Grade 5 · Math · Unit 12 of 14
Patterns & Equations
Pattern rules and mystery numbers
What your child practises
Describing growing and shrinking patterns with rules and expressions like 3n + 1, using input–output tables, and solving one-step equations such as n + 37 = 92 or 6 × n = 54.
Alberta Curriculum learning outcome: 5P1.1, 5A1.3 · arithmetic sequences, position and term, and solving equations
How we explain it
Children can open this short lesson before they practise.
- 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
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?
53, 75, 97, 119,
answer box
Show answer
141
Hint: Find how much the pattern grows from one number to the next, then apply that change once more.
Question 2
What number comes next in the pattern?
409, 394, 379, 364,
answer box
Show answer
349
Hint: Find how much the pattern shrinks from one number to the next, then apply that change once more.
Question 3
The table follows a rule. What is the output when n = 10?
Input and output Input (n) Output 1 2 2 4 3 6 4 8 answer box
Show answer
20
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 4
Which expression matches the rule in the table?
Input and output Input (n) Output 1 8 2 16 3 24 4 32 - 9n
- 8n + 1
- 8n
- n + 8
Show answer
8n
Hint: Test each expression with every row: replace n with the input and see if you get the output. (3n means 3 × n.)
Question 5
Solve for b.
10 × b = 90
answer box
Show answer
9
Hint: Think: 10 times what number makes 90? Divide 90 by 10 to undo the multiplying.
Question 6
Zoe shared some grapes equally among 6 friends. Each friend got 12 grapes. Which equation can find g, the total number of grapes?
- 6 ÷ g = 12
- g ÷ 6 = 12
- g − 6 = 12
- g × 6 = 12
Show answer
g ÷ 6 = 12
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 ÷.