Mathematics K–6 · Years 5–6

Ordering fractions with different denominators

Number and algebra

Practical, model not builtLow risk

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The idea

Fractions with different denominators are compared by placing them on the same number line or by renaming them with a common denominator, and a benchmark such as one half settles many comparisons at once.

What you need

a fraction wall printed with rows for halves, thirds, quarters, fifths, sixths, eighths and tenths
a 1.2 m strip of paper as a number line from 0 to 1 (120 cm chosen because it divides by 2, 3, 4, 5, 6, 8 and 10)
fraction cards: 2/3, 3/8, 5/8, 3/5, 7/10, 1/2, 2/5, 4/6, 3/4, 5/6
pegs and a ruler

How to do it

Sort the fraction cards into three piles: less than one half, equal to one half, more than one half, using the wall to check.
Mark the 120 cm line at every fraction on the cards by measuring (for example 2/3 of 120 cm is 80 cm). Peg the cards on the line.
Read the order from the line. Compare 5/8 and 3/4 and explain the order with the wall by renaming 3/4 in eighths.
Add 1/2 and 1/4 on the line by measuring one quarter of 120 cm (30 cm) on from the 1/2 mark, and read the result. Check with the wall that it is 3/4.
Find every card that is equivalent to another on the wall (4/6 and 2/3) and check they land on the same peg.

What you should see

On the 120 cm line the cards sit at 45 cm (3/8), 48 cm (2/5), 60 cm (1/2), 72 cm (3/5), 75 cm (5/8), 80 cm (2/3 and 4/6), 84 cm (7/10), 90 cm (3/4) and 100 cm (5/6). Against the benchmark, 3/8 and 2/5 are less than one half, 1/2 is equal to it and the other seven cards are more, so each of the three piles holds at least one card. The order from smallest is 3/8, 2/5, 1/2, 3/5, 5/8, 2/3 and 4/6 together, 7/10, 3/4, 5/6. 3/4 is 6/8, so 3/4 is larger than 5/8 by 1/8, which is 15 cm on the line (90 cm against 75 cm). 1/2 plus 1/4 lands at 90 cm, the 3/4 mark.

What changes

This activity lists no variables to change, measure and keep the same.

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

The fraction with the bigger denominator is the bigger fraction.
To add fractions, add the tops and add the bottoms.

Safety card

Low riskLearners carry it out

Hazards

none beyond ordinary classroom materials

Controls

none needed

Note

No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package is not needed; ordinary classroom supervision under the school's usual risk management.

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

Mathematics K-10 Syllabus (2022), NSW Education Standards AuthorityMA3-RQF-01 MAO-WM-01
Australian Curriculum v9AC9M5N03AC9M6N03AC9M6N05

Sources

The pages the author read to write this activity.

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