Divide Shapes into Equal Parts

In order to divide shapes into equal parts, your child must first understand that this can only be achieved in “regular” shapes. A regular shape’s sides and interior angles are equal to the shape’s other sides or angles.

Once this rule has been established, your child can utilize symmetry to divide shapes into equal parts. This concept serves as a fundamental foundation to master more advanced principles such as fractions and probability. To tell whether a shape can be broken into two or more equal parts, try cutting out a symmetrical figure of that shape, for example, a rectangle, and fold the shape. If the two parts of the shape match exactly, then you can include the shape in your instruction.

Rectangle Fold Rectangle Folded Rectangle

The most common divisions we use in daily life are halves, thirds, and quarters. For simplicity, a circle will be used to demonstrate dividing a shape equally into halves or quarters.


This term refers to dividing the shape into two equal parts. The easiest way to understand this concept is by cutting a circle out of a piece of paper. Fold it right down the middle of the circle so both sides overlap each other completely. Make sure the mark passes through the center of the circle. You can find the center by measuring the diameter of the circle with a ruler and then divide the measurement by two to find the mid-point.The mark you get from folding the piece of paper divides the shape into two perfect halves.

Circle Circle Half


For this measurement, you want to get four equal parts. You can show a quarter, or a fourth of a shape by using the circle you already cut out previously and simply fold it so it overlaps perfectly again, but this time, on the other side of the circle. Now, you have created four equal parts of a circle, and each part is referred to as “a quarter of” or “one-fourth” of a circle. Make sure the second mark intersects with the first mark at the center of the circle.

Circle Quarter


It will be difficult for young children to divide a circle into three equal parts, which involves using a protractor to measure the angles and finding the center of the circle with a ruler. Therefore, use a simpler shape, such as a rectangle, to demonstrate how you create three equal parts. Measure and cut out a rectangle that has a 6 cm length and a width that is anything shorter than 6 cm. Then, use a ruler to measure 2 cm intervals on one length of the rectangle. As you make a straight line from one length of the rectangle to the other, make sure the line is perpendicular, which means the line forms a 90° angle when it intersects with the edge. A third of a shape refers to three equal parts of a shape, which is why you had to divide the entire length (6 cm) by three, and you get the intervals you are looking for (2 cm).

Rectangle Thirds

Encourage your child to practice this concept using other regular shapes such as a square, triangle, or octagon.

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