📍 British Columbia · Grade 7 Mathematics

Your complete companion to Grade 7 Math

Every unit has an instructional video, worked examples, printable practice and extension worksheets, and a levelled interactive quiz. Choose a unit from the sidebar to get started.

10Units
38Weeks
100+Quiz Questions
4Levels
How to use this site
📺
Watch the Video
Start each unit by watching the concept video before working through examples.
✏️
Study Examples
Work through the step-by-step examples before trying questions on your own.
📄
Print & Practise
Print practice worksheets to strengthen your skills, or tackle extension questions for a challenge.
🎯
Take the Quiz
Test your knowledge with a 10+ question levelled quiz and get instant feedback.
Level guide
⬢ Level 1 — Foundational
Core skills with guided practice. Build confidence here first.
⬢ Level 2 — Developing
Apply skills in slightly more complex situations.
⬢ Level 3 — Proficient
Multi-step problems and word problems with real context.
⬢ Level 4 — Extending
Challenging extensions that go beyond the expected standard.
1

Number Sense & Place Value

📅 Week 1

Place value, divisibility rules, prime & composite numbers, prime factorization, GCF and LCM — the building blocks of all number work in Grade 7.

Concept Video
GCF: Greatest Common Factor — Math Antics. After watching, explore the related videos below for LCM and prime factorization.
LCM using the Birthday Cake method
LCM vs GCF — Math with Mr. J

Big Ideas

  • Every digit has a specific place value — changing one digit can dramatically change a number's value.
  • Divisibility rules are shortcuts rooted in our base-ten number system.
  • Every whole number > 1 is either prime (exactly 2 factors) or composite (more than 2).
  • Prime factorization gives every composite number a unique set of building blocks.
  • GCF and LCM connect number sense to real-world situations like sharing and scheduling.
Worked Examples
1
Place Value
Find the value of the underlined digit in 4703 821.
1
Write out the place value columns: 4 millions | 7 hundred-thousands | 0 ten-thousands…
2
The underlined digit 7 sits in the hundred-thousands column.
3
Value = 7 × 100 000 = 700 000
Answer: 700 000
2
Divisibility Rules
Is 7 236 divisible by 9? Show the digit-sum check.
1
Add all digits: 7 + 2 + 3 + 6 = 18
2
Is 18 divisible by 9? 18 ÷ 9 = 2 ✓ Yes.
3
Therefore 7 236 is divisible by 9.
Answer: Yes — digit sum 18 is divisible by 9
3
Prime Factorization
Write the prime factorization of 48 using exponents.
1
Build a factor tree: 48 = 2 × 24 = 2 × 2 × 12 = 2 × 2 × 2 × 6 = 2 × 2 × 2 × 2 × 3
2
Count the 2s: four 2s and one 3.
3
Write with exponents: 2⁴ × 3
Answer: 48 = 2⁴ × 3
4
Finding GCF
Find GCF(24, 36) using prime factorization.
1
24 = 2³ × 3 and 36 = 2² × 3²
2
Take the lowest power of each shared prime factor.
3
Shared: 2 (lowest power 2²) and 3 (lowest power 3¹)
4
GCF = 2² × 3 = 4 × 3 = 12
Answer: GCF(24, 36) = 12
5
Finding LCM
Find LCM(6, 9) using prime factorization.
1
6 = 2 × 3 and 9 = 3²
2
Take the highest power of each prime that appears in either number.
3
Primes involved: 2¹ and 3²
4
LCM = 2 × 9 = 18
Answer: LCM(6, 9) = 18
6
GCF Word Problem
A farmer has 24 red and 36 white flowers. What is the greatest number of identical bouquets she can make using ALL the flowers?
1
"Greatest number of identical bouquets using all flowers" → find GCF.
2
GCF(24, 36) = 12 (from Example 4)
3
Each bouquet: 24÷12 = 2 red, 36÷12 = 3 white flowers.
Answer: 12 bouquets (2 red + 3 white each)
🪶 First Peoples Connection
Cedar baskets made by Coast Salish weavers often use repeating patterns with rows of exactly the same design. If a weaver uses 48 cedar strips and 36 bark strips to create identical rows, GCF(48, 36) = 12 tells her she can make 12 identical rows — each using 4 cedar strips and 3 bark strips. Mathematics supports design decisions that have been part of cultural practice for thousands of years.
📝 Practice Worksheet Practice

