Ashdale Secondary College · T2 Weeks 3–6 · 16 Lessons
L1 · T2 Week 3
What is Pythagoras' Theorem?
Identify the hypotenuse, write the theorem and verify right-angled triangles
⚡ Do Now 8 min · display on board as students enter
1
Write the formula for the area of a rectangle
Answer: A = l × w
2
Find the area: length = 8 cm, width = 3 cm
Answer: 24 cm²
3
What is 5²?
Answer: 25
4
What is 12²?
Answer: 144
5
What is √36?
Answer: 6
6
What is √100?
Answer: 10
📖 Key Vocabulary
Right angle
90° — shown by the small square □
Hypotenuse
Longest side — always OPPOSITE the right angle
Legs (a and b)
The two shorter sides — they FORM the right angle
📐 Formula / Rule
a² + b² = c² where c = hypotenuse
📐 Diagrams
Basic right triangle
Verify: does (3, 4, 5) work?
✏️ Worked Examples teacher-led · reveal steps one at a time
Verify that 3, 4, 5 is a right-angled triangle
→Longest side = 5 → c = 5, a = 3, b = 4
→a² + b² = 3² + 4² = 9 + 16 = 25
→c² = 5² = 25
→25 = 25 ✓ It IS right-angled
Verify that 6, 7, 8 is a right-angled triangle
→Longest side = 8 → c = 8, a = 6, b = 7
→a² + b² = 6² + 7² = 36 + 49 = 85
→c² = 8² = 64
→85 ≠ 64 ✗ NOT right-angled
📝 Practice Questions
1
What is 7²?
✓ 49
2
What is √81?
✓ 9
3
What is 11²?
✓ 121
4
Write Pythagoras' theorem from memory.
✓ a² + b² = c²
5
Does (8, 15, 17) form a right triangle? Show working.
✓ 64 + 225 = 289 = 17² ✓
6
Does (4, 5, 6) form a right triangle? Show working.
✓ 16 + 25 = 41 ≠ 36 ✗
7
Does (7, 24, 25) form a right triangle? Show working.
✓ 49 + 576 = 625 = 25² ✓
8
Does (9, 10, 14) form a right triangle? Show working.
✓ 81 + 100 = 181 ≠ 196 ✗
🎯 Exit Ticket
1
Write Pythagoras' theorem.
✓ a² + b² = c²
2
Does (6, 8, 10) form a right triangle? Show all working.
✓ 36 + 64 = 100 = 10² ✓ Yes
💡 Teacher note: Keep diagrams BIG. Re-draw for every example. Ahmed A — speak steps aloud as you write.
L2 · T2 Week 3
Finding the Hypotenuse
Use a² + b² = c² to find the hypotenuse, showing all working
⚡ Do Now 8 min · display on board as students enter
1
What is 6²?
Answer: 36
2
What is 9²?
Answer: 81
3
What is √49?
Answer: 7
4
What is √144?
Answer: 12
5
Write Pythagoras' theorem from memory.
Answer: a² + b² = c²
6
Which side is the hypotenuse? Sketch a right triangle and label it.
Answer:
📖 Key Vocabulary
Hypotenuse (c)
The side we are FINDING — longest, opposite 90°
a and b
The two known short sides — substitute these in
√ (square root)
The inverse of squaring — use the √ button on calculator
📐 Formula / Rule
c = √(a² + b²)
📐 Diagrams
c is always opposite the right angle
Example: find c when a=5, b=7
✏️ Worked Examples teacher-led · reveal steps one at a time
Find the hypotenuse when a = 3, b = 4
→c² = a² + b²
→c² = 3² + 4² = 9 + 16 = 25
→c = √25 = 5
Find the hypotenuse when a = 5, b = 7
→c² = 5² + 7²
→c² = 25 + 49 = 74
→c = √74 ≈ 8.60 (2 d.p.)
📝 Practice Questions
1
a = 6, b = 8. Find c.
✓ 10
2
a = 9, b = 12. Find c.
✓ 15
3
a = 5, b = 10. Find c (1 d.p.)
✓ 11.2
4
a = 7, b = 7. Find c (2 d.p.)
✓ 9.90
5
a = 2.5, b = 6. Find c (2 d.p.)
✓ 6.50
6
a = 11, b = 4. Find c (2 d.p.)
✓ 11.70
7
a = 9, b = 40. Find c.
✓ 41
8
a = 8, b = 8. Find c (2 d.p.)
✓ 11.31
🎯 Exit Ticket
1
Find c when a = 8, b = 15.
✓ 17
2
Find c when a = 4, b = 9. Round to 2 d.p.
✓ 9.85
💡 Teacher note: Insist on every line of working: c² = ... on one line, c = ... on the next.
L3 · T2 Week 3
Finding a Short Side
Rearrange Pythagoras' theorem to find a missing leg
⚡ Do Now 8 min · display on board as students enter
1
Find c: a = 6, b = 8
Answer: 10
2
Find c: a = 5, b = 12
Answer: 13
3
What is √64?
Answer: 8
4
100 − 36 = ?
Answer: 64
5
169 − 25 = ?
Answer: 144
📖 Key Vocabulary
Rearranging
Moving parts of the formula to isolate what we want to find
a² = c² − b²
Subtract the known leg² FROM the hypotenuse²
Inverse operation
Square rooting undoes squaring
📐 Formula / Rule
a = √(c² − b²) or b = √(c² − a²)
📐 Diagrams
Finding the missing leg
Example: find a when c=13, b=5
✏️ Worked Examples teacher-led · reveal steps one at a time
Find the missing leg when c = 13, b = 5
→a² + b² = c²
→a² + 5² = 13²
→a² + 25 = 169
→a² = 169 − 25 = 144
→a = √144 = 12
Find the missing leg when c = 10, b = 6
→a² = c² − b²
→a² = 10² − 6² = 100 − 36 = 64
→a = √64 = 8
📝 Practice Questions
1
c = 10, b = 6. Find a.
✓ 8
2
c = 17, b = 8. Find a.
✓ 15
3
c = 15, b = 9. Find a.
✓ 12
4
c = 20, b = 12. Find a.
✓ 16
5
c = 11, b = 5. Find a (2 d.p.)
✓ 9.80
6
c = 8, b = 3. Find a (2 d.p.)
✓ 7.42
7
c = 25, b = 7. Find a.
✓ 24
8
c = 30, b = 18. Find a.
✓ 24
🎯 Exit Ticket
1
Find a when c = 26, b = 10.
✓ 24
2
Find b when c = 14, a = 9. Round to 2 d.p.
✓ 10.44
💡 Teacher note: Common error: students ADD instead of SUBTRACT. Say: 'We already have the big side — we go DOWN.' Leave both rearrangements on the board all lesson.
L4 · T2 Week 3
Pythagoras + Area & Perimeter
Use Pythagoras to find a missing dimension, then calculate area and perimeter
⚡ Do Now 8 min · display on board as students enter
1
Write the formula for area of a triangle.
Answer: A = ½ × b × h
2
Triangle: base 10 cm, height 6 cm. Area?
Answer: 30 cm²
3
Find c: a = 8, b = 15
Answer: 17
4
Find the missing leg: c = 13, b = 5
Answer: 12
📖 Key Vocabulary
Strategy
Find the unknown side with Pythagoras FIRST — then use area or perimeter
Exact form
Leave as a surd — e.g. √112 cm
Approximate form
Rounded decimal — e.g. 10.58 cm
📐 Formula / Rule
Step 1: Find unknown side (Pythagoras) → Step 2: Area = ½ × b × h → Step 3: P = sum of all sides
📐 Diagrams
Right triangle: find height first
Isosceles: split into two right triangles
✏️ Worked Examples teacher-led · reveal steps one at a time
Right triangle: base 12 cm, hypotenuse 16 cm. Find height, area and perimeter.
