5th grade · Math · Unit 6 of 15
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.
Alabama Course of Study content standard: 5.2 · making numerical patterns from rules and completing input/output tables
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 Alabama
In the Alabama Course of Study, this is unit 6 of 15 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?
83, 103, 123, 143,
answer box
163
Hint: Find how much the pattern grows from one number to the next, then apply that change once more.
Question 2
The table follows a rule. What is the output when n = 9?
Input and output Input (n) Output 1 12 2 24 3 36 4 48 answer box
108
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 3
What number comes next in the pattern?
359, 348, 337, 326,
answer box
315
Hint: Find how much the pattern shrinks from one number to the next, then apply that change once more.
Question 4
Which rule describes this pattern?
110, 102, 94, 86, …
- Start at 110 and subtract 8 each time.
- Start at 102 and subtract 8 each time.
- Start at 8 and subtract 110 each time.
- Start at 110 and subtract 9 each time.
Start at 110 and subtract 8 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 5
Ana 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
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 ÷.
Question 6
Solve for p.
p ÷ 8 = 4
answer box
32
Hint: Undo dividing by 8: multiply 4 by 8.