A MATH GUIDE FOR PARENTS

Help your child add fractions with different denominators

Before teaching a rule, make the pieces the same size. One picture can help your child explain why the rule works.

You only need a pencil and a strip of paper. Read the example together, then let your child draw and explain the next one.

The idea to keep

The denominator tells us how many equal parts make one whole. The numerator tells us how many of those parts we have. To add, we count parts of the same size.

ONE EXAMPLE, THREE STEPS

What is one third plus one sixth?

$\displaystyle \frac{1}{3} + \frac{1}{6} = ?$

Start with the same whole
Let one strip of paper be the whole. Every bar below represents that same-sized strip, divided into six equal parts. Each box is one sixth of the whole.
Ask: “If the boxes had different sizes, could each one be called a sixth?”
Give the fractions the same kind of part
A third is bigger than a sixth. Split each third into two equal pieces: the whole now has six pieces, and one third covers two of them. We have changed the way we count, not the amount.
First amount $\displaystyle \frac{1}{3} = \frac{2}{6}$
Amount to add $\displaystyle \frac{1}{6}$
Each box has the same size: one sixth. The first amount covers two boxes; the second covers one.
Ask: “Where can you see two sixths inside one third?”
Count the pieces, then name the amount
Two sixths plus one sixth makes three sixths. The denominator stays six because each piece is still one sixth. Three of the six equal parts cover half the whole.
Together $\displaystyle \frac{2}{6} + \frac{1}{6} = \frac{3}{6}$
$\displaystyle \frac{3}{6} = \frac{1}{2}$ . Three marked boxes, three unmarked boxes: two equal halves.
Ask: “Did the pieces get bigger when we added, or did we count more pieces?”

Why not add the bottom numbers too?

It is tempting to add $\displaystyle 1 + 1$ and $\displaystyle 3 + 6$ and write $\displaystyle \frac{2}{9}$ . But the 3 and 6 describe different-sized pieces. Adding those numbers does not turn thirds and sixths into ninths.

Try a quick size check: adding a positive $\displaystyle \frac{1}{6}$ must give more than $\displaystyle \frac{1}{3}$ . Yet $\displaystyle \frac{2}{9}$ is less than $\displaystyle \frac{1}{3}$ , because $\displaystyle \frac{1}{3} = \frac{3}{9}$ . So $\displaystyle \frac{2}{9}$ cannot be the sum.

If your child says “two ninths,” ask: “Can you point to a ninth in our picture?” Then return to the six equal boxes.

LET YOUR CHILD DO THE EXPLAINING

Two questions to check understanding

Give your child time to draw or talk before revealing an answer. Listen for what one part means, not just the final number.

1. Use the six boxes again

What is $\displaystyle \frac{1}{2} + \frac{1}{6}$ ? How many sixths are in the half?

Reveal the answer and reasoning

$\displaystyle \frac{1}{2} = \frac{3}{6}$

$\displaystyle \frac{3}{6} + \frac{1}{6} = \frac{4}{6} = \frac{2}{3}$

Half the strip covers three boxes. Add one more: four of the six boxes are marked. Group the six boxes into three equal pairs; two pairs are marked, so the result is two thirds.

2. Choose a different-sized part

What is $\displaystyle \frac{1}{4} + \frac{1}{2}$ ? Could four equal boxes work? Explain why.

Reveal the answer and reasoning

$\displaystyle \frac{1}{2} = \frac{2}{4}$

$\displaystyle \frac{1}{4} + \frac{2}{4} = \frac{3}{4}$

Yes. One quarter is one box and one half is two boxes, so together they cover three of four. We need a common denominator, but we do not always need to multiply the original denominators.

When your child gets stuck

Try one prompt at a time. Let your child point, shade or fold before asking for symbols.

“Show me what counts as one whole.”
“How could we cut the pieces so they all match?”
“Can you explain why the amount stayed the same?”

If the same example still feels confusing, stop with the picture and come back later. A useful next step is explaining one equal part clearly.