→Step 1 — Height: h = √(16² − 12²) = √(256 − 144) = √112 ≈ 10.58 cm
→Step 2 — Area: A = ½ × 12 × 10.58 = 63.50 cm²
→Step 3 — Perimeter: P = 12 + 16 + 10.58 = 38.58 cm
Isosceles triangle: base 16 cm, equal sides 10 cm. Find the height then area.
→Step 1 — Split in half: base half = 8 cm, hyp = 10 cm
→Step 2 — Height: h² = 10² − 8² = 100 − 64 = 36 → h = 6 cm
→Step 3 — Area: A = ½ × 16 × 6 = 48 cm²
📝 Practice Questions
1
Right triangle: legs 9 cm and 12 cm. Find (a) hypotenuse (b) perimeter (c) area.
✓ (a) 15 cm (b) 36 cm (c) 54 cm²
2
Right triangle: hyp = 20 cm, one leg = 12 cm. Find the other leg then the area.
✓ leg = 16 cm, A = 96 cm²
3
Isosceles triangle: base = 10 cm, equal sides = 13 cm. Find height then area.
✓ h = 12 cm, A = 60 cm²
4
Right triangle: legs 7 cm and 7 cm. Find hyp (2 d.p.), perimeter (2 d.p.) and area.
✓ c ≈ 9.90 cm, P ≈ 23.90 cm, A = 24.5 cm²
🎯 Exit Ticket
1
Right triangle: legs 6 cm and 8 cm. Find the hypotenuse, then the area.
✓ c = 10 cm, A = 24 cm²
💡 Teacher note: Find unknown side FIRST is the key habit. Ahmed A — write each step on a new line.
L5 · T2 Week 3
Is it Right-Angled? (The Converse)
Use the converse of Pythagoras to test whether a triangle is right-angled
⚡ Do Now 8 min · display on board as students enter
1
Find c: a = 6, b = 8
Answer: 10
2
Find a: c = 25, b = 24
Answer: 7
3
What does the □ symbol mean on a diagram?
Answer: 90° right angle
4
What is 15²?
Answer: 225
📖 Key Vocabulary
Converse
The REVERSE of the theorem — use it to TEST a triangle
Pythagorean triad
Three whole numbers satisfying a² + b² = c²
📐 Formula / Rule
If a² + b² = c² → RIGHT-ANGLED ✓ If a² + b² ≠ c² → NOT right-angled ✗
📐 Diagrams
Always use the LONGEST side as c
Check: (8, 15, 17)
✏️ Worked Examples teacher-led · reveal steps one at a time
Are sides 7, 24, 25 a right-angled triangle?
→Longest side = 25 → c = 25, a = 7, b = 24
→a² + b² = 49 + 576 = 625
→c² = 625
→625 = 625 ✓ RIGHT-ANGLED
Are sides 5, 7, 9 a right-angled triangle?
→Longest side = 9 → c = 9, a = 5, b = 7
→a² + b² = 25 + 49 = 74
→c² = 81
→74 ≠ 81 ✗ NOT right-angled
📝 Practice Questions
1
8, 15, 17 — right-angled?
✓ 64 + 225 = 289 = 17² ✓ Yes
2
6, 9, 11 — right-angled?
✓ 36 + 81 = 117 ≠ 121 ✗ No
3
20, 21, 29 — right-angled?
✓ 400 + 441 = 841 = 29² ✓ Yes
4
4, 7, 8 — right-angled?
✓ 16 + 49 = 65 ≠ 64 ✗ No
5
9, 40, 41 — right-angled?
✓ 81 + 1600 = 1681 = 41² ✓ Yes
6
10, 12, 15 — right-angled?
✓ 100 + 144 = 244 ≠ 225 ✗ No
🎯 Exit Ticket
1
Are sides 11, 60, 61 a right triangle? Show full working.
✓ 121 + 3600 = 3721 = 61² ✓ Yes
💡 Teacher note: Always use the LONGEST side as c — students who pick the wrong side get the wrong answer.
L6 · T2 Week 3
Word Problems & Drawing Diagrams
Draw a labelled diagram from a word problem and solve using Pythagoras
⚡ Do Now 8 min · display on board as students enter
1
Find c: a = 5, b = 12
Answer: 13
2
Are 8, 15, 17 right-angled?
Answer: Yes: 64 + 225 = 289 = 17² ✓
3
A triangle has sides 3, 4 and 5. Which is the hypotenuse?
Answer: 5
📖 Key Vocabulary
4-Step Method
Read → Draw → Identify → Solve
Diagram
Always sketch and label — no diagram, no marks
Units
Always include cm / m / km in the answer
📐 Formula / Rule
READ the problem → DRAW and label → IDENTIFY what to find → SOLVE with Pythagoras
📐 Diagrams
Problem 1: ladder against wall
Problem 2: diagonal of a rectangle
✏️ Worked Examples teacher-led · reveal steps one at a time
A ladder leans against a wall. Base is 1.5 m from wall, wall is 3.5 m high. How long is the ladder?
→Draw: right triangle — base = 1.5 m, vertical = 3.5 m, ladder = c
→c² = 1.5² + 3.5² = 2.25 + 12.25 = 14.5
→c = √14.5 ≈ 3.81 m
A field is 40 m long and 30 m wide. How long is the diagonal path?
→Draw: rectangle — diagonal is the hypotenuse
→c² = 40² + 30² = 1600 + 900 = 2500
→c = √2500 = 50 m
📝 Practice Questions
1
A ramp is 4 m long and reaches 1.5 m high. How far does it extend horizontally? (2 d.p.)
✓ √(16 − 2.25) = √13.75 ≈ 3.71 m
2
A screen is 55 cm wide and 31 cm tall. Find its diagonal. (2 d.p.)
✓ √(3025 + 961) = √3986 ≈ 63.13 cm
3
Two friends walk from the same corner — one 6 km east, one 8 km north. How far apart?
✓ √(36 + 64) = 10 km
4
A 12 m rope goes from the top of a 9 m pole to a peg. How far is the peg from the base?
✓ √(144 − 81) = √63 ≈ 7.94 m
🎯 Exit Ticket
1
A TV is 90 cm wide and 50 cm tall. Find the diagonal. Round to 1 d.p.
✓ √10600 ≈ 103.0 cm
💡 Teacher note: No diagram = no marks. Non-negotiable. Ahmed A — a rough sketch is fine.
L7 · T2 Week 3
Pythagoras — Mixed Practice
Apply all Pythagoras skills: hypotenuse, short side, converse and word problems
⚡ Do Now 8 min · display on board as students enter
1
Find c: a = 7, b = 24
Answer: 25
2
Find a: c = 17, b = 15
Answer: 8
3
Are 6, 8, 10 right-angled?
Answer: Yes: 36 + 64 = 100 ✓
4
Write the 4-step word problem method.
Answer: Read, Draw, Identify, Solve
📖 Key Vocabulary
Exact answer
Leave as a surd — e.g. √74
Approximate answer
Rounded decimal — e.g. 8.60 cm
📐 Formula / Rule
a² + b² = c² | a = √(c² − b²) | Converse: test if a² + b² = c²
📐 Diagrams
Find c
Find a
Is it right-angled?
✏️ Worked Examples teacher-led · reveal steps one at a time
Right triangle with legs 6 m and 6 m. Find hypotenuse, area and perimeter.
→c = √(6² + 6²) = √72 ≈ 8.49 m
→Area = ½ × 6 × 6 = 18 m²
→Perimeter = 6 + 6 + 8.49 = 20.49 m
📝 Practice Questions
1
Find c: a = 9, b = 12
✓ 15
2
Find a: c = 10, b = 8
✓ 6
3
Are 5, 12, 13 right-angled? Show working.
