Compare fractions

What the tool shows

Two fractions, one blue and one red, appear side by side as bars or circles of the same size. Set each numerator and denominator with the buttons, look at the shaded amounts, and tap <, = or > to say how they compare. The tool says whether you are right and why, using a common denominator or the size of the parts. The hint button draws a line at one half on both models and says whether each fraction is less than, equal to or more than 1/2 and, when both are more than 1/2, how far each is from 1. Play 5 rounds gives random pairs and keeps score.

Why seeing both helps

Comparing fractions is where whole-number thinking trips children up most. 1/8 has a bigger number than 1/3 but is a smaller piece, and 5/6 against 7/8 looks hard until you notice each is one piece away from a whole. Two wholes of the same size side by side let a child check their reasoning against a picture, and choosing the sign before any answer appears keeps the thinking with the child. Over time, the benchmarks 1/2 and 1 become a quick mental strategy that needs no picture at all.

Common mix-ups

• Comparing denominators like whole numbers. 1/8 is less than 1/3, because the whole is cut into more, smaller pieces.
• Comparing only the numerators. 3/10 has a bigger numerator than 2/5 but is smaller, since 2/5 = 4/10.
• Comparing parts of different wholes. Half of a large pizza is more than half of a small one, so fractions are compared using the same whole. The models here are always the same size.
• Mixing up < and >. The wide, open side of the sign faces the greater fraction.

A 10-minute activity

• Minutes 1 to 2: compare 1/2 with 1/2 so the child sees the = sign, then change the red fraction to 1/3 and then 1/4.
• Minutes 3 to 5: compare two fractions with the same denominator, such as 3/8 and 5/8, then two with the same numerator, such as 2/3 and 2/5. Ask for a rule for each case.
• Minutes 6 to 8: turn on the hint and compare 3/8 with 5/9. One is less than 1/2 and one is more, so no common denominator is needed.
• Minutes 9 to 10: play 5 rounds. Ask the child to explain each answer out loud before tapping the sign.

Where it fits by grade

• Grade 3: comparing two fractions with the same numerator or the same denominator by reasoning about their size, and recording the result with <, = or > (Common Core 3.NF.A.3d).
• Grade 4: comparing fractions with different numerators and denominators by creating common denominators or numerators, or by comparing to a benchmark such as 1/2 (4.NF.A.2).
• England: Year 3 pupils compare and order unit fractions and fractions with the same denominator, Year 5 pupils compare fractions whose denominators are multiples of the same number, and Year 6 pupils compare and order any fractions, including fractions greater than 1.

Learning more

Comparing fractions is a skill on Eurekami's skill map, next to equivalent fractions and ordering. Lessons draw the fractions in each question as bars, and Daily Practice brings comparing back when it starts to fade.