Your complete companion to Grade 7 Math

I am a 6-digit number. My digits sum to 27. I am divisible by 9 but not 6. My thousands digit is prime. My hundreds digit is twice my units digit. What numbers could I be? Find all possibilities and explain your reasoning.

Create your own number puzzle with exactly one solution. Test it on a partner.

List all numbers from 1 to 50 and count how many factors each has. Which number in this range has the most factors? What is special about its prime factorization? Predict: among 51–100, which number will have the most factors?

Why do perfect squares have an odd number of factors? Prove it using an example.

Two numbers have GCF = 12 and LCM = 180. Use exactly the digits 1, 2, 3, 4, 5, 6 (each once) to form two 3-digit numbers whose GCF is as large as possible. Record all attempts.

If GCF(a,b) = g, then both a and b are multiples of g. Use this to explain why GCF × LCM = a × b for any two numbers a and b.

A Coast Salish weaver has 48 red strips, 60 yellow strips, and 36 black strips. She wants to make identical bundles using ALL strips with the same colour ratio in each. (a) How many bundles can she make? (b) What is the colour ratio per bundle? (c) If she adds 24 more of one colour to make the most bundles possible, which colour should she add and why?

Generalize: if three quantities have a GCF of g, write a formula for the number of identical bundles and the amount of each quantity per bundle.

Each student gets a 10×10 grid (1–100). Starting from 2, cross out all multiples (but not 2 itself). Move to the next un-crossed number and repeat. What remains are primes.

Count the primes up to 100. How many are there? Predict: roughly how many primes exist between 100 and 200? Between 200 and 300? Research the Prime Number Theorem and explain what it says about how primes thin out.

Design a flowchart that takes any whole number as input and outputs which of these it is divisible by: 2, 3, 4, 5, 6, 9, 10. Your flowchart must use the fewest possible yes/no decisions. Test it on 360, 225, and 1001.

Why does the rule "divisible by 6 if divisible by both 2 and 3" work? Use prime factorization to explain.

Three First Nations drummers play at intervals of 4 seconds, 6 seconds, and 10 seconds. They all start together. (a) After how many seconds do all three play at the same time again? (b) In 2 minutes, how many times do exactly two of the three play together (but not all three)? (c) Create your own "timing coincidence" problem using three BC contexts.

What is the minimum interval set (three numbers) that would make all three drummers coincide exactly once per minute?

Use the digits 1, 2, 3, 4, 5, 6, 7 exactly once to form a 7-digit number. Version A: make it as large as possible while being divisible by 9. Version B: make it as small as possible while being divisible by 6. Version C: make a number divisible by both 4 and 5.

For divisibility by 9, why does only the digit sum matter, regardless of digit order? Use expanded form to explain.

Find a fraction between ⅓ and ½. Now find one between ⅓ and your answer. Keep going — how many times can you repeat this? Is there a limit? This property (that there is always a fraction between any two fractions) is called density. Explain why it is true using equivalent fractions.

Find a fraction between 0.499 and 0.5. Express it as both a fraction and a decimal.

Convert 0.3̄, 0.6̄, 0.12̄, and 0.142857142857… to fractions using the "let x = …, multiply by 10ⁿ" method. What patterns do you notice? Can you predict what fraction 0.09̄ equals without calculating?

Why do fractions with denominators whose only prime factors are 2 and 5 produce terminating decimals? Prove it using prime factorization.

A First Nations community has a quota of ³⁄₈ of the total salmon count. This week 4 800 salmon were counted, but the count has a ¹⁄₁₀ margin of error. (a) What is the quota range (min and max fish)? (b) If the community took ¹⁵⁰⁰ fish last week, what fraction of this week's quota remains? (c) Express the remaining quota as a decimal and a percent.

If the quota fraction changes to 40% next season, what is the percentage increase in the quota compared to ³⁄₈? Show using both fraction and percent methods.

Use the digits 1, 2, 3, 4, 5 exactly once to create two decimals (one with 2 decimal places, one with 3) that multiply as close to 10 as possible. Record all attempts. Then arrange them to get the largest possible product and smallest possible product.

