Halves, quarters and eighths by folding · Concept Studio

The idea

Folding a whole in half again and again makes 2, 4 then 8 equal parts, each part half the size of the one before.

What you need

6 paper strips 32 cm long and 3 cm wide per child
3 paper circles 16 cm across per child
a 30 cm ruler
coloured pencils

How to do it

Fold one strip in half so the ends meet exactly. Open it and colour one part. Say one half and measure each part.
Fold a second strip in half and in half again. Open it, count the parts, colour one part and measure it. Say one quarter.
Fold a third strip in half three times. Open it, count the parts and measure one part. Say one eighth.
Lay the quarter strip on the half strip and show that two quarters cover one half exactly. Lay the eighth strip on the quarter strip and count how many eighths cover one quarter.
Fold a paper circle into halves and another into quarters. Cut the quartered circle along its folds and check that the four pieces make the whole circle again.

What you should see

Each part of the 32 cm strip measures 16 cm after one fold, 8 cm after two and 4 cm after three, and the number of parts goes 2, 4, 8. Two quarters lie exactly on one half and two eighths on one quarter. Four quarter pieces of the circle reassemble into the whole with no gap. A strip folded unevenly gives parts of different lengths, and the child sees why those parts are not halves.

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.

Any two pieces are halves, even when they are different sizes.
Eighths are bigger than quarters because eight is bigger than four.

Safety card

Low riskLearners carry it out

Hazards

scissors

Controls

rounded-tip scissors; an adult cuts for the youngest children

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 AuthorityMA1-GM-03 MAO-WM-01
Australian Curriculum v9AC9M2N03AC9M2M02

Sources

The pages the author read to write this activity.