Lesson 1

Which one doesn’t belong? 

 

1. Which rectangle has the greatest perimeter?
2. Which rectangle has the greatest area?
3. Find a rectangle with the same perimeter, but an even greater area than the previous answer.
4. For the remaining questions, tables are provided to organize your work. Rectangle D has a perimeter of 32 units.
   1. Find the side lengths of three different possible rectangles that have this perimeter.
   2. Find a pair of side lengths for rectangle D that give the greatest area in square units.
   3. Find a pair of side lengths for rectangle D that give the smallest area in square units.

      length (units)	width (units)	perimeter (units)	area (square units)

5. Rectangle E has an area of 36 square units.
   1. Find 3 pairs of side lengths that give this area.
   2. Find a pair of side lengths for rectangle E that give the greatest perimeter in whole-number units.
   3. Find a pair of side lengths for rectangle E that give the smallest perimeter in whole-number units.

      length (units)	width (units)	perimeter (units)	area (square units)

 

Here are two tables. The first shows some measurements for Rectangle A, with a side length of 5 cm. The second shows some measurements of Rectangle B, which is a square.

1. Complete the table for Rectangle A and be prepared to explain your reasoning.

   length (cm)	width (cm)	perimeter (cm)	area (sq cm)
   5	1
   5	2
   5	4
   5		20
   5			40
   5		28
   5			50
   5	\(x\)

2. Complete the table for Rectangle B and be prepared to explain your reasoning.

   length (cm)	width (cm)	perimeter (cm)	area (sq cm)
   1	1
   2	2
   3	3
   4		16
   	8
   			100
   	\(x\)

3. Sketch the graph of each pair of quantities, where the width is plotted along the \(x\)-axis.

   1. \(x\) and the perimeter of Rectangle A

   2. \(x\) and the area of Rectangle A

   3. \(x\) and the perimeter of Rectangle B

   4. \(x\) and the area of Rectangle B