Fractions as parts of a whole

What it looks like when your child can do it

• — Shown a pan of brownies cut into 8 equal pieces with 3 eaten, your child says 3/8 of the pan is gone and 5/8 is left.
• — Your child points out when pieces are not the same size, and says a fraction only counts equal parts.
• — Asked what 2/5 means, your child says something like "the whole is cut into 5 equal parts and we have 2 of them."

How to teach it at the kitchen table

1. 01

   Start with something you can fold

   Fold a sheet of paper into 4 equal strips and shade 3. Say it together: the whole is cut into 4 equal parts and 3 are shaded, so 3/4 is shaded.

2. 02

   Name the job of each number

   The bottom number says how many equal parts the whole was cut into. The top number says how many of those parts you are talking about.

3. 03

   Insist on equal parts

   Cut a sandwich into one big piece and one small piece and ask if each is 1/2. It is not, because halves have to be the same size. Everything else rests on this.

4. 04

   Find the whole of a group first

   A whole can be a set. A carton holds 7 brown eggs and 5 white eggs, so the whole is 12 eggs and the brown ones are 7/12. Add the parts to find the whole before writing the bottom number.

You will need: Paper to fold · Crayons or colored pencils · Something to cut into equal pieces, like a sandwich

Try it together

1. Try 1

   Cut a sandwich or an apple into 6 equal pieces. Eat 1. Ask what fraction of it is left.

   Listen for  5/6. The bottom number stays 6, the pieces the whole was cut into. Watch that your child names what is left, and does not answer 1/6, which is the part that was eaten.

2. Try 2

   A bag holds 4 red marbles and 5 blue marbles. What fraction of the marbles are red?

   Listen for  4/9. The whole is all 9 marbles, 4 + 5. Writing 4/5 is the classic slip: that compares red to blue instead of red to the whole bag.

3. Try 3

   Draw a rectangle, split it into 4 equal parts, and shade 2. Ask for two different names for the shaded part.

   Listen for  2/4, which is also 1/2. If your child sees that half the rectangle is shaded, they are reading the picture and not only counting.

4. Try 4

   A pizza is cut into 8 equal slices and your family eats 5. What fraction was eaten, and what fraction is left?

   Listen for  5/8 eaten and 3/8 left. The two top numbers add back to 8, the whole pizza, which is a good way for your child to check.

Watch for

• — Using the other part as the bottom number, so 4 red and 5 blue marbles becomes 4/5. The bottom number is the whole group, 9.

If it is not there yet

• — Go back to folding paper strips into halves, fourths and eighths, naming each piece out loud, until the bottom number clearly means the size of the piece.
• — Use real food cut into equal pieces and ask only "how many pieces is the whole cut into?" before any fraction gets written.

A few days of this is normal, and it is time well spent. The lesson will still be there, and it will go faster.

Where this skill comes up

• Grade 6 Math Practice Workbook · Lesson 4

  What a Ratio Says

  Needs it because a ratio written as a fraction reuses that notation with a new meaning, so the old meaning has to be solid first.