5th grade foundations (Eureka Math/EngageNY)
Lindsay creates a rectangle that has the same area (but different side lengths) than a given rectangle. Created by Lindsay Spears.
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- So, here is our given rectangle, and we want to draw a rectangle with the same area, the same area, so what is the area of this rectangle? Area is the amount of space a shape covers, so how much space, or how many square units does this shape cover, does our rectangle cover? Each of these is one square unit, so our rectangle covers one, two, three, four, five, six, seven, eight square units. It has an area of eight square units. So, we want to draw another rectangle that also covers eight square units. If it covers eight square units, than it has an area of eight square units, but we can't just draw the identical rectangle, because we're also told that it should have, our rectangle should have no side lengths the same, so what are the side lengths of our rectangle? Over here on the left, it's one unit long, and going across the top is eight units long. This rectangle had eight square units, and they were broken up into one row of eight, so we need to think of another way that we can break up eight square units. One idea would be two rows of four, 'cause two rows of four would also cover eight, so let's try that. Let's create a rectangle here, two rows of four, and we can just spread this out a little bit so it covers the whole square units, and so this rectangle also covers one, two, three, four, five, six, seven, eight square units, so the given rectangle, and our rectangle have the same area because they cover the same amount of space, but they have different side lengths, because our new rectangle is, has a side length of two over here on the side, it's two units long, and going across the top is four units long, so it has new side lengths, so here's one way that we could draw a rectangle with the same area, but different side lengths.