Embedded Files
My daughter is a dedicated artist. Recently, I walked into the room and saw her arranging items on the floor like this. I asked what she was doing and she explained that she was using sketchbooks and paper to outline an area on the floor equal to 18 by 24 inches, the size of a new canvas she wants to use for a painting.
Measuring a Rectangular Area
Measuring a Rectangular Area
Measurement: Area Units
Measurement: Area Units
I had cut a piece of cardboard for a different project that was 12 inches square, so 1 square foot. What would the area of an 18-by-24-inch canvas be in square feet, we wondered?
We placed the square foot in the region my daughter had outlined; in the picture, I outlined it in red to make it easy to see. We could see that another whole square foot would fit beneath it and that two more halves together would fill the remaining space to the right and my daughter quickly declared that it would be 3 square feet in area altogether!
Multiplication with Mixed Numbers and Decimal Numbers
Multiplication with Mixed Numbers and Decimal Numbers
We know that the dimensions of the canvas, in feet, would be 1 1/2 feet by 2 feet, so how could we express the area of the canvas as a product of those dimensions?
Well, 1 1/2 foot x 2 feet = 3 square feet.
Or, in decimals, 1.5 feet x 2 feet = 3 square feet.
We can look at the picture to see how we get that total area by thinking about the whole and half square feet we visualized.
Measurement: Converting Area Units
Measurement: Converting Area Units
Soooo ... coming back to inches. You can see in this picture how 1 square inch (the orange tile) compares to 1 square foot. It would take 144 tiles that size to cover 1 square foot! What would the area of the canvas be in square inches?
We could think of it in many ways. One way would be to think about the 144 square inches in each square foot ... so it would be 3 x 144 or 300 + 130 + 12 = 432 square inches. Some people might like to do that mentally.
We could also multiply 18 inches x 24 inches to get a total area of 432 square inches.
Also ... can you visualize a cubic foot? How many cubic inches would fill it? ... We can come back to that one in a different post!
Calculating: Multiplying 18 x 24
Calculating: Multiplying 18 x 24
We talked about 18 x 24. How can you multiply those numbers? How many different ways can you find to do it?
There are lots of ways to think about multiplying 18 and 24! We noticed that 18 and 24 are both multiples of 6, so we played that idea for a minute:
18 x 24 = (6 x 3) x (6 x 4)
= 6 x 6 x 3 x 4
= 36 x 12
= 36 x (10 + 2)
= 360 + 72
= 432!
(That's an exclamation point for excitement, not a factorial symbol!)
This might look like a bunch of numbers that make some people cringe, but we thought it was pretty fun and cool! The picture shows how you can make sense of those numbers and understand why our strategy works: math is not magic, even though it's really magical sometimes!
You can actually see how the associative and distributive properties are at work here, which is so awesome! When you understand how and why they work (not magic), you have the power to take numbers apart and put them back together in different ways to find elegant or efficient ways to calculate. So much fun! 18 and 24 are really versatile numbers, so you can probably find other ways to multiply them! Tell us about them. See if you can show them with a picture ... we can help you think about that if you want!
Page updated
Google Sites
Report abuse