Name: _________________________    Date: _____________    Score: ___/20

Level 1 — Place Value & Divisibility
  1. Write the value of the underlined digit in 5728 304. L1
  2. Write 3 045 807 in expanded form. L1
  3. Order from least to greatest: 2 040 500, 2 400 050, 2 004 500, 2 400 500. L1
  4. Is 4 824 divisible by 4? Show your test. L1
  5. Is 3 531 divisible by 9? Show the digit-sum check. L1
Level 2 — Primes, GCF & LCM
  1. Is 83 prime or composite? Explain how you know. L2
  2. Write the prime factorization of 72 using exponents. Show your factor tree. L2
  3. Find GCF(30, 45). Show your method. L2
  4. Find LCM(8, 12). Show your method. L2
  5. List the first 6 multiples of 7 and the first 6 multiples of 9. Circle any that appear in both lists. L2
Level 3 — Word Problems
  1. Two school buses leave a depot at 7:00 am. Bus A returns every 15 minutes, Bus B every 20 minutes. When is the next time both leave the depot together? L3
  2. A woodworker has 60 cm and 84 cm lengths of cedar. She wants to cut both lengths into equal pieces with no waste. What is the longest possible piece length? How many pieces of each does she get? L3
  3. A number is divisible by both 3 and 8. What is the smallest such number greater than 1? Explain. L3
Level 4 — Extending
  1. Three First Peoples drummers beat at different intervals: every 4, 6, and 9 seconds. They all beat together at time 0. How many seconds until they next all beat together? L4
  2. Find two numbers whose GCF is 12 and whose LCM is 60. Explain how you know your answer is correct. L4
🚀 Extension Worksheet Extension

Name: _________________________    Date: _____________

Challenge yourself: These questions require creative thinking, multi-step reasoning, and connections beyond the standard curriculum.
  1. A number N has exactly three distinct prime factors: 2, 3, and 5. The prime factorization includes 2³, 3², and 5¹. What is N? List ALL factors of N.
  2. The GCF of two numbers is 18 and their LCM is 540. One of the numbers is 54. Find the other number. Show algebraic reasoning.
  3. A digital clock shows hours from 1–12. Starting at 12:00, the hour hand has turned exactly 1/3 of a full rotation. What time is shown? What fraction of a full rotation does the hour hand make in 4 hours?
  4. A salmon counting fence records exactly 4 200 salmon in the first week, and the count is divisible by 2, 3, 4, 5, 6, 7, and 10. What is the smallest number of additional salmon that could arrive in Week 2 so the two-week total is also divisible by 11?
  5. Cryptography connection: The RSA encryption system uses products of two large prime numbers as a "public key." Why does using primes make this secure? Research and write a 4–6 sentence explanation connecting prime factorization to digital security.
Levelled Quiz
2

Fractions, Decimals & Percents

📅 Weeks 2–7

Operations with fractions, decimal place value, terminating vs repeating decimals, and fluent conversion between all three forms.

Concept Videos
Math Antics — Fractions and Decimals. Watch this first, then the percentages video below.
What Are Percentages? — Math Antics
Converting Any Fraction to a Decimal — Math Antics
Worked Examples
1
Adding Fractions — Unlike Denominators
Calculate: ¾ + ⅝
1
Find the LCD of 4 and 8: LCD = 8
2
Convert: ¾ = ⁶⁄₈
3
⁶⁄₈ + ⁵⁄₈ = ¹¹⁄₈ = 1³⁄₈
Answer: 1³⁄₈
2
Subtracting Mixed Numbers
Calculate: 2⅓ − 1¾
1
Convert to improper: 2⅓ = ⁷⁄₃, 1¾ = ⁷⁄₄
2
LCD = 12: ²⁸⁄₁₂ − ²¹⁄₁₂ = ⁷⁄₁₂
Answer: ⁷⁄₁₂
3
Multiplying Fractions
Calculate: ⅔ × ⁹⁄₄
1
Cross-cancel: ⅔ × ⁹⁄₄ → ²⁄₁ × ³⁄₄ (cancel 3s)
2
Multiply: 2 × 3 = 6, 1 × 4 = 4 → ⁶⁄₄ = 1½
Answer: 1½
4
Dividing Fractions
Calculate: 3½ ÷ ¾
1
Convert: 3½ = ⁷⁄₂
2
Multiply by the reciprocal: ⁷⁄₂ × ⁴⁄₃ = ²⁸⁄₆ = 4²⁄₃
Answer: 4⅔
5
Decimal Multiplication
Calculate: 4.85 × 3.2
1
Multiply ignoring decimals: 485 × 32 = 15 520
2
Count decimal places: 2 + 1 = 3 → place decimal 3 from right.
3
15 520 → 15.520
Answer: 15.52
6
Fraction → Decimal → Percent
Convert ⁷⁄₈ to a decimal and percent.
1
Divide: 7 ÷ 8 = 0.875
2
Multiply by 100: 0.875 × 100 = 87.5%
Answer: 0.875 = 87.5%
🪶 First Peoples Connection
A Fraser River salmon population of 6 400 decreases by ¼ due to low water levels. Calculating: ¼ × 6 400 = 1 600 fish lost. Remaining: 6 400 − 1 600 = 4 800. BC First Nations fisheries managers use proportional reasoning like this every season to make decisions about harvest limits and habitat restoration.
📝 Practice Worksheet Practice

