Slide 1
Rate of Change
Complete this table according to the information given. Type your answers in the blanks.
One batch of a cake recipe will feed 8 people.
Description of work area: A two-column table appears. The left column of the table is titled “Batch” and has the numbers 0, 1, 2, 3, 4. The right side of the table is titled “People Fed” and contains five answer blanks.
Correct answers: 0, 8, 16, 24, 32
Slide 2
Complete this table according to the information given. Type your answers in the blanks.
A cake recipe calls for one point five cups of flour per batch.
Description of work area: A two-column table appears. The left column of the table is titled “Batch” and has the numbers 0, 1, 2, 3, 4. The right side of the table is titled “Flour (cups)” and contains five answer blanks.
Correct answers: 0, 1.5, 3, 4.5, 6
Slide 3
Complete this table according to the information given. Type your answers in the blanks.
In an eating contest, Tim eats one batch of cake in half a minute. Every batch after that takes twice as long to eat as the prior batch.
*Note that increments of half a minute should be recorded as a decimal in the table.
For example, 30 seconds would be written as zero point five.
Description of work area: A two-column table appears. The left column of the table is titled “Batch” and has the numbers 0, 1, 2, 3, 4. The right side of the table is titled “Time (min.)” and contains five answer blanks.
Correct answers: 0, 0.5, 1, 2
Slide 4
Find the rate of change in this table of values. Include the appropriate operation. For example, type plus one in the blank to indicate a common difference of 1 more, and type minus one to indicate a common difference of 1 less.
Description of work area: A two-column table appears. The left column of the table is titled “Batch” and has the numbers 0, 1, 2, 3, 4. The right side of the table is titled “People Fed” and has the numbers 0,8,16, 24, 32. There are four answer blanks outside both columns of the table to enter the common differences for both columns in the table.
Correct answers: +1, +1, +1, +1, +8, +8, +8, +8
Slide 5
Find the rate of change in this table of values. Include the appropriate operation. Be sure to add plus or minus as needed.
Description of work area: A two-column table appears. The left column of the table is titled “Batch” and has the numbers 0, 1, 2, 3, 4. The right side of the table is titled “Flour (cups)” and has the numbers 0, 1.5, 3, 4.5, 6. There are four answer blanks outside both columns of the table to enter the common differences for both columns in the table.
Correct answers: +1, +1, +1, +1, +1.5, +1.5, +1.5, +1.5
Slide 6
Find the rate of change in this table of values. Include the appropriate operation. Be sure to add plus or minus as needed.
Description of work area: A two-column table appears. The left column of the table is titled “Batch” and has the numbers 0, 1, 2, 3, 4. The right side of the table is titled “Time (min.)” and has the numbers 0, 0.5, 1, 2, 4. There are four answer blanks outside both columns of the table to enter the common differences for both columns in the table.
Correct answers: +1, +1, +1, +1, +0.5, +0.5, +1, +2
Slide 7
Graph the scenario on the grid provided. Drag each point to the appropriate 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 “Batches” and is numbered from negative one to five, in increments of one. The y-axis is labeled “Number of People Fed” and extends from zero to thirty-six, in increments of four. On the bottom right of the screen is a two-column table. The first column is labeled “Batch” and has the numbers 0, 1, 2, 3, 4. The second column is labeled “People Fed” and has the numbers 0, 8, 16, 24, 32. At the top right of the screen is a collection of five points that 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 “Batches” and is numbered from negative one to five, in increments of one. The y-axis is labeled “Number of People Fed” and extends from zero to thirty-six, in increments of four. Five points are plotted at (0, 0), (1, 8), (2, 16), (3, 24) and (4, 32).
Slide 8
Graph the scenario on the grid provided. Drag each point to the appropriate 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 “Batches” and is numbered from negative one to five, in increments of one. The y-axis is labeled “Cups of Flour” and extends from zero to eight, in increments of one. On the bottom right of the screen is a two-column table. The first column is labeled “Batch” and has the numbers 0, 1, 2, 3, 4. The second column is labeled “Flour (cups)” and has the numbers 0, 1.5, 3, 4.5, 6. At the top right of the screen is a collection of five points that 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 “Batches” and is numbered from negative one to five, in increments of one. The y-axis is labeled “Cups of Flour” and extends from zero to eight, in increments of one. Five points are plotted at (0, 0), (1, 1.5), (2, 3), (3, 4.5) and (4, 6).
