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.
Arizona Academic Standards learning standard: 5.OA.B.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 Arizona
In the Arizona Academic 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: Arizona Department of Education
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
Which expression matches the rule in the table?
Input and output Input (n) Output 1 10 2 20 3 30 4 40 - 11n
- 10n
- n + 10
- 2n + 8
10n
Hint: Test each expression with every row: replace n with the input and see if you get the output. (3n means 3 × n.)
Question 2
Solve for k.
k ÷ 6 = 11
answer box
66
Hint: Undo dividing by 6: multiply 11 by 6.
Question 3
Sam bought 5 packs of pencils with the same number in each pack. There are 20 pencils in all. Which equation can find p, the number of pencils in each pack?
- 5 × p = 20
- p + 5 = 20
- p − 5 = 20
- p ÷ 5 = 20
5 × p = 20
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 4
The table follows a rule. What is the output when n = 12?
Input and output Input (n) Output 1 10 2 20 3 30 4 40 answer box
120
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 5
Solve for p.
p × 9 = 72
answer box
8
Hint: Think: 9 times what number makes 72? Divide 72 by 9 to undo the multiplying.
Question 6
What number comes next in the pattern?
525, 503, 481, 459,
answer box
437
Hint: Find how much the pattern shrinks from one number to the next, then apply that change once more.