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.
Maine Learning Results 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 Maine
In the Maine Learning Results, 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: Maine 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
Solve for b.
b ÷ 2 = 7
answer box
14
Hint: Undo dividing by 2: multiply 7 by 2.
Question 2
What number comes next in the pattern?
358, 345, 332, 319,
answer box
306
Hint: Find how much the pattern shrinks from one number to the next, then apply that change once more.
Question 3
What number comes next in the pattern?
67, 87, 107, 127,
answer box
147
Hint: Find how much the pattern grows from one number to the next, then apply that change once more.
Question 4
Solve for m.
m × 12 = 72
answer box
6
Hint: Think: 12 times what number makes 72? Divide 72 by 12 to undo the multiplying.
Question 5
Priya shared some grapes equally among 7 friends. Each friend got 11 grapes. Which equation can find g, the total number of grapes?
- g ÷ 7 = 11
- g × 7 = 11
- 7 ÷ g = 11
- g − 7 = 11
g ÷ 7 = 11
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
Which rule describes this pattern?
29, 42, 55, 68, …
- Start at 13 and add 29 each time.
- Start at 29 and add 13 each time.
- Start at 29 and add 14 each time.
- Start at 29 and subtract 13 each time.
Start at 29 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.