge

30 minutes

For today's activity, I provide each student a stack of 6 cups.  Because I typically seat four students to a table, I have four different brands of cups that I use.  That way, students can still support each other in the activity without giving each other data since each person at the table has a different set of 'prototype' cups.

Once everyone has their cups and lab sheet, I introduce today's scenario:

You have been hired by a box company to design a box that holds 50 cups. You have only been given a small number of cups as prototypes.  You must gather data about the cups you stack and organize it in a table. Then, using your data, graph the information. Use your table, graph, or rule to determine the height of the box you need to design for your stack of cups.

I explain that accuracy in measurement is critical in today's task, so we will be using Mathematical Practice 4: Attend to precision.  I call the students' attention to the fact that the table is already labeled in centimeters and ask, "Is centimeters precise enough or should we measure to tenths of a centimeter (mm)? What do you think the company would like?"

I then explain that I intentionally gave each student a stack of cups that is different from others at their table.  However, I still want to encourage them to support each other during the task as needed.

I ask for clarifying questions and set the task timer for 30 minutes.

## Closure

10 minutes

When the task timer sounds, I ask for volunteers to share the equations they found for their cup type.  On the SmartBoard, I wrote three equations for each type in a table, so students could easily compare them. I asked students to talk at their table for one minute about what would cause the differences in the equations of the same cup types. After a minute, students shared their ideas with the larger group. Most groups cited precision in measuring as the main cause.

To close the lesson, I wanted to see how well students were connecting their equations to the situation, so I posed the following questions for students to answer in their journals:

-What does the slope of your equation represent?

-What does the y-intercept of your equation represent?

Because more than half of my students speak English as a second language, I like to provide opportunities to write about their thinking, even if it's just a sentence or two, every day. As students leave class, I read over their responses, stacking their journals into two stacks:  One of students who demonstrate understanding and one for those who do not.  This will help me keep track of students who need additional support through after school tutoring.