Grade 6 Patterns & Graphs worksheet
from Gradelings · Name: ______________________
How to explain it
- 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
Question 1
The points show the height of a bean plant (cm) after each week. Between which two weeks did it change the most?
- Week 0 to 1
- Week 3 to 4
- Week 4 to 5
- Week 1 to 2
- Week 2 to 3
Week 4 to 5
Hint: Look for the biggest jump between neighbouring points. On a line graph, that's the steepest part of the line.
Question 2
A rain barrel holds 193 L of water. A tap drains 9 L every minute. How many litres are left after 4 minutes?
answer box
157
Hint: This is a decreasing pattern: start at 193 and subtract 9 each time. After 4 times, that's 193 − 4 × 9.
Question 3
The points show the distance a hiker has walked (km) at the start (x = 0) and after each hour. How much did it increase from hour 3 to hour 5?
answer box
2
Hint: Read the y-value above x = 3 and above x = 5. Subtract the smaller value from the larger one.
Question 4
Which expression gives the output for any input n?
Pattern rule Input (n) Output 1 11 2 15 3 19 4 23 - 11n
- n + 11
- 7n + 4
- 4n + 7
4n + 7
Hint: The output changes by 4 each time the input goes up by 1, so the rule starts with 4n. Then check n = 1 and adjust with + or −.
Question 5
What number comes next in the pattern?
62, 52, 42, 32,
answer box
22
Hint: Find the change from one number to the next. Each number goes down by the same amount.
Question 6
These points follow a growing linear pattern. If it continues, what is y when x = 4?
answer box
4
Hint: Each time x goes up by 1, y goes up by 1. Keep going from the last point, (3, 3).
Question 7
A taxi charges $5 per kilometre plus a starting fee of $2. Which expression gives the total cost, in dollars, for k kilometres?
- 7k
- 2k + 5
- 5k
- 5k + 2
5k + 2
Hint: The cost that repeats ($5 each time) is multiplied by k. The one-time cost ($2) is added only once.
Question 8
Find the pattern rule. What is the output when the input is 12?
Input and output Input (n) Output 1 16 2 23 3 30 4 37 12 ? answer box
93
Hint: The output goes up by 7 each time, so the rule is 7 × n, plus or minus a fixed number. Check it with n = 1, then use n = 12.
Question 9
The points show the height of a burning candle (cm) after each hour. Between which two hours did it change the most?
- Hour 2 to 3
- Hour 3 to 4
- Hour 0 to 1
- Hour 1 to 2
- Hour 4 to 5
Hour 1 to 2
Hint: Look for the biggest jump between neighbouring points. On a line graph, that's the steepest part of the line.
Question 10
A climbing gym charges $6 per visit plus a one-time membership fee of $7. Which expression gives the total cost, in dollars, for v visits?
- 7v + 6
- 6v
- 13v
- 6v + 7
6v + 7
Hint: The cost that repeats ($6 each time) is multiplied by v. The one-time cost ($7) is added only once.
Answer key
- 1. Week 4 to 5
- 2. 157
- 3. 2
- 4. 4n + 7
- 5. 22
- 6. 4
- 7. 5k + 2
- 8. 93
- 9. Hour 1 to 2
- 10. 6v + 7
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