What students learn in AC9M6A01
This unit helps students build a clear, usable understanding of And use rules that generate visually growing patterns and number.... The goal is not to memorise one answer pattern. Students should be able to explain the idea, recognise it in a new example and apply it in a short practice or worksheet task.
- Start with the main idea: recognise and use rules that generate visually growing patterns and number patterns involving rational numbers.
- Use concrete examples, pictures, oral explanation and short written responses before moving to independent practice.
- investigating patterns such as the number of tiles in a geometric pattern, or the number of dots or other shapes in successive repeats of a strip or border pattern; looking for patterns in the way the numbers increase/decrease using a calculator or spreadsheet to experiment with number patterns that result from multiplying or dividing; for example, 1 ÷ 9, 2 ÷ 9, 3 ÷ 9…, 210 \times 11, 211 \times 11, 212 \times 11…, 111 \times 11, 222 \times 11, 333 \times 11…, or 100 ÷ 99, 101 ÷ 99, 102 ÷ 99…
- Finish with mixed questions so students must choose the correct strategy rather than copy the last example.
Curriculum coverage and elaborations
The content description and elaborations below show the curriculum ideas taught in this unit. Items marked as teaching context support lesson planning but may not appear in the initial eight-question activity.
- Content description: recognise and use rules that generate visually growing patterns and number patterns involving rational numbers
- E1: investigating patterns such as the number of tiles in a geometric pattern, or the number of dots or other shapes in successive repeats of a strip or border pattern; looking for patterns in the way the numbers increase/decrease
- E2: using a calculator or spreadsheet to experiment with number patterns that result from multiplying or dividing; for example, 1 ÷ 9, 2 ÷ 9, 3 ÷ 9…, 210 \times 11, 211 \times 11, 212 \times 11…, 111 \times 11, 222 \times 11, 333 \times 11…, or 100 ÷ 99, 101 ÷ 99, 102 ÷ 99…
- E3: creating an extended number sequence that represents an additive pattern using decimals; for example, representing the additive pattern formed as students pay their \$2.50 for an incursion as 2.50, 5.00, 7.50, 10.00, 12.50, 15.00, 17.50 …
- E4: investigating the number of regions created by successive folds of a sheet of paper: one fold, 2 regions; 2 folds, 4 regions; 3 folds, 8 regions, and describing the pattern using everyday language
- E5: creating a pattern sequence with materials, writing the associated number sequence and then describing the sequence with a rule so someone else can replicate it with different materials; for example, using matchsticks or toothpicks to create a growing pattern of triangles using 3 for one triangle, 5 for 2 triangles, 7 for 3 triangles and describing the pattern as, “Multiply the number of triangles by 2 and then add one for the extra toothpick in the first triangle”
How to use this unit
Read the topic guide, use the teacher slide for instruction, then complete the Worksheet, Practice and Test. These three activities use the same eight-question unit bank.
Teacher resource
AC9M6A01 teacher slide
Use this one-page PDF to introduce the key idea, vocabulary and teaching sequence before students begin the activities.
Open teacher slide (PDF)Common mistakes to watch for
- Rushing to a rule before checking the concrete model, drawing or number sentence.
- Using the correct answer once but not being able to explain why it works.
- Mixing up similar vocabulary such as more/less, before/after, longer/shorter or equal groups/sharing.
International curriculum mapping
This table gives closest-topic mapping for search and planning. The Australian Curriculum code is exact; overseas entries are broad equivalents because each jurisdiction structures outcomes differently.
| Region | Curriculum | Closest mapping |
|---|---|---|
| Australia | Australian Curriculum v9.0 | AC9M6A01 — recognise and use rules that generate visually growing patterns and number patterns involving rational numbers |
| Victoria | Victorian Curriculum F-10 | Year 6 Maths: closest match in Algebra. Use this page as a VIC-aligned practice and worksheet reference. |
| NSW | NSW Curriculum | Stage 3 Maths: closest content focus for And use rules that generate visually growing patterns and number... and related outcomes. |
| United States | Common Core / NGSS | Grade 6 Common Core Mathematics/ELA closest topic match for And use rules that generate visually growing patterns and number.... |
| England / UK | National Curriculum | Key Stage 2 / Year 6: closest programme-of-study match for And use rules that generate visually growing patterns and number.... |
| Canada | Provincial and territory curricula | Grade 6 closest topic match. Canada varies by province, so use this as a broad Ontario/BC-style learning outcome reference. |
| New Zealand | New Zealand Curriculum | Level 3 Maths: closest achievement-objective topic for And use rules that generate visually growing patterns and number.... |
| India | NCERT / CBSE | Class 6 closest NCERT/CBSE topic match for And use rules that generate visually growing patterns and number.... |