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
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.