3rd Grade - Use Cubes To Find Volume And Area

 
     
 
     
 
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3rd
Shapes and Geometry
Use Cubes to Find Volume and Area
Estimate or determine the area and volume of solid figures by covering them with squares or by counting the number of cubes that would fill them.
Measurement and Geometry: volume and area of solid figures The ability to determine a number representation of the space inside a shape. The object of this lesson is to show your child a way to calculate the area or volume of a polygon or solid shape without just learning a formula that would perform that calculation. When children use hands-on methods to perform calculations before they are taught a formula (recipe) for completing the task they are more apt to remember how to do it, even when they have not used the information for some time.
 

Sample Problems

(1)

Define area. (Count of how many square units fit inside a figure as a way of determining area.)

(2)

Can you use what you learned when you placed the square papers to figure out how we could write a rule for determining area? If we had to cut little squares for everything it would take a long time!


Answer: The formula for the area of a rectangle/square is its width times its height. When we used the little squares each had a width of 1 and a height of 1 so we just counted them up. Because each was worth “1” we counted how many there were in each direction and multiplied them together. We could just as easily use the measurement for each direction and multiply those numbers together. .

(3)

Advanced: How do I find the surface area of a cube? To find the surface area of a cube, find the surface area of one side (the length of a side squared) and then multiply by 6. Children can begin to explore this concept by creating a cube shape out of sugar cubes.

(4)

What is the formula for the volume of a cube? (a x a x a)

(5)

What is the difference between the area of a shape and the volume of a solid object? (area refers to the area of the surface (2D) of an object, whereas volume measures the amount of 3D space an object takes up)

Learning Tips

(1)

Have children take an index card and cover it with cut out cm squares. Children can also cover the card with dimes or pennies and a discussion can take place regarding which covers the card better (squares because there are no gaps). Children then count how many squares cover the card = area. Cover other shapes with the squares and children can see that different figures can have the same area. Measure perimeter of each figure, too. Children can see that figures with the same area can also have different perimeters.

(2)

Use geoboards, square shaped crackers or candy bars to calculate area. Place the items as you would tiles, filling up the space that you have marked. Count how many items it takes to completely fill the space.


Children can have fun with the challenge of creating a label for their answer, since the result will not be measured in feet, inches, centimeters, or any other conventional measure. Perhaps the label could be square candies? Square crackers?


Children can then measure the space occupied conventionally, calculate the area using paper squares of a known size and then convert their answer to square feet inches or centimeters, depending upon the measure of the paper squares.

(3)

Mark off (with masking tape) a square section of your kitchen or living room floor. Ask the child to sit on the floor with a package of rulers. Have the child take the rulers and mark off square feet and then calculate the area of the section of floor in square feet.

(4)

Children can explore volume/area by using base ten one cube blocks or cubes of sugar. Have the child make a cube (many layers) out of ones blocks. It is easier to see the middle of the cube if ones blocks are used.

(5)

Ask the child to trace a hand on a piece of graph paper and then count the number of squares inside the outline. The child will need to put together ½ and ¼ squares to make a whole and get an accurate count. If the paper is cm graph paper, the number the child gets would be the area in cubic cm. The child can try this activity with their foot or other household objects, too.

Extra Help Problems

(1)

The attached worksheet has 24 problems: 12 involve finding area by covering with 1 cm paper squares and 12 involve finding area by pretending that there are additional layers of cubes on top of the 2-dimensional areas calculated on the other page.

 

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