Rockdale County Public Schools: MSP Courses

1
Rockdale County Public Schools MSP Courses

• Day 1 7th Grade

2
Unit 5 Staying in Shape

• Students will be able to
• create similar shapes by enlarging or reducing
  a geometric figure in a coordinate plane
• describe similarities by listing corresponding
  parts
• find missing side lengths or areas in similar
  figures

3
Part 1 Create similar shapes by enlarging or
reducing a geometric figure in a coordinate plane

• Unit 5

4
Similar Figures

• Similar figures are figures that have the same
  shape but may be of different sizes. In similar
  figures, corresponding angles are congruent and
  corresponding segments are in proportion.

5
Similarity

• Which figure is similar to this one?

6
Similarity

• Which figure is similar to this one?

Math.com (Similar Figures) http//www.math.com/sch
ool/subject1/lessons/S1U2L4GL.html
7
Scaling

• A scale of 11 implies that the drawing of the
  grasshopper is the same as the actual object. The
  scale 12 implies that the drawing is smaller
  (half the size) than the actual object (in other
  words, the dimensions are multiplied by a scale
  factor of 0.5). The scale 21 suggests that the
  drawing is larger than the actual grasshopper --
  twice as long and twice as high (we say the
  dimensions are multiplied by a scale factor of
  2).

8
Scale Drawings

• Copy the picture onto graph paper and label the
  coordinates. Multiply the coordinates of each
  point by 2, creating points A H. Plot these
  points on the same grid.
• What is the ratio of proportionality?

9
Similar Figures

• Similar figures are figures that have the same
  shape but may be of different sizes. In similar
  figures, corresponding angles are congruent and
  corresponding segments are in proportion.

10
Similarity

• Which figure is similar to this one?

Math.com (Similar Figures) http//www.math.com/sch
ool/subject1/lessons/S1U2L4GL.html
11
Scaling

• A scale of 11 implies that the drawing of the
  grasshopper is the same as the actual object. The
  scale 12 implies that the drawing is smaller
  (half the size) than the actual object (in other
  words, the dimensions are multiplied by a scale
  factor of 0.5). The scale 21 suggests that the
  drawing is larger than the actual grasshopper --
  twice as long and twice as high (we say the
  dimensions are multiplied by a scale factor of
  2).

12
Scale Drawings

• Copy the picture onto graph paper and label the
  coordinates. Multiply the coordinates of each
  point by 2, creating points A H. Plot these
  points on the same grid.
• What is the ratio of proportionality?

13
Activities

• Interactive Activity Quad Person
• http//www.learner.org/channel/courses/learningmat
  h/algebra/session4/part_c/index.html
• NLVM Transformation-Dilation
• Illuminations Shape Tool
• GSP Dilations
• Similar Figures
• Comic Expansions/Inca Birds

14
Part 2 Compare geometric figures for similarity
and describe similarities by listing
corresponding parts

• Unit 5

15
Congruent Triangles
Two triangles are congruent when they have the
same shape and the same size. Corresponding
angles are equal, and corresponding sides are
equal.
equal angles
a 6
c 11
d 6
e 11
b 9
f 9
equal angles
equal angles
16
Similar Triangles
Similar triangles are found in art, engineering,
architecture, biology, and chemistry. Two
triangles are similar when they have the same
shape (but not necessarily the same size) meaning
that one is a scaled up or down version of the
other.
17
In similar triangles, the measures of
corresponding angles are equal and corresponding
sides are in proportion.
d 6
a 3
e 10
b 5
c 8
f 16
Side a corresponds to side d, side b corresponds
to side e, and side c corresponds to side f.
18
Similar Geometric Figures?
Are these triangles similar?
What geometric figures are always similar?
19
Part 3 Find missing side lengths or areas in
similar figures

• Unit 5

20
Scaling Factors Proportions

• Since, similar figures have equal angles and
  proportional sides. the sides of one figure can
  be obtained by multiplying the other by the
  scaling factor or by setting up proportions.

