Tile Patterns
Tables
Graphs
Equations
Miscellaneous
100
Examine the pattern below. Sketch Figure 0 and Figure 4.
See sketches.
100
Fill in the missing values in the table. 
Missing values: 18;210;150
100
Find a rule that represent the graph below.
y=-2x+3
100
In the equation y = mx + b, what do the letters m and b represent?
m is slope and b is y-intercept
100
Simplify the expression 2x2 - 6 when x = -3.
12
200
Write a rule for the tile pattern below.
y = 6x + 5
200
Write a rule for the table.
y = 2x +10
200
Give two ways you can tell that the rule y = 2x − 3 does not match the graph.
The slope must be negative because the line is going down from left to right. The y-intercept is a positive 3 but is represented as -3 in the equation.
200
Consider the rule y = 5x + 7. How many are in figure 0?
7
200
Simplify 20 + 3xy − 4xy + y2 + 10 − y2
-xy + 30
300
Find the number of tiles in figure 100.
605 tiles
300
Using the table below, what is the y-intercept? What is the growth factor?
y-intercept (0, -2)
Growth factor: 5
300
Richard is frustrated. He knows the line to the right should have a 3 and a 4 in the equation but he can’t remember if it is 
y = 4x + 3. Explanations may vary.
300
Consider the rule y = 5x + 7. How many tiles for the 100 figure have?
507 tiles
300
Solve for x.
7x - 3 = 4x + 3
x = 2
400
Find the rule for the tile pattern below. Then find the number of tiles in Figure 100.
y = 2x + 1; figure 100 has 201 tiles.
400
Using the table below, if the output number (y) is −52, what was the input number (x)?
-10
400
Write a rule for the following graph using two different methods. Show your work and explain each method.
y = 6x - 4
400
Consider the rule y = 5x + 7. Which figure has 37 tiles?
Figure 6
400
Solve for x.
6( - 2 - x) = -5( 2x + 4)
x = -2
500
Write the rule for the tile pattern below. How many tiles are in figure 100?
y = (n + 1)2 ; figure 100 has 10,201 tiles
500
Stardollars Coffee hosted a coffee-cup-stacking contest. Anthony noticed a pattern. He told the judges that Figure 100 would have 203 coffee cups stacked up. Was he correct? Use mathematics to prove or disprove Anthony’s claim. Include a table, a graph, and a rule (equation) in your explanation.
Answers may vary.
500
he graphs at right represent two tile patterns A and B. Describe the similarities and differences between each tile pattern based on the graphs? Justify your conclusions.
Answers may vary.
500
Monique and Jesus studied the pattern and the graph below to see if they could make a table and a rule. Jesus thinks that the rule must be y = 3x + 2 because the figure has 3 tiles on the bottom row and 2 tiles on the corners. Monique does not agree. She says that the graph shows that Figure 0 has two tiles and that each new figure in the pattern grows by 1 tile. Her rule is y = 1x + 2. Who is correct? How do you know?
Monique. Answers may vary for explanation.
500
Solve for x.
-2 - 3k - 2 = -2k + 8 - k
No Solution