Exploring Factors: Real-Life Applications for 8th Graders

A gardener has 48 square feet of space to plant flowers. If he wants to plant them in a rectangular area, what are the possible dimensions (length and width) he can choose that are factors of 48?

• (7, 7)

• (5, 9)

• (10, 5)

• (1, 48), (2, 24), (3, 16), (4, 12), (6, 8)

A rectangular garden has an area of 72 square feet. If the length is 8 feet, what is the width? Can you express the area as a product of its factors?

• 12 feet

• 10 feet

• 9 feet

• 6 feet

A school is organizing a field trip for 120 students. They want to arrange them in equal groups. What are the possible group sizes that can be formed using the factors of 120?

• 7

• 9

• 11

• [1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120]

A rectangular pool has a length of 10 meters and an area of 150 square meters. What is the width of the pool? Can you factor the area to find the dimensions?

• 12 meters

• 20 meters

• 15 meters

• 8 meters

A farmer has a rectangular plot of land with an area of 200 square meters. If the length is 20 meters, what is the width? Can you express the area as a product of its factors?

• 15 meters

• 5 meters

• 10 meters

• 25 meters

A box has a volume of 216 cubic inches. If the height is 6 inches, what is the area of the base? Can you factor the volume to find possible dimensions of the base?

• 24 square inches

• 36 square inches

• 48 square inches

• 54 square inches

A rectangular classroom has an area of 96 square feet. If the length is 12 feet, what is the width? Can you list the factors of 96 to find other possible dimensions?

• 12 feet

• 6 feet

• 10 feet

• 8 feet

A company produces 1800 units of a product. They want to package them in boxes that hold the same number of units. What are the possible box sizes based on the factors of 1800?

• 8

• [1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 60, 75, 90, 100, 150, 180, 225, 300, 450, 600, 900, 1800]

• 7

• 11

A rectangular garden has an area of 50 square meters. If the length is 10 meters, what is the width? Can you express the area as a product of its factors?

• 6 meters

• 5 meters

• 4 meters

• 8 meters

A rectangular piece of land has an area of 144 square meters. If the length is 12 meters, what is the width? Can you factor the area to find other possible dimensions?

• Width is 12 meters.

• Width is 8 meters.

• Width is 10 meters.

• Width is 6 meters.