21
Finding Unknown Lengths of Sides in Similar
Triangles
EXAMPLE
Find the length of the side labeled n of the
following pair of similar triangles.
n
9
8
14
SOLUTION
Since the triangles are similar, corresponding
sides are in proportion. Thus, the ratio of 8 to
14 is the same as the ratio of 9 to n.
22
Find Missing Side Lengths

• Why are the two triangles similar? (how were the
  angles formed?) How can you find the height of
  the lamp post?

How tall is the lamp post if it has a shadow 5
meters long, your friend is 2 meters tall and
your friends shadow is 1 meter long?
23
Shadows

• Because the suns rays are parallel, the
  triangles are similar.

24
Scale Factor

• NCTM E-Ex. Side Length Area of Similar Figures
• http//standards.nctm.org/document/eexamples/chap6
  /6.3/index.htm
• NCTM E-Ex Side Length, Volume, Surface Area
• http//standards.nctm.org/document/eexamples/chap6
  /6.3/part2.htm
• NCTM E-Ex Ratios of Areas
• http//standards.nctm.org/document/eexamples/chap7
  /7.3/index.htm

25
Scaling Laws

• Lengths always scale with the scale factor.
• Areas always scale with the square of the scale
  factor.
• Volumes always scale with the cube of the scale
  factor.

26
Unit 6 Values that Vary

• Students will be able to
• draw pictures and use manipulatives to
  demonstrate a conceptual understanding of
  proportion
• solve problems using proportional reasoning
• represent and recognize direct proportions and
  inverse proportions graphically, numerically, and
  symbolically
• determine and interpret the constant of
  proportionality in direct and inverse
  relationships and
• explain how a change in one variable affects
  another variable.

27
Part 1 Draw pictures and use manipulatives to
demonstrate a conceptual understanding of
proportion

• Unit 6

28
Ratios
A ratio is the quotient of two quantities. A
ratio is no different than a fraction except that
a ratio is sometimes written using notation other
than fractional notation.
The ratio of 1 to 3 can be written as
1 to 3
1 3
or
or
fractional notation
colon notation
The order of the quantities is important when
writing ratios. To write a ratio as a fraction,
write the first number of the ratio as the
numerator of the fraction and the second number
as the denominator.
29
Comparing Ratios

• The scientists at the research lab for Whodunit
  Jeans are trying to decide on just the right
  shade of blue for a new line of jeans. Being
  scientists, not mathematicians, the researchers
  decide to choose a color by mixing pure blue
  liquid and clear water together until they get
  just the right shade.
• The scientists have several beakers of liquid,
  some with blue liquid and some with clear water.
  They plan to mix these together in big bowls.
  Before they mix the liquids, they guess how blue
  the mixture will be.
• In each of the following problems, there are two
  sets (A and B) of blue-clear combinations to mix.
  Predict which set will be bluer, and explain your
  reasoning.

2
30
Mixture Blues
31
Proportions

• Figure 1 below shows two out of the three circles
  shaded, and Figure 2 below shows four out of the
  six circles shaded. Although Figure 2 has more
  circles, the ratio of shaded circles to total
  circles is the same. That is,

• A statement such as this, stating that one ratio
  is equal to another is called a proportion. It
  can be written in two ways as two equal
  fractions a/b c/d or using a colon, ab cd.
  The proportion is read as two is to three as
  four is to six."