✓ 25 + 144 = 169 = 13² ✓ Yes
4
Ladder 5 m long, base 2 m from wall. How high does it reach?
✓ √(25 − 4) = √21 ≈ 4.58 m
5
Right triangle legs 9 cm, 12 cm: find hyp, area and perimeter.
✓ c=15, A=54 cm², P=36 cm
6
a = 7, b = 9. Find c (2 d.p.)
✓ 11.40
7
c = 20, b = 13. Find a (2 d.p.)
✓ 15.20
8
Are 8, 9, 12 right-angled?
✓ 64 + 81 = 145 ≠ 144 ✗ No
🎯 Exit Ticket
1
Find c when a = 20, b = 21.
✓ 29
2
A rope of 10 m is pegged 6 m from a pole. How high up the pole does it reach?
✓ 8 m
💡 Teacher note: Circulate actively. Use levelled prompts: 'What do you know? What are you finding?'
L8 · T2 Week 3
Pythagoras — Consolidation & Test Prep
Review all Pythagoras skills and prepare for the Measurement Test
⚡ Do Now 8 min · display on board as students enter
1
Find c: a = 8, b = 6
Answer: 10
2
Find a: c = 13, b = 5
Answer: 12
3
Are 9, 40, 41 right-angled?
Answer: Yes ✓
4
Ladder 5 m, base 2 m from wall. Height?
Answer: √21 ≈ 4.58 m
5
Right triangle legs 3 m, 4 m: perimeter?
Answer: 12 m
📖 Key Vocabulary
Measurement Test
NEXT WEEK — covers area, perimeter, composite shapes and Pythagoras
📐 Formula / Rule
a² + b² = c² | a = √(c²−b²) | Converse | Word problems with diagram
📐 Diagrams
Finding sides
Converse — is it right-angled?
📝 Practice Questions
1
a = 3, b = 4 → c = ?
✓ 5
2
a = 5, b = 12 → c = ?
✓ 13
3
c = 10, b = 6 → a = ?
✓ 8
4
c = 26, b = 10 → a = ?
✓ 24
5
a = 7, b = 9 → c (2 d.p.)
✓ 11.40
6
c = 14, b = 11 → a (2 d.p.)
✓ 8.66
7
Right tri legs 9, 12 cm: find hyp, area, perimeter.
✓ c=15, A=54 cm², P=36 cm
8
Ladder 5 m, base 2 m from wall. How high does it reach?
✓ √21 ≈ 4.58 m
🎯 Exit Ticket
1
What topics are on the Measurement Test? List all of them.
✓ Area, perimeter, composite shapes, Pythagoras, converse, word problems
💡 Teacher note: REMINDER: Measurement Test is Lesson 10 (T2 Week 4, second lesson). Write test topics on board at end of this lesson.
L9 · T2 Week 4
Ways to Earn Money
Name and calculate different types of income: wages, salary, commission, piecework
⚡ Do Now 8 min · display on board as students enter
✏️ Worked Examples teacher-led · reveal steps one at a time
After test — Sam earns $22/hr and works 38 hours. Weekly pay?
→Pay = $22 × 38 = $836
📝 Practice Questions
1
$18/hr × 40 hrs = ?
✓ $720
2
Salary $52,000/year. Weekly pay?
✓ $1,000
3
$23.50/hr × 6 hrs = ?
✓ $141
4
Salary $78,000/year. Fortnightly pay?
✓ $3,000
🎯 Exit Ticket
1
You earn $20/hr. You work 9 hours. How much do you earn?
✓ $180
💡 Teacher note: TEST: seating plan strictly enforced, clear desks, formula sheet provided. Ahmed A — extra time if needed. After test: keep intro light and engaging.
L11 · T2 Week 4
Wages & Penalty Rates
Calculate wages including time and a half, double time and mixed weeks
⚡ Do Now 8 min · display on board as students enter
1
$18 × 6 = ?
Answer: $108
2
$18 × 1.5 = ?
Answer: $27
3
$18 × 2 = ?
Answer: $36
4
$22.50 × 8 = ?
Answer: $180
5
What does 'time and a half' mean? Write in your own words.
Answer: 1.5× normal rate
📖 Key Vocabulary
Normal time
×1 — standard hourly rate
Time and a half
×1.5 — common for Saturday shifts
Double time
×2 — common for Sunday and public holidays
Double time and a half
×2.5 — public holiday premium
📐 Formula / Rule
Penalty pay = hourly rate × multiplier × hours worked
✏️ Worked Examples teacher-led · reveal steps one at a time
Jake earns $17/hr. Mon–Fri 8 hrs/day, Sat 4 hrs (T&H), Sun 3 hrs (DT). Total?
Mia $19.50/hr. Tue–Sat 8 hrs. Sat = time & half. Total?
✓ $624 + $234 = $858
6
$24/hr. 3 hrs double time and a half. Pay?
✓ $24 × 2.5 × 3 = $180
🎯 Exit Ticket
1
You earn $21/hr. 6 hours on Sunday at double time. How much?
✓ $21 × 2 × 6 = $252
2
What multiplier is used for time and a half?
✓ 1.5
💡 Teacher note: Real-world connection: which shifts pay the most and why? The 'Your Roster' activity works well here.
L12 · T2 Week 4
Payslips — Reading & Calculating
Read a payslip and calculate gross pay, tax, super and net pay
⚡ Do Now 8 min · display on board as students enter
1
$850 − $125 = ?
Answer: $725
2
10% of $960 = ?
Answer: $96
3
11% of $840 = ?
Answer: $92.40
4
$1,200 − $312 − $96 = ?
Answer: $792
📖 Key Vocabulary
Gross Pay
Total earnings BEFORE any deductions
Tax
Money withheld for the government (ATO)
Superannuation (Super)
11% employer contribution — goes into your retirement fund
Net Pay
What you actually receive — gross minus deductions
YTD
Year to Date — total earned since 1 July
📐 Formula / Rule
Net Pay = Gross − Tax − Other Deductions | Super = 11% × Gross (employer pays this separately)
✏️ Worked Examples teacher-led · reveal steps one at a time
Gross = $1,400. Tax = $285. Super = 11% of gross. Find net pay and super.
→Super = 11% × $1,400 = $154 (employer pays this on top)
→Net Pay = $1,400 − $285 = $1,115
📝 Practice Questions
1
Gross=$960, Tax=$142, Other=$20. Net pay?
✓ $798
2
Gross=$2,100, Tax=$385. Net pay?
✓ $1,715
3
Gross=$780. Super=11%. How much super does employer pay?
✓ $85.80
4
Net=$1,260. Tax=$194. What was the gross?
✓ $1,454
5
Jake: 38 hrs at $23/hr. Tax=18% of gross. Find gross, tax, net.
✓ Gross=$874, Tax=$157.32, Net=$716.68
🎯 Exit Ticket
1
What is the difference between gross and net pay?
✓ Gross = before deductions, Net = take-home after tax etc.
2
Gross=$1,050, Tax=$210, Super=11%. Find net pay and employer super.
✓ Net=$840, Super=$115.50
💡 Teacher note: Key misconception: super is paid BY the employer ON TOP of gross — not deducted from wages. Say: 'It's a bonus put into a retirement account you can't touch yet.'
L13 · T2 Week 5
Commission & Piecework
Calculate commission (with and without base pay) and piecework earnings
⚡ Do Now 8 min · display on board as students enter
1
4% of $30,000 = ?
Answer: $1,200
2
2.5% of $12,000 = ?
Answer: $300
3
$3.20 × 45 = ?
Answer: $144
4
Gross=$920, Tax=$158. Net pay?
