Teaching children about the properties of three-dimensional shapes is often more difficult than teaching them about two-dimensional shapes. This is especially true when you use two-dimensional illustrations to represent three-dimensional shapes, as it can be difficult for children to grasp the relationship between the represented depth on the page and the depth of an actual 3D object. To help children understand this relationship, use actual 3D objects in an exercise. This will help them associate the mathematical properties of the shapes with the actual concept of three dimensions.

- Skill level:
- Moderately Challenging

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### Things you need

- Dice
- Deck of cards

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## Instructions

- 1
Show the children dice as a representation of three-dimensional cubes. Though any cubic object will work, dice are especially apt, as the numerical inscriptions on the dice give children a way to visually differentiate between the sides of the cube. Point out that the surface of the dice is essentially six two-dimensional squares linked together. This will help children apply their knowledge of 2D shapes to 3D objects.

- 2
Draw a three-dimensional representation of the dice on a piece of paper. Include the numerical dice values on the drawing to help the children associate it with the actual dice. Explain that the drawing represents the entire dice, including the material that makes up the centre of the dice.

- 3
Use a deck of cards to further establish the concept of three-dimensional volume. Each individual card can be seen as a two-dimensional rectangle. As you stack the cards, the deck begins to take on a three-dimensional shape. Seeing this process in action will help the children understand the relationship between 2D and 3D shapes. Allow the children to cut the deck of cards into multiple stacks so that they can see different three-dimensional volumes for themselves. For children who have trouble with calculation, have them count the cards of each stack. Explain that the greater number of cards represents a greater volume.

- 4
Teach the mathematical properties of a three-dimensional shape. Explain that the area of any individual square that makes up the cube can be calculated with the multiplication of the square's length and height. This area will feature an exponent of 2, as it is a 2D shape. Then, show how the volume of a cube can be calculated similarly by multiplying the cube's length, width and height. The volume will feature an exponent of 3, as it is a 3D shape. This relationship between the area of a square and cube, as well as the correlated exponents, show the children the mathematical difference between a 2D and 3D shape.