Grade 8 · Math · Unit 7 of 18
Growing & Shrinking Patterns
Rates, initial values and rules
What your child practises
Finding the constant rate and initial value of a pattern, comparing patterns, writing a rule such as 5n + 2 or 40 − 3n, and using the rule to predict later terms.
Ontario Curriculum expectation: C1.1–C1.4 · repeating, growing and shrinking patterns, rates of change, initial values, and rules as algebraic expressions
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
Pattern A starts at 6 and grows by 5 each term. Pattern B starts at 4 and grows by 6 each term. Which statement is true?
- A grows faster and B starts higher
- A grows faster and A starts higher
- B grows faster and A starts higher
- B grows faster and B starts higher
Show answer
B grows faster and A starts higher
Hint: Compare the rates of change to see which grows faster, and compare the initial values to see which starts higher.
Question 2
A pattern follows the rule value = 2n + 5. Which term has a value of 17?
answer box
Show answer
6
Hint: Solve 2n + 5 = 17. Subtract 5, then divide by 2.
Question 3
Sam has $87 and spends $7 each day. Which rule gives the amount M after n days?
- M = 87 − 7n
- M = 87 + 7n
- M = 7n − 87
- M = 7 − 87n
Show answer
M = 87 − 7n
Hint: Start with the initial amount, then subtract the rate times n.
Question 4
The table shows a shrinking pattern. What is the value of term 10?
Term (n) Value 1 31 2 29 3 27 4 25 answer box
Show answer
13
Hint: The value goes down by 2 each term. Find the rule, then put n = 10 into it.
Question 5
A growing pattern is shown in the table. What is the initial value (the value when n = 0)?
Term (n) Value 1 7 2 11 3 15 4 19 answer box
Show answer
3
Hint: The value goes up by 4 each term. Work backwards from term 1: 7 − 4 = 3.
Question 6
A shrinking pattern follows the rule value = 29 − 2n. What is the value of term 5?
answer box
Show answer
19
Hint: Put n = 5 into the rule: 29 − 2 × 5.