Slide 1
Common Difference
Fill in the blanks of the table to show the common differences in the cake diameter and the cake layer.
Description of work area:
On the right is a layered cake. The bottom layer (layer one) has a ten-inch diameter, the middle layer (layer two) has an eight-inch diameter, and the top layer (layer three) has a six-inch diameter.
On the left is a two-column table. The first column is labeled “Cake Layer” and has the numbers 1, 2, 3. The second column is labeled “Diameter in Inches” and has the numbers 10, 8, and 6. On the sides of the columns are blanks to enter in the common differences for each column.
Correct answers: (for Cake Layer column) 1, 1; (for Diameter column) minus 2, - minus2
Slide 2
Continue the pattern in the table to find the diameter of the next cake layers. Type your answers in the blanks.
Description of work area:
On the left is a two-column table. The first column is labeled “Cake Layer” and has the numbers 1, 2, 3, 4, 5. The second column is labeled “Diameter in Inches” and has the numbers 10, 8, and 6. Two more numbers belong in this column beneath these first numbers, and there are blanks to be filled in. On the sides of the columns are blanks to enter in the common differences for each column.
Correct answers: Common differences: (for Cake Layer column) 1, 1; (for Diameter column) minus 2, minus 2; Table (Diameter column): 4, 2
Slide 3
Type your answers in the blanks.
Description of work area:
On the right is a two-column table. The first column is labeled “Cake Layer” and has the numbers 1, 2, 3, 4, 5. The second column is labeled “Diameter in Inches” and has the numbers 10, 8, 6, 4, 2. The common differences are shown, which are plus 1 for the left column of the table and minus two for the right column in the table.
(text on slide) What would be the diameter of a cake at Layer 6?
How many total layers high could this cake be?
Description of quiz area: two blanks are provided to respond to the two questions.
Correct answers: 0, 5
Slide 4
Type your answer in the blank.
The cake is placed on a plate such that the diameter of the plate follows the pattern in the cake layers. If the cake plate is considered Cake Layer 0, what would its diameter be?
Description of work area:
On the right is a two-column table. The first column is labeled “Cake Layer” and has the numbers 1, 2, 3, 4, 5. The second column is labeled “Diameter in Inches” and has the numbers 10, 8, 6, 4, 2. The common differences are shown, which are plus 1 for the left column of the table and minus two for the right column in the table.
Description of quiz area: one blank is provided to respond to the question.
Correct answer: 12
Slide 5
The pattern or change in the diameter is a decrease of 2 inches per layer, or negative 2.
Therefore, the ratio of the change in the diameter to the change in the cake layer is negative 2 to 1.
This is the unit rate, defined at the change in the dependent variable (the quantity in the given situation that is affected by previous outcomes) for every one unit change in the independent variable (the quantity in the given situation that is not affected by the previous outcomes). It is the rate of change - defined as the change in the dependent variable (the quantity in the given situation that is affected by previous outcomes) with respect to the change in the independent variable (the quantity in the given situation that is not affected by previous outcomes - in the diameter with respect to the cake layer.
Description of table:
On the right is a two-column table. The first column is labeled “Cake Layer” and has the numbers 1, 2, 3, 4, 5. The second column is labeled “Diameter in Inches” and has the numbers 10, 8, 6, 4, 2. The common differences are shown, which are plus 1 for the left column of the table and minus two for the right column in the table.
Slide 6
Graph the relationship between the diameter and the cake layer by dragging and dropping the points to the correct location on the coordinate grid.
Description of work area:
The work area is divided into three sections. On the left of the screen is a coordinate grid. The x-axis is labeled “Cake Layer” and is numbered from zero to ten, in increments of one. The y-axis is labeled “Diameter in Inches” and extends from zero to sixteen, in increments of one. On the bottom right of the screen is a two-column table. The first column is labeled “Cake Layer” and has the numbers 0, 1, 2, 3, 4, 5, 6. The second column is labeled “Diameter in Inches” and has the numbers 12, 10, 8, 6, 4, 2, 0. At the top right of the screen is a collection of seven points which can be clicked and dragged onto the coordinate grid to the appropriate locations.
Correct Answer: A coordinate grid is shown. The x-axis is labeled “Cake Layer” and is numbered from zero to ten, in increments of one. The y-axis is labeled “Diameter in Inches” and extends from zero to sixteen, in increments of one. Seven points are plotted at (0, 12), (1, 10), (2, 8), (3, 6), (4, 4), (5, 2), and (6, 0).
Slide 7
Which of the following accurately describes the pattern shown in the graph?
Description of work area: The work area is divided into three sections. On the right of the screen is a coordinate grid is shown. The x-axis is labeled “Cake Layer” and is numbered from zero to ten, in increments of one. The y-axis is labeled “Diameter in Inches” and extends from zero to sixteen, in increments of one. Seven points are plotted at (0, 12), (1, 10), (2, 8), (3, 6), (4, 4), (5, 2), and (6, 0).
On the left of the screen are three answer choices:
A hint box is provided below the answer choices:
Hint:
A linear pattern follows a path of a straight line.
A non-linear pattern follows a pattern but the pattern is not in a straight line.
Slide 8
Slide 8:
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