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.
New York State Learning Standards learning standard: NY-5.OA.3 · making number patterns from rules and finding how they are related
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 New York
In the New York State Learning Standards, 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
Solve for p.
p × 11 = 66
answer box
6
Hint: Think: 11 times what number makes 66? Divide 66 by 11 to undo the multiplying.
Question 2
What number comes next in the pattern?
43, 64, 85, 106,
answer box
127
Hint: Find how much the pattern grows from one number to the next, then apply that change once more.
Question 3
Solve for n.
n ÷ 4 = 7
answer box
28
Hint: Undo dividing by 4: multiply 7 by 4.
Question 4
Kenji bought 3 packs of pencils with the same number in each pack. There are 24 pencils in all. Which equation can find p, the number of pencils in each pack?
- 3 × p = 24
- p ÷ 3 = 24
- p + 3 = 24
- p − 3 = 24
3 × p = 24
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?
4, 15, 26, 37, …
- Start at 15 and add 11 each time.
- Start at 4 and subtract 11 each time.
- Start at 4 and add 12 each time.
- Start at 4 and add 11 each time.
Start at 4 and add 11 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
Which expression matches the rule in the table?
Input and output Input (n) Output 1 5 2 10 3 15 4 20 - 6n
- 5n
- 2n + 3
- 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.)