Helping your child understand fractions: find the right starting point

Ask your child to show the fraction and explain the whole. “Draw one half” gives you more information than “Do you understand halves?” Watch whether the parts are equal, whether the child can identify the whole and whether their explanation matches the picture they have drawn.

Avoid correcting every line immediately. Ask, “How did you decide?” and give them time to point or draw. Their reasoning may reveal a specific missing connection even when the final answer is wrong. Keep one dated example to share with the teacher instead of describing the child as simply bad at fractions.

Choose familiar, low-pressure materials: equal paper strips, a pencil and a blank number line are enough. If drawing or cutting is difficult, prepare the materials yourself so that the activity still tests the mathematical idea. You are exploring understanding, not speed or neat handwriting.

Use two same-sized paper strips to compare an equal split with an unequal split. Fold one into two matching parts and divide the other unevenly. Ask which strip shows halves and why. The important idea is that a denominator describes equal parts of a chosen whole, not just any collection of pieces.

Next fold a fresh strip into four equal parts and shade one. Ask your child to name the fraction, identify the whole and explain what the four counts. If they call any shaded piece “one half,” return to matching parts before introducing more fraction symbols.

Compare unit fractions using the same whole. With identical strips, one divided into four equal parts and another into eight, one quarter is larger than one eighth. The activity below makes the comparison visible. Avoid comparing differently sized cakes or shapes, because that introduces a second changing quantity.

Ask your child to explain before introducing a rule: “We split the same strip into more equal pieces, so each piece is smaller.” Then ask whether the explanation still works for one third and one sixth. Keep the numerator at one while practising this particular idea.

Once that feels secure, explain the limit of the shortcut. A larger denominator alone does not decide every comparison when numerators also change. For instance, three quarters is larger than one half. A drawing or common number line helps your child compare the amounts rather than individual digits.

Place fractions as numbers between whole numbers rather than treating them only as shaded pieces. The IES fractions practice guide recommends number lines as a central teaching representation. Draw a line from 0 to 1, divide the interval into four equal lengths and ask your child to identify each position.

Count the spaces, not just the marks. Four equal intervals require the two endpoints and three internal marks. Ask where one quarter belongs, then three quarters. If your child places three quarters at the third mark without identifying zero, return to counting the lengths travelled from the starting point.

Extend the line to 2 when your child is ready. Five quarters lies one quarter beyond 1, so fractions do not have to be less than one. This extension helps keep the meaning connected: the denominator still describes the size of the fractional unit.

Show equivalence by keeping the shaded amount fixed while changing how it is partitioned. Shade one half of a strip, then divide the whole strip into four equal parts. The same shaded area now covers two quarters. Repeat with eight equal parts to see four eighths without changing the amount.

Ask, “What changed, and what stayed the same?” The number of named pieces changed; the total shaded length did not. This comparison separates the physical amount from the notation. It gives a reason for equivalent fractions before the child learns a written procedure for generating them.

Try the idea in reverse. If three of six equal parts are shaded, ask whether the shaded length reaches the halfway point. Accept a drawing or an explanation as evidence. A child who can recite “divide top and bottom” may still benefit from showing why the value stays unchanged.

Choose the activity that exposed the first unclear idea and repeat it with a different drawing or material. If equal parts are still uncertain, adding fraction calculations may make the task harder to interpret. If comparisons are secure, move to equivalence or number-line positions and ask for an explanation.

Use these practice answers to check a fresh attempt: two shaded parts out of five equal parts is 2/5; one third is larger than one sixth of the same whole; three sixths equals one half; and seven quarters is one and three quarters. Ask for a picture alongside one answer.

Share a concrete observation with your child’s teacher: “They identify quarters on a strip but count marks incorrectly on a number line.” Ask which representation and notation the school uses. If you seek a mathematics tutor, look for someone who listens to the child’s explanation and adjusts the next task from that evidence.