Name: _________________________    Date: _____________    Score: ___/20

Level 1 — Fraction Operations
  1. Convert ¹⁷⁄₅ to a mixed number. L1
  2. Simplify ¹²⁄₁₆ to lowest terms. Show the GCF. L1
  3. Write three equivalent fractions for ²⁄₅. L1
  4. Order from least to greatest: ²⁄₃, ³⁄₅, ⁷⁄₁₀, ½. Show your common denominator. L1
  5. Calculate: ³⁄₄ + ⅝. Show all steps. L1
Level 2 — Mixed Operations
  1. Calculate: 2½ − 1¾. Convert to improper fractions first. L2
  2. Calculate: ³⁄₅ × ¹⁰⁄₉. Simplify your answer. L2
  3. Calculate: ⅔ ÷ ⅘. Show the "multiply by the reciprocal" step. L2
  4. Calculate: 6.4 × 2.5. Show how you place the decimal. L2
  5. Calculate: 9.36 ÷ 0.4. Convert the divisor to a whole number first. L2
Level 3 — Conversions & Ordering
  1. Convert ⅝ to a decimal and a percent. Show both steps. L3
  2. Write 4.307 in expanded form showing decimal place values. L3
  3. Order on a number line: 0.6, ⅝, 63%, ⁷⁄₁₂. Show your working. L3
  4. A salmon population of 6 400 decreases by ¼. How many remain? L3
Level 4 — Extending
  1. A fraction has a decimal equal to 0.4̄ (0.4444…). Write it as a simplified fraction and explain how repeating decimals connect to fractions with denominators that have prime factors other than 2 and 5. L4
🚀 Extension Worksheet Extension
Extension Challenge: These questions explore fractions and decimals at a deeper level — perfect for students who want to go further.
  1. A recipe calls for 2¼ cups of flour for every 1½ cups of sugar. How much flour is needed for 4 cups of sugar? Write and solve a proportion.
  2. Show algebraically why 0.9̄ (0.999…) equals exactly 1. Use the "let x = 0.999…" approach and multiply by 10.
  3. A First Nations weaver mixes ⅔ of one dye colour with ¾ of another. If the total mixture must be exactly 2 litres, how much of each colour does she need? Set up and solve an equation.
  4. Investigate: which fractions with denominators from 1 to 20 produce terminating decimals, and which produce repeating decimals? Write a general rule based on the prime factorization of the denominator.
  5. A store sells two types of salmon at different prices per 100g. Store A: 3/8 kg for $6.75. Store B: 0.45 kg for $8.10. Calculate the unit price per 100g for each and determine the better value. Show all steps.
Levelled Quiz
3

Integers

📅 Weeks 8–10

Extending the number line below zero — integer concepts, all four operations with integers, and BEDMAS with negative numbers.

Introduction to Negative Numbers. Covers the concept of integers on a number line with real-world contexts.
Order of Operations (BEDMAS/PEMDAS) — Math Antics. Essential for simplifying integer expressions.
Worked Examples
1
Adding Integers
(+8) + (−5) = ?
1
Different signs → subtract magnitudes: 8 − 5 = 3
2
Larger magnitude is positive (+8), so answer is positive.
Answer: +3
2
Subtracting Integers
(+3) − (−9) = ?
1
Subtracting a negative = adding a positive: (+3) + (+9)
2
Same signs → add: 3 + 9 = 12
Answer: +12
3
Multiplying Integers
(−6) × (−7) = ?
1
Multiply the magnitudes: 6 × 7 = 42
2
Sign rule: negative × negative = positive.
Answer: +42
4
Dividing Integers
(+48) ÷ (−6) = ?
1
Divide magnitudes: 48 ÷ 6 = 8
2
Sign rule: positive ÷ negative = negative.
Answer: −8
5
BEDMAS with Integers
Simplify: (−3) × (4 + (−7)) − 8 ÷ (−2)
1
Brackets: 4 + (−7) = −3
2
Now: (−3) × (−3) − 8 ÷ (−2)
3
Division: 8 ÷ (−2) = −4
4
Multiplication: (−3) × (−3) = +9
5
Subtraction: 9 − (−4) = 9 + 4 = 13
Answer: +13
6
Real World: Temperature
Temperature at midnight: −8°C. It drops 3°C every hour for 4 hours. What is the temperature at 4 am?
1
Change over 4 hours: (−3) × 4 = −12°C
2
Final: (−8) + (−12) = −20°C
Answer: −20°C at 4 am
📝 Practice Worksheet Practice