32
Determining Whether Proportions are True
Sandy made some iced tea from a mix, using 12
tablespoons of mix and 20 cups of water. Chris
and Pat thought it tasted great, but they needed
30 cups of tea for their party. Lee arrived, and
they found they disagreed about how to make 30
cups that tasted just the same Chris It's
easy Just add 10 tablespoons of tea and 10 cups
of water. Increase everything by 10. Pat Wait a
minute. 30 is just 1 and a 1/2 times 20, so since
you add 1/2 as much water, add 1/2 the tea add
10 cups of water and 6 tablespoons of
tea. Sandy I think about it this way We used 12
tablespoons for 20 cups, so 12/20 3/5
tablespoons for 1 cup, so for 30 cups we should
use 30 x 3/5 18 tablespoons. Lee Wait 20 - 12
8, so you want to keep the difference between
water and tea at 8. Since there are 30 cups of
water, we should use 30 - 8 22 tablespoons of
tea. That will keep everything the
same. Critique each of these methods. Which
methods are the same? Which methods will really
produce tea that tastes the same?
33
Determining Whether Proportions are True
Like other mathematical statements, a proportion
may be either true or false. A proportion is true
if its ratios are equal. You can check if a
proportion is true by finding the decimal
equivalent on both sides. Also, in a true
proportion, the product of its means is equal to
the product of its extremes. These products are
called cross products.
if
then
product of extremes
product of means
34
Why Does it Work?

• The reason cross multiplication works is because
  you are really multiplying both sides of an
  equation by the product of the two denominators.
  This cross product property only works when
  solving a proportion. It does not apply when
  doing operations with fractions, such as
  multiplying or dividing fractions. Using cross
  multiplying inappropriately is a common mistake
  many students make.

35
Solve Proportions

• Capture-Recapture
• Wildlife biologists use a method called
  capture-recapture to estimate animal
  populations. This method involves tagging some
  animals and then releasing them to mingle with
  the larger population. Later, a sample is taken.
  Using the ratio of tagged animals in the sample
  to total animals in the sample, biologists can
  estimate the animal population.
• Activity Use a bag of white beans to represent
  the population of fish in a lake. Reach into the
  lake and grab a handful of fish. Replace
  these white beans with red beans to represent the
  tagged fish. Allow the new fish to mingle and
  then take several samples. Record your results.
  Set up a proportion to estimate the entire
  population using the samples.

36
Absolute vs Relative Comparisons

• Suppose there are two classes in a school, one
  with 20 students and one with 25. If the first
  class has 10 girls and the second class has 12,
  which class has more girls?
• If you said that the second class has more girls,
  you're making an absolute comparison. You
  probably thought that 12 is 2 more than 10, so
  there are more girls in the class with 12.
• If you said that the first class has more girls,
  you're making a relative comparison. You probably
  thought 10 is half of 20, and 12 is less then
  half of 25, so there are more girls in the class
  with 10.
• Clearly these are two different interpretations
  of "more." Although both interpretations are
  correct, in some cases it is more appropriate to
  look at relative rather than absolute
  comparisons. For example, compare an all-girl
  class of 20 students with a class of 25 students,
  22 of whom are girls. In a sense, there are
  "more" girls in the class with 20.
• http//www.learner.org/channel/courses/learningmat
  h/algebra/session4/part_c/index.html

37
Absolute vs Relative Scaling

• Draw a right triangle ABC with legs 3 and 4 cm
  and hypotenuse 5 cm.
• Draw a second triangle whose legs are double the
  first triangle (6, 8, 10 units).
• Draw a third triangle whose side lengths are each
  2 cm more than those of the first triangle. That
  is, the lengths are 5 cm, 6 cm, and 7 cm.
• Which of the new triangles looks similar to the
  original triangle?

38
Part 2 Represent and recognize direct
proportions and inverse proportions

• Unit 6

39
Converting Measurements

• This table shows the lengths, in both miles and
  kilometers, of the worlds longest ship canals.
  Two values are missing from the table. In this
  investigation youll learn several ways to find
  the missing values.
• This graph shows the lengths, in both miles and
  kilometers, of eight of the worlds longest ship
  canals. Use the graph to estimate the length in
  kilometers of the Suez Canal, which is 101 miles
  long.
• Notice that if we extend the line, the line will
  go through the origin.

40
Direct Variation

• The relationship between kilometers and miles is
  an example of a type of relationship called a
  direct variation. In a direct variation, the
  ratio of two variables is constant.
• An equation of the form ykx is a direct
  variation. The quantities represented by x and y
  are directly proportional, and k is the constant
  of variation.