Answer: $762
📖 Key Vocabulary
Base + commission
Fixed amount plus a % of sales on top
Piecework rate
Fixed $ per item or task completed
Compare income
Calculate totals for each option — then decide
📐 Formula / Rule
Commission = rate% × total sales | Piecework = rate per item × number of items
✏️ Worked Examples teacher-led · reveal steps one at a time
Real estate agent: base $800/week + 1.5% commission. Sold a house for $620,000.
$3,500 at 4.2% p.a. for 2 yrs. Interest and total.
✓ I=$294, A=$3,794
🎯 Exit Ticket
1
List 5 formulas or rules from this Finance unit.
✓ Wage, penalty rates, net pay, super=11%, I=PRT, A=P+I
💡 Teacher note: FINANCE TEST: confirm exact timing with class teacher. Covers all income types, payslips and simple interest.
L1 · T2 Week 3
What is Pythagoras' Theorem?
Objective: Identify the hypotenuse, write the theorem and verify right-angled triangles
🅃 Daily Riddle
1 / 9
💬 Word Puzzle
🔺
I have 3 sides, one angle that is EXACTLY 90°, and my longest side has a very special name. I'm found in every building, every ramp, every roof. What is my longest side called?
90
It's the side directly opposite the right angle — and today's entire lesson is named after it...
The HYPOTENUSE! From the Greek 'hypoteinousa' meaning 'stretching under'. Every right triangle has one.
⚡ Do Now
2 / 9
1
Write the formula for the area of a rectangle
A = l × w
2
Find the area: length = 8 cm, width = 3 cm
24 cm²
3
What is 5²?
25
4
What is 12²?
144
5
What is √36?
6
6
What is √100?
10
📘 Key Vocabulary
3 / 9
Right angle
90° — shown by the small square □
Hypotenuse
Longest side — always OPPOSITE the right angle
Legs (a and b)
The two shorter sides — they FORM the right angle
📐 Formula
4 / 9
a² + b² = c² where c = hypotenuse
Copy this into your book.
📐 Diagram
5 / 9
Basic right triangle
Verify: does (3, 4, 5) work?
✏️ Worked Example 1
6 / 9
Verify that 3, 4, 5 is a right-angled triangle
Step 1
Longest side = 5 → c = 5, a = 3, b = 4
Step 2
a² + b² = 3² + 4² = 9 + 16 = 25
Step 3
c² = 5² = 25
Step 4
25 = 25 ✓ It IS right-angled
✏️ Worked Example 2
7 / 9
Verify that 6, 7, 8 is a right-angled triangle
Step 1
Longest side = 8 → c = 8, a = 6, b = 7
Step 2
a² + b² = 6² + 7² = 36 + 49 = 85
Step 3
c² = 8² = 64
Step 4
85 ≠ 64 ✗ NOT right-angled
📝 Practice Questions
8 / 9
1
What is 7²?
49
2
What is √81?
9
3
What is 11²?
121
4
Write Pythagoras' theorem from memory.
a² + b² = c²
5
Does (8, 15, 17) form a right triangle? Show working.
64 + 225 = 289 = 17² ✓
6
Does (4, 5, 6) form a right triangle? Show working.
16 + 25 = 41 ≠ 36 ✗
7
Does (7, 24, 25) form a right triangle? Show working.
49 + 576 = 625 = 25² ✓
8
Does (9, 10, 14) form a right triangle? Show working.
81 + 100 = 181 ≠ 196 ✗
🎯 Exit Ticket
9 / 9
1
Write Pythagoras' theorem.
a² + b² = c²
2
Does (6, 8, 10) form a right triangle? Show all working.
36 + 64 = 100 = 10² ✓ Yes
← → arrow keys to navigate
L2 · T2 Week 3
Finding the Hypotenuse
Objective: Use a² + b² = c² to find the hypotenuse, showing all working
🅃 Daily Riddle
1 / 9
🧮 Maths Challenge
🧮
A farmer has a square paddock. Each side is 5 km. He walks diagonally corner to corner instead of along the edges. Without a calculator — is the diagonal longer or shorter than 5 km? By how much roughly?
90
Think about what a diagonal of a square creates — two triangles. What do you know about those triangles?
LONGER! The diagonal is √(5²+5²) = √50 ≈ 7.07 km. He saves 2.93 km vs walking two sides (10 km total)!
⚡ Do Now
2 / 9
1
What is 6²?
36
2
What is 9²?
81
3
What is √49?
7
4
What is √144?
12
5
Write Pythagoras' theorem from memory.
a² + b² = c²
6
Which side is the hypotenuse? Sketch a right triangle and label it.
📘 Key Vocabulary
3 / 9
Hypotenuse (c)
The side we are FINDING — longest, opposite 90°
a and b
The two known short sides — substitute these in
√ (square root)
The inverse of squaring — use the √ button on calculator
📐 Formula
4 / 9
c = √(a² + b²)
Copy this into your book.
📐 Diagram
5 / 9
c is always opposite the right angle
Example: find c when a=5, b=7
✏️ Worked Example 1
6 / 9
Find the hypotenuse when a = 3, b = 4
Step 1
c² = a² + b²
Step 2
c² = 3² + 4² = 9 + 16 = 25
Step 3
c = √25 = 5
✏️ Worked Example 2
7 / 9
Find the hypotenuse when a = 5, b = 7
Step 1
c² = 5² + 7²
Step 2
c² = 25 + 49 = 74
Step 3
c = √74 ≈ 8.60 (2 d.p.)
📝 Practice Questions
8 / 9
1
a = 6, b = 8. Find c.
10
2
a = 9, b = 12. Find c.
15
3
a = 5, b = 10. Find c (1 d.p.)
11.2
4
a = 7, b = 7. Find c (2 d.p.)
9.90
5
a = 2.5, b = 6. Find c (2 d.p.)
6.50
6
a = 11, b = 4. Find c (2 d.p.)
11.70
7
a = 9, b = 40. Find c.
41
8
a = 8, b = 8. Find c (2 d.p.)
11.31
🎯 Exit Ticket
9 / 9
1
Find c when a = 8, b = 15.
17
2
Find c when a = 4, b = 9. Round to 2 d.p.
9.85
← → arrow keys to navigate
L3 · T2 Week 3
Finding a Short Side
Objective: Rearrange Pythagoras' theorem to find a missing leg
🅃 Daily Riddle
1 / 9
🔢 Spot the Pattern
🎯
A right triangle has a hypotenuse of 10 and one leg of 6. Here's the catch: you are NOT allowed to use a calculator. How fast can you find the missing side?
90
Psst — have you seen the numbers 3, 4, 5 before? What if you doubled them all...?
8! It's the 6-8-10 triangle — which is just the famous 3-4-5 triple multiplied by 2. These number combos are called Pythagorean triples.
⚡ Do Now
2 / 9
1
Find c: a = 6, b = 8
10
2
Find c: a = 5, b = 12
13
3
What is √64?
8
4
100 − 36 = ?
64
5
169 − 25 = ?
144
📘 Key Vocabulary
3 / 9
Rearranging
Moving parts of the formula to isolate what we want to find
a² = c² − b²
Subtract the known leg² FROM the hypotenuse²
Inverse operation
Square rooting undoes squaring
📐 Formula
4 / 9
a = √(c² − b²) or b = √(c² − a²)
Copy this into your book.
📐 Diagram
5 / 9
Finding the missing leg
Example: find a when c=13, b=5
✏️ Worked Example 1
6 / 9
Find the missing leg when c = 13, b = 5
Step 1
a² + b² = c²
Step 2
a² + 5² = 13²
Step 3
a² + 25 = 169
Step 4
a² = 169 − 25 = 144
Step 5
a = √144 = 12
✏️ Worked Example 2
7 / 9
Find the missing leg when c = 10, b = 6
Step 1
a² = c² − b²
Step 2
a² = 10² − 6² = 100 − 36 = 64
Step 3
a = √64 = 8
📝 Practice Questions
8 / 9
1
c = 10, b = 6. Find a.
