Grade 6 · Math · Unit 9 of 13
Patterns & Graphs
Rules, tables and line graphs
What your child practises
Describing growing and shrinking patterns with rules like 3n + 2, using tables and graphs to predict values, and reading change over time from line graphs.
Alberta Curriculum learning outcome: 6P1.1 · functions as tables of values, expressions and graphs
How we explain it
Children can open this short lesson before they practise.
- A rule links x and y, like y = 2x + 1.
- Put a number in for x to find y.
- Plot each (x, y) point. A straight line shows a steady pattern.
Example: For y = 2x + 1, what is y when x = 3? Replace x with 3. 2 × 3 = 6. 6 + 1 = 7. Answer: 7
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
What number comes next in the pattern?
63, 56, 49, 42,
answer box
Show answer
35
Hint: Find the change from one number to the next. Each number goes down by the same amount.
Question 2
These points follow a growing linear pattern. If it continues, what is y when x = 4?
answer box
Show answer
6
Hint: Each time x goes up by 1, y goes up by 1. Keep going from the last point, (3, 5).
Question 3
Find the pattern rule. What is the output when the input is 14?
Input and output Input (n) Output 1 11 2 19 3 27 4 35 14 ? answer box
Show answer
115
Hint: The output goes up by 8 each time, so the rule is 8 × n, plus or minus a fixed number. Check it with n = 1, then use n = 14.
Question 4
A taxi charges $6 per kilometre plus a starting fee of $5. Which expression gives the total cost, in dollars, for k kilometres?
- 5k + 6
- k + 11
- 6k + 5
- 11k
Show answer
6k + 5
Hint: The cost that repeats ($6 each time) is multiplied by k. The one-time cost ($5) is added only once.
Question 5
A tablet battery is at 85% and drops 12% every hour of video. What percent is left after 4 hours?
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37
Hint: This is a decreasing pattern: start at 85 and subtract 12 each time. After 4 times, that's 85 − 4 × 12.
Question 6
The points show the height of a bean plant (cm) at the start (x = 0) and after each week. How much did it increase from week 1 to week 5?
answer box
Show answer
7
Hint: Read the y-value above x = 1 and above x = 5. Subtract the smaller value from the larger one.