Balancing with cubes: mass in uniform informal units · Concept Studio

The idea

The mass of an object can be measured by how many identical units balance it, and a heavier unit gives a smaller count.

What you need

an equal-arm bucket balance
200 interlocking centimetre cubes of one kind
40 wooden cubes of one larger kind
a mandarin, a glue stick, an eraser and a small toy

How to do it

Heft the four objects and predict their order from lightest to heaviest.
Put the mandarin in one pan and add small cubes to the other until the pans level. Count the cubes. Do it again from empty and compare the two counts.
Balance the other three objects the same way. Order them by cube count and compare with the predicted order.
Find how many small cubes balance one large cube. Then balance the mandarin with large cubes and compare the count with the small-cube count.
Record every result in a table: object, small cubes, large cubes.

What you should see

Repeat counts for the same object agree closely when the pans are read level the same way each time. The order by cube count matches hefting for objects that differ a lot and corrects it for objects that feel similar. If one large cube balances four small cubes, an object that needed 12 small cubes needs 3 large cubes, and the pair can predict the large-cube count before testing it. Adding cubes past the level point tips the pan the other way, which shows the balance point has been passed; a bucket balance may need a few extra cubes before the tip shows, so the count is read as closely as the balance allows.

What changes

What you change: the unit placed in the pan (small cube or large cube)
What you measure: the number of units that balance the object
What you keep the same: the same object
the balance checked to be level when empty
units added one at a time

Common misconceptions

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

A bigger count always means a heavier object, whatever unit was used.
The balance measures size, so the bigger object always needs more cubes.

Safety card

Low riskLearners carry it out

Hazards

pans can swing and pinch fingers

Controls

keep fingers clear of the pivot; steady the balance before adding cubes

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-NSM-01 MAO-WM-01
Australian Curriculum v9AC9M2M01

Sources

The pages the author read to write this activity.