8
2
c = 17, b = 8. Find a.
15
3
c = 15, b = 9. Find a.
12
4
c = 20, b = 12. Find a.
16
5
c = 11, b = 5. Find a (2 d.p.)
9.80
6
c = 8, b = 3. Find a (2 d.p.)
7.42
7
c = 25, b = 7. Find a.
24
8
c = 30, b = 18. Find a.
24
🎯 Exit Ticket
9 / 9
1
Find a when c = 26, b = 10.
24
2
Find b when c = 14, a = 9. Round to 2 d.p.
10.44
← → arrow keys to navigate
L4 · T2 Week 3
Pythagoras + Area & Perimeter
Objective: Use Pythagoras to find a missing dimension, then calculate area and perimeter
🅃 Daily Riddle
1 / 9
🧠 Lateral Thinking
🏠
Ancient Egyptians had NO calculators, NO computers, and NO set squares — but they still built PERFECTLY square pyramid bases. How did they guarantee 90° corners using only a rope?
90
They tied 12 equally-spaced knots in a rope to make a triangle with sides of 3, 4 and 5 knots...
They used a rope with 12 segments tied into a 3-4-5 triangle! Pull it tight and you get a perfect right angle every time. Pythagoras didn't invent this — Egyptians used it 1500 years earlier!
⚡ Do Now
2 / 9
1
Write the formula for area of a triangle.
A = ½ × b × h
2
Triangle: base 10 cm, height 6 cm. Area?
30 cm²
3
Find c: a = 8, b = 15
17
4
Find the missing leg: c = 13, b = 5
12
📘 Key Vocabulary
3 / 9
Strategy
Find the unknown side with Pythagoras FIRST — then use area or perimeter
Exact form
Leave as a surd — e.g. √112 cm
Approximate form
Rounded decimal — e.g. 10.58 cm
📐 Formula
4 / 9
Step 1: Find unknown side (Pythagoras) → Step 2: Area = ½ × b × h → Step 3: P = sum of all sides
Copy this into your book.
📐 Diagram
5 / 9
Right triangle: find height first
Isosceles: split into two right triangles
✏️ Worked Example 1
6 / 9
Right triangle: base 12 cm, hypotenuse 16 cm. Find height, area and perimeter.
Step 1
Step 1 — Height: h = √(16² − 12²) = √(256 − 144) = √112 ≈ 10.58 cm
Step 2
Step 2 — Area: A = ½ × 12 × 10.58 = 63.50 cm²
Step 3
Step 3 — Perimeter: P = 12 + 16 + 10.58 = 38.58 cm
✏️ Worked Example 2
7 / 9
Isosceles triangle: base 16 cm, equal sides 10 cm. Find the height then area.
Step 1
Step 1 — Split in half: base half = 8 cm, hyp = 10 cm
Step 2
Step 2 — Height: h² = 10² − 8² = 100 − 64 = 36 → h = 6 cm
Step 3
Step 3 — Area: A = ½ × 16 × 6 = 48 cm²
📝 Practice Questions
8 / 9
1
Right triangle: legs 9 cm and 12 cm. Find (a) hypotenuse (b) perimeter (c) area.
(a) 15 cm (b) 36 cm (c) 54 cm²
2
Right triangle: hyp = 20 cm, one leg = 12 cm. Find the other leg then the area.
leg = 16 cm, A = 96 cm²
3
Isosceles triangle: base = 10 cm, equal sides = 13 cm. Find height then area.
h = 12 cm, A = 60 cm²
4
Right triangle: legs 7 cm and 7 cm. Find hyp (2 d.p.), perimeter (2 d.p.) and area.
c ≈ 9.90 cm, P ≈ 23.90 cm, A = 24.5 cm²
🎯 Exit Ticket
9 / 9
1
Right triangle: legs 6 cm and 8 cm. Find the hypotenuse, then the area.
c = 10 cm, A = 24 cm²
← → arrow keys to navigate
L5 · T2 Week 3
Is it Right-Angled? (The Converse)
Objective: Use the converse of Pythagoras to test whether a triangle is right-angled
🅃 Daily Riddle
1 / 9
🕵️ Spot the Mistake
🕵️
A student wrote on their test: '5²+8²=13², so 5,8,13 is a right triangle✓' — Their teacher gave zero marks. Why?
90
Grab a calculator and actually check both sides of that equation...
5²+8² = 25+64 = 89. But 13² = 169. So 89 ≠ 169. The student just guessed 5+8=13 and didn't check! Always substitute and calculate BOTH sides.
⚡ Do Now
2 / 9
1
Find c: a = 6, b = 8
10
2
Find a: c = 25, b = 24
7
3
What does the □ symbol mean on a diagram?
90° right angle
4
What is 15²?
225
📘 Key Vocabulary
3 / 9
Converse
The REVERSE of the theorem — use it to TEST a triangle
Pythagorean triad
Three whole numbers satisfying a² + b² = c²
📐 Formula
4 / 9
If a² + b² = c² → RIGHT-ANGLED ✓ If a² + b² ≠ c² → NOT right-angled ✗
Copy this into your book.
📐 Diagram
5 / 9
Always use the LONGEST side as c
Check: (8, 15, 17)
✏️ Worked Example 1
6 / 9
Are sides 7, 24, 25 a right-angled triangle?
Step 1
Longest side = 25 → c = 25, a = 7, b = 24
Step 2
a² + b² = 49 + 576 = 625
Step 3
c² = 625
Step 4
625 = 625 ✓ RIGHT-ANGLED
✏️ Worked Example 2
7 / 9
Are sides 5, 7, 9 a right-angled triangle?
Step 1
Longest side = 9 → c = 9, a = 5, b = 7
Step 2
a² + b² = 25 + 49 = 74
Step 3
c² = 81
Step 4
74 ≠ 81 ✗ NOT right-angled
📝 Practice Questions
8 / 9
1
8, 15, 17 — right-angled?
64 + 225 = 289 = 17² ✓ Yes
2
6, 9, 11 — right-angled?
36 + 81 = 117 ≠ 121 ✗ No
3
20, 21, 29 — right-angled?
400 + 441 = 841 = 29² ✓ Yes
4
4, 7, 8 — right-angled?
16 + 49 = 65 ≠ 64 ✗ No
5
9, 40, 41 — right-angled?
81 + 1600 = 1681 = 41² ✓ Yes
6
10, 12, 15 — right-angled?
100 + 144 = 244 ≠ 225 ✗ No
🎯 Exit Ticket
9 / 9
1
Are sides 11, 60, 61 a right triangle? Show full working.
121 + 3600 = 3721 = 61² ✓ Yes
← → arrow keys to navigate
L6 · T2 Week 3
Word Problems & Drawing Diagrams
Objective: Draw a labelled diagram from a word problem and solve using Pythagoras
🅃 Daily Riddle
1 / 9
🧮 Maths Challenge
📺
Samsung advertises a TV as '65 inches'. Your mate says that's the screen width. You say it's the diagonal. Who's right — and what are the actual dimensions if the height is 32 inches?
90
TV screens have a 16:9 aspect ratio. If height = 32 inches, what is the width? Then use Pythagoras to find the diagonal...
YOU'RE right — it's the diagonal! Width ≈ 56.9 inches. Diagonal = √(56.9²+32²) ≈ 65 inches ✓ All TV sizes are quoted diagonally.
⚡ Do Now
2 / 9
1
Find c: a = 5, b = 12
13
2
Are 8, 15, 17 right-angled?
Yes: 64 + 225 = 289 = 17² ✓
3
A triangle has sides 3, 4 and 5. Which is the hypotenuse?