Name: _________________________    Date: _____________

Level 1 — Integer Concepts
  1. Write an integer for each: (a) 15 m below sea level (b) gain of $45 (c) 7°C below zero (d) sea level. L1
  2. Order from least to greatest: +5, −3, 0, −8, +1, −1. L1
  3. Which is greater: −4 or −7? Explain using the number line. L1
Level 2 — Operations
  1. (+8) + (−5) = ___   (+7) + (−12) = ___   (−9) + (−6) = ___ L2
  2. (+3) − (−7) = ___   (−5) − (−2) = ___   (−8) − (+4) = ___ L2
  3. (−4) × (+9) = ___   (−6) × (−7) = ___   (+5) × (−8) = ___ L2
  4. (−45) ÷ (+5) = ___   (−56) ÷ (−8) = ___   (+72) ÷ (−9) = ___ L2
Level 3 — BEDMAS & Word Problems
  1. Simplify using BEDMAS: (−3) × (4 + (−7)) ÷ (−2) + (−1). Show every step. L3
  2. A submarine is at −120 m. It ascends 45 m, then descends 30 m. What is its final depth? L3
  3. Mon: −8°C, Tue: −3°C, Wed: +2°C, Thu: −1°C, Fri: +5°C. Find the mean temperature. L3
Level 4 — Extending
  1. The difference in elevation between a mountain peak (+2 954 m) and a valley floor (−83 m) is ___. Create a similar real BC example and calculate it. L4
  2. Create and solve a word problem using integers that involves a BC First Nations context (e.g., tide levels, temperature changes, elevation). Show all mathematical steps. L4
🚀 Extension Worksheet Extension
Challenge yourself with these deeper integer problems.
  1. Find all integer values of n such that (−3) × n + 15 is between −12 and +12 (inclusive).
  2. A tide table shows: High tide +2.8 m, Low tide −1.4 m. (a) What is the tidal range? (b) If a boat needs at least 1.5 m of water and the harbour floor is at −0.8 m from mean sea level, during what portion of the tide cycle can the boat safely enter?
  3. Explain why "negative times negative equals positive" using the pattern: (+3)×(−2)=−6, (+2)×(−2)=−4, (+1)×(−2)=−2, 0×(−2)=0, (−1)×(−2)=___. What must the next result be to continue the pattern?
  4. Stock market challenge: A stock starts at $24. On consecutive days it changes: −$3, +$5, −$8, +$2, −$6. Write the calculation, find the final price, and determine the total absolute change (sum of magnitudes of each change).
Levelled Quiz
4

Ratio, Rate & Percent

📅 Weeks 11–14

Multiplicative relationships through ratios, rates, proportional reasoning, scale, percent of a number, and percent change.

What Are Percentages? — Math Antics. Covers percent as a ratio out of 100.
What Percent Is It? — Math Antics. Solving for the percent in different problem types.
Worked Examples
1
Writing & Simplifying Ratios
A bag has 8 red and 6 blue marbles. Write the ratio in all three forms and simplify.
1
Three forms: 8:6, ⁸⁄₆, "8 to 6"
2
GCF(8,6) = 2. Divide both: 4:3
Answer: 4:3 (simplified)
2
Unit Rate
A car travels 340 km in 4 hours. Find the unit rate (km/h).
1
Unit rate = rate per ONE unit: 340 ÷ 4 = 85
Answer: 85 km/h
3
Solving a Proportion
Solve: ³⁄₅ = n⁄₂₅
1
Cross-multiply: 3 × 25 = 5 × n
2
75 = 5n → n = 15
Answer: n = 15
4
Percent Change
A salmon population rises from 4 200 to 5 040. What is the percent increase?
1
Change: 5 040 − 4 200 = 840
2
% Change = 840 ÷ 4 200 × 100 = 20%
Answer: 20% increase
5
Map Scale
A BC map has scale 1:50 000. Two cities are 8.4 cm apart. Actual distance in km?
1
Actual cm: 8.4 × 50 000 = 420 000 cm
2
Convert: 420 000 cm ÷ 100 000 = 4.2 km
Answer: 4.2 km
6
Best Buy
750 mL juice for $3.29 or 1.25 L for $5.49? Which is better value?
1
A: $3.29 ÷ 7.5 = $0.439/100mL
2
B: $5.49 ÷ 12.5 = $0.439/100mL
Answer: Equal value! (both ≈ $0.44/100 mL)
📝 Practice Worksheet Practice

Name: _________________________    Date: _____________

  1. Write the ratio 18:24 in lowest terms. Show the GCF. L1
  2. A car travels 360 km in 4 hours. Find the unit rate. L1
  3. Solve the proportion: ⁴⁄₆ = n⁄₃₀. L2
  4. Find 35% of $280. Show two methods. L2
  5. A BC map has scale 1:50 000. Two towns are 6.4 cm apart. Actual distance in km? L2
  6. A sweater costs $64 after a 20% discount. What was the original price? L3
  7. A population drops from $150 to $112.50. What percent decrease? L3
  8. In a Grade 7 class, 18 of 30 students own a pet. If the school has 360 students, how many own a pet? L3
  9. A recipe uses 3 cups of flour for 2 cups of sugar. For 9 cups of flour, how much sugar is needed? L3
  10. Best buy: 750 mL for $3.00 or 1.25 L for $4.75? Calculate price per 100 mL for each. L4
🚀 Extension Extension
  1. A BC First Nations community harvests salmon using a traditional practice ensuring only 60% of the counted fish are taken. If 4 800 salmon are counted, and the count has a 15% margin of error, what is the range of fish that might be harvested? Explain why the margin of error matters for sustainable fisheries management.
  2. A store marks up an item by 40% to get the selling price, then offers a "20% off sale." Show algebraically that this is NOT the same as a 20% markup. What is the actual percent increase from cost to final sale price?
  3. Two hikers start at the same trailhead. Hiker A walks at 4.5 km/h. Hiker B walks at 6 km/h but starts 45 minutes later. How long after Hiker B starts will they be at the same distance from the trailhead?
  4. A map of Vancouver Island has scale 1:250 000. The island is approximately 460 km long and 80 km wide. What are its dimensions on the map in cm?
5

Patterns & Algebra

📅 Weeks 15–19

Linear patterns, T-tables, four-quadrant graphing, expressions, BEDMAS, one- and two-step equations.

