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.
Alaska content standards learning standard: 6.EE.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 Alaska
In the Alaska content 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: Alaska Department of Education and Early Development
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 9 2 15 3 21 4 27 12 ? answer box
75
Hint: The output goes up by 6 each time, so the rule is 6 × n, plus or minus a fixed number. Check it with n = 1, then use n = 12.
Question 2
The points show the height of a bean plant (cm) after each week. Between which two weeks did it change the most?
- Week 3 to 4
- Week 1 to 2
- Week 4 to 5
- Week 0 to 1
- Week 2 to 3
Week 2 to 3
Hint: Look for the biggest jump between neighboring points. On a line graph, that's the steepest part of the line.
Question 3
These points follow a growing linear pattern. If it continues, what is y when x = 4?
answer box
5
Hint: Each time x goes up by 1, y goes up by 1. Keep going from the last point, (3, 4).
Question 4
Which expression gives the output for any input n?
Pattern rule Input (n) Output 1 9 2 11 3 13 4 15 - 3n + 6
- 2n + 8
- n + 9
- 2n + 7
2n + 7
Hint: The output changes by 2 each time the input goes up by 1, so the rule starts with 2n. Then check n = 1 and adjust with + or −.
Question 5
The points show the height of a burning candle (cm) at the start (x = 0) and after each hour. How much did it decrease from hour 0 to hour 4?
answer box
7
Hint: Read the y-value above x = 0 and above x = 4. Subtract the smaller value from the larger one.
Question 6
Amir has 281 pages left to read and reads 12 pages every day. How many pages are left after 5 days?
answer box
221
Hint: This is a decreasing pattern: start at 281 and subtract 12 each time. After 5 times, that's 281 − 5 × 12.