Mathematics K–6 · Years 1–2

Cube towers: skip counting by twos, fives and tens

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

Equal towers turn counting by ones into counting by twos, fives or tens, and a staircase of towers that grow by the same step is an additive pattern whose missing terms can be predicted.

What you need

100 interlocking cubes (2 cm) per pair in at least two colours
a 100 chart and 70 transparent counters in two colours
number cards for labelling towers

How to do it

Snap 30 cubes into towers of 5. Count the towers by fives and write the count.
Break the same 30 cubes into towers of 2 and count by twos, then into towers of 10 and count by tens. Record the number of towers each time.
Share the 30 cubes one at a time among 3 people and count each share.
Build a staircase of towers 2, 4, 6, 8 and 10 cubes tall. Say how much each step grows, predict the heights of the next two towers and build them to check.
A partner builds a staircase that grows by 3 and hides one tower (3, 6, _, 12, 15). Name the hidden height, then build a staircase that shrinks by 3 from 20.
Place a counter on every fifth square of the 100 chart and, in the other colour, on every second square. Describe where each colour lands.

What you should see

30 cubes make 6 towers of 5, 15 towers of 2 and 3 towers of 10, and the count is 30 every time, so grouping does not change the total. Shared among 3 people, each share is 10. The staircase 2, 4, 6, 8, 10 grows by 2 at each step and uses 30 cubes, and the next two towers are 12 and 14. The hidden tower is 9, and the shrinking staircase reads 20, 17, 14, 11, 8, 5, 2. On the 100 chart the fives fill two columns (numbers ending in 5 and 0), 20 counters, and the twos fill every second column, 50 counters.

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.

Counting the same cubes by fives gives a different total from counting them by ones.
In 3, 6, _, 12 the missing number is 7 because 7 comes after 6.

Safety card

Low riskLearners carry it out

Hazards

cubes dropped on the floor

Controls

work on a table or a mat

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-FG-01 MAO-WM-01
Australian Curriculum v9AC9M1A01AC9M2A01AC9M1N06

Sources

The pages the author read to write this activity.

All Concept Studio activities