Solving Basic Equations — covers the inverse operations approach to one- and two-step equations.
Introduction to Algebra — variables, expressions, and what equations mean.
Worked Examples
1
Pattern Rule & Expression
Sequence: 4, 7, 10, 13, … Write the rule and expression for the nth term.
1
Common difference: +3
2
Start at 4 when n=1: 3(1)+1=4 ✓
3
Expression: 3n + 1
Answer: Rule: add 3. Expression: 3n + 1
2
Solving a Two-Step Equation
Solve: 3x − 5 = 16. Verify your answer.
1
Add 5 to both sides: 3x = 21
2
Divide by 3: x = 7
3
Verify: 3(7)−5 = 21−5 = 16 ✓
Answer: x = 7
3
Four-Quadrant Coordinates
Name the quadrant for: A(3,−2), B(−4,5), C(−1,−3).
1
A(3,−2): x positive, y negative → Quadrant IV
2
B(−4,5): x negative, y positive → Quadrant II
3
C(−1,−3): both negative → Quadrant III
A: Q IV, B: Q II, C: Q III
4
Rate of Change
A linear relation passes through (0, 3) and (1, 7). Find the rate of change and write the equation.
1
Rate of change = (7−3)÷(1−0) = 4
2
y-intercept = 3 (the point when x = 0)
3
Equation: y = 4x + 3
Answer: Rate = 4, Equation: y = 4x + 3
📝 Practice Worksheet Practice

Name: _________________________    Date: _____________

  1. Continue the pattern and write the rule: 4, 7, 10, 13, ___, ___, ___. L1
  2. Complete the T-table for the rule y = 3n − 2. Use n = 1, 2, 3, 4, 5. L1
  3. Is 1, 4, 9, 16, 25 linear or non-linear? How do you know? L2
  4. Write an expression for "three more than twice a number n." L2
  5. Evaluate 4n − 3 when n = 5. Show your substitution. L2
  6. Simplify using BEDMAS: 3 + 4 × (6 − 2) ÷ 2. L2
  7. Solve: x + 8 = 15. Verify your answer. L2
  8. Solve: 3x − 5 = 16. Show both steps. Verify. L3
  9. Solve: 4x + 7 = 31. Show all steps. Verify. L3
  10. A canoe carries 6 people per trip. After n trips, 30 people have crossed. Write and solve an equation. L3
  11. A linear relation has rate of change 3 and y-intercept −2. Write the equation, make a T-table for n = 0 to 5, and identify the coordinates of the y-intercept. L4
  12. Solve and explain: 2(3x − 4) = 16. What does "distributing" mean here? L4
🚀 Extension Extension
  1. A traditional First Nations basket design grows in a pattern. Row 1 has 3 beads, each subsequent row has 5 more. Write an expression for the number of beads in row n, and find which row first has more than 100 beads.
  2. Two linear relations are: y = 2x + 1 and y = −x + 7. Determine the point where they intersect by setting the expressions equal and solving for x, then finding y.
  3. A raven can fly 3 km in 6 minutes. Write an equation for distance d in terms of time t (in minutes). If a salmon swims at 0.8 km/min, how long until the raven has flown exactly twice the distance the salmon has swum (both starting at t = 0)?
  4. Create your own "growing pattern" using toothpicks or squares. Draw the first 4 terms, write a T-table, write the expression for the nth term, and use your expression to predict the 20th term.
6

Geometry

📅 Weeks 20–22

Angle relationships, triangle and polygon properties, transformations, circles — circumference using π.

Angles — supplementary, complementary, vertically opposite, and angles on a straight line.
Circles, Circumference & π — Math Antics. The most important constant in geometry.
Worked Examples
1
Supplementary & Complementary Angles
Two angles are supplementary. One is 64°. Find the other.
1
Supplementary angles sum to 180°.
2
180° − 64° = 116°
Answer: 116°
2
Interior Angles of a Triangle
A triangle has angles 48°, 65°, and x°. Find x.
1
Interior angles of a triangle sum to 180°.
2
48 + 65 + x = 180 → x = 67°
Answer: x = 67°
3
Circumference of a Circle
A circle has radius 5 cm. Calculate the circumference (π ≈ 3.14).
1
Formula: C = 2πr
2
C = 2 × 3.14 × 5 = 31.4 cm
Answer: C = 31.4 cm
4
Translation
A shape at (2, 3) is translated 4 left and 2 down. New coordinates?
1
x: 2 − 4 = −2
2
y: 3 − 2 = 1
Answer: (−2, 1)
📝 Practice Worksheet Practice