When multiplying decimals, why does the number of decimal places in the product equal the total decimal places in both factors? Use expanded form to explain.

Each student places ³ fractions on a shared 0–2 number line: one that is a terminating decimal, one repeating, and one whose decimal they must calculate. The class checks positions using equivalent forms.

Find 5 fractions that are all equivalent to 0.625. How many different denominators (from 1 to 20) produce this value? What do they have in common?

A store applies a 30% discount, then adds BC tax (12%). A second store adds tax first, then applies 30% off. Does the order matter? Prove algebraically that the final price is the same either way. Then find a discount + tax combination where a small rounding difference could occur.

If an item is discounted by x%, then another y%, what single discount is equivalent? Write a formula in terms of x and y.

A Musqueam weaver creates a blanket pattern using rows of three colours. Row 1: ½ red, ⅓ black, rest yellow. Row 2: ⅖ red, ¼ black, rest yellow. (a) What fraction is yellow in each row? (b) Which row has more yellow? By how much? (c) If the blanket is 180 cm wide, how wide is each colour in row 1 and row 2 in centimetres?

Design your own 3-colour row where no fraction has denominator greater than 12 and all three colours appear in equal amounts. Is this possible? Prove or disprove.

Order these from least to greatest using three different methods — common denominator, decimal conversion, and number line estimation — then compare efficiency: ⅗, 0.62, 63%, ⁷⁄₁₁, 0.6̄, ⁵⁄₈.

For which type of number is each method most efficient? Create a decision guide: "Use method X when…"

Create an "integer portrait" on a number line from −20 to +20. Choose 10 pairs of integers that are zero pairs. For each pair, write an addition equation and mark both numbers. Then create a single expression using all 20 numbers that equals a target value of your choice. Show all working.

If you have n zero pairs and add one more positive integer p, write a formula for the sum of all 2n + 1 numbers.

Research the average monthly temperatures for a BC city (e.g., Prince George or Smithers). Record 12 months. (a) Find the mean annual temperature. (b) Find the range. (c) Write an integer equation for the temperature change from the coldest to the warmest month. (d) If global warming raises each temperature by 1.5°C, recalculate the mean.

In which months are temperatures negative? Write the total "degree-months below zero" as a single integer calculation.

A BC harbour has tides: High tide +3.2 m, Low tide −1.4 m. A boat with 2 m draft needs at least 0.5 m clearance above the harbour floor (at −0.9 m). (a) At what minimum tide height can the boat safely dock? (b) Write an integer expression for the total tidal change over 3 complete cycles. (c) The tide drops ¼ of its range every 3 hours. Model the tide at hours 0, 3, 6, 9.

Create a table showing "safe" and "unsafe" docking times using your model. Express safety as an integer inequality.

Complete the pattern and explain each step: (+4)×(−3)=−12, (+3)×(−3)=−9, (+2)×(−3)=−6, (+1)×(−3)=−3, (0)×(−3)=0, (−1)×(−3)=___, (−2)×(−3)=___. What rule must hold to keep the pattern consistent? Now build the same type of pattern for division and for (−)×(+).

Write a formal "proof by pattern" that negative × negative = positive. Why isn't this a complete mathematical proof? What would a complete proof require?

Student A writes a two-integer expression. Student B adds one more operation (keeping BEDMAS in mind). Student C adds brackets that change the answer. Student D evaluates the final expression.

Create expressions using integers from −10 to +10 that equal exactly 0, exactly 1, and exactly −7. Use at least 5 numbers and 4 operations in each.

Use BC geography: Mt. Fairweather (+4 663 m), Death Valley in California (−86 m for comparison), Marianas Trench (−10 935 m, for scale). (a) Calculate the total elevation difference between BC's highest peak and BC's deepest point (Douglas Channel floor: −670 m). (b) If you descend from Fairweather at 200 m per hour, write an integer sequence for your elevation every 2 hours. (c) When are you below sea level?

Write a linear equation for elevation e after t hours of descent. When does e = 0? Solve algebraically.

