1
Understand rational numbers
Recognise numbers that can be written as p/q where p and q are integers and q is not zero.
Chapter route
Number System
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2
Sort numbers into sets
Place given numbers into the correct number set and explain the inclusion relationship between sets.
3
Find equivalent rational forms
Generate and recognise equivalent forms of the same rational number.
4
Compare rational numbers
Use common denominators or cross multiplication to order rational numbers.
5
Plot positive rational numbers
Divide unit intervals correctly to place positive rational numbers.
6
Plot negative rational numbers
Use direction and equal partitions to place negative rational numbers.
7
Place fractions between integers
Identify the correct interval for a given rational number.
8
Estimate decimal positions
Use decimal place value to approximate a point on the number line.
9
Why rationals are dense
Show that there is always another rational number between any two rational numbers.
10
Find numbers in between
Use averages or equivalent fractions to generate rational numbers between two values.
11
Create many rationals in an interval
Construct several rational numbers within a specified range using systematic methods.
12
Convert to terminating decimals
Use division and denominator factors to identify and compute terminating decimal forms.
13
Convert to recurring decimals
Perform long division to identify repeating decimal patterns.
14
Predict decimal type
Use prime factors of the denominator in lowest form to classify decimal expansions.
15
Write recurring decimals as fractions
Use algebraic steps to express recurring decimals in p/q form.
16
Spot irrational numbers
Distinguish irrational numbers from rational numbers using decimal behaviour and known roots.
17
Compare real number types
Explain how rational and irrational numbers differ in representation and properties.
18
Approximate square roots
Use nearby perfect squares and decimals to estimate irrational values.
19
Prove √2 is irrational
Follow contradiction-based reasoning for the irrationality of √2.
20
Prove √3 is irrational
Apply contradiction-based reasoning to show √3 is irrational.
21
Build a square root spiral
Use right triangles and the Pythagorean theorem to construct lengths √2, √3, √4 and beyond.
22
Generate decimals systematically
Describe a step-by-step procedure for obtaining decimal expansions of rational numbers.
23
Classify numbers by algorithm
Apply a decision process to identify whether a number is rational or irrational.
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