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Variables and Relationships

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Variables and Relationships

A fete stall is tracking how sales change with the number of items sold. Complete the activities to investigate variables, rules and relationships. Show calculations where useful.

Spot the variables

A variable is a quantity that can change. Use the fete and other everyday situations to identify variables and describe how they are related.

1.At a fruit stall, the total price depends on how many apples are bought. Which pair names the two variables?

Number of apples and total price
Colour of the stall and total price
Seller’s name and number of apples
Day of the week and apple variety

2.A water tank is being filled at a steady rate. Name two variables that could be tracked and explain how one changes as the other increases.

3.Match each situation to the relationship that best describes it. Situations: (1) More identical tickets are bought, so the total cost rises. (2) A fixed distance is travelled at a faster speed, so travel time falls. (3) More hours of daylight may mean less time a household needs its lights on.

1. Tickets bought and total cost
2. Speed and travel time for a fixed distance
3. Daylight hours and time lights are used

As one increases, the other decreases
As one increases, the other decreases
As one increases, the other increases

Build and use rules

A relationship can be described by a rule. Use the rule to make a table, then interpret what it tells you.

4.The fete’s badge stall charges $3 to set up a badge design, then $2 for each badge. Let b be the number of badges and C be the total cost in dollars. Write a rule for C in terms of b.

5.Use the badge-stall rule C = 3 + 2b to complete the table. What is the total cost for 0, 1, 3 and 5 badges?

Badges, b: 0 | 1 | 3 | 5

Cost, C ($): _____ | _____ | _____ | _____

6.A juice stall starts with 24 cups of juice and sells 3 cups each minute. Let J be the number of cups left after m minutes. Write a rule and find how many cups remain after 4 minutes.

7.A square garden bed has side length s metres. Its area A in square metres is given by A = s × s. Find A when s = 2, 3 and 5 metres. What happens to the area as the side length increases?

Explain and investigate

Think about what the numbers and rules mean, not just how to calculate them.

8.For the badge stall, explain what the 3 and the 2 represent in C = 3 + 2b. Then find the cost of 8 badges.

9.A student says, “In the rule T = 5n, T is always 5.” Is the student correct? Explain what T and n could represent and why.

10.Create a real-life situation with two variables that follow the rule y = 4x + 2. State what x and y represent, and explain what the 4 and 2 mean in your situation.