41
Representations of Direct Variation

• If two variables change so that their ratio is
  constant, the variables vary directly.
• From the table we can see that the variable y is
  always 4 times the variable x. 
• Direct variation can be expressed as a linear
  equation. A formula for this relationship is
• y 4 x or y/x 4
• Graphically, we can see that y increases when x
  increases and that y increases four times as fast
  as x and the line goes through the origin.

42
Examples of Direct Variation

• The circumference of a circle varies directly as
  the diameter, C kD
• The distance an object will fall varies directly
  as the square of the time, d kt2
• The volume of a gas in a container at a constant
  pressure varies directly as the absolute temp, V
  kT

43
Speed vs. Time

• The time it took to walk 2 meters by 6
  individuals was recorded in the table above and
  the average speeds were computed. (How?) Write an
  equation to represent this relationship. (Hint
  How are the numbers related?)

44
Inverse / Indirect Variation

• In the speed versus time investigation, the
  product of the speed and total time was constant.
  Such a relationship is called an inverse
  variation, and the variables are said to be
  inversely proportional.
• An equation of the form y k/x is an inverse
  variation. Quantities represented by x and y are
  inversely proportional, and k is the constant of
  variation.

45
Representations of Inverse Variation

• If two variables change so that one equals a
  constant divided by the other, the variables vary
  indirectly or inversely.
• From the table we can see that xy is always 28
• Symbolically, y varies indirectly with x when 
• xy k or y k/x.  
• Graphically an indirect variation is a curve, not
  a straight line as in the direct variation.

46
Examples of Inverse Variation

• The lengths of the base and height of a triangle
  with constant area.
• The volume of a gas in a container with a
  constant temperature varies indirectly with the
  pressure, V P k
• When a constant force is applied to a massive
  object the acceleration experienced by the object
  varies indirectly with the mass, m a k
• To travel a certain distance at a constant speed,
  the speed varies indirectly with the time it
  takes to make the trip, s t k
• The severity of an itch varies indirectly with
  the ability to reach it, S R k

47
Part 3 Solve problems using proportional
reasoning

• Unit 6

48
Proportional Relationships

• All proportional relationships have the equation
  y kx, where k is some constant number. A line
  graph represents a proportional relationship only
  when the line goes through the origin (0, 0).

49
An Astros baseball player makes 3 hits in every 8
times at bat. At this rate, if he made 12 hits,
find how many times he batted.
Problem 1

• Understand.

• Solve.

3x 3x 96 x 32

• Translate. Let x number times at bat.

• Interpret

At this rate, the player would make 12 hits in 32
at bats.
50
More Problems

• Problem 1 Exhausted Examiners Elke and Faye
  corrected final exams at the same rate but Elke
  got a head start. When Elke had completed 12
  exams Faye had finished only 4. When Elke had
  finished 60 exams, how many exams had Faye
  completed? Problem 2 A Metric Conversion If 6
  inches is 15.24 cm, 9 inches is how many
  centimeters? Problem 3 An Exchange Rate If 5
  Canadian dollars can be exchanged for 4 US
  dollars, what is 35 Canadian dollars worth in US
  dollars? Problem 4 Taken for a Ride A taxicab
  charged 1 plus 50 cents a mile. If it costs 3
  to go four miles, how much would it cost to go 6
  miles? Of Problems 1-4, which are proportion
  problems and which are not? Briefly justify your
  answers. To distinguish between problems having
  a direct proportion and nonproportion problems,
  it can be helpful to record the data in a table
  and graph it. Draw a line connecting the dots of
  the graph and if necessary, extend the line so
  that it intersects the left or bottom side of the
  graph. Graph Problems 1-4. Graphs of directly
  proportional relationships have what
  characteristics? Why do these graphs have these
  characteristics? In what way are they different
  from graphs of nonproportional situations?
  (Source Adapted from Fostering Children's
  Mathematical Power. An Investigative Approach to
  K-12 Mathematics, Arthur J. Baroody, with Ronald
  T. Coslick, c. 1998 by Lawrence Erlbaum
  Associates, Mahwah, NJ.)