5
📘 Key Vocabulary
3 / 9
4-Step Method
Read → Draw → Identify → Solve
Diagram
Always sketch and label — no diagram, no marks
Units
Always include cm / m / km in the answer
📐 Formula
4 / 9
READ the problem → DRAW and label → IDENTIFY what to find → SOLVE with Pythagoras
Copy this into your book.
📐 Diagram
5 / 9
Problem 1: ladder against wall
Problem 2: diagonal of a rectangle
✏️ Worked Example 1
6 / 9
A ladder leans against a wall. Base is 1.5 m from wall, wall is 3.5 m high. How long is the ladder?
Step 1
Draw: right triangle — base = 1.5 m, vertical = 3.5 m, ladder = c
Step 2
c² = 1.5² + 3.5² = 2.25 + 12.25 = 14.5
Step 3
c = √14.5 ≈ 3.81 m
✏️ Worked Example 2
7 / 9
A field is 40 m long and 30 m wide. How long is the diagonal path?
Step 1
Draw: rectangle — diagonal is the hypotenuse
Step 2
c² = 40² + 30² = 1600 + 900 = 2500
Step 3
c = √2500 = 50 m
📝 Practice Questions
8 / 9
1
A ramp is 4 m long and reaches 1.5 m high. How far does it extend horizontally? (2 d.p.)
√(16 − 2.25) = √13.75 ≈ 3.71 m
2
A screen is 55 cm wide and 31 cm tall. Find its diagonal. (2 d.p.)
√(3025 + 961) = √3986 ≈ 63.13 cm
3
Two friends walk from the same corner — one 6 km east, one 8 km north. How far apart?
√(36 + 64) = 10 km
4
A 12 m rope goes from the top of a 9 m pole to a peg. How far is the peg from the base?
√(144 − 81) = √63 ≈ 7.94 m
🎯 Exit Ticket
9 / 9
1
A TV is 90 cm wide and 50 cm tall. Find the diagonal. Round to 1 d.p.
√10600 ≈ 103.0 cm
← → arrow keys to navigate
L7 · T2 Week 3
Pythagoras — Mixed Practice
Objective: Apply all Pythagoras skills: hypotenuse, short side, converse and word problems
🅃 Daily Riddle
1 / 8
🔢 Spot the Pattern
🧩
Here are the first three Pythagorean triples: 3-4-5, 5-12-13, 8-15-17. What is the pattern in the LARGEST numbers only: 5, 13, 17, ...? What comes next?
90
Look at the differences between 5, 13, 17... they go up by 8, then 4... or is there another pattern? Try squaring the middle numbers...
The next ones are 7-24-25 and 9-40-41. Notice the largest number is always just ONE more than one of the other sides! These are called 'primitive Pythagorean triples'.
⚡ Do Now
2 / 8
1
Find c: a = 7, b = 24
25
2
Find a: c = 17, b = 15
8
3
Are 6, 8, 10 right-angled?
Yes: 36 + 64 = 100 ✓
4
Write the 4-step word problem method.
Read, Draw, Identify, Solve
📘 Key Vocabulary
3 / 8
Exact answer
Leave as a surd — e.g. √74
Approximate answer
Rounded decimal — e.g. 8.60 cm
📐 Formula
4 / 8
a² + b² = c² | a = √(c² − b²) | Converse: test if a² + b² = c²
Copy this into your book.
📐 Diagram
5 / 8
Find c
Find a
Is it right-angled?
✏️ Worked Example 1
6 / 8
Right triangle with legs 6 m and 6 m. Find hypotenuse, area and perimeter.
Step 1
c = √(6² + 6²) = √72 ≈ 8.49 m
Step 2
Area = ½ × 6 × 6 = 18 m²
Step 3
Perimeter = 6 + 6 + 8.49 = 20.49 m
📝 Practice Questions
7 / 8
1
Find c: a = 9, b = 12
15
2
Find a: c = 10, b = 8
6
3
Are 5, 12, 13 right-angled? Show working.
25 + 144 = 169 = 13² ✓ Yes
4
Ladder 5 m long, base 2 m from wall. How high does it reach?
√(25 − 4) = √21 ≈ 4.58 m
5
Right triangle legs 9 cm, 12 cm: find hyp, area and perimeter.
c=15, A=54 cm², P=36 cm
6
a = 7, b = 9. Find c (2 d.p.)
11.40
7
c = 20, b = 13. Find a (2 d.p.)
15.20
8
Are 8, 9, 12 right-angled?
64 + 81 = 145 ≠ 144 ✗ No
🎯 Exit Ticket
8 / 8
1
Find c when a = 20, b = 21.
29
2
A rope of 10 m is pegged 6 m from a pole. How high up the pole does it reach?
8 m
← → arrow keys to navigate
L8 · T2 Week 3
Pythagoras — Consolidation & Test Prep
Objective: Review all Pythagoras skills and prepare for the Measurement Test
🅃 Daily Riddle
1 / 7
🧠 Lateral Thinking
⚡
You are a spy. You need to cross a rectangular courtyard without being seen on the diagonal security camera path. The courtyard is 30m × 40m. What is the SHORTEST distance you can travel crossing it diagonally?
90
Draw a rectangle. The diagonal is the hypotenuse of a right triangle with legs 30 and 40...
50 metres! √(30²+40²) = √(900+1600) = √2500 = 50 m. It's a 3-4-5 triple multiplied by 10. Mission accomplished.
⚡ Do Now
2 / 7
1
Find c: a = 8, b = 6
10
2
Find a: c = 13, b = 5
12
3
Are 9, 40, 41 right-angled?
Yes ✓
4
Ladder 5 m, base 2 m from wall. Height?
√21 ≈ 4.58 m
5
Right triangle legs 3 m, 4 m: perimeter?
12 m
📘 Key Vocabulary
3 / 7
Measurement Test
NEXT WEEK — covers area, perimeter, composite shapes and Pythagoras
📐 Formula
4 / 7
a² + b² = c² | a = √(c²−b²) | Converse | Word problems with diagram
Copy this into your book.
📐 Diagram
5 / 7
Finding sides
Converse — is it right-angled?
📝 Practice Questions
6 / 7
1
a = 3, b = 4 → c = ?
5
2
a = 5, b = 12 → c = ?
13
3
c = 10, b = 6 → a = ?
8
4
c = 26, b = 10 → a = ?
24
5
a = 7, b = 9 → c (2 d.p.)
11.40
6
c = 14, b = 11 → a (2 d.p.)
8.66
7
Right tri legs 9, 12 cm: find hyp, area, perimeter.
c=15, A=54 cm², P=36 cm
8
Ladder 5 m, base 2 m from wall. How high does it reach?
√21 ≈ 4.58 m
🎯 Exit Ticket
7 / 7
1
What topics are on the Measurement Test? List all of them.
Area, perimeter, composite shapes, Pythagoras, converse, word problems
← → arrow keys to navigate
L9 · T2 Week 4
Ways to Earn Money
Objective: Name and calculate different types of income: wages, salary, commission, piecework
🅃 Daily Riddle
1 / 9
🧮 Maths Challenge
💸
You work at Maccas for $15/hr. Your friend works at KFC for $14.50/hr but gets a FREE meal worth $12 every shift (4 hrs). Who actually earns more per shift — you or your friend?
90
Calculate total earnings per 4-hour shift for BOTH people, including the meal value for your friend...
Your friend wins! You: $15×4 = $60. Friend: $14.50×4 + $12 = $58+$12 = $70. Free food counts as income!
Alex earns $19.50/hr and works 8 hours. Total pay?
Step 1
Pay = rate × hours
Step 2
Pay = $19.50 × 8 = $156
✏️ Worked Example 2
6 / 9
Salary = $72,800/year. Weekly pay?
