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.
Maine Learning Results 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 Maine
In the Maine Learning Results, 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: 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
Jay has 219 pages left to read and reads 8 pages every day. How many pages are left after 7 days?
answer box
163
Hint: This is a decreasing pattern: start at 219 and subtract 8 each time. After 7 times, that's 219 − 7 × 8.
Question 2
Find the pattern rule. What is the output when the input is 11?
Input and output Input (n) Output 1 6 2 8 3 10 4 12 11 ? answer box
26
Hint: The output goes up by 2 each time, so the rule is 2 × n, plus or minus a fixed number. Check it with n = 1, then use n = 11.
Question 3
What number comes next in the pattern?
120, 113, 106, 99,
answer box
92
Hint: Find the change from one number to the next. Each number goes down by the same amount.
Question 4
Which expression gives the output for any input n?
Pattern rule Input (n) Output 1 8 2 14 3 20 4 26 - 6n + 2
- 8n
- 6n + 3
- n + 8
6n + 2
Hint: The output changes by 6 each time the input goes up by 1, so the rule starts with 6n. Then check n = 1 and adjust with + or −.
Question 5
A taxi charges $8 per kilometer plus a starting fee of $9. Which expression gives the total cost, in dollars, for k kilometers?
- 17k
- 8k
- 8k + 9
- 9k + 8
8k + 9
Hint: The cost that repeats ($8 each time) is multiplied by k. The one-time cost ($9) is added only once.
Question 6
These points follow a shrinking linear pattern. If it continues, what is y when x = 4?
answer box
6
Hint: Each time x goes up by 1, y goes down by 1. Keep going from the last point, (3, 7).