Use the integers −5, −3, −2, 0, +1, +4, +6 (each at most once) and any operations (including brackets) to make every integer from −10 to +10. Which target integers are impossible? Why?

What is the maximum possible value you can make from these seven integers using only addition and subtraction? What about multiplication? What is the minimum?

A stock starts at $50. Over 5 days: Day 1: −$8, Day 2: +$12, Day 3: −$5, Day 4: −$3, Day 5: +$7. (a) Final price? (b) Greatest single-day loss expressed as a negative integer. (c) Absolute total change (sum of all magnitudes). (d) Mean daily change. (e) If each change is doubled, what is the new final price?

Design a 5-day change sequence where the final price equals the starting price but the absolute total change is maximized. What is the maximum possible absolute change?

Compare unit prices for 5 pairs of BC products (e.g., BC salmon: 400g for $8.99 vs 750g for $15.49; blueberries: 1 pint for $4.50 vs 2 pints for $7.99). Calculate the price per 100g or per unit for each. Which offers better value? Are there non-price factors a shopper should consider?

A store offers "buy 2 get 1 free" on a $6.99 item. Calculate the effective unit rate. Compare to a competing store selling 3 of the same item for $14.49.

Choose a scale (e.g., 1:500) and create a scale diagram of part of your school grounds. Mark at least 5 key points, measure 4 distances on your map, and calculate actual distances. Include a scale bar and compass rose.

If you change the scale to 1:1000, how do all measurements on your map change? What stays the same?

A salmon run: Year 1: 12 000 fish. Year 2: increases 15%. Year 3: decreases 20%. Year 4: increases 8%. (a) Calculate the population each year. (b) Overall percent change from Year 1 to Year 4. (c) What single percent change from Year 1 would give the same Year 4 result? (d) At what percent increase in Year 3 would the population return to Year 1 levels?

If a population decreases by 50% then increases by 50%, does it return to its original value? Prove algebraically. This is called the "percent change trap."

Student A sets up a proportion from a real context. Student B solves it and creates a new context where the answer becomes one of the given values. Student C solves and extends. Continue for 4 rounds.

Create a proportion chain involving at least 3 of these contexts: map scale, recipe scaling, speed/distance/time, population density, exchange rates.

A jacket costs $200. Store A applies 30% off, then 10% off. Store B applies 10% off, then 30% off. Store C applies 40% off. (a) Calculate the final price at each store. (b) Which is cheapest? (c) Show algebraically that two sequential discounts of x% and y% are equivalent to a single discount of (x + y − xy/100)%.

Find two discount percentages that together are equivalent to exactly 50% off.

A canoe travels downstream at rate r + 3 km/h and upstream at r − 3 km/h, where r is the paddler's rate in still water. The canoe travels 24 km downstream and 12 km upstream in the same total time. Set up and solve a proportion equation to find r.

What does it mean for the canoe's rate to equal the current's rate? What happens mathematically and physically?

BC is approximately 944 735 km² in area. On a 1:5 000 000 scale map, (a) a river appears 18.4 cm long — find its actual length; (b) two cities are actually 340 km apart — find their map distance; (c) a lake appears as a 6 cm × 4 cm rectangle — estimate its actual area.

If the map scale changes to 1:10 000 000, by what factor do all distances change? By what factor does area change? Generalize for any scale change from 1:a to 1:b.

A family's meal in Vancouver costs $84.60 before tax. BC GST = 5%, PST = 7% (food is GST-exempt in BC but not all items are). (a) The drinks ($18.40) are taxable — calculate the bill with full tax on drinks only. (b) They want to leave exactly 18% tip on the pre-tax total. What is the tip? (c) They split the bill 3 ways equally. What does each person pay? (d) If one person pays with a $50 bill, what change do they receive?

Research which BC food items are GST-exempt and which are not. Create a "tax guide" for a typical school cafeteria menu.

Design a growing pattern using shapes (toothpicks, dots, or tiles). Draw the first 4 terms. Complete a T-table for terms 1–10. Write an algebraic expression for term n. Use your expression to predict term 50 and term 100. Create a graph of the first 10 terms and label the rate of change and y-intercept.

