GRADE 9 · ALBERTAOUTCOME AB-G9-9N1
L5 · Real numbers clinic
Learning goal
“I can classify, notate, order and combine real numbers and sets without falling for the unit's standard traps: disguised values, boundary errors, double-counted unions and repeating decimals.”
Number-set chain — N ⊆ whole ⊆ Z ⊆ Q ⊆ R, with Q′ ⊆ R and Q ∩ Q′ = ∅.
Set-builder notation — {x | domain, rule}: apply BOTH parts; test the boundary.
Subset — A ⊆ B when every element of A is in B; one counterexample defeats it.
Venn diagram — nested regions for the number sets; overlapping regions for two sets' union and intersection.
Worked example
Classify -√16. Step 1: Evaluate the disguise: √16 = 4, so -√16 = -4. Step 2: Classify the VALUE: -4 is an integer (also rational and real). Say it plainly: sign and root symbol are decoration. Value first, set second.
Check yourself — explain it
Why is 5/5 a natural number?
Paired problem — example still visible
Smallest set for √25 -> √25 = 5: natural (N).
Faded completion — last step is yours
"-0.75 belongs to ______ and ______ only." -> rationals (Q); reals (R)
Ready to practise?
10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.