5th grade · Math · Unit 7 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.
Texas Essential Knowledge and Skills (TEKS) teks student expectation: 5.4(C); 5.4(D) · number patterns from a rule, and additive and multiplicative 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 Texas
In the Texas Essential Knowledge and Skills (TEKS), this is unit 7 of 15 in 5th grade Math, after Expressions & Equations and before Parentheses & Expressions.
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: Texas Education Agency (TEA)
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?
118, 141, 164, 187,
answer box
210
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 7 2 14 3 21 4 28 answer box
63
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
Solve for b.
b ÷ 4 = 5
answer box
20
Hint: Undo dividing by 4: multiply 5 by 4.
Question 4
Ravi bought 3 packs of pencils with the same number in each pack. There are 27 pencils in all. Which equation can find p, the number of pencils in each pack?
- p + 3 = 27
- p − 3 = 27
- p ÷ 3 = 27
- 3 × p = 27
3 × p = 27
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 5
Which rule describes this pattern?
21, 34, 47, 60, …
- Start at 34 and add 13 each time.
- Start at 13 and add 21 each time.
- Start at 21 and add 14 each time.
- Start at 21 and add 13 each time.
Start at 21 and add 13 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 6
What number comes next in the pattern?
311, 290, 269, 248,
answer box
227
Hint: Find how much the pattern shrinks from one number to the next, then apply that change once more.