Name: _________________________    Date: _____________

  1. Two angles are supplementary. One is 73°. Find the other. L1
  2. Two angles are complementary. One is 37°. Find the other. L1
  3. A triangle has angles 48°, 65°, and x°. Find x. Verify. L1
  4. A circle has diameter 14 cm. Find the radius and circumference. Use π ≈ 3.14. L2
  5. A circular track has circumference 400 m. Find its diameter. Use π ≈ 3.14. L2
  6. Vertically opposite angles: one is 112°. Name the measure of each of the other three angles. L2
  7. A quadrilateral has angles 90°, 85°, 110°. Find the fourth angle. L3
  8. A point at (3, −2) is reflected in the y-axis. New coordinates? L3
  9. Classify the triangle with sides 7 cm, 7 cm, 10 cm by both sides and angles. L3
  10. Angles at a point: x°, 2x°, 3x°. Find x and each angle. Show working. L4
  11. A traditional First Nations pattern on a drum uses a circle of diameter 46 cm. Find the circumference and the area of the circular face. L4
🚀 Extension Extension
  1. Research: Why does the interior angle sum of a polygon with n sides equal (n−2) × 180°? Use triangles to explain. Apply this to a regular hexagon (like a beehive cell). Why might hexagons be an efficient shape for tessellation?
  2. A Coast Salish basket uses a repeating tessellating pattern based on equilateral triangles. Explain why equilateral triangles tessellate using the interior angle sum rule.
  3. A circle is inscribed in a square (touches all four sides). If the square has side length 10 cm, find the area of the region inside the square but outside the circle. Use π ≈ 3.14.
  4. A rotation of 90° clockwise maps point (x, y) to (y, −x). Apply this rule to triangle with vertices A(1,3), B(4,3), C(4,1). Then reflect the result in the x-axis. What are the final coordinates?
7

Measurement

📅 Weeks 23–25

Area of circles & composite figures, volume of rectangular prisms and cylinders, surface area of rectangular prisms.

Area & Perimeter — Math Antics. Reviews area of standard polygons before extending to circles.
Volume of Rectangular Prisms & Cylinders — connects base area × height concept.
Worked Examples
1
Area of a Circle
Circle with radius 6 cm. Find the area. (π ≈ 3.14)
1
Formula: A = πr²
2
A = 3.14 × 6² = 3.14 × 36 = 113.04 cm²
Answer: A = 113.04 cm²
2
Volume of a Cylinder
Cylinder: r = 4 cm, h = 10 cm. Find volume. (π ≈ 3.14)
1
Base area: A = πr² = 3.14 × 16 = 50.24 cm²
2
Volume: V = A × h = 50.24 × 10 = 502.4 cm³
Answer: V = 502.4 cm³
3
Surface Area of a Rectangular Prism
Rectangular prism: 6 cm × 4 cm × 3 cm. Find the surface area.
1
3 pairs of faces: lw, lh, wh
2
6×4=24, 6×3=18, 4×3=12
3
SA = 2(24+18+12) = 2(54) = 108 cm²
Answer: SA = 108 cm²
4
Volume to Capacity
A fish tank holds 60 000 cm³. How many litres?
1
Conversion: 1 L = 1 000 cm³
2
60 000 ÷ 1 000 = 60 L
Answer: 60 litres
📝 Practice Worksheet Practice

Name: _________________________    Date: _____________

  1. Find the area of a circle with radius 5 cm. (π ≈ 3.14) L1
  2. Find the area of a circle with diameter 12 m. L1
  3. A rectangular box: 8 cm × 5 cm × 4 cm. Find the volume. L2
  4. A cylinder has r = 3 cm, h = 8 cm. Find the volume. (π ≈ 3.14) L2
  5. A cube has side length 5 cm. Find the surface area. L2
  6. A juice can has r = 3.5 cm, h = 12 cm. Estimate the volume without a calculator. Explain your strategy. L3
  7. A circular fish pond has diameter 6 m. Find the area of the water surface and the volume if the water is 1.5 m deep. L3
  8. A composite figure has a rectangle (10 cm × 4 cm) with a semicircle on top (diameter 4 cm). Find the total area. L3
  9. A fish tank holds 54 litres. It is 60 cm long and 30 cm wide. How deep is the water? L4
  10. A totem pole base is a cylinder of radius 35 cm and height 1.2 m. Calculate the curved surface area of the base in cm². (π ≈ 3.14) L4
🚀 Extension Extension
  1. A drum used in a BC First Nations ceremony has a circular face of diameter 55 cm. The cedar rim is 4 cm wide. Find (a) the area of the circular face, (b) the area of just the rim, (c) what percent of the total circle the rim takes up.
  2. A cylindrical water storage tank holds exactly 10 000 litres. The height is 2.5 m. Calculate the radius of the tank. (Use π ≈ 3.14; remember 1 m³ = 1000 L.)
  3. Optimization: A canning company wants to design a cylinder that holds exactly 500 cm³ using the least amount of metal (minimum surface area). Using the formula SA = 2πr² + 2πrh with V = πr²h = 500, investigate different radius values (1 cm, 2 cm, 3 cm, 4 cm) to find the optimal dimensions.
  4. A composite solid is made of a rectangular prism (l = 10, w = 6, h = 4 cm) with a cylinder (r = 2 cm, h = 3 cm) drilled through from top to bottom. Find the remaining volume.
8

Data & Probability

📅 Weeks 26–29

Data collection, circle graphs, central tendency, outliers, theoretical vs experimental probability, two independent events.

