Grade 5 Patterns & Equations worksheet
from Gradelings · Name: ______________________
How to explain it
- A pattern rule tells how each term changes.
- A letter, like n, stands for a mystery number.
- Do the opposite operation to find it: the opposite of × is ÷.
Example: n × 4 = 28 Undo × 4 by dividing by 4. 28 ÷ 4 = 7. Answer: n = 7
Question 1
Solve for n.
3 × n = 21
answer box
7
Hint: Think: 3 times what number makes 21? Divide 21 by 3 to undo the multiplying.
Question 2
What number comes next in the pattern?
305, 286, 267, 248,
answer box
229
Hint: Find how much the pattern shrinks from one number to the next, then apply that change once more.
Question 3
Solve for a.
a ÷ 4 = 11
answer box
44
Hint: Undo dividing by 4: multiply 11 by 4.
Question 4
Kenji shared some grapes equally among 3 friends. Each friend got 11 grapes. Which equation can find g, the total number of grapes?
- g × 3 = 11
- g ÷ 3 = 11
- g − 3 = 11
- 3 ÷ g = 11
g ÷ 3 = 11
Hint: Read the story in order and write the actions you see: getting more is +, spending or losing is −, equal groups is ×, sharing equally is ÷.
Question 5
Which rule describes this pattern?
2, 16, 30, 44, …
- Start at 2 and add 15 each time.
- Start at 2 and add 14 each time.
- Start at 2 and subtract 14 each time.
- Start at 16 and add 14 each time.
Start at 2 and add 14 each time.
Hint: A pattern rule tells the starting number and how the pattern changes each step. Check the first number, then find the difference between neighbours.
Question 6
The table follows a rule. What is the output when n = 8?
Input and output Input (n) Output 1 8 2 16 3 24 4 32 answer box
64
Hint: Compare each output with its input and find a rule that works for every row (like “add 5”, “multiply by 3” or “multiply by 2, then add 1”). Then use the rule on the new input.
Question 7
Which expression matches the rule in the table?
Input and output Input (n) Output 1 9 2 18 3 27 4 36 - 9n + 1
- 9n
- 10n
- n + 9
9n
Hint: Test each expression with every row: replace n with the input and see if you get the output. (3n means 3 × n.)
Question 8
Priya had some stickers. After getting 26 more, Priya has 64. Which equation can find s, the number of stickers Priya started with?
- s + 26 = 64
- s − 26 = 64
- s + 64 = 26
- 26 × s = 64
s + 26 = 64
Hint: Read the story in order and write the actions you see: getting more is +, spending or losing is −, equal groups is ×, sharing equally is ÷.
Question 9
Solve for y.
17 + y = 71
answer box
54
Hint: Undo adding 17: subtract 17 from 71.
Question 10
The table follows a rule. What is the output when n = 10?
Input and output Input (n) Output 1 21 2 22 3 23 4 24 answer box
30
Hint: Compare each output with its input and find a rule that works for every row (like “add 5”, “multiply by 3” or “multiply by 2, then add 1”). Then use the rule on the new input.
Answer key
- 1. 7
- 2. 229
- 3. 44
- 4. g ÷ 3 = 11
- 5. Start at 2 and add 14 each time.
- 6. 64
- 7. 9n
- 8. s + 26 = 64
- 9. 54
- 10. 30
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