Modify your pattern so the expression becomes 2n + 5 instead of 3n − 1. What visual change creates this new rule?

Create cards for 5 linear relations — each set has a word problem, a T-table, an equation, and a graph. Mix all 20 cards. Partners must re-sort them into 5 matched sets.

For the BC-context set: "A cedar canoe travels at a constant 6 km/h" — write the equation, T-table (for 0–5 hours), and graph. Add an equation for a salmon swimming at 4 km/h from the same start. Find when the canoe has travelled twice the distance of the salmon.

Relations: y = 3x − 2 and y = −x + 10. (a) Complete T-tables for each (x from 0 to 5). (b) Find the intersection point algebraically. (c) Verify by substituting into both equations. (d) Create a BC story where these two relations represent two hikers starting from different points.

Find all pairs of equations from y = 2x + 1, y = 3x − 4, y = x + 5 that intersect at a point with integer coordinates.

Using the integers −3, −1, 2, 4, 6 (each at most once) and any operations and brackets, make every integer from −10 to +10. Record your expression for each. Which target values need brackets? Which work without?

Without brackets, can changing the order of the same numbers and operations produce different results? Give 3 examples using these integers.

A First Nations family paddles 24 km along a river in a traditional canoe. They start at 8:00 am. (a) At 4 km/h, write an equation for distance remaining d after t hours. When do they arrive? (b) If they rest for 30 minutes at the halfway point, rewrite the equation for each leg separately. (c) Plot both legs on a distance-time graph. (d) A second canoe leaves the same point 90 minutes later at 6 km/h — when does it overtake the first canoe?

Write a system of equations and solve algebraically for the overtaking time and distance.

The solution is x = 5. Create 6 different two-step equations that have x = 5 as the solution, using at least 3 different operations. Make one easy (L1), two medium (L2/L3), and three difficult (L4). Verify each by substituting x = 5.

The solution is x = −3. Create 4 two-step equations with this solution. Why is it harder when the solution is negative?

A totem pole carver charges a $500 base fee plus $120 per figure carved. (a) Write an equation for total cost C in terms of figures f. (b) Complete a T-table for 1–10 figures. (c) Graph the relation. (d) What does the y-intercept represent? (e) If a community has a budget of $1500, how many figures can they afford? (f) A second carver charges $300 + $150/figure. Under what conditions is each carver cheaper?

Solve the system algebraically to find when both carvers cost the same. Interpret this point on the graph.

Without listing all terms, find term 100 of: (a) 7, 11, 15, 19, … (b) 3, 6, 12, 24, … (c) a pattern where each term = previous term + 2n. For (a) and (b), write the general expression and explain how you derived it. For (c), first figure out the first 6 terms, then find term 100.

For (b), this is a geometric sequence (multiply by a constant). Why can't it be represented by a linear equation y = mn + b? What type of equation would it need?

Create a set of points on a Cartesian grid so that, across your whole set, you have satisfied every condition below at least once:

• one point in each quadrant
• one point on the x-axis and one on the y-axis
• two points with the same x-coordinate
• two points with the same y-coordinate
• a pair that are reflections across the y-axis
• a pair that are reflections across the x-axis
• three points that form a right triangle
• two points whose midpoint is the origin

Goal: use the fewest possible points. Be ready to defend why your design is efficient.

Add one new condition without increasing the number of points.

Use the numbers 1, 2, 3, 4, 5, 6, 7, 8 exactly once to make four ordered pairs. Put one point in each quadrant.

Version A: make the quadrilateral formed by joining the points in order have the greatest possible perimeter.

Version B: make the quadrilateral have the smallest possible perimeter.

Which digits should be used far from the axes? When does symmetry help? Can two different-looking solutions have the same perimeter?

Find all possible fourth vertices for each shape. Sketch and justify every answer.

• A(-2, 1), B(2, 1), C(2, 5) are three vertices of a rectangle.
• P(-3, 0), Q(0, 3), R(3, 0) are three vertices of a kite.
• M(-4, -1), N(0, 3), O(4, -1) are three vertices of a symmetric quadrilateral.

