Optimizing a Rectangle

Overview: Students determine the optimal swimming area for a fixed swimming perimeter, selecting from a variety of tools/resources to support their investigation.

Curriculum Expectation(s):

• Linear Relations: apply data-management techniques to investigate relationships between two variables
• Measurement and Geometry: determine, through investigation, the optimal values of various measurements of rectangles

Learning Goal(s):

• To investigate the area of different rectangles given a fixed perimeter, where one side is bounded by an obstruction
• To determine the maximum area of a rectangle with a fixed perimeter, where one side is bounded by an obstruction
• To use data management strategies to organize data

Linking Cube Race

Overview: Students race to link as many cubes as possible in certain time intervals. Using the collected data, students make a scatterplot to make inferences.

Curriculum Expectations:

• Linear Relations: Apply data-management techniques to investigate relationships between two variables.

• Number Sense and Algebra: Solve problems involving proportional reasoning.

Learning Goal:

• To collect and organize data
• Collecting data is useful for making inferences
• To learn about rates and to use them in decision-making