Larry and Gary are discussing whose garden has the most area to plant flowers. Larry claims that all they have to do is walk around the two gardens to get the perimeter and the one with the greatest perimeter has the greatest area. How would you help these students?
Well, Larry and Gary, you certainly seem to have a garden rivalry going on! But let me tell you, determining the greatest area just by measuring the perimeter is like judging a book by its cover - it doesn't really give you the full picture!
To accurately compare the garden areas, you'll need to measure the length and width of each garden separately. Then you can use the formula for finding the area, which is length multiplied by width. The garden with the greatest product of length and width will have the largest area for planting flowers.
So, put that tape measure away from the perimeter and grab a ruler to measure those dimensions, Larry and Gary! Happy gardening, and may the best area win!
I would start by explaining the difference between perimeter and area to Larry and Gary.
Perimeter is the distance around the outside of a shape, while area is the amount of space inside a shape.
Then, I would explain that Larry's claim is incorrect. The perimeter measures the length of the boundary of a shape, but it does not tell us anything about the area. We cannot determine the area just by knowing the perimeter.
To find out which garden has the greatest area, we need to calculate the actual area of each garden separately. The area is found by multiplying the length and width of each garden.
Once we have the areas of both gardens, we can compare them to see which one has the greater area.
To help Larry and Gary understand the relationship between perimeter and area accurately, you can explain the difference between the two concepts and how they are related.
1. Explain the concept of perimeter: The perimeter of a shape is the distance around its outer boundary. To find the perimeter of a garden, you need to measure the length of each side and add up the measurements. Walking around the garden will indeed give you the perimeter.
2. Introduce the concept of area: The area of a shape is the amount of space it covers. To find the area of a garden, you need to measure the length and width of the garden and multiply those values together. Walking around the garden will not give you the area.
3. Emphasize that perimeter and area are two different measurements: Perimeter is about the distance around an object, while area is about the space inside that object.
4. Demonstrate the relationship between perimeter and area: Consider two squares— one with sides measuring 4 units and another with sides measuring 6 units. Both squares will have different perimeters (16 units and 24 units) but the same area (16 square units). This shows that having a larger perimeter doesn't necessarily mean a larger area.
5. Provide an example with gardens: Show Larry and Gary two different gardens—one with a large perimeter but a small area, and another with a small perimeter but a large area. By calculating the area for each garden, they can compare the values to determine which garden has the greatest area for planting flowers.
By explaining the distinction between perimeter and area and providing examples, Larry and Gary will understand that the length of the perimeter doesn't directly determine the size of the area.
I would send them back to third grade, or at least Larry. I wonder what Gary said.
consider this
a garden by 24x6 area: 144 perimeter:60
a garden by 12x13 area: 156 perimeter:50
Larrys argument is shot down.