Create your own “three vertices are given” puzzle that has exactly two correct answers.

Student A draws a simple polygon with integer coordinates and writes only the starting coordinates. Student B secretly chooses two transformations from this list: reflect in x-axis, reflect in y-axis, rotate 90° clockwise, rotate 180°, translate by a whole-number vector.

Student C must determine the final coordinates without seeing the drawing, then explain the rules that were used.

Find two different two-step transformation sequences that land the shape in the same final position.

You may use regular triangles, squares, pentagons, hexagons, octagons, and decagons. Build as many different “vertex recipes” as you can where the angles add to exactly 360°.

Record each successful recipe in a compact way, such as 3.3.3.3.3.3 for six triangles or 8.8.4 for two octagons and a square.

Which combinations are impossible? Why do pentagons keep causing trouble? Can a combination work at one vertex but still fail to tessellate as a full pattern?

You have exactly 100 ext{ cm} of willow to make one large dreamcatcher hoop or two smaller hoops.

• Option 1: design one circle using as much of the willow as possible.
• Option 2: design two circles with different diameters.
• Option 3: design two equal circles.

For each option, find the diameter(s) and radius/radii, then decide which design gives the largest total diameter and which gives the largest total radius.

What stays the same and what changes if you switch from “total willow” to “total diameter” as the quantity you want to maximize?

Plot at least 8 points with integer coordinates to create a closed design that has:

• one line of symmetry
• at least one vertex in each quadrant
• at least one vertex on an axis
• one pair of points related by a 180° rotation about the origin

After students finish, add one surprise condition such as “it must also have rotational symmetry” or “you may only move one point.”

Start with triangle A(1,1), B(4,1), C(2,3). Compare these sequences:

• reflect in the y-axis, then reflect in the x-axis
• rotate 180° about the origin
• rotate 90° clockwise twice

Do all three produce the same image? Prove it with coordinates. Then invent another pair of different-looking sequences that always agree.

A can must hold exactly 330 cm³. You want to minimize the amount of metal used (surface area = 2πr² + 2πrh). Test radius values r = 1, 2, 3, 4, 5, 6 cm. For each, find h from V = πr²h = 330, then calculate SA. Which r minimizes material? Sketch the "best" can. How does it compare to a real soft drink can?

Prove that the minimum surface area for a cylinder with fixed volume occurs when h = 2r (i.e., the height equals the diameter). Use the data from your table to support this.

Design a BC-inspired composite shape (e.g., a totem pole silhouette, a salmon shape, a coast outline) made up of at least 3 different polygons and one circle/semicircle. Target total area: between 200 and 250 cm². Label all dimensions, show area calculations for each part, and verify the total.

Calculate the perimeter of your composite shape. Explain which boundaries count as perimeter and which are internal dividing lines.

A Haida artist builds traditional cedar boxes. Each box is 30 cm × 20 cm × 15 cm. (a) Calculate the surface area of one box. (b) Cedar planks cost $0.85/100 cm². How much does one box cost in materials? (c) She makes 12 boxes for a gallery — total material cost? (d) If she increases each dimension by 50%, by what factor does the surface area increase? By what factor does the volume increase?

Prove algebraically that when all dimensions are multiplied by k, surface area multiplies by k² and volume multiplies by k³.

A BC fish hatchery uses cylindrical tanks. Tank A: r = 80 cm, h = 120 cm. Tank B: r = 60 cm, h = 200 cm. (a) Which holds more water? By how many litres? (b) Both tanks are filled at 20 litres/minute. Which fills first? How much sooner? (c) If salmon need 15 litres each, how many salmon can each tank support?

A new tank must hold exactly 3000 litres and have h = 2r. Find the dimensions of this tank (use π ≈ 3.14 and estimate to 2 decimal places).

Create 3 different rectangular prisms that all have volume = 24 cm³ (using integer dimensions). For each, calculate the surface area. Which has the smallest surface area? Which has the largest? What shape approaches the minimum surface area for a fixed volume?

