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.
Minnesota K-12 Academic Standards benchmark: 6.3.7.1 · relating two changing quantities with an equation, a table and a graph
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 Minnesota
In the Minnesota K-12 Academic 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.
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 10?
Input and output Input (n) Output 1 7 2 14 3 21 4 28 10 ? answer box
70
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 = 10.
Question 2
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 0 to 1
- Hour 4 to 5
- Hour 3 to 4
- Hour 2 to 3
Hour 3 to 4
Hint: Look for the biggest jump between neighboring points. On a line graph, that's the steepest part of the line.
Question 3
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 5?
answer box
7
Hint: Read the y-value above x = 0 and above x = 5. Subtract the smaller value from the larger one.
Question 4
A pottery class costs $8 per session plus $6 for supplies. Which expression gives the total cost, in dollars, for s sessions?
- 8s + 6
- 8s
- 14s
- s + 14
8s + 6
Hint: The cost that repeats ($8 each time) is multiplied by s. The one-time cost ($6) is added only once.
Question 5
These points follow a growing linear pattern. If it continues, what is y when x = 4?
answer box
9
Hint: Each time x goes up by 1, y goes up by 2. Keep going from the last point, (3, 7).
Question 6
What number comes next in the pattern?
76, 69, 62, 55,
answer box
48
Hint: Find the change from one number to the next. Each number goes down by the same amount.