Mathematics K–6 · Years 5–6

Fraction strips on a 24 cm whole: adding and subtracting

Number and algebra

Practical, model not builtLow risk

This site has no interactive model of its own. Where a step or a material names a Concept Studio model, simulation or tool, it has not been built; an external simulation a step names (for example PhET) is not part of this site.

The idea

Fractions with the same or related denominators are added and subtracted by measuring them as lengths of the same whole, which gives the same result as renaming them with a common denominator.

What you need

7 strips of card 24 cm long and 3 cm wide per learner
a ruler marked in millimetres
coloured pencils and scissors
a number line from 0 to 2 drawn 48 cm long (24 cm for each whole)

How to do it

Keep one strip whole. Mark and cut the others into halves (12 cm), thirds (8 cm), quarters (6 cm), sixths (4 cm), eighths (3 cm) and twelfths (2 cm). Label every piece.
Lay 1/2 and 1/4 end to end under the whole strip and read the total as a fraction of 24 cm.
Lay 2/3 and 1/6 end to end and find every family of pieces that matches the total exactly.
Show 3/4 - 3/8 by laying 3/8 over 3/4 and measuring what is left.
Add 1/2 and 3/4 on the 0 to 2 number line and write the total as an improper fraction and as a mixed numeral.
Add 1/4 and 3/8, find the family that matches the total, and write each step with a common denominator.

What you should see

1/2 + 1/4 lies 18 cm long, which is 3/4 of 24 cm. 2/3 + 1/6 is 16 cm + 4 cm = 20 cm, matched by five sixths and also by ten twelfths. 3/4 - 3/8 is 18 cm - 9 cm = 9 cm, which is 3/8. 1/2 + 3/4 is 30 cm, 6 cm past one whole, so 5/4 = 1 1/4. 1/4 + 3/8 is 6 cm + 9 cm = 15 cm, matched only by eighths: 2/8 + 3/8 = 5/8. Each total measured in centimetres agrees with the total found by renaming with a common denominator.

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.

1/2 + 1/4 = 2/6 because the numerators and the denominators are each added.
Fractions with different denominators cannot be added.

Safety card

Low riskLearners carry it out

Hazards

scissors

Controls

cut seated at a table and pass scissors handle first

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 v9AC9M5N05AC9M6N05

Sources

The pages the author read to write this activity.

All Concept Studio activities