Why do animals in cold climates tend to be rounder (more sphere-like)? How does the ratio of surface area to volume relate to heat loss? Connect to BC wildlife (e.g., Pacific salmon vs arctic fish).

A dreamcatcher hoop is made from a willow branch bent into a circle. The hoop has outer diameter 25 cm and the willow is 1.5 cm thick. (a) Find the area of the circular face of the hoop (annulus = outer circle − inner circle). (b) Find the circumference of the outer and inner circles. (c) If the hoop is decorated with beads placed every 3 cm along the outer circumference, how many beads are needed? (d) Web strings cross the inner circle 8 times — what is the total length of web strings if each crosses from edge to edge through the centre?

If the hoop diameter doubles, by what factor does the annulus area change? By what factor does the circumference change? Generalize for any scale factor k.

Find all rectangular prisms with integer dimensions where Volume = 60 cm³. List them systematically. Which has the largest surface area? Which has the smallest? For which prism is the surface area closest to a cube's (i.e., most "cubic")?

How does prime factorization help you find all the dimension combinations systematically? Use 60 = 2² × 3 × 5 as your starting point.

Provide 5 real objects (water bottle, textbook, eraser, roll of tape, tissue box). Each student estimates volume and surface area before measuring. Calculate percent error for each estimate.

Develop a "personal benchmark" system: find a part of your body or an everyday object that is approximately 1 cm, 10 cm, and 100 cm². Use these benchmarks to estimate 5 more objects' measurements without measuring directly.

Design a 3-question survey about outdoor activities in BC. Collect data from at least 20 people. Display results as a circle graph. Calculate mean, median, mode, and range for one numerical question. Write a 3-sentence conclusion about what your data shows.

Identify one potential source of bias in your survey design and explain how it could be corrected. How might your results differ if you surveyed a different group?

Start with the dataset: 12, 14, 15, 16, 13, 14, 15. Calculate mean, median, mode, range. Now add these values one at a time and recalculate each time: (a) 14, (b) 100, (c) 0. Which measure changed the most each time? Write a rule for when to use mean vs median to represent "typical."

A dataset has 8 values and a mean of 15. What single value could you add to make the mean exactly 18? Show the algebra.

Two players roll a die. Player A wins if the result is prime. Player B wins if the result is composite. (a) Is this fair? Calculate P(A wins) and P(B wins). (b) Redesign the game so both players have P(win) = ½. (c) Create a new two-dice game that is fair but uses addition instead of individual rolls. Prove it's fair using a sample space table.

For the original game, if Player A wins $3 and Player B wins $2, what is the expected earning per game for each player? Which player has the advantage?

A BC Ministry of Fisheries wants to estimate the salmon population in a river system. Propose a sampling method. (a) Describe your sampling strategy (random, systematic, or stratified). (b) What potential biases exist? (c) If a sample of 200 fish is tagged and released, and 15 of 120 fish caught later are tagged, estimate the total population using the capture-recapture method (Population ≈ first catch × second catch ÷ recaptured). (d) What assumptions does this method require?

If the estimated population is 1 600 and the sustainable harvest is 35%, how many fish can be harvested? What if the estimate has a 20% margin of error — what is the safe harvest range?

Build the complete sample space for: (a) rolling two dice and recording the sum; (b) spinning a spinner with sections 1, 2, 3 and flipping a coin. For each: count total outcomes, find the most likely outcome, calculate P(sum > 6) or P(spinner > 1 AND heads). Compare theoretical probability to 30 simulated trials.

Why does "sum = 7" have the highest probability in (a)? Prove it using the sample space table. How many ways can each sum from 2–12 be made?

Collect data on how Grade 7 students spend a typical weekend day (categories: sleep, screen time, outdoors, homework, meals, other). Create a circle graph with correct central angles. Then swap graphs with a partner and write 5 interpretation statements about their graph — each must include a calculation.

Combine your graph and your partner's graph into a class average. How do you calculate the combined central angles when the sample sizes are different?