Basic Probability — covers single events, sample space, and expressing probability as fractions, decimals, and percents.
Mean, Median, Mode & Range — measures of central tendency with examples.
Worked Examples
1
Central Tendency
Dataset: 4, 7, 9, 3, 7, 12, 5, 7, 8. Find mean, median, mode, range.
1
Order: 3, 4, 5, 7, 7, 7, 8, 9, 12
2
Mean: (3+4+5+7+7+7+8+9+12) ÷ 9 = 62 ÷ 9 ≈ 6.9
3
Median: middle value (5th of 9) = 7
4
Mode: 7 (appears 3 times)
5
Range: 12 − 3 = 9
Mean ≈ 6.9, Median = 7, Mode = 7, Range = 9
2
Two Independent Events
Flip a coin and roll a die. Find P(heads AND a 4).
1
Total outcomes: 2 × 6 = 12
2
Favourable outcomes: (H,4) = 1
3
P = 1/12
Answer: P(H and 4) = 1/12
3
Circle Graph — Central Angles
A survey of 400 students: 140 prefer hiking. Find the central angle for hiking.
1
Percent: 140 ÷ 400 = 35%
2
Central angle: 35% × 360° = 0.35 × 360 = 126°
Answer: 126°
4
Theoretical vs Experimental
A die is rolled 60 times; 6 appears 14 times. Compare theoretical and experimental probability.
1
Theoretical: P(6) = 1/6 ≈ 16.7%
2
Experimental: 14/60 ≈ 23.3%
3
These differ — that's normal! With more trials, results get closer to theoretical.
Theoretical ≠ Experimental (but both are valid)
📝 Practice Worksheet Practice

Name: _________________________    Date: _____________

  1. A bag has 5 red, 3 blue, 2 green marbles. Write P(red) as fraction, decimal, percent. L1
  2. Flip a coin and roll a die. List the complete sample space. How many outcomes? L1
  3. Dataset: 4, 7, 9, 3, 7, 12, 5, 7, 8. Find mean, median, mode, and range. L2
  4. If 52 is added to the dataset above, which measure of central tendency is most affected? Why? L2
  5. A circle graph shows 40% of 250 students prefer soccer. How many is that? L2
  6. A survey has sections: 50%, 25%, 15%, x%. Find x. Find the central angle of the 25% section. L3
  7. Using the coin-and-die sample space: find P(tails AND even number). L3
  8. A student rolls a die 60 times and gets a 3 on 12 occasions. Compare theoretical and experimental probability. L3
  9. Write a biased survey question about screen time. Rewrite it as an unbiased question. Explain what makes the first biased. L4
  10. What is the difference between a population and a sample? Give a BC example of each and explain when a sample is better to use. L4
🚀 Extension Extension
  1. Design a survey to investigate Grade 7 students' favourite outdoor activities in BC. Write 3 unbiased questions, describe how you would select a representative sample of 60 students from a school of 300, and explain what sampling method you used.
  2. Roll two dice and add the results. List all 36 possible outcomes. Find: P(sum = 7), P(sum > 9), P(sum is prime). Which sum is most likely? Explain why.
  3. A First Nations salmon monitoring program records the following weekly counts: 320, 285, 410, 290, 350, 315, 390. Calculate the mean and median. Which better represents the "typical" week and why? What would happen to the mean if one week recorded 850?
  4. Create a tree diagram for drawing 2 beads (without replacement) from a bag containing 1 red, 1 blue, 1 yellow bead. List all outcomes and find the probability that both beads are different colours.
9

Financial Literacy

📅 Weeks 30–32

BC GST & PST, discounts & sale price, tips, income types, budgeting, and simple interest — all grounded in real BC financial contexts.

Calculating Tax, Tip & Discount — applying percent skills to everyday financial situations.
Simple Interest — the formula I = Prt explained with examples.
Worked Examples
1
BC Sales Tax (GST + PST)
Running shoes cost $120.00 in BC. Find GST, PST, and total price.
1
GST (5%): $120 × 0.05 = $6.00
2
PST (7%): $120 × 0.07 = $8.40
3
Total tax: $6.00 + $8.40 = $14.40
4
Total price: $120 + $14.40 = $134.40
Answer: Total = $134.40
2
Discount & Sale Price
A snowboard costs $280 with 30% off. Find the sale price.
1
Discount: $280 × 0.30 = $84
2
Sale price: $280 − $84 = $196
3
Shortcut: $280 × 0.70 = $196 ✓
Answer: Sale price = $196
3
Finding the Original Price
A jacket costs $68 after a 20% discount. What was the original price?
1
$68 = 80% of original (100% − 20%)
2
Original = $68 ÷ 0.80 = $85
Answer: Original price = $85
4
Simple Interest
$500 deposited at 3% simple interest per year. Interest after 2 years?
1
Formula: I = P × r × t
2
I = $500 × 0.03 × 2 = $30
Answer: Interest = $30. Total = $530.
🪶 First Peoples Connection — Traditional Economy
Many BC First Nations historically used potlatch ceremonies involving redistribution of wealth — a system where surplus resources were shared with the community. Compare this to modern concepts of budgeting and saving: how do both systems balance having enough for today vs. saving for future needs? Discuss with a partner.
📝 Practice Worksheet Practice

