Mathematics K–6 · Years 1–2
The twentieth bead: finding the unit of repeat
Measurement and space
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
A repeating pattern is fixed by its unit of repeat, so the length of the unit tells you the element at any position without building the whole pattern.
What you need
- 37 interlocking cubes or threading beads at least 35 mm across per pair: 10 red, 20 blue and 7 yellow (enough to build either pattern to 30)
- a lace for threading beads
- position cards numbered 1 to 30
- sound and action cards: clap, stamp, click
How to do it
- Build a red, blue, blue pattern to 12 cubes. Frame one unit of repeat with two fingers and say how many cubes it holds.
- Place position cards under the cubes. Name the colour at positions 3, 6, 9 and 12 and say what those positions have in common.
- Predict the colour of the 20th cube before building, then build to 20 to check.
- Perform the same pattern as sounds (clap, stamp, stamp) and match it to the cube pattern by its unit.
- A partner builds a pattern with a unit of 4 (red, blue, blue, yellow) and puts one mistake in it. Find the mistake by checking one unit at a time.
What you should see
The red, blue, blue unit holds 3 cubes, so positions 3, 6, 9 and 12 are each the last blue of a unit. The 20th cube is blue: position 18 ends the sixth unit, 19 is red and 20 is blue. A pattern of 24 cubes holds 8 whole units, so 8 reds and 16 blues. The clap, stamp, stamp pattern matches the cube pattern because both have a unit of 3 whose first element differs from the other two. In the unit-of-4 pattern the 30th cube is blue, because position 28 ends the seventh unit and 30 is the second element of the next.
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 unit of a red, blue, blue pattern is red, blue because the pattern starts with those two colours.
- The only way to know the 20th element is to build all twenty.
Safety card
Hazards
- small beads near young children
Controls
- use interlocking cubes, or only threading beads too big to fit wholly inside a small-parts test cylinder (31 mm across and 57 mm long), the ACCC test for choking hazards
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 AuthorityMA1-2DS-01MAO-WM-01
- Australian Curriculum v9AC9M1A02
Sources
The pages the author read to write this activity.