By the end of this unit, students are expected to:
Deepen their understanding of area and perimeter of rectangular and non-rectangular shapes.
Relate area to covering a figure
Relate perimeter to surrounding a figure
Analyze what it means to measure area and perimeter
Develop and use formulas for calculating area and perimeter
Develop techniques for estimating the area and perimeter of an irregular figure
Explore relationships between perimeter and area, including that one can vary considerably while the other stays fixed
Visually represent relationships between perimeter and area on a graph
Solve problems involving area and perimeter of rectangles
Analyze how the area of a triangle and the area of a parallelogram are related to each other and to the area of a rectangle.
Recognize that a triangle can be thought of as half of a rectangle whose sides are equal to the base and height of the triangle
Recognize that a parallelogram can be decomposed into two triangles. Thus the area of a parallelogram is twice the area of a triangle with the same base and height as the parallelogram
Know that the choice of base of a triangle (or parallelogram) is arbitrary but that the choice of the base determines the height
Recognize that there are many triangles (or parallelograms) that can be drawn with the same base and height
Develop formulas and strategies, stated in words or symbols, for finding the area and perimeter of triangles and parallelograms
Find the side lengths and area of polygons on a coordinate grid
Solve problems involving area and perimeter of parallelograms and triangles
Solve problems involving area and perimeter of polygons by composing into rectangles or decomposing into triangles
Extend their understanding of the volume of rectangular prisms.
Relate volume to filling a three-dimensional figure
Extend understanding of the strategies for finding the volume of rectangular prisms to accommodate fractional side lengths
Relate finding area of two-dimensional shapes to finding the surface area of three-dimensional objects
Develop strategies for finding the surface area of three-dimensional objects made from rectangles and triangles
Solve problems involving surface area of prisms and pyramids and volume of rectangular prisms
Pattern Blocks - Build bumper-car floor plans out of individual tiles.
Billy the Bug - Practice plotting point on a graph with Billy the Bug!
Data and Graphs - Graph and analyze your data (side length, perimeter, area, etc.).
Areas and Perimeters of Shapes and Images - Visualize and calculate the area and perimeter of triangles and parallelograms.
Geoboard - Create triangle families by keeping the base fixed and sliding the third vertex along a line parallel to the base.
Coordinate Grapher - Plot points and find the coordinates of the vertices of a polygon on a coordinate grid.
Virtual Box - Explore rectangular prisms and unfold them into nets. Use these resulting nets to find the surface area of the prism. Or, unfold the sides of a rectangular prism and fill with unit cubes or half-unit cubes to calculate volume.
Cube Nets - Examine various nets to decide if they form cubes when folded.
3D Geometry Tool - Arrange the two-dimensional faces of a prism or pyramid into a net, then print and fold to test your net. Also, find the surface area of the object by calculating the area of each of its two-dimensional faces or find the volume using a method developed in class.