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.
Alabama Course of Study content standard: 6.21 · two quantities that change together, shown 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 Alabama
In the Alabama Course of Study, 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.
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
Find the pattern rule. What is the output when the input is 12?
Input and output Input (n) Output 1 12 2 16 3 20 4 24 12 ? answer box
56
Hint: The output goes up by 4 each time, so the rule is 4 × n, plus or minus a fixed number. Check it with n = 1, then use n = 12.
Question 2
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).
Question 3
The points show the height of a burning candle (cm) after each hour. Between which two hours did it change the most?
- Hour 1 to 2
- Hour 4 to 5
- Hour 2 to 3
- Hour 3 to 4
- Hour 0 to 1
Hour 1 to 2
Hint: Look for the biggest jump between neighboring points. On a line graph, that's the steepest part of the line.
Question 4
The points show the height of a bean plant (cm) at the start (x = 0) and after each week. How much did it increase from week 2 to week 5?
answer box
4
Hint: Read the y-value above x = 2 and above x = 5. Subtract the smaller value from the larger one.
Question 5
A taxi charges $8 per kilometer plus a starting fee of $3. Which expression gives the total cost, in dollars, for k kilometers?
- k + 11
- 11k
- 8k + 3
- 8k
8k + 3
Hint: The cost that repeats ($8 each time) is multiplied by k. The one-time cost ($3) is added only once.
Question 6
Which expression gives the output for any input n?
Pattern rule Input (n) Output 1 9 2 14 3 19 4 24 - 4n + 5
- n + 9
- 5n + 5
- 5n + 4
5n + 4
Hint: The output changes by 5 each time the input goes up by 1, so the rule starts with 5n. Then check n = 1 and adjust with + or −.