What students learn in AC9M9N01
This unit helps students build a clear, usable understanding of That the real number system includes the rational numbers and.... 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 that the real number system includes the rational numbers and the irrational numbers, and solve problems involving real numbers using digital tools.
- Use concrete examples, pictures, oral explanation and short written responses before moving to independent practice.
- investigating the real number system by representing the relationships between irrationals, rationals, integers and natural numbers and discussing the difference between exact representations and approximate decimal representations of irrational numbers using a real number line to indicate the solution interval for inequalities of the form ax+b c; for example, 1.2x-5.4>10.8
- 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 that the real number system includes the rational numbers and the irrational numbers, and solve problems involving real numbers using digital tools
- E1: investigating the real number system by representing the relationships between irrationals, rationals, integers and natural numbers and discussing the difference between exact representations and approximate decimal representations of irrational numbers
- E2: using a real number line to indicate the solution interval for inequalities of the form ax+b c; for example, 1.2x-5.4>10.8
- E3: using positive and negative rational numbers to solve problems; for example, for financial planning such as budgeting
- E4: solving problems involving the substitution of real numbers into formulas, understanding that solutions can be represented in exact form or as a decimal approximation, such as calculating the area of a circle using the formula A=\mathrm{π}r^2 and specifying the answer in terms of π as an exact real number; for example, the circumference of a circle with diameter 5 units is 5\mathrm\pi units, and the exact area is \mathrm\pi(\frac52)^2=\frac{25}4\mathrm\pi square units which rounds to 19.63 square units, correct to 2 decimal places
- E5: investigating the position of rational and irrational numbers on the real number line, using geometric constructions to locate rational numbers and square roots on a number line; for example, \sqrt2 is located at the intersection of an arc and the number line, where the radius of the arc is the length of the diagonal of a one-unit square
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
AC9M9N01 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 | AC9M9N01 — recognise that the real number system includes the rational numbers and the irrational numbers, and solve problems involving real numbers using digital tools |
| Victoria | Victorian Curriculum F-10 | Year 9 Maths: closest match in Number. Use this page as a VIC-aligned practice and worksheet reference. |
| NSW | NSW Curriculum | Stage 5 Maths: closest content focus for That the real number system includes the rational numbers and... and related outcomes. |
| United States | Common Core / NGSS | Grade 9 Common Core Mathematics/ELA closest topic match for That the real number system includes the rational numbers and.... |
| England / UK | National Curriculum | Key Stage 3 / Year 9: closest programme-of-study match for That the real number system includes the rational numbers and.... |
| Canada | Provincial and territory curricula | Grade 9 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 5 Maths: closest achievement-objective topic for That the real number system includes the rational numbers and.... |
| India | NCERT / CBSE | Class 9 closest NCERT/CBSE topic match for That the real number system includes the rational numbers and.... |