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

Angles in Polygons Activity

Overview: Students investigate the interior angles of polygons and generalize to a pattern rule.

Curriculum Expectations:

• Measurement and Geometry: Determine, through investigation facilitated by dynamic geometry software, geometric properties and relationships involving two-dimensional shapes, and apply the results to solving problems

Learning Goal:

• To explore/identify the relationship between the sum of the interior angles and the number of sides in a polygon.
  

Building Squares and Cubes

Overview: Students time themselves building squares and cubes. Then predict the effect on time needed to build the squares and cubes if the side length is increased.

Curriculum Expectations

• Number sense and algebra: Solve problems involving proportional reasoning
• Measurement and geometry: Solve problems involving the measurements of two-dimensional shapes and the volumes of three-dimensional figures

Learning Goal:

• If the side length of a square doubles the area is four times larger.
• If the side length of a cube doubles the volume is eight times larger.
• The time it takes to build a square or cube will be proportional to its area or volume