Open Middle®
Directions: Draw three rectangles with a perimeter of 20 units.
Hint
How can we tell whether a rectangle has a perimeter of 20 units? How can we adjust our rectangle if it doesn’t have a perimeter of 20 units?
Answer
There are an infinite number of answers as long as the side lengths add up to 20 units.
Source: Dan Meyer
My students struggled with similar problems from Math Expressios this year. I tried using inch tiles, but found students confusing counting the units along the sides with counting the tiles. My idea for this year is to cut one inch lengths from straws & string them on yarn. Students could work together in small groups & each one have 20 lengths of straw on their strings. They must each make a rectangle which is different from their partners.
Thanks for the implementation suggestion Nancy!
EXCELLENT idea, Nancy!!
Also, this can be simplified to realizing that half the perimeter must be 10, so the height and width must sum to 10.
How can there be an infinite number of rectangles with a perimeter or 20 units?
If the side lengths are not whole numbers, then you can have lengths of 5.1, 5.01, 5.001, etc.