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You have named flat shapes and solids. Mia makes a gate display with a rectangle drawing and a cube-shaped toy.
How many straight sides does the rectangle drawing have?
Comparing 2-D and 3-D shapes
Analyse and compare 2-D and 3-D shapes using informal language to describe sides, vertices, and other attributes
What a learner can do afterwards
- Describe and count straight sides and corners of flat shapes, including a circle with none
- Compare flat shapes using side and corner counts, including triangles, rectangles and squares
- Compare flat shapes with solids using faces, curved parts and corners, including a cube's square faces
1 · Read
On a flat shape, a straight side runs from one corner to the next. A corner is where sides meet. A circle has no straight sides or corners. Choose a starting place when counting. Count each side or corner once. Stop when you get back to the start.
Try it together
The playground gate is a rectangle with 4 sides and 4 corners. It has two longer sides and two shorter sides. A square also has 4 sides and 4 corners, but all its sides have the same length. A square is a special rectangle. The gate has one more side than the triangle. Turning a shape does not change its counts.
A square is flat. A cube-shaped toy is solid. A face is a flat part of a solid's outside. A cube has six square faces and corners, with no curved parts. Each face has the shape of a flat square. A sphere is solid too, but it curves all the way around and has no corners.
Try it together
One square face of a cube has 4 corners. The whole cube has 8: 4 on top and 4 underneath. Count the top corners, then keep counting the bottom corners: 5, 6, 7, 8. Include corners hidden in a picture. For the gate display, Mia compares a flat rectangle drawing with a whole cube-shaped toy.
Compare the same kind of part: sides with sides, or corners with corners. A face is not a corner. Matching counts do not always mean matching shapes. A square and a rectangle that is not square both have 4 corners.
Try it together
For separate shapes, keep counting as you move to the next shape. Count a triangle's sides: 1, 2, 3. Then count a square's sides: 4, 5, 6, 7. There are 7 sides altogether. Each dot below stands for one counted side.
Tap each dot and count out loud.
Covering a corner does not remove it. Use the whole shape's count to find hidden corners. If a rectangle has 2 corners showing, count on to its full count of 4. Two more corners are hidden.
Try it together
You can compare side and corner counts on one flat shape. Count the sides first. Then start a new count for the corners. A rectangle has 4 sides and 4 corners, so these counts match. Keep the counts separate rather than adding them together.
Count each part once. Compare sides with sides and corners with corners. A square is flat; a cube is solid with square faces.
Geometry lesson and questions written for this dataset.
Readings and questions written for this dataset. Linked videos: Khan Academy.
More to read
Stop at the start
Choose a corner on a triangle drawing. Trace one side to the next corner. Keep going around the boundary. Count each side once.
Then count the corners. Returning to the starting corner does not add a new corner. Stop before counting it again. You find three sides and three corners.
Matching counts
A square and a rectangle that is not square both have four sides and four corners. Their counts match even though their side lengths differ.
A square's four sides are equal. The other rectangle has two longer sides and two shorter sides. Count sides with sides, or corners with corners, when comparing them.
A face and a whole solid
Look at one square face of a cube. It has four corners. Now check the whole cube. It has four corners on top and four underneath, making eight.
Some corners may be hidden in a drawing. They still belong to the cube. Counting just one face misses part of the solid.
Separate shapes
Draw two shapes with a gap between them. Count the sides on one shape, then keep counting on the next. The empty gap is not a side.
Check which part the question asks you to count. A face, a straight side and a corner are different things. Counting the right kind of part comes before finding the total.
Explore more
2 · Watch
3 · Play
Take it off screen
Print a worksheetA4 with an answer key page for grown-ups. No screen, no internet.
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
Then practise
18 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.