Mad Cow FarmInvestigation #2:

Changing Area, Changing Perimeter

Problem 2.1: Constant Area, Changing Perimeter Bessie needs to fence in her pasture. The

pasture needs to have an area of 24 square meters.

A.Experiment with different rectangles that have whole-number sides. Sketch each possible pasture plan on grid paper.

B. Record your data in the ”Constant Area” table. Look for patterns in the data.

Ponder the FollowingC. Each fence section is 1 meter in

length.• What determines how many fence

sections are needed, area or perimeter? Explain.

• Which design would need the most panels? Explain.

• Which design would need the least panels? Explain.

D.Use the axes on your graph paper to make a graph for various rectangles with an area of 24 square meters.

•When you are done graphing, describe the graph. How do the patterns you observe in your table, show up in your graph?

E. Repeat the process, because Bessie changed her mind and wants a pasture with an area of 36 square meters.

Constant Perimeter,

Changing Area

Constant Perimeter,

Changing Area

More Mad Decisions at the Mad Cow Farm

Bessie’s friend Bob has a set budget and bought 24 meters of fencing to build a pasture for his cows.

A. Find all the pasture sizes (perimeters) Bob can make with his 24 meters of fencing. Sketch all possible pasture plans on the grid paper.

B. Record your data in the ”Constant Perimeter” table. Look for patterns in the data.

1. Which rectangle has the least area? What is the area?

2. Which rectangle has the greatest area? What is the area?

C. Make a graph from your table.

1. Describe the graph. How do the patterns that you saw in your table show up in the graph?

2. Compare the graph to the “Length and Perimeter” graph.

Even More Mad Decisions at the Mad Cow Farm

Bessie’s friend Bob had a smaller budget than he thought. He was only able to buy 20 meters of fencing.

D. Repeat the process for the 20 meters of fencing.

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