Elementary Math: Introduction to Volume and Area
It is typically in third grade that children are first introduced to volume and area. To help your child get a head start on these concepts, use the following methods.
How Can I Introduce My Child to Area and Volume?
Start with Area
Third graders are typically introduced to area using 2dimensional figures. Teaching this can be a lot of fun because it lends itself to handson lessons. Give your child a sheet of graph paper and let him draw fun shapes. You can also look at teacher supply stores for geoboards, which are used to explore area, or find virtual or printable ones online. YouTube.com features several video tutorials about geoboards.
Next, your child can figure out the area of his shapes on the graph paper or geoboard by counting the number of squares enclosed within the shape outline. Teach him that the number of squares inside the shape, called the area, equals the length times the width. The formula for this is A = l x w.
Once your child is comfortable using the formula for area, ask him to design a house. He can draw the floor plan on graph paper and figure how much carpet or tile he would need to buy for various rooms in square feet. Give him some home decorating magazines so he can cut out pictures showing the kind of flooring he would want in different rooms.
Add Volume
You can use blocks or cubes to help your child comprehend volume. You can find special cubes for modeling math problems at teacher supply stores. Start by making a base of cubes. For example, if you make a base that's four across and five down (4 x 5), you'll use 20 cubes. Ask your child to count the cubes and determine the area.
Put a layer of cubes on top of these. Show her that you have another layer of 20 cubes and that if you add the two layers together, you have a total of 40 cubes. Demonstrate that if you multiply the area of the first layer by two  the number of layers you have  you also get 40. State that this is called the volume, and you would say you have 40 cubic units.
Encourage your child to spend time working with the cubes and adding more layers. With each layer, she can count how many blocks she has used. She can then multiply the area of the base with the number of layers and see if it gives her the same number of blocks that she counted. Teach her that the formula for volume is length times width times height, which is written as V = l x w x h.
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