Slide 9
Graph the scenario on the grid provided. Drag each point to the appropriate 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 “Batches” and is numbered from negative one to five, in increments of one. The y-axis is labeled “Time (minutes)” and extends from zero to five, in increments of one. On the bottom right of the screen is a two-column table. The first column is labeled “Batch” and has the numbers 0, 1, 2, 3, 4. The second column is labeled “Time (min)” and has the numbers 0, 0.5, 1, 2, 4. At the top right of the screen is a collection of five points that 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 “Batches” and is numbered from negative one to five, in increments of one. The y-axis is labeled “Time (minutes)” and extends from zero to five, in increments of one. Five points are plotted at (0, 0), (1, 0.5), (2, 1), (3, 2) and (4, 4).
Slide 10
Which scenario does NOT follow a linear pattern?
Description of quiz area:
Three graphs are shown, and one is to be selected as the correct answer.
Graph A: The x-axis is labeled “Batches” and is numbered from negative one to five, in increments of one. The y-axis is labeled “Number of People Fed” and extends from zero to thirty-six, in increments of four. Five points are plotted at (0, 0), (1, 8), (2, 16), (3, 24) and (4, 32).
Graph B: The x-axis is labeled “Batches” and is numbered from negative one to five, in increments of one. The y-axis is labeled “Cups of Flour” and extends from zero to eight, in increments of one. Five points are plotted at (0, 0), (1, 1.5), (2, 3), (3, 4.5) and (4, 6).
Graph C: The x-axis is labeled “Batches” and is numbered from negative one to five, in increments of one. The y-axis is labeled “Time (minutes)” and extends from zero to five, in increments of one. Five points are plotted at (0, 0), (1, 0.5), (2, 1), (3, 2) and (4, 4).
Correct Answer: C
Slide 11
Now let’s determine the unit rate for the scenarios that follow a linear pattern.
It is the unit rate in these proportional relationships that form the linear pattern. The unit rate is the constant change in the dependent variable with respect to the change in the independent variable.
The unit rate is the slope of the line. The slope of a line is the ratio of the change in the dependent variable to the change in the independent variable. The slope of this line is one point five over 1.
Descriptions of Graphs:
Two graphs are shown. Both graphs have the x-axis labeled “Batches” and numbered from negative one to five, in increments of one. The y-axis is labeled “Cups of Flour” and extends from zero to eight, in increments of one. Five points are plotted at (0, 0), (1, 1.5), (2, 3), (3, 4.5) and (4, 6). Both graphs show how the ‘rise’ (or vertical movement) to move from one plotted point to the next is “+1.5” and the ‘run’ (or horizontal movement) to move from one plotted point to the next is “+1”. The graph on the right connects the five points with a line that has a positive slope and crosses through the origin.
Slide 12
Here is the other linear pattern.
Descriptions of Graphs:
Two graphs are shown. Both graphs have the x-axis labeled “Batches” and are numbered from negative one to five, in increments of one. The y-axis is labeled “Number of People Fed” and extends from zero to thirty-six, in increments of four. Five points are plotted at (0, 0), (1, 8), (2, 16), (3, 24) and (4, 32). Both graphs show how the ‘rise’ (or vertical movement) to move from one plotted point to the next is “+8” and the ‘run’ (or horizontal movement) to move from one plotted point to the next is “+1”. The graph on the right connects the five points with a line that has a positive slope and crosses through the origin.
(text on slide) What is the slope of the line formed by this proportional relationship? Type your answer in the blank. Enter a fraction using a slash mark. For example, the fraction one-half would be entered as one slash two.
Correct answer: 8/1
Slide 13
This scenario did not have a unit rate. It does not follow a linear pattern, thus, no slope.
Description of graph: A coordinate grid is shown. The x-axis is labeled “Batches” and is numbered from negative one to five, in increments of one. The y-axis is labeled “Time (minutes)” and extends from zero to five, in increments of one. Five points are plotted at (0, 0), (1, 0.5), (2, 1), (3, 2) and (4, 4).
Slide 14
You have finished this part of the activity. Return to the main activity to continue.