Exploring Volume

by on March 20, 2012

The volume of a 3-D solid is the space inside of it; that is, how many cubes of a certain size it would take to fill it.  For this reason, volume is measured in cubic units (ex: in3 or cm3).  Volume can be a very confusing concept to children.  If your child is learning about volume, she has already had the opportunity to explore the concept of area of shapes.  Be sure you explain to her that we find the volume of 3-D solids (sometimes called 3-D shapes), and not flat shapes such as squares, triangles and rectangles.

BUILDING BLOCKS

If your child happens to own some building blocks, dig them out as you explore volume together.  Get a small, empty cardboard box (a tissue box works well), and ask your child to begin filling the bottom of the box with her blocks.  Once the blocks are completely covering the bottom (or as close as you can given the size of your blocks), ask her to count the number of blocks.  Write down that number.  Next, ask her to add another layer of blocks so it completely covers the first layer, and ask her to count the blocks in that layer (it should equal the number of blocks in the bottom layer!).  Continue filling the box with cubes until the box is completely filled up.  Add up the total number of blocks that she placed in the box.  If there are ex: 64 blocks, you can tell her that the box has a volume of 64 cubic units.  Note: If your blocks happen to be exactly 1 inch cubed, you can tell her that the volume of the box is 64 inches cubed.

SUGAR CUBES

If you do not have building blocks at your house, you can use sugar cubes to fill various containers to explore volume.

FORMULA FOR VOLUME

When children begin learning about volume, they first find the volume of rectangular prisms (boxes).  Once your child has had opportunities to fill containers with cubes to understand what volume looks like, she will be ready for the formula to calculate the volume of rectangular prisms.  The formula is simply Base x height  (B x h).  The Base is one side (we usually think of the Base as the bottom, but it doesn’t have to be).  To find the area of the base (which will be a square or a rectangle), multiply the length x the width.  Then, multiply this number times the height.  So, B x h is the same thing as length x width x height.  We usually express the formula as simply B x h because we can use this same formula later on for other solids (ex: triangular prisms and cylinders).

CALCULATING VOLUME OF A STACK OF BLOCKS

Once your child has learned the formula for calculating the volume of a rectangular prism, have her build some freestanding structures using blocks.  Be sure the structure is completely closed in. It should look like a closed in box.  Ask her to figure out the volume of her structure without counting all the cubes.  If she needs a hint, tell her to figure out how many blocks are in one layer of her structure (easiest to count the top layer).  Then, ask her how many layers she has.  Tell her it’s like slices of cubes stacked on top of each other.  So, if there are 12 cubes in one layer or “slice”, and there are 4 layers/slices, then there will be 12 x 4 cubes, or 48 cubes.  The volume of her structure would be 48 cubic units.

WANT MORE?

• As always, playing math games at home is a great way to reinforce math skills learned in school.