Theoretical P(heads) = ½. Flip a coin 10 times, 30 times, 100 times. Record the experimental probability after each set. Plot "number of flips" on the x-axis and "experimental P(heads)" on the y-axis. What do you notice as the number of flips grows? Describe the pattern in words and connect it to the Law of Large Numbers.

If a coin lands heads 7 times in a row, what is P(heads on the next flip)? Why do many people get this wrong?

Create a dataset of exactly 8 values (all integers from 1–20) that satisfies ALL of: mean = 11, median = 10.5, mode = 8, range = 14. Prove your dataset works. Then change exactly one value to make the mean = 12 while keeping median and mode the same.

Prove that if a dataset has an even number of values, the median is always the mean of the two middle values. Why can't the median equal a value not in the dataset for an odd-sized dataset?

You earn $15/hour and work 8 hours per week. Create a monthly budget. Research actual BC prices for: transportation (bus pass), phone plan, school supplies, food (3 lunches/week), entertainment, savings. Use GST/PST where applicable. Calculate percent of income for each category. Is your budget balanced?

Your hours are cut to 6/week. Adjust your budget. Which category do you cut first, and why? Calculate the percent reduction in total spending.

Research BC's GST and PST exemptions. Create a "tax classification table" for 20 items (at least 5 from each category: food, clothing, electronics, sports equipment, books). Calculate the total tax on a $200 shopping cart with 10 different items — some exempt, some not. Compare to a fictional province with a flat 10% tax on everything.

Why does BC exempt basic groceries from GST? What is the policy argument? Who benefits most from this exemption?

Scenario A: You save $50/month at 3% simple annual interest for 5 years. Scenario B: You borrow $3000 at 8% simple annual interest and pay it back over 5 years. (a) For Scenario A, calculate total saved including interest each year for 5 years. (b) For Scenario B, calculate total interest paid. (c) Compare: how much more do you pay in interest in Scenario B vs earn in Scenario A? (d) What monthly savings rate would earn the same as the loan costs?

Research compound interest. If Scenario A used compound interest instead, how much more would be earned over 5 years? (Compound annually: A = P(1 + r)ⁿ)

A Haida artist sells carved pendants. Materials cost $18 each, she spends 2.5 hours making each, and values her time at $22/hour. (a) What is her total cost per pendant? (b) She wants to make 40% profit — what price should she charge (before tax)? (c) What does a customer pay with BC taxes? (d) She sells 12 pendants at a craft fair with a $75 table fee. Calculate net profit. (e) At what number of pendants sold does she break even (cover table fee)?

If she increases her hourly rate by 10%, what new price maintains the same 40% profit margin? By what percent does the selling price increase?

Three job offers: Job A: $14/hour, 30 hours/week. Job B: $1600/month flat salary. Job C: $0.45/item produced, typically 3000 items/month. (a) Calculate weekly/monthly gross pay for each. (b) Which pays most per month? (c) Job C is unpredictable — in a slow month you produce 2000 items. Recalculate. (d) After 15% tax deductions, what is net monthly pay for each job?

At what hourly rate (for 30 hours/week) does Job A equal Job B? Set up and solve an equation.

A snowboard is $349.99 regularly. Deals throughout the year: January — 30% off + BC taxes; March — 15% off + no PST; October — buy 1 get 1 at 50% off (need one board). (a) Calculate the final price in each sale. (b) Which is cheapest? (c) In March, is saving PST better than the January extra discount? By how much? (d) If you buy two boards in October, what is each board's effective price?

Create a general formula: for what discount percentage does "no PST" (7% off) give a better deal than an extra x% regular discount?

List 20 purchases a Grade 7 student might make. Each student categorizes them as Need or Want and assigns a priority rank 1–5. Compare rankings in groups of 4 — discuss disagreements.

You have $500 and a ranked list of 15 potential purchases with prices (including BC taxes). You must include at least 2 "needs." Select items to maximize your total priority score while staying within budget. Set up and solve this as a constrained optimization — which combination wins?

