Video: KS2-M19 • Paper 2 • Question 21

Adam has this piece of rectangular card. It is marked with grid lines. Adam makes two straight cuts along the grid lines. The two cuts divide the rectangle into 3 shapes: 2 squares of different size, 1 rectangle. Using the grid lines, draw two lines that show where Adam could have made his cuts. Use a ruler.

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Video Transcript

Adam has this piece of rectangular card. It is marked with grid lines. Adam makes two straight cuts along the grid lines. The two cuts divide the rectangle into three shapes: two squares of different size, one rectangle. Using the grid lines, draw two lines that show where Adam could have made his cuts. Use a ruler.

The first piece of important information in this question tells us that the piece of card is rectangular. The rectangle is seven squares long and five squares wide. We know that Adam makes two straight cuts along the grid lines. And those cuts create three shapes: two squares of different size and a rectangle.

Let’s think about how we could create a square. We could make a square which measures five by five. Adam could make a straight cut along the pink line to make this square. With the remaining piece of card, Adam needs to make a square and a rectangle. This piece of card measures two by five. So if the square is two squares long, it must be two squares wide. So Adam could make his second cut here.

Now we have two squares of different size and a rectangle. So Adam could make his cuts on the grid where the pink lines are shown. We used our knowledge of 2D shapes to help us find the answer. We knew the piece of card was a rectangle, which measured seven by five. We knew we had to make two squares and a rectangle from the card. So first, we made a square which measures five by five because we know that squares have sides which are equal in length. So if the width of the square is five, the length has to be five.

We were left with a rectangle measuring two by five squares. We used our knowledge of geometry again to draw a square which was two by two. If the length of the square was two, the width of the square must be two. So we drew a five-by-five square, a two-by two-square, which left us with a rectangle. We used two lines to divide the rectangle into three shapes: two squares of different size and a rectangle.

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