51
Tortoise and the Hare

• Achilles runs at a constant rate of 9 miles per
  hour, and the tortoise moves at 1 mile per hour.
  a) Suppose that Achilles catches up to the
  tortoise in 1 1/2 hours. How much of a head start
  did the tortoise get?b) The tortoise has taken
  some "turtle speedup potion" and can now walk at
  2 miles per hour. If Achilles still runs at 9
  miles per hour and catches up to the tortoise in
  3 hours, how much of a head start did the
  tortoise get?c) Use Excel to graph the
  relationships for parts a and b.

52
Distance, Rate, and Time
Seven cars are near an intersection. The graph
below show the distances between cars and the
intersection as time passes.
In what direction is each car moving in relation
to the intersection? How do the cars speeds
relate to the steepness of the lines? Is the
relationship between distance and time
proportional for any of the cars?
53
Five Brother Race

• Five brothers ran a race. The twins began at the
  starting line. Their older brother began behind
  the starting line, and their two younger brothers
  began at different distances ahead of the
  starting line. Each boy ran at a fairly uniform
  speed. Here are the rules for the relationship
  between distance (d meters) from the starting
  line and time (t seconds) for each boy
• Adam d 6t
• Brett d 4t 7
• Caleb d 5t 4
• David d 5t
• Eric d 7t 5

54
Five Brother Race (cont.)

• Which line above represents which brother? (label
  the graph)
• For each brother, describe how far from the
  starting line he began the race and how fast he
  ran.
• Which brothers relationships between distance
  from the starting line and time are proportional?
  How do you know?
• Which two brothers stay the same distance apart
  throughout the race? How do you know, based on
  their graphs? How do you know, based on their
  equations?
• If the finish line was 30 meters from the
  starting line, who won the race?

55
Part 4 Determine and interpret the constant of
proportionality in direct and inverse
relationships

• Unit 6

56
Direct Proportions

• Proportional relationships are the relationships
  between two variables in which the ratio remains
  constant. An example of direct proportional
  quantities is the relationship between the hours
  worked and the amount of money a worker earns. If
  you earn 12 dollars per hour, then you will earn
  12 dollars in 1 hour. If you earn 6 dollars per
  hour, then it will take you twice as long to earn
  the same 12 dollars.
• Directly proportional relationships have a
  constant of proportionality. It can be found from
  the ratio of the outputs to the inputs. What is
  the constant of proportionality for the above
  relationship? How does this relate to the graph
  of the data? How long will it take you to earn 60
  dollars if you earn 5 dollars per hour? 10
  dollars per hour? How much must you make in order
  to earn 60 dollars in 5 hours? 3 hours?

57
y kx or y/x k

• 1. Write the equation for the following
  conditions y varies directly with x and when x
  12, y 36. 
• Solution The equation in most general form is y
  kx.  Replace x with 12 and y with 36 to find
  the value of k 36 12k.  Solving for k, we get k
  3 and the equation becomes y 3x.
• 2. Suppose that y varies directly with x. When x
  10, y 25. Find y when x 6.
• Solution Use the first conditions to find the
  constant of variation in y kx. We substitute
  known values to get 25 k (10). So k 25/10
  5/2 2.5. Now replace k and the value given for
  x in the equation to obtain y 2.5 (6) 15.

58
Inverse Proportions

• Inverse relationships are the relationships
  between two variables in which the product is
  held constant. An example of inversely
  proportional quantities is the relationship
  between the speed and time it takes to travel a
  fixed distance. If you drive 60 mph, you can
  drive 60 miles in 1 hour. If you drive 30 mph, it
  will take you 2 hours to drive the same 60 miles.
  
• Inversely proportional relationships have a
  constant of proportionality. It can be found from
  a combination of the speed and time that works
  for all pairs of speed and time. What is the
  constant of proportionality for the above
  relationship? How does this relate to the graph
  of the data? How long will it take you to drive
  60 miles if you drive at 2 mph? 25 mph? 65 mph?
  How fast must you drive to cover the 60 miles in
  5 hours? 3 hours?

