6th grade · Math · Unit 5 of 21
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.
New York State Learning Standards learning standard: NY-6.EE.9 · relating two changing 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 New York
In the New York State Learning Standards, this is unit 5 of 21 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 19 3 26 4 33 12 ? answer box
89
Hint: The output goes up by 7 each time, so the rule is 7 × n, plus or minus a fixed number. Check it with n = 1, then use n = 12.
Question 2
A pottery class costs $9 per session plus $15 for supplies. Which expression gives the total cost, in dollars, for s sessions?
- s + 24
- 9s
- 24s
- 9s + 15
9s + 15
Hint: The cost that repeats ($9 each time) is multiplied by s. The one-time cost ($15) is added only once.
Question 3
What number comes next in the pattern?
117, 106, 95, 84,
answer box
73
Hint: Find the change from one number to the next. Each number goes down by the same amount.
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 0 to week 2?
answer box
4
Hint: Read the y-value above x = 0 and above x = 2. Subtract the smaller value from the larger one.
Question 5
These points follow a growing linear pattern. If it continues, what is y when x = 4?
answer box
6
Hint: Each time x goes up by 1, y goes up by 1. Keep going from the last point, (3, 5).
Question 6
A tablet battery is at 83% and drops 11% every hour of video. What percent is left after 6 hours?
answer box
17
Hint: This is a decreasing pattern: start at 83 and subtract 11 each time. After 6 times, that's 83 − 6 × 11.