# Linear Progression Worksheets

Worksheet A

The M&M Bucket

Name: _____________________________________________

Partner(s):__________________________________________

Problem Introduction: Tape the spring at the edge of your table. Attach the bucket to the bottom of the spring. You will fill your bucket with M&M’s in order to write a mathematical model of the relationship between the number of M&Ms in the bucket and the distance the bucket stretches from the table’s edge.

Describe the experiment:

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Conduct the experiment and collect the data.

Place the M&Ms in your bucket in multiples of 3, 4 or 5 and measure the distance from the top of the spring to the bottom of the bucket. Take seven measurements and record all information on a table of values.

The independent variable is _______________________ , measured in the units of ___________.

The dependent variable is ______________________, measured in the units of ______________.

Create a scatter plot of your data.

Using graph paper, plot your data carefully, labeling the axes and units. Then draw a line that best represents, or models your data.

Questions:

- How long would the spring stretch if 11 weights were used? ______________________ Explain how you arrived at this answer.

- If the total length of the spring and bucket is 36cm (or 16 in.), how many weights are in the bucket? _____________________ Explain how you arrived at this answer.

- If the total length of the spring and basket is 67 cm (or 25 in.), how many weights are in the bucket? ________________ Explain how you arrived at this answer.

- What is the meaning of the point where your line crosses the y-axis? Explain.

Choose two points that fall directly on or very close to your best fit line.

The points chosen are: __________________ and ______________________

Explain the data.

Using your graph and your data from your table, explain why the graph has this shape. Describe the shape of the graph. What factors influence this shape? How could this shape be different?

Using the points listed above, determine the slope between these two points.

Find the point where your line crosses your y-axis. (y-intercept)

Determine the equation of your line that models your data.

How much does the spring stretch for every one weight that is added to the bucket? ___________ Explain how you know this and demonstrate with an example.

What is the meaning of the rate of change in this model?

Is there a point where your line crosses the x-axis? If so, what is it and what does it mean? If not, why not? Explain.

Worksheet B

WHAT IF?

Suppose you were to use heavier weights in the bucket. How would this change your graph?

How would this change your equation?

Conduct the experiment with the new conditions. Sketch a scatter plot of your data, list some of the values of the lists and write an equation that represents your scatter plot.

EXTENSION

Predict how your graph would look if the experiment was conducted, however, instead of measuring the distance of the bucket from the meterstick, measure the distance of the bucket to the floor. Predict what your graph would look like, and predict what your equation may look like.

Write your predictions using ClarisWorks or Microsoft Word. Be sure to answer the following questions in your predictions. Write in complete sentences and in paragraphs.

How are your graphs similar? How are they different? Explain your reasoning.

How are the equations similar? How are they different? Explain your reasoning.

Do the y-intercepts mean the same in each equation? Explain your reasoning.

Do the slopes mean the same in each equation? Explain your reasoning.

If time permits, conduct this experiment and compare your data with your prediction.

How do your results compare with your predictions? Explain.