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Mathematics notes, unit 7

Shapes

Textbook Mathematics Year 1 (DLP), Textbook Part 1 and Part 2, pages Part 2, 61–74

What this chapter covers

  • You can name a cube, a cuboid, a pyramid, a cylinder, a cone and a sphere, and find them in real objects (7.1.1)
  • You can count the flat faces, vertices and straight edges of 3-D shapes, and say which have a curved face (7.1.2)
  • You can find the missing shape in a pattern of 3-D shapes, and name the shapes in a model (7.1.3, 7.1.4)
  • You can name a square, a rectangle, a triangle and a circle, and know they come from the flat faces of 3-D shapes (7.2.1)
  • You can count the straight sides, curved sides and corners of 2-D shapes (7.2.2)
  • You can find the missing shape in a pattern of 2-D shapes and make your own pattern (7.2.3, 7.2.4)
  • You can solve a simple shape problem by guess and check (7.3.1)

7.13-D shapes

A 3-D shape is a solid shape. You can hold it. It has length, breadth and height.

Textbook picture of a cube, a cuboid and a pyramid with their names
Cube, cuboid and pyramid.

Textbook figure: Mathematics Year 1, Part 2, p.62.

A cube, a pyramid, a cylinder, a cone and a sphere in a row
Cube, pyramid, cylinder, cone, sphere.
ShapeThings that look like it
Cubedice, gift box
Cuboidtissue box, cake box
Pyramida pyramid gift, a tent
Cylindertin can, drum
Coneparty hat, ice-cream cone
Sphereball, marble
A tissue box is a cuboid. A ball is a sphere.
What shape is a tin can? What shape is a ball?
Show answerHide answer
A tin can is a cylinder. A ball is a sphere.

7.2Faces, vertices and edges

Flat face: a flat side you can put on the table.
Vertex: a corner where edges meet.
Straight edge: a line where two faces meet.
Curved face: a face that is round, not flat.
Cube with a vertex, an edge and a flat face labelled
Cube
Cone with a curved face and a vertex labelled
Cone
Cylinder with a flat face and a curved face labelled
Cylinder
ShapeFlat facesCurved facesVerticesStraight edges
Cube60812
Cuboid60812
Pyramid5058
Cylinder2100
Cone1110
Sphere0100

Textbook facts: Mathematics Year 1, Part 2, pp. 64-65. Figures drawn for this site.

In a cube all 6 faces are the same size. Only a cube has this.
Careful! A sphere has no flat face. It has only 1 curved face.
How many flat faces does a cone have? How many vertices does a cylinder have?
Show answerHide answer
A cone has 1 flat face. A cylinder has 0 vertices.

7.33-D patterns and models

A pattern is shapes arranged again and again. Find the part that repeats.

Pattern of a cube, a cone, a cube, a cone, a cube and a cone
Cube, cone, cube, cone ... The next shape is a cube.

We can build a model from 3-D shapes. Then we count how many of each shape we used.

Example
A castle model uses 2 cones, 3 cylinders, 2 cubes, 1 cuboid and 1 pyramid. Count all: 2 + 3 + 2 + 1 + 1 = 9 shapes.
Cube, cone, cube, cone, cube, ___. What is the missing shape?
Show answerHide answer
The pattern is cube, cone. The missing shape is a cone.

7.42-D shapes

A 2-D shape is flat. 2-D shapes are on the flat faces of 3-D shapes. Trace round a flat face to draw one.

Children trace a flat face of a box to make a square and trace a cone to make a circle
Trace a flat face: a square from a box, a circle from a cone.

Textbook figure: Mathematics Year 1, Part 2, p.68.

A square, a rectangle, a triangle and a circle in a row
Square, rectangle, triangle, circle.
Which 3-D shape gives a circle when you trace its flat face?
Show answerHide answer
A cone (or a cylinder).

7.5Sides and corners

ShapeStraight sidesCurved sidesCorners
Square404
Rectangle404
Triangle303
Circle010

Textbook facts: Mathematics Year 1, Part 2, p.69.

A circle is the only one with a curved side and no corners.
How many corners does a triangle have? Which shape has 1 curved side?
Show answerHide answer
A triangle has 3 corners. The circle has 1 curved side.

7.62-D patterns

Pattern of triangle, square, triangle, square, triangle, square
Triangle, square, triangle, square ...

Say the pattern aloud. Then find the shape that comes next.

Triangle, square, triangle, square, triangle, ___. What comes next?
Show answerHide answer
A square.

7.7Solve a shape problem

Example
A shape has 1 vertex and 1 flat face. Guess a cone: 1 vertex, 1 flat face. Yes! It is a cone.
Example
Two shapes have 7 sides in all. Try 4 + 4 = 8, no. Try 4 + 3 = 7, yes! It is a square (or rectangle) and a triangle.
Guess, then check. If it is wrong, try again.
Two shapes have 6 sides in all. Both are triangles. Is this right?
Show answerHide answer
3 + 3 = 6. Yes.

Summary

  • 3-D shapes: cube, cuboid, pyramid, cylinder, cone, sphere.
  • Cube and cuboid: 6 flat faces, 8 vertices, 12 edges. Pyramid: 5 flat faces, 5 vertices.
  • 2-D shapes: square, rectangle, triangle, circle.
  • Triangle 3 sides, square and rectangle 4 sides, circle 1 curved side.