Explore the Effect of Side Lengths of a Rectangle on the Area.
(1.) Adjust the sliders so l = 5 and w = 3. How many squares fit inside the rectangle?
(2.) When we say that the area of the rectangle is “32 square cm” or “32 cm squared”, what do we really mean by that?
(3.) What measurements of the rectangle would give you an area of 32 square cm?
(4.) What is the formula for the area of a rectangle? Your answer should be in terms of l and w.
Explore Rectangles with Fractional Dimensions.
(1.) From the graph, how many squares with side lengths of inch can fit in a square with side lengths of 1 inch?
(2.) What is the area of a square with side lengths of inch? Explain or show your reasoning.
In the app below, draw a rectangle that is 3 ½ inches by 2 ¼ inches.
(1.) How many inch segments are in a length of inches?
(2.) How many inch segments are in a length of inches
(3.) Each of these multiplication expressions below represents the area of a rectangle. All regions shaded in light blue have the same area.
(4.) Explain your reasoning for the matches above.
Complete a Table with the Ratio of Side Lengths of a Rectangle.
The following rectangles in the applet below are composed of squares, and each rectangle is constructed using the previous rectangle. The side length of the first square is 1 unit.
(1.) Describe the values of the fraction of the longer side over the shorter side.
(2.) What happens to the fraction as the pattern continues?
Noah would like to cover a rectangular tray with rectangular tiles. The tray has a width of inches and an area of square inches.
(1.) Find the length of the tray in inches.
(2.) If the tiles are inch by inch, how many would Noah need to cover the tray completely, without gaps or overlaps? Explain your reasoning.
Find the unknown side length of the rectangle below.
Select all the equations that represent the relationship of the side lengths and area of the television below.