Geometry

Shapes and Partitioning Equal Shares

Grade 2

✓By the end of this lesson students will be able to recognize and draw shapes based on their attributes, such as the number of sides and vertices.
✓By the end of this lesson students will be able to identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
✓By the end of this lesson students will be able to partition circles and rectangles into two, three, or four equal shares.
✓By the end of this lesson students will be able to describe the shares using terms like halves, thirds, and fourths (or quarters).
✓By the end of this lesson students will be able to understand that equal shares of identical wholes do not always have to be the same shape.

Key concepts

Recognizing Shapes by Attributes

Shapes can be recognized and named by their attributes, which are their special features. Important attributes for 2D shapes are the number of sides and the number of vertices (corners). A side is a straight line segment that forms part of the boundary of a shape. A vertex is the point where two sides meet. Here are some common shapes and their attributes:\n- A **triangle** has 3 sides and 3 vertices.\n- A **quadrilateral** has 4 sides and 4 vertices. Squares and rectangles are examples of quadrilaterals.\n- A **pentagon** has 5 sides and 5 vertices.\n- A **hexagon** has 6 sides and 6 vertices.\nWe also learn about 3D shapes like a **cube**, which has 6 square faces, 12 edges, and 8 vertices.

Partitioning Shapes into Equal Shares

To partition a shape means to divide it into smaller parts. When we partition a shape into **equal shares**, it means all the parts are exactly the same size. We can partition circles and rectangles into two, three, or four equal shares.\n- When a shape is divided into 2 equal shares, each share is called a **half**. We say 'one half' or '1/2'. The whole is 'two halves'.\n- When a shape is divided into 3 equal shares, each share is called a **third**. We say 'one third' or '1/3'. The whole is 'three thirds'.\n- When a shape is divided into 4 equal shares, each share is called a **fourth** or a **quarter**. We say 'one fourth' or '1/4'. The whole is 'four fourths' or 'four quarters'.\nIt's important to remember that equal shares of the same whole do not always have to look exactly alike in shape, as long as their size (area) is the same.

Key facts to remember

1Shapes are recognized by their attributes, such as the number of sides and vertices.
2A triangle has 3 sides and 3 vertices.
3A quadrilateral has 4 sides and 4 vertices (e.g., squares, rectangles).
4A pentagon has 5 sides and 5 vertices.
5A hexagon has 6 sides and 6 vertices.
6A cube is a 3D shape with 6 square faces, 12 edges, and 8 vertices.
7To partition a shape means to divide it into smaller parts.
8Equal shares are parts that are exactly the same size.
9Two equal shares are called halves, three equal shares are called thirds, and four equal shares are called fourths or quarters.

Worked examples

Example 1

Look at the shape described below. It has 4 straight sides and 4 vertices. All of its sides are the same length, and all of its vertices are square corners. What is the name of this shape?

IStep 1: Count the number of sides. The description states it has 4 sides.

IIStep 2: Count the number of vertices. The description states it has 4 vertices.

IIIStep 3: Recall the names of shapes based on their attributes. A shape with 4 sides and 4 vertices is a quadrilateral. Since all sides are the same length and all corners are square, it is a special type of quadrilateral.

IVStep 4: Identify the specific name. A quadrilateral with 4 equal sides and 4 square corners is a square.

Answer

The shape is a square.

A square is also a type of quadrilateral.

Example 2

Draw a rectangle and partition it into three equal shares. Shade one of the shares. What fraction of the rectangle is shaded?

IStep 1: Draw a rectangle.

IIStep 2: Divide the rectangle into three parts that are exactly the same size. You can do this by drawing two lines across the rectangle.

IIIStep 3: Shade one of the three equal parts.

IVStep 4: Identify the fraction. Since one out of three equal parts is shaded, the fraction is one third.

Answer

Drawing of a rectangle partitioned into three equal shares with one share shaded. The shaded fraction is one third (1/3).

Make sure your three parts are as equal in size as possible.

Example 3

Draw a circle and partition it into four equal shares. Label each share with its fraction name.

IStep 1: Draw a circle.

IIStep 2: Divide the circle into four parts that are exactly the same size. You can do this by drawing a plus sign (+) inside the circle, with the lines crossing at the center.

IIIStep 3: Label each of the four equal parts. Each part represents one fourth or one quarter.

Answer

Drawing of a circle partitioned into four equal shares. Each share is labeled 'one fourth' or '1/4'.

All four parts must be the same size to be 'equal shares'.

Common mistakes

✗Confusing the names of shapes, especially pentagons and hexagons, by miscounting sides or vertices.
✗Drawing unequal shares when asked to partition a shape into equal shares.
✗Not understanding that 'halves' means two equal parts, 'thirds' means three equal parts, and 'fourths' means four equal parts.
✗Believing that equal shares must always look identical in shape, even when partitioning the same whole in different ways.

Exam tips

★Always count the sides and vertices carefully when identifying and naming shapes.
★When partitioning shapes, use a ruler or straight edge for rectangles to help make your shares as equal as possible.
★Read the question carefully to know exactly how many equal shares you need to create (two, three, or four).
★Practice drawing different ways to partition circles and rectangles into equal shares to understand that shapes of shares can vary.

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