5th grade · Math · Unit 6 of 12
Patterns & Equations
Pattern rules and mystery numbers
What your child practices
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.
Minnesota K-12 Academic Standards benchmark: 5.3.7.2; 5.3.7.5 · relationships between two patterns, and rules for visual patterns
How we explain it
Children can open this short lesson before they practice.
- 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
Patterns & Equations in Minnesota
In the Minnesota K-12 Academic Standards, this is unit 6 of 12 in 5th grade Math, after Decimals and before Mental Math Tricks.
Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.
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, 75, 87, 99,
answer box
111
Hint: Find how much the pattern grows from one number to the next, then apply that change once more.
Question 2
Which rule describes this pattern?
5, 14, 23, 32, …
- Start at 5 and add 9 each time.
- Start at 9 and add 5 each time.
- Start at 14 and add 9 each time.
- Start at 5 and add 10 each time.
Start at 5 and add 9 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 neighbors.
Question 3
The table follows a rule. What is the output when n = 8?
Input and output Input (n) Output 1 11 2 22 3 33 4 44 answer box
88
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
Solve for k.
k ÷ 2 = 12
answer box
24
Hint: Undo dividing by 2: multiply 12 by 2.
Question 5
What number comes next in the pattern?
521, 501, 481, 461,
answer box
441
Hint: Find how much the pattern shrinks from one number to the next, then apply that change once more.
Question 6
Which expression matches the rule in the table?
Input and output Input (n) Output 1 2 2 4 3 6 4 8 - n + 2
- 2n
- 3n
- 2n + 1
2n
Hint: Test each expression with every row: replace n with the input and see if you get the output. (3n means 3 × n.)