Fraction Activities Using Models, Not Rules

By Laura Lurns · Reviewed by Philip Weaver · Last reviewed 2026-10-23

Models and steps, together

The guides pair models with the steps, so the steps make sense. A model shows what the numbers stand for. Each guide grades its own evidence. We give each grade beside its advice.

What the 2021 guide says about models

A US federal guide on extra math help came out in 2021 (Fuchs and colleagues). It covers children who struggle with math, from kindergarten to sixth grade. It is about help in small groups or one to one, at school.

It is not a guide to dyscalculia. Its studies were of help given in school, not at home. Nothing in the guide tests Learning Success.

Each study tested a whole package of help. So the guide cannot say what one step adds on its own.

For fractions, its examples include fraction tiles and strips. They are linked to number lines. The guide rates the evidence for hands-on and drawn models, linked to the numbers, as strong. Strong means its studies kept finding gains, across different groups of children. The grade is for the advice as a whole, not for each step in it. Which model suits which topic is the panel's advice.

The guide also uses number lines for fractions. It rates the evidence for number lines as strong. That grade is for the advice as a whole, not for each step in it. Of its 14 number-line studies, eight were on fractions. Its steps include using 0, one half and 1 as markers. Equal fractions, like one half and two fourths, sit at one point.

The panel advises against relying on cross-multiplying to compare fractions.

What the 2010 fractions guide says

A second federal guide, on fractions, came out in 2010 (Siegler and colleagues). It is a guide to classroom teaching, from kindergarten to eighth grade. It found rigorous studies of fraction teaching "especially scarce." We hold no study of its advice used by a parent at home. Nothing in the guide tests Learning Success.

Start from sharing. The guide suggests sharing first. Share a set of things, like 12 cookies among 3 children. Then share things that must be cut, like 5 apples between 2. It suggests sharing among 2, 4 or 8 first, so halving works. More sharers means smaller pieces. The guide rates its sharing advice as minimal. Minimal means the advice rests on the panel's judgment, not on a body of tested studies.

Fractions are numbers. The guide says fractions are numbers, with a place on a number line. One step is measuring with fraction strips. A desk might be three strips and a half. That is measuring used to show fractions as amounts. The guide rates its advice that fractions are numbers as moderate. Moderate means some good studies, but it is less clear the practice itself caused the gains. In that guide, the number-line evidence came mainly from whole numbers.

Why the steps work

The title says models, not rules. That does not mean skip the steps. The 2010 guide wants children to see why the steps make sense.

It suggests models to show why you need the same bottom number, the common denominator, to add. It suggests a guess first, using 0, one half and 1. It also names common mistakes to tackle head on. Here are two. One is adding the tops and adding the bottoms. Another is using only the whole numbers in a mixed number. The guide rates its advice on why the steps work as moderate. Moderate means some good studies, but it is less clear the practice itself caused the gains. Three of the studies behind that advice were small, and on decimals.

A picture can mislead, too. In one study, dot paper led more children to add fractions without a common denominator. So the choice of picture matters.

For ratio problems, the guide says to build the reasoning first. Cross-multiplying comes after that. The guide rates this advice as minimal. Minimal means the advice rests on the panel's judgment, not on a body of tested studies.

Fraction activities to try at home

The home routines on this page are ours. We hold no study that tests them at home. Do them alongside your child's math instruction, not in place of it.

Share a sandwich. Cut one sandwich in half for two people. Cut another in four parts for four people. Ask who gets more. In our view, a child can see that more sharers means smaller pieces.

Paper strips. Cut four strips of paper, all the same length. Keep one whole. Fold one in half, one in fourths and one in eighths. Label each part. Lay the strips in a stack. Ask your child what two fourths covers. Then measure a book with the whole strip. Is it two strips and a half?

A line on tape. Put tape on the floor. Mark 0 at one end and 1 at the other. Ask where one half goes. Lay the fourths strip along it, and mark each fourth. Is two fourths in the same place as one half?

Guess first. Before a fraction sum, ask: more than one half, or less? Then work it out and check.

Look at a mistake together. Say your child writes 1/2 + 1/2 = 2/4. Lay two half strips end to end. They make one whole strip. In our view, the strips let your child see the mistake. Then teach the step, and say why it works.

When to ask for help

Each of these is a reason to ask for help on its own.

• Little change, even with steady practice and good teaching.
• Math well below your child's other schoolwork.
• A teacher who raises a concern about math.
• Extreme upset about math.
• Complete avoidance of math.
• Worry about math that spreads into the rest of learning.
• Sadness or worry that lasts.
• A skill that was there and has gone. Our position is that a lost skill goes to a doctor first, not a tutor.

If no skill has gone, start with the teacher. Say what you are seeing at home, and what you have tried. Beyond the teacher, the right person depends on what it turns out to be about. If the work is too hard, someone who works on that school skill. If worry or mood is the thing, someone who works with children's mental health. In our view, if you are worried enough to ask, a professional evaluation is worth asking about.

Any talk of hurting themselves is a same-day call to your doctor or a crisis line.