5th grade · Math · Unit 6 of 14
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.
Alaska content standards learning standard: 5.OA.3 · generating numerical patterns from rules and finding relationships between them
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 Alaska
In the Alaska content standards, this is unit 6 of 14 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.
Source: Alaska Department of Education and Early Development
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
Maya bought 9 packs of pencils with the same number in each pack. There are 99 pencils in all. Which equation can find p, the number of pencils in each pack?
- p + 9 = 99
- p ÷ 9 = 99
- 9 × p = 99
- p − 9 = 99
9 × p = 99
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 2
Which expression matches the rule in the table?
Input and output Input (n) Output 1 5 2 10 3 15 4 20 - 6n
- 5n
- 5n + 1
- n + 5
5n
Hint: Test each expression with every row: replace n with the input and see if you get the output. (3n means 3 × n.)
Question 3
The table follows a rule. What is the output when n = 10?
Input and output Input (n) Output 1 8 2 16 3 24 4 32 answer box
80
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
What number comes next in the pattern?
84, 109, 134, 159,
answer box
184
Hint: Find how much the pattern grows from one number to the next, then apply that change once more.
Question 5
What number comes next in the pattern?
468, 455, 442, 429,
answer box
416
Hint: Find how much the pattern shrinks from one number to the next, then apply that change once more.
Question 6
Which rule describes this pattern?
35, 41, 47, 53, …
- Start at 35 and add 6 each time.
- Start at 35 and add 7 each time.
- Start at 6 and add 35 each time.
- Start at 41 and add 6 each time.
Start at 35 and add 6 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.