59
y k / x or xy k

• 1. Find the constant of variation if y varies
  indirectly with x and y 30 when x 5. 
• Solution The most general equation is xy k. 
  Substitute x and y to get k  5(30) k, and k
  150.  The equation for the given conditions is 
  xy 150.
• 2. Suppose that h varies indirectly with g.  When
  g 3, h 12.  Find h when g 15.
• Solution First, we find the constant of
  variation. The equation is hg k, so (12)(3) k
  36.  Now substitue for g and k to get h(15)
  36. The solution is h 36/15 2.4.

60
Part 5 Explain how a change in one variable
affects another variable

• Unit 6

61
Tulip Walkathon Race Announcement

• A Tulip Walkathon is to be held the morning of
  your schools tulip bulb sale, with all finishers
  receiving a shirt with the winning tulip logo
  imprinted on it. Several students are planning to
  participate in the 10K race, but they arent sure
  how long it might take them to walk this
  distance.

• GPS Grade 7 Webcast TI-83 Plus - Algebra
• http//www.georgiastandards.org/mathframework.aspx
  

62
Preparing for the Tulip Race I

• Three students conduct an experiment to determine
  their walking rates.

63
Preparing for the Tulip Race II

• Organize a table that shows the distance walked
  by each of the students after various numbers of
  seconds.

64
Determining Walking Rates for the Tulip Race

• Complete the table.
• What is each students walking rate in terms of
  t?

65
Preparing to Visualize Walking Rates for the
Tulip Race

• Before a scatter plot of the walking rates can be
  viewed,
• Clear all existing lists.
• 2nd CATALOG, Down Arrow to ClrAllLists (or press
  C to move to the commands beginning with C),
  press ENTER to paste the command to the home
  screen, and press ENTER again.

66
Entering Walking Rate Data

• Enter the time into L1.
• Enter Joshs distance (y-coordinates) into L2.
• Move the cursor above the horizontal line to L2
  and press ENTER.
• Paste L1 (2nd 1) after the and press ENTER.
• Enter Jennis distance (y-coordinates) into L3.
• Enter Janelles distance (y-coordinates) into L4.

67
Plotting Walking Rate Data for Josh

• Plot a scatter plot for all three students on the
  same graph.
• Press 2ND STAT PLOT (Y).
• Select 1Plot1 by pressing ENTER.
• Move cursor to On using the left arrow and press
  ENTER.
• Down arrow to Type, arrow to scatter plot, and
  press ENTER.
• Down arrow to XList, press 2nd L1 (above 1), and
  press ENTER.
• For YList, press 2nd L2 (above 2), and press
  ENTER.
• Select the point as the Mark and press ENTER.

68
Plotting Walking Rate Data for Jenni

• Plot a scatter plot for all three students on the
  same graph.
• From the Plot1 screen up and right arrow to Plot2
  and press ENTER.
• Move cursor to On using the left arrow and press
  ENTER.
• Down arrow to Type, arrow to scatter plot, and
  press ENTER.
• Use L1 for XList.
• For YList, press 2nd L3 (above 3), and press
  ENTER.
• Select the as the Mark and press ENTER.

69
Plotting Walking Rate Data for Janelle

• Plot a scatter plot for all three students on the
  same graph.
• From the Plot2 screen up and right arrow to Plot3
  and press ENTER.
• Move cursor to On using the left arrow and press
  ENTER.
• Down arrow to Type, arrow to scatter plot, and
  press ENTER.
• Use L1 for XList.
• For YList, press 2nd L4 (above 4), and press
  ENTER.
• Select the ? as the Mark and press ENTER.

70
Visualizing Walking Rates for the Tulip Race

• Press Y to make certain that no equations are
  turned on.
• Use ZOOM, 9 ZoomStat or Adjust WINDOW settings
  and press GRAPH.