Step 1
Weekly = $72,800 ÷ 52 = $1,400
✏️ Worked Example 3
7 / 9
Commission 3% on a $24,000 sale.
Step 1
Commission = 3% × $24,000 = 0.03 × 24,000 = $720
📝 Practice Questions
8 / 9
1
Emma earns $24/hr and works 35 hrs. Weekly pay?
$840
2
Salary $46,800/year. Fortnightly pay (÷ 26)?
$1,800
3
Commission rate 4%. Sales = $15,000. Commission?
$600
4
Piecework: $2.80 per item. 75 items. Pay?
$210
5
Jordan earns $21.60/hr and works 12 hours. Total?
$259.20
6
Salary $58,500/year. Weekly pay?
$1,125
7
Commission 5% on $32,000 in sales.
$1,600
8
Piecework: $3.50 per box × 120 boxes.
$420
🎯 Exit Ticket
9 / 9
1
Name 3 types of income with a real-life example of each.
Wage, salary, commission, piecework — any 3 with examples
2
Jordan earns $21.60/hr and works 12 hours. How much does she earn?
$259.20
← → arrow keys to navigate
L10 · T2 Week 4
⚠️ Measurement Test + Wages Intro
Objective: Complete the Measurement Test, then begin wage and salary calculations
🅃 Daily Riddle
1 / 7
🧮 Maths Challenge
🎰
A job ad says '$78,000 per annum'. Your friend gets paid $1,600 per fortnight. Another friend earns $720 per week. Rank them from highest to lowest annual income — no calculator!
90
Convert everything to yearly: fortnightly × 26, weekly × 52, or annual stays the same...
1st: $78,000/yr. 2nd: $1,600×26 = $41,600/yr. 3rd: $720×52 = $37,440/yr. Always convert to the same unit to compare!
⚡ Do Now
2 / 7
Test this lesson - see lesson plan.
📘 Key Vocabulary
3 / 7
Measurement Test
Covers: area, perimeter, composite shapes, Pythagoras, converse, word problems
After test — Sam earns $22/hr and works 38 hours. Weekly pay?
Step 1
Pay = $22 × 38 = $836
📝 Practice Questions
6 / 7
1
$18/hr × 40 hrs = ?
$720
2
Salary $52,000/year. Weekly pay?
$1,000
3
$23.50/hr × 6 hrs = ?
$141
4
Salary $78,000/year. Fortnightly pay?
$3,000
🎯 Exit Ticket
7 / 7
1
You earn $20/hr. You work 9 hours. How much do you earn?
$180
← → arrow keys to navigate
L11 · T2 Week 4
Wages & Penalty Rates
Objective: Calculate wages including time and a half, double time and mixed weeks
🅃 Daily Riddle
1 / 7
🧠 Lateral Thinking
⏰
Your normal rate is $22/hr. On Sunday you earn double time. Your coworker works twice as many hours as you on Sunday but only at normal rate. Who earns more on Sunday?
90
You work X hours at $44/hr. Coworker works 2X hours at $22/hr. Compare the totals...
It's a TIE! You: X × $44. Coworker: 2X × $22 = X × $44. Same total! Double time for half the hours = normal time for double the hours.
⚡ Do Now
2 / 7
1
$18 × 6 = ?
$108
2
$18 × 1.5 = ?
$27
3
$18 × 2 = ?
$36
4
$22.50 × 8 = ?
$180
5
What does 'time and a half' mean? Write in your own words.
1.5× normal rate
📘 Key Vocabulary
3 / 7
Normal time
×1 — standard hourly rate
Time and a half
×1.5 — common for Saturday shifts
Double time
×2 — common for Sunday and public holidays
Double time and a half
×2.5 — public holiday premium
📐 Formula
4 / 7
Penalty pay = hourly rate × multiplier × hours worked
Copy this into your book.
✏️ Worked Example 1
5 / 7
Jake earns $17/hr. Mon–Fri 8 hrs/day, Sat 4 hrs (T&H), Sun 3 hrs (DT). Total?
Mia $19.50/hr. Tue–Sat 8 hrs. Sat = time & half. Total?
$624 + $234 = $858
6
$24/hr. 3 hrs double time and a half. Pay?
$24 × 2.5 × 3 = $180
🎯 Exit Ticket
7 / 7
1
You earn $21/hr. 6 hours on Sunday at double time. How much?
$21 × 2 × 6 = $252
2
What multiplier is used for time and a half?
1.5
← → arrow keys to navigate
L12 · T2 Week 4
Payslips — Reading & Calculating
Objective: Read a payslip and calculate gross pay, tax, super and net pay
🅃 Daily Riddle
1 / 7
🕵️ Spot the Mistake
🧾
A payslip shows: Gross $1,400 · Tax $280 · Super 11%. A student calculates net pay as $1,400 - $280 - $154 = $966. Their teacher says they're wrong. Who is right?
90
Where does super actually come from — the employee's wages, or the employer's pocket?
The STUDENT made an error — but the teacher is only half right too! Super ($154) is paid BY the employer on TOP of wages, not deducted. Net pay = $1,400 - $280 = $1,120. Super is a bonus, not a deduction!
⚡ Do Now
2 / 7
1
$850 − $125 = ?
$725
2
10% of $960 = ?
$96
3
11% of $840 = ?
$92.40
4
$1,200 − $312 − $96 = ?
$792
📘 Key Vocabulary
3 / 7
Gross Pay
Total earnings BEFORE any deductions
Tax
Money withheld for the government (ATO)
Superannuation (Super)
11% employer contribution — goes into your retirement fund
Net Pay
What you actually receive — gross minus deductions
YTD
Year to Date — total earned since 1 July
📐 Formula
4 / 7
Net Pay = Gross − Tax − Other Deductions | Super = 11% × Gross (employer pays this separately)
Copy this into your book.
✏️ Worked Example 1
5 / 7
Gross = $1,400. Tax = $285. Super = 11% of gross. Find net pay and super.
Step 1
Super = 11% × $1,400 = $154 (employer pays this on top)
Step 2
Net Pay = $1,400 − $285 = $1,115
📝 Practice Questions
6 / 7
1
Gross=$960, Tax=$142, Other=$20. Net pay?
$798
2
Gross=$2,100, Tax=$385. Net pay?
$1,715
3
Gross=$780. Super=11%. How much super does employer pay?
$85.80
4
Net=$1,260. Tax=$194. What was the gross?
$1,454
5
Jake: 38 hrs at $23/hr. Tax=18% of gross. Find gross, tax, net.
Gross=$874, Tax=$157.32, Net=$716.68
🎯 Exit Ticket
7 / 7
1
What is the difference between gross and net pay?
Gross = before deductions, Net = take-home after tax etc.
2
Gross=$1,050, Tax=$210, Super=11%. Find net pay and employer super.
Net=$840, Super=$115.50
← → arrow keys to navigate
L13 · T2 Week 5
Commission & Piecework
Objective: Calculate commission (with and without base pay) and piecework earnings
🅃 Daily Riddle
1 / 8
🕵️ Spot the Mistake
🔍
A car salesperson says: 'I earned $3,200 commission this month! I sold $80,000 of cars at a 4% rate.' Is their maths correct?
90
Calculate 4% of $80,000 yourself...
YES — correct! 0.04 × $80,000 = $3,200 ✓ Don't always assume there's a mistake. Sometimes the maths checks out!
⚡ Do Now
2 / 8
1
4% of $30,000 = ?
$1,200
2
2.5% of $12,000 = ?
$300
3
$3.20 × 45 = ?
$144
4
Gross=$920, Tax=$158. Net pay?
$762
📘 Key Vocabulary
3 / 8
Base + commission
Fixed amount plus a % of sales on top
Piecework rate
Fixed $ per item or task completed
Compare income
Calculate totals for each option — then decide
📐 Formula
4 / 8
Commission = rate% × total sales | Piecework = rate per item × number of items
Copy this into your book.