Name: _________________________    Date: _____________

Level 1 — BC Tax Calculations
  1. A bicycle costs $349.99 in BC. Calculate GST (5%), PST (7%), and total price. L1
  2. A video game costs $64.99. How much GST is charged? How much PST? L1
  3. Convert: 7% as a decimal = ___ ; 12% as a fraction = ___ ; 0.05 as % = ___. L1
Level 2 — Discount & Sale Price
  1. A ski jacket is $195.00 with 40% off. Find the discount amount and sale price. L2
  2. A tablet is $420 with 15% off. (a) What is the sale price? (b) Add BC tax. Final price? L2
  3. A meal costs $56. Calculate a 15% tip. L2
Level 3 — Income & Reverse Percent
  1. A worker earns $16.50/hour and works 36 hours this week. Calculate gross weekly pay. L3
  2. An item is on sale for $68 after a 20% discount. What was the original price? L3
  3. Calculate simple interest: $800 at 4% for 3 years. What is the total amount? L3
Level 4 — Budget & Complex Problems
  1. A Grade 7 student earns $12/hour babysitting, works 6 hours per week, and wants to save 40% of their earnings. After 12 weeks, how much have they saved? If they want to buy a $250 snowboard (before tax), how many more weeks do they need to work? L4
🚀 Extension Extension
  1. Research BC's actual GST-exempt items. List 5 things that are GST-exempt and 5 that are PST-exempt. Explain the policy reasoning behind at least one exemption. Why might groceries be exempt from GST?
  2. Compound interest preview: $1000 invested at 5% annually for 3 years with compound interest vs simple interest. Calculate both and find the difference. (Compound: each year's interest is added to the principal before the next year's interest is calculated.)
  3. Budget challenge: You have $2000 to plan a 5-day camping trip to BC's backcountry for 4 people. Research realistic costs for food, transportation, permits, and gear. Create a detailed budget with categories, showing GST/PST where applicable, and determine if $2000 is enough.
  4. A First Nations artisan sells cedar baskets. The materials cost $45 each. She sells them at a 120% markup. A gallery then marks up her price by 35% for their commission. What does the final customer pay? What percent of the final price goes to the artisan?
10

Review & Consolidation

📅 Weeks 33–38

Final review across all units — Number & Operations, Algebra, Geometry, Measurement, Data & Probability. Build your portfolio and prepare for the end-of-year assessment.

Year in Review — Topics Covered

  • Units 1–4 & 9: Number Sense, Fractions, Integers, Ratio/Rate/Percent, Financial Literacy
  • Unit 5: Patterns, Expressions, Two-Step Equations, Linear Relations
  • Units 6–7: Geometry (Angles, Circles, Transformations) and Measurement (Area, Volume, SA)
  • Unit 8: Data Collection, Central Tendency, Circle Graphs, Probability

Revisit any unit's video tab to review a specific concept. Use the mixed quiz below to test your readiness across all strands.

📝 Mixed Review Worksheet All Units

Name: _________________________    Date: _____________

Number & Operations (Units 1–4, 9)
  1. ¾ + ⅝ = ___ ; 2⅓ − 1¾ = ___ ; ⅔ × ⁹⁄₄ = ___ ; 3½ ÷ ¾ = ___ L2
  2. Order: 0.625, ⅝, 63%, ⁶⁄₁₀. L2
  3. (−8)+(+5) = ___ ; (+3)−(−9) = ___ ; (−6)×(−7) = ___ ; (+48)÷(−6) = ___ L2
  4. A population rises from 4 500 to 5 400. % increase? A price drops from $250 to $175. % decrease? L3
  5. In BC: GST=5%, PST=7%. A book costs $25. Total price including both taxes? L3
Algebra & Patterns (Unit 5)
  1. Solve: 4x + 7 = 31. Show all steps. Verify. L3
  2. A linear relation: y = 2n − 1. Complete for n = 1, 2, 3, 4, 5. What is the rate of change? L3
Geometry & Measurement (Units 6–7)
  1. A circle has r = 5 cm. Find circumference and area. (π ≈ 3.14) L3
  2. A cylinder has r = 3 cm, h = 10 cm. Find volume. A rectangular prism: 6 × 4 × 3 cm. Find SA. L3
Data & Probability (Unit 8)
  1. Flip a coin and roll a die. Total outcomes? P(heads AND 4)? P(tails AND even)? L3
  2. Dataset: Mon −8°C, Tue −3°C, Wed +2°C, Thu −1°C, Fri +5°C. Find mean temperature. L3
  3. Create a circle graph for: Hiking 35%, Skiing 20%, Kayaking 25%, Other 20%. What is the central angle for Kayaking? L4