Composing Shapes · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Building New Shapes from Shapes

Mathematics · Geometry · ages 6-7
Name ______________________   Date ____________

  1. Two half-circles can be put together to make one whole circle.

    Circle one:   True   False

  2. Ben has two right triangles that are the same size and shape. He puts them together so their longest sides touch. Which new shape can he make?

    • A rectangle
    • A circle
    • An oval

  3. Leo has two same-size right triangles. He flips one over and slides it next to the other so their long slanted sides touch with no gaps. What shape do they make together?

    • A rectangle
    • A circle
    • A pentagon

  4. Once you build a shape by putting two triangles together, you can use that new shape to help build something even bigger.

    Circle one:   True   False

  5. Mia builds a rocket from shapes. She uses 1 triangle on top, 1 rectangle in the middle, and 2 small triangles for the fins. How many shapes did Mia use in all?

    Answer: ______________

  6. Look at a shape made of one rectangle with one triangle on top, like a little house. Which two shapes were used to build it?

    • A rectangle and a triangle
    • A circle and a square
    • Two half-circles

  7. Two quarter-circles fit together to make one half-circle. How many quarter-circles does Tia need to make one whole circle?

    Answer: ______________

  8. Leah is picking shapes for her picture. Which one of these shapes is NOT made of 4 straight sides?

    • A trapezoid
    • A circle
    • A rectangle

  9. Leo has a big rectangle. He makes one straight cut from one corner to the corner across from it. Which two shapes does he get?

    • Two triangles
    • Two squares
    • Two circles

  10. Ben looks at a shape made of a rectangle and a triangle on top. He says, 'This is just one plain shape, it wasn't built from anything.' What is wrong with what Ben said?

    • Nothing, Ben is right
    • Ben is wrong: rectangle plus triangle
    • Ben is wrong: it was built from four circles
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Building New Shapes from Shapes W1-mt_MqqR7VUoz1-s1

  1. True · A half-circle is a circle cut down the middle, so two half-circles fit back together into a whole circle.
  2. A rectangle · When two matching triangles join along their longest side, they make a rectangle.
  3. A rectangle · The two straight sides line up to form four right-angle corners, so together the triangles make a rectangle.
  4. True · Yes. A shape you build, like a rectangle made from two triangles, can be used again just like any other piece.
  5. 4 · Count each shape she used: 1 triangle plus 1 rectangle plus 2 triangles makes 4 shapes.
  6. A rectangle and a triangle · The flat bottom part is a rectangle, and the pointy roof part is a triangle.
  7. 4 · A whole circle is made of 2 half-circles, and each half-circle takes 2 quarter-circles, so 2 plus 2 makes 4.
  8. A circle · Trapezoids and rectangles are both 4-sided shapes, but a circle is one smooth curve with no straight sides at all.
  9. Two triangles · A cut from corner to corner splits a rectangle into two triangles, and those two triangles could be pushed back together to remake the rectangle.
  10. Ben is wrong: rectangle plus triangle · Even though it looks like one shape, it is a composite shape built from a rectangle and a triangle.
Worksheet · LightMySky