✏️ Worked Example 1
5 / 8
Real estate agent: base $800/week + 1.5% commission. Sold a house for $620,000.
Piecework: $4.20 per board. 180 boards Monday, 210 Tuesday. Total pay?
Step 1
Total boards: 180 + 210 = 390
Step 2
Pay: 390 × $4.20 = $1,638
📝 Practice Questions
7 / 8
1
Commission 6% on sales of $45,000.
$2,700
2
Base $500/week + 2% commission on $28,000.
$500 + $560 = $1,060
3
Piecework: $1.80/item × 340 items.
$612
4
Which is better: (A) $25/hr × 40 hrs OR (B) $5/item × 220 items?
A=$1,000 B=$1,100 → B is better
5
Commission 3.5% on $80,000 + base $1,200/month. Monthly total?
$1,200 + $2,800 = $4,000
6
Piecework: $2.10/kg × 670 kg (380 Mon + 290 Tue).
$1,407
🎯 Exit Ticket
8 / 8
1
Commission rate 5% on $32,000 sales. Calculate.
$1,600
2
Which pays more: $28/hr × 38 hrs OR $20/hr × 38 hrs + Sat 5 hrs T&H?
A=$1,064 B=$910 → A pays more
← → arrow keys to navigate
L14 · T2 Week 5
Percentages Review + Intro to Interest
Objective: Identify P, R and T in interest problems and convert time periods correctly
🅃 Daily Riddle
1 / 8
🧮 Maths Challenge
🏦
Your grandma offers you one of two deals: (A) $1,000 now, or (B) $200 saved per month for 5 months with 3% p.a. simple interest for 2 years. Which do you take?
90
For option B: total saved = $200×5 = $1,000. Then calculate simple interest: I = PRT where P=1000, R=0.03, T=2...
Take option B! You still get $1,000 but ALSO earn $60 interest. Total = $1,060. Free money from grandma AND a maths lesson.
⚡ Do Now
2 / 8
1
5% of $600 = ?
$30
2
8% of $2,500 = ?
$200
3
12.5% of $800 = ?
$100
4
Write 4.5% as a decimal.
0.045
5
Write 0.075 as a percentage.
7.5%
📘 Key Vocabulary
3 / 8
Principal (P)
The original amount borrowed or saved
Rate (R)
Annual interest rate — always convert to a decimal
Identify P, R and T: 'Sarah borrows $5,000 at 6% per year for 3 years.'
Step 1
P = $5,000
Step 2
R = 6% = 0.06
Step 3
T = 3 years
✏️ Worked Example 2
6 / 8
Identify P, R and T: '$1,500 saved at 3.5% p.a. for 18 months.'
Step 1
P = $1,500
Step 2
R = 3.5% = 0.035
Step 3
T = 18 ÷ 12 = 1.5 years
📝 Practice Questions
7 / 8
1
Identify P, R, T: $8,000 at 4% p.a. for 2 years.
P=$8,000 R=0.04 T=2
2
Identify P, R, T: $12,000 at 7.2% p.a. for 4 years.
P=$12,000 R=0.072 T=4
3
Identify P, R, T: $500 at 2% p.a. for 9 months.
P=$500 R=0.02 T=0.75
4
Identify P, R, T: $25,000 at 9.25% p.a. for 3 years.
P=$25,000 R=0.0925 T=3
5
Convert: 15 months to years.
1.25
6
Convert: 8% to a decimal.
0.08
🎯 Exit Ticket
8 / 8
1
Write the simple interest formula and explain each letter.
I = P × R × T — principal, rate (decimal), time (years)
2
Identify P, R, T: '$3,000 at 5.5% p.a. for 30 months'
P=$3,000 R=0.055 T=2.5
← → arrow keys to navigate
L15 · T2 Week 6
Simple Interest Formula: I = PRT
Objective: Calculate simple interest and total amount using I = P × R × T
🅃 Daily Riddle
1 / 8
🧮 Maths Challenge
🚗
You want a $18,000 car. Option A: Pay cash now. Option B: $3,000 deposit + borrow the rest at 6% p.a. for 3 years. How much EXTRA do you pay with option B compared to cash?
90
Borrowed amount = $18,000 - $3,000 = $15,000. Use I = PRT to find the interest...
You pay $2,700 extra! I = $15,000 × 0.06 × 3 = $2,700 in interest. Total cost = $3,000 + $15,000 + $2,700 = $20,700 vs $18,000 cash.
⚡ Do Now
2 / 8
1
Write I = PRT in full words.
Interest = Principal × Rate × Time
2
Convert 9 months to years.
0.75
3
Write 7.5% as a decimal.
0.075
4
$2,000 × 0.05 × 3 = ?
$300
📘 Key Vocabulary
3 / 8
I = PRT
Simple Interest = Principal × Rate × Time
A = P + I
Total Amount = Principal + Interest
p.a.
Per annum = per year
📐 Formula
4 / 8
I = P × R × T A = P + I (R as decimal, T in years)
Copy this into your book.
✏️ Worked Example 1
5 / 8
Find the interest on $4,000 at 5% p.a. for 3 years.
Step 1
P = $4,000 R = 0.05 T = 3
Step 2
I = 4000 × 0.05 × 3 = $600
Step 3
A = $4,000 + $600 = $4,600
✏️ Worked Example 2
6 / 8
$9,000 at 4.5% p.a. for 18 months. Find I and A.
Step 1
P = $9,000 R = 0.045 T = 1.5 (18 ÷ 12)
Step 2
I = 9000 × 0.045 × 1.5 = $607.50
Step 3
A = $9,000 + $607.50 = $9,607.50
📝 Practice Questions
7 / 8
1
P=$3,000, R=4%, T=2 yrs. Find I and A.
I=$240, A=$3,240
2
P=$7,500, R=6%, T=3 yrs. Find I and A.
I=$1,350, A=$8,850
3
P=$1,200, R=8%, T=6 months. Find I.
T=0.5, I=$48
4
P=$5,000, R=3.5%, T=4 yrs. Find I and A.
I=$700, A=$5,700
5
P=$2,500, R=5%, T=30 months. Find I and A.
T=2.5, I=$312.50, A=$2,812.50
6
P=$10,000, R=9.25%, T=3 yrs. Find I then monthly interest.
I=$2,775, per month=$77.08
🎯 Exit Ticket
8 / 8
1
Car loan: $14,500 at 9.25% p.a. for 3 years. Find total interest and total amount.
I=$4,026.75, A=$18,526.75
2
How much interest per month on the loan above?
$4,026.75 ÷ 36 = $111.85/month
← → arrow keys to navigate
L16 · T2 Week 6
⚠️ Finance Test Prep + Review
Objective: Review all financial maths topics and prepare for the Finance Test
🅃 Daily Riddle
1 / 6
🧠 Lateral Thinking
🧠
Banks are sneaky. Bank A offers '6% p.a. for 1 year'. Bank B offers '0.5% per month'. If you invest $1,000, which bank gives you more? Most people get this wrong!
90
For Bank B: 0.5% per month × 12 months = ? % per year? Now compare to Bank A's 6%...
They're IDENTICAL! 0.5%/month × 12 = 6%/year. Same rate, just expressed differently. Banks love confusing customers with different time periods. Always convert to annual to compare!
⚡ Do Now
2 / 6
1
Write the simple interest formula.
I = P × R × T
2
Write the total amount formula.
A = P + I
3
What multiplier is time and a half?
1.5
4
Difference between gross and net pay?
Gross = before deductions, Net = take-home
5
Convert 9 months to years.
0.75
📘 Key Vocabulary
3 / 6
Finance Test
THIS WEEK — covers all income types, payslips and simple interest