Math · Pre-K – Grade 5

Fractions and Decimals

Parts of a whole, parts of a set, and decimal notation for tenths, hundredths, and beyond.

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A fraction names equal parts of one whole, and a decimal writes those same parts in place-value columns to the right of the point. Children rarely get stuck on the arithmetic. They get stuck on two ideas underneath it: the pieces have to be equal, and the whole has to be named before the fraction means anything at all.

What your child is really saying when they say three fourths

Three fourths is not three pieces. It is three of the four equal pieces that one whole was cut into. That one sentence carries most of the difficulty in this topic. A child who can say it can also work out why one eighth is smaller than one fourth: cutting the same whole into more pieces makes every piece smaller, so a bigger bottom number means a smaller share.

Decimals are those same parts written in columns. A dime is one tenth of a dollar, so 0.1 and one tenth are one amount said two ways. Once a child sees the tenths column as the next step to the right of the ones column, comparing 0.7 and 0.25 stops being a contest between seven and twenty-five and becomes a question about which column you are standing in.

A fifteen-minute routine with paper strips

Fractions need hands before symbols, and hands work best on the same material every day for a few weeks. Cut strips of copy paper, all exactly the same length, and keep a stack of them where you work. Fold, name, write, compare. Stopping while your child is still willing matters more than finishing the page.

  1. Hand over one strip and say: this whole strip is one. Fold it into two matching pieces and tell me what one piece is called.
  2. Have your child write the name on the piece in pencil, one half. Fold again for one fourth, again for one eighth, writing each time.
  3. Lay two strips side by side and ask how many eighths it takes to cover one fourth, so 2/8 and 1/4 land on top of each other instead of being declared equal.
  4. Draw a line, mark 0 at one end and 1 at the other, and ask them to put 3/4 on it. Then 0.75. Then three quarters from the coin jar.
  5. Finish with one real kitchen question: the recipe wants 3/4 cup and only the 1/4 cup is clean, so what do we do?

Five things in your kitchen that do this better than a printout

Nesting measuring cups, a chocolate bar with a scored grid, a jar of coins, a ruler marked in quarter inches, and a bag of identical bricks will carry a child from halves to hundredths. Coins are the most useful of the five, because they are the bridge into decimals: four quarters, ten dimes, and a hundred pennies all build the same one dollar.

Printed practice belongs after the folding, not instead of it. Once your child can show a fraction with a strip or a cup and explain it out loud, worksheets are the right tool for building speed and coverage. The fraction and decimal sets in the practice library open the first three sheets of every set, which is enough to check the level before you print a stack.

Two fourths, one half, and 0.5: signs the idea has landed

Listen for the word fourths rather than four, for a check that the pieces are equal before anything is named, and for the observation that half of a large pizza is more food than half of a small one while both are still one half. Naming the same amount two ways without being asked, two fourths and one half and 0.5, tells you more than any correct answer on a page.

The reverse signs are just as plain. Adding straight across, so 1/2 plus 1/4 comes out as 2/6. Judging 0.7 to be smaller than 0.25. Carrying out a procedure correctly and then being unable to draw what it means. Asking for a drawing is the fastest test you have, because a memorized rule collapses the moment a child has to show what it stands for.

If it will not hold, go back to halves and fourths

Put the symbols away for a week or two and work with halves and fourths only, folded and spoken aloud, answering the question a half of what every single time. If the real trouble sits underneath in division or in the place-value columns, repair that first. Fractions built on shaky place value will not stand up, however much fraction practice you add on top.

As for how long: halves and fourths of shapes usually appear in first grade, real fraction work in third, and decimal notation in fourth and fifth. Comparing fractions and finding equivalents confidently is a matter of weeks of short regular sessions rather than days, and adding unlike denominators fluently takes considerably longer. Going back to the paper strips at any point is normal and not a setback.

First, your child should already…

This skill builds directly on:

What your child is learning

Fractions and decimals extend number sense beyond whole numbers. The child must understand equal parts before procedures like comparing, simplifying, or operating.

Signs your child is ready

  • Can split shapes into equal parts
  • Understands halves and fourths
  • Can compare sizes visually

The common stumbling point

Counting pieces without checking whether the parts are equal, or assuming a larger denominator always means a larger amount.

Practice this skill

Worksheets and decodable practice for Fractions and Decimals are in the library.

Every set opens its first three worksheets to everyone; the rest are included with All Access.

Browse the whole practice library

How to know it’s mastered

The child names, compares, represents, and solves grade-level fraction and decimal problems with a visual or numerical model.

Common questions

Why does my child think 1/8 is bigger than 1/4?
Because eight is bigger than four, and nothing in the symbols contradicts that. The bottom number counts how many pieces the whole was cut into, so counting higher there means cutting smaller. Fix it with material rather than a rule: fold one strip into fourths and an identical strip into eighths, lay them together, and let your child watch one eighth disappear under one fourth. Repeat with different wholes until the reversal feels obvious.
When should a child start learning fractions?
Informally at five or six, with equal sharing: cutting a sandwich into two matching pieces, splitting crackers fairly between three children. Halves and fourths of shapes are usually a first-grade target. Formal work with naming, comparing and equivalence generally belongs in third grade, and decimal notation in fourth. Sharing food fairly at four years old is genuine fraction work and needs no worksheet attached to it.
Should I teach fractions or decimals first?
Fractions first, because a fraction can be shown by folding something and a decimal cannot. Once halves, fourths and tenths are secure as pieces of a whole, decimals become a way of writing tenths and hundredths in place-value columns rather than a new topic. Money is the useful overlap: a dime is one tenth of a dollar in either notation, so coins let you move between the two without a rule to memorize.
My fifth grader still cannot add fractions. Where do I start?
Not with more addition practice. Check the layer underneath: ask for a drawing of 2/3, then ask which is larger, 2/3 or 3/4, and why. If the drawing or the reason will not come, the gap is in equal parts and equivalence, and that is where four to six weeks of strip work belongs. Older children move through this quickly once the idea lands, because the arithmetic itself was never the obstacle.

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