6th grade · Math · Unit 5 of 17
Patterns & Graphs
Rules, tables and line graphs
What your child practices
Describing growing and shrinking patterns with rules like 3n + 2, using tables and graphs to predict values, and reading change over time from line graphs.
Arizona Academic Standards learning standard: 6.EE.C.9 · relating two quantities with tables, graphs and equations
How we explain it
Children can open this short lesson before they practice.
- A rule links x and y, like y = 2x + 1.
- Put a number in for x to find y.
- Plot each (x, y) point. A straight line shows a steady pattern.
Example: For y = 2x + 1, what is y when x = 3? Replace x with 3. 2 × 3 = 6. 6 + 1 = 7. Answer: 7
Patterns & Graphs in Arizona
In the Arizona Academic Standards, this is unit 5 of 17 in 6th grade Math, after Percents & Budgets and before Equations.
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
A tablet battery is at 69% and drops 5% every hour of video. What percent is left after 8 hours?
answer box
29
Hint: This is a decreasing pattern: start at 69 and subtract 5 each time. After 8 times, that's 69 − 8 × 5.
Question 2
A bowling alley charges $2 per game plus $13 for shoe rental. Which expression gives the total cost, in dollars, for g games?
- 2g
- 15g
- 2g + 13
- g + 15
2g + 13
Hint: The cost that repeats ($2 each time) is multiplied by g. The one-time cost ($13) is added only once.
Question 3
What number comes next in the pattern?
102, 96, 90, 84,
answer box
78
Hint: Find the change from one number to the next. Each number goes down by the same amount.
Question 4
Find the pattern rule. What is the output when the input is 14?
Input and output Input (n) Output 1 12 2 21 3 30 4 39 14 ? answer box
129
Hint: The output goes up by 9 each time, so the rule is 9 × n, plus or minus a fixed number. Check it with n = 1, then use n = 14.
Question 5
Which expression gives the output for any input n?
Pattern rule Input (n) Output 1 10 2 14 3 18 4 22 - 4n + 6
- n + 10
- 6n + 4
- 10n
4n + 6
Hint: The output changes by 4 each time the input goes up by 1, so the rule starts with 4n. Then check n = 1 and adjust with + or −.
Question 6
These points follow a shrinking linear pattern. If it continues, what is y when x = 4?
answer box
1
Hint: Each time x goes up by 1, y goes down by 2. Keep going from the last point, (3, 3).