6th grade · Math · Unit 7 of 19
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.
Texas Essential Knowledge and Skills (TEKS) teks student expectation: 6.6(A); 6.6(B); 6.6(C) · independent and dependent quantities in 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 Texas
In the Texas Essential Knowledge and Skills (TEKS), this is unit 7 of 19 in 6th grade Math, after Percents & Budgets and before Powers and Common Factors.
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: Texas Education Agency (TEA)
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
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 2 to hour 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 2
These points follow a shrinking linear pattern. If it continues, what is y when x = 4?
answer box
5
Hint: Each time x goes up by 1, y goes down by 1. Keep going from the last point, (3, 6).
Question 3
Find the pattern rule. What is the output when the input is 12?
Input and output Input (n) Output 1 11 2 14 3 17 4 20 12 ? answer box
44
Hint: The output goes up by 3 each time, so the rule is 3 × n, plus or minus a fixed number. Check it with n = 1, then use n = 12.
Question 4
Which expression gives the output for any input n?
Pattern rule Input (n) Output 1 8 2 14 3 20 4 26 - n + 8
- 6n + 2
- 2n + 6
- 8n
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
The points show the height of a bean plant (cm) after each week. Between which two weeks did it change the most?
- Week 4 to 5
- Week 0 to 1
- Week 2 to 3
- Week 3 to 4
- Week 1 to 2
Week 0 to 1
Hint: Look for the biggest jump between neighboring points. On a line graph, that's the steepest part of the line.
Question 6
A climbing gym charges $4 per visit plus a one-time membership fee of $9. Which expression gives the total cost, in dollars, for v visits?
- 13v
- 9v + 4
- 4v + 9
- 4v
4v + 9
Hint: The cost that repeats ($4 each time) is multiplied by v. The one-time cost ($9) is added only once.