71
Interpreting the Walking Rate Graph

• TASKS FOR STUDENTS
• For each of the three students, describe the
  relationship between the time and the distance
  walked.
• What equation do you think models each
  relationship if d represents distance in meters
  and t represents time in seconds?
• Josh d t
• Jenni d 1.5t
• Janelle d 2t
• Describe how the walking rate affects the
  steepness of the graph and the equation.

72
Testing Your Tulip Walkathon Equation for Janelle

• Turn off Joshs plot and Jennis plot.
• Press Y, up and right arrow to Plot1 and press
  ENTER.
• Right arrow to Plot2 and press ENTER.
• Type Janelles proposed equation in Y3 with Y3
  representing distance and x representing time.
• Press GRAPH.
• Question for Students
• How well does your equation fit Janelles data?

73
Testing Your Tulip Walkathon Equation for Jenni

• Turn off Janelles plot.
• Press Y, up and right arrow to Plot3 and press
  ENTER.
• Turn on Jennis plot
• Arrow to Plot2 and press ENTER.
• Turn off Janelles equation by moving the cursor
  on top of the after Y3 and pressing ENTER.
• Type Jennis proposed equation in Y2.
• Press GRAPH.
• Question for Students
• How well does your equation fit Jennis data?

74
Testing Your Tulip Walkathon Equation for Josh

• Turn off Jennis plot.
• Press Y, arrow to Plot2, and press ENTER.
• Turn on Joshs plot.
• Arrow to Plot1 and press ENTER.
• Turn off Jennis equation by moving the cursor on
  top of the after Y2 and pressing ENTER.
• Type Joshs proposed equation in Y1.
• Press GRAPH.
• Question for Students
• How well does your equation fit Joshs data?

75
Viewing and Predicting Total Walking Time from
Graphs

• Turn on all PLOTS and Y equations.
• Press GRAPH.
• Press TRACE and up arrow to view the Y
  (predicting) equations.
• Type 11 on Jennis equation (Y2) and press ENTER.
• Note that entering a number larger than the xmax
  in the WINDOW settings will produce an error
  message.
• Increase the xmax value to fix this problem.

76
Viewing and Tracing on Line Plots for Josh,
Jenni, Janelle

• Turn off all Y equations
• Move cursor to and press ENTER.
• Turn on all PLOTS and change plot type to
  connected (line plot) rather than scatter.
• Press GRAPH.
• Press TRACE and left or right arrow to move along
  the plot.
• Up or down arrow to toggle between Plot1, Plot2,
  and Plot3 and then right or left arrow to move
  along the plot.

77
Predicting Total Walking Time

• Go to the HOME screen (2nd QUIT).
• Determine the distance traveled by each student
  in 30 minutes.
• Select VARS, right arrow to Y-VARS, and press
  ENTER.
• Select Y1 and press ENTER.

78
Predicting Total Walking Time for Josh

• If Josh takes 30 min to walk 1800 m, how long
  will it take him to walk 10K (10,000 m), assuming
  he maintains the same pace throughout the race?
• How should you interpret the calculator answer?
• Exactly how long in terms of hours, minutes, and
  seconds will it take Josh to walk 10K?
• 2 hours, 46 minutes, and 40 seconds (2/3 of a
  minute)
• Note MATH 1gtFrac converts decimals to fractions.

79
Predicting Total Walking Time for Jenni and
Janelle

• If Jenni takes 30 min to walk 2700 m, how long
  will it take her to walk 10K (10,000 m), assuming
  she maintains the same pace throughout the race?
• Exactly how long in terms of hours, minutes, and
  seconds will it take Jenni to walk 10K?
• 1 hour, 51 minutes, and 7 seconds (1/9 of a
  minute)
• Recall MATH 1gtFrac converts decimals to
  fractions.
• If Janelle takes 30 min to walk 3600 m, how long
  will it take her to walk 10K (10,000 m), assuming
  she maintains the same pace throughout the race?
• Exactly how long in terms of hours, minutes, and
  seconds will it take Janelle to walk 10K?
• 1 hours, 23 minutes, and 20 seconds (1/3 of a
  minute)