You want to buy a mountain bike that costs $680 + BC taxes. You have $200 saved at 3% simple annual interest. You can also save $35/month from earnings. (a) How long until you can afford the bike counting only savings (no interest)? (b) How much interest does your $200 earn during this time? (c) With interest included, how much sooner do you reach your goal? (d) If the bike goes on sale for 20% off at a specific date, set up an equation to find whether it's worth waiting for the sale.

Build a month-by-month savings tracker spreadsheet (table) for 18 months showing: savings balance, monthly interest, cumulative total, and distance to goal.

Write a 1-page mathematical autobiography. Include: (a) The unit or concept you found most challenging and how you overcame it. (b) A specific problem you solved that you are proud of — explain your solution. (c) A real-world connection you made between math class and your everyday life. (d) One mathematical question you still wonder about. Use at least 3 mathematical terms from the year.

Select your best piece of mathematical work from the year. Write a 1-paragraph reflection explaining what mathematical thinking it demonstrates and what you would do differently.

A BC First Nations community plans a salmon festival. 480 guests attend. Food costs $18.75/person (+ BC taxes). A circular performance area has diameter 20 m. Tickets are sold at a 15% markup on cost. A fundraising game uses a spinner with 5 equal sections. Plan the festival by: (a) calculating total food cost with tax; (b) setting the ticket price; (c) finding the area and circumference of the performance space; (d) calculating P(winning) and expected earnings per 100 game plays if the prize is $5 and the game costs $2 to play.

This problem uses Units 2 (fractions/percent), 4 (ratio/percent), 6 (circles), 7 (area), and 8 (probability). Identify which calculation belongs to which unit.

In groups of 4, each person writes 3 questions: one L1, one L3, and one L4, from a different unit (divide units 1–4 among the group). Compile into a 12-question "peer test." Exchange tests between groups. Mark using an answer key you create together.

Write a marking rubric for your L4 question. What earns full marks, partial marks, and no marks? Use mathematical vocabulary in your rubric.

Choose one BC context from this list: salmon fisheries, cedar basket weaving, BC mountain hiking, a First Nations community feast. Create a portfolio page that includes: (a) One number/fraction/percent problem; (b) One algebraic equation or pattern; (c) One geometry or measurement calculation; (d) One probability or data display. All must use realistic numbers from your chosen context.

Connect two of your four problems with a "bridge" — a sentence explaining how the answer from one is used in another.

Closest estimate wins each event: (a) Number Sense — estimate GCF(144, 252) without calculating; (b) Measurement — estimate the area of the classroom floor in m²; (c) Data — estimate the mean of 20 values shown for 10 seconds; (d) Probability — estimate P(sum = 7) for two dice as a percent without a table; (e) Geometry — estimate the circumference of a circle with diameter 37 cm.

Which estimation required the most mathematical reasoning vs experience? Which benchmarks or strategies were most useful?

Each card shows a worked solution with one mathematical error. For each: (a) identify the error; (b) explain why it is wrong; (c) show the correct solution. Cards cover: adding fractions incorrectly, wrong percent change direction, BEDMAS error with integers, incorrect surface area setup, biased probability claim.

Create your own "error card" for a concept you found tricky. Write a plausible but wrong solution and the correct one. Include a hint that helps without giving away the error.

Find 5 real-life linear relations (e.g., taxi fare vs distance, cell phone data cost vs GB used, temperature vs elevation, BC ferry cost vs passengers). For each: write the equation y = mx + b; identify m and b and explain what they mean in context; create a T-table; determine at what point the cost/quantity crosses a threshold of your choosing.

Two of your five relations must come from BC-specific contexts (e.g., BC Ferries pricing, BC hydro rates, or local transit costs). Source your data from real websites and cite them.

Design a "mathematical postcard" that represents everything you learned in Grade 7 Math. Include: (a) One equation or formula from each of the 4 strands; (b) A visual (graph, diagram, or geometric figure); (c) One BC context connection; (d) Your "mathematical motto" for Grade 8. Use colour, symbols, and mathematical notation — make it visually striking and mathematically accurate.

Display these in the classroom or compile into a class "Year in Math" booklet. These make excellent portfolio cover pages.