
Seesaw Nickels
Jim Roderick
7th grade
North Whitfield Middle School
Whitfield County Schools
Task

Overview
In this task, students will focus on extending their conceptual understanding of proportional relationships and direct variation to include inverse relationships. Students will use manipulatives, completed charts, and graphs to further their understanding.
Illustrative Task
Source: Jerald Murdock, Ellen Kamischke, and Eric Kamischke,
Discovering Algebra: An Investigative Approach, Key Curriculum Press
If a grown man and a small child sit on opposite ends of a seesaw, what happens? Would changing or moving the weight on one end of the seesaw affect the balance? You will find out as you do the experiment in this investigation.
 Step 1: On a flat desk or table, try to balance a ruler across a pencil that is taped to the desk, near the ruler’s 6inch mark.
 Step 2: Stack two nickels on the ruler so that they are centered 3 inches to the right of the pencil. You may need to tape them in place.
 Step 3: Place one nickel on the ruler to the left of the pencil so that it balances the two rightside nickels. Be sure the ruler stays centered over the pencil. How far from the pencil is this one nickel centered?
 Step 4: Repeat Step 3 for two, three, four, and six nickels on the ruler to the left of the pencil. Measure to the nearest ½ inch. Copy and complete the following table.
Left Side   Right Side  Number of nickels  Distance from pencil  Number of nickels  Distance from pencil  1   2   2   2   3   2  
 Step 5: As you increase the number of nickels on the left side, how does the distance from the balance point change? What relationships do you notice?
 Step 6: Make a new table and repeat the investigation with three nickels stacked 3 inches to the right of center. Does the same relationship seem to hold true?
 Step 7: Review the data in your tables. How does the number of nickels on the left and their distance from the pencil compare to the number of nickels on the right and their distance from the pencil? Write a sentence using the words left nickels, right nickels, left distance, and right distance to explain the relationship between the quantities in this investigation. Define variables and rewrite your sentence as an equation.
 Step 8: Graph the equation you wrote in Step 7. How is this graph similar to or different from the graph of a direct variation?


GPS Addressed

M7A3. Students will understand relationships between two variables.
 Plot points on a coordinate plane.
 Represent, describe, and analyze relations from tables, graphs, and formulas.
 Describe how change in one variable affects the other variable.
 Describe patterns in the graphs of proportional relationships, both direct (y=kx) and inverse (y=k/x)


Video Information


Use these questions to guide your thinking about some of the important teacher ideas in the lesson featured in the video clip.
 What kinds of questions does the teacher ask to promote students’ problem solving?
 How is the teacher gauging students’ current understandings and building from those understandings?
 Consider the GPS standards listed with this video.
 What makes this lesson different from lessons you have taught on this topic?


