1. What are the next three numbers in
the list?
• 1, 2, 3, 4, 5, …
6, 7, 8
• 7, 9, 11, 13, 15, …
17, 19, 21
• 2, 4, 7, 11, 16, …
22, 29, 37
• 0, 1, 4, 9, 16, 25, …
36, 49, 64
• 10, 7, 4, 1, -2, …
-5, -8, -11

2. Some Special patterns
• Arithmetic
1, 2, 3, 4, 5, …
7, 9, 11, 13, 15, …
• Geometric
1, 3, 9, 27, 81, …
• Fibonacci
1, 1, 2, 3, 5, 8, …
32, 16, 8, 4, 2, …

3. Toothpick Patterns
1st
2nd
3rd
4th
Number of boxes
(x, input, independent variable)
1
2
3
4
20
50
Number of toothpicks
(y, output, dependent variable)
4
7
10
13
61
151 301
Unit rate of change (pattern): +3
Function: y = 3x + 1
100

4. Toothpick Patterns
1st
2nd
3rd
4th
Number of boxes
(x, input, independent variable)
1
2
3
4
20
50
Number of toothpicks
(y, output, dependent variable)
3
5
7
9
41
101 201
Unit rate of change (pattern): +2
Function: y = 2x + 1
100

5. POD 5 Dec
• Does the table below represent a function?
• What is the independent variable?
# of
boxes
1
2
• What is the dependent variable?
3
• Can you write a rule for the table? 4
5
# of
toothpicks
4
7
10
13
16

6. Mathematize
Input (x)
Output (y)
1
2
3
4
5
4
10
16
22
28
Unit rate of change (pattern): +6
Function: y = 6x – 2

7. Mathematize
input 1
output 7
2
3
4
5
9
11
13
15
Unit rate of change (pattern): +2
Function: y = 2x + 5

8. Mathematize
input 1
output 10
2
3
4
5
7
4
1
-2
Unit rate of change (pattern): -3
Function: y = -3x + 13

9. Linear Functions
Your smart phone plan costs 35 dollars a month, plus 10 dollars per
GB of data used. Fill out a table, create a graph, and write an equation
to model the money you will spend each month on your phone.
Table
Graph
GBs of
Data
0
1
45
2
55
3
65
4
75
5
85
6
95
7
Unit rate of
change:
+10
Total
Cost
35
105
Total
Cost
Equation:
y = 10x + 35
GBs of Data

10. Linear Functions
You want to ship math textbooks from Singapore. They cost 45 dollars
each, plus 25 dollars total for shipping. Fill out a table, create a graph,
and write an equation to model the cost of the textbooks.
Graph
Table
Books
Cost
1
70
2
115
3
160
4
205
5
250
6
295
7
340
8
385
Unit Rate of
Change:
+45
Total
Cost
Equation:
y = 45x + 25
Books

11. Linear Functions
A taxi service charges an initial three dollar fee, plus two dollars per
mile driven. Fill out a table, create a graph, and write an equation to
model the cost of the taxi service.
Graph
Table
Miles
Cost
0
3
1
5
2
7
3
9
4
11
5
13
6
15
7
17
Unit Rate of
Change:
+2
Total
Cost
Equation:
y = 2x + 3
Miles