Middle School Workbook 2015

Middle School Workbook
2015
Page 1
Note to the Teacher:
Our 2015 workbook is designed for students to engage in activities as they
explore Kings Dominion. Rocket Research and How High is High? are activities
intended for education days with the MathScience Innovation Center. The rest
of the activities that follow can be completed any day in the park. One goal of
the activities is to encourage students to see how mathematics and science are
everywhere – and that includes fun places like Kings Dominion.
Please note that the activities in this workbook are open-ended to allow for
exploration and discovery. Another important aspect of students’ work that you
will see in this workbook is the central role of explanation and the sharing of
ideas. Collaboration on activities and tasks is highly encouraged and all
members of the team must be able to understand and explain how their team
arrived at their results.
Finally, please encourage students to try. Many times students wait for exact
instruction from a teacher before they engage in a task only to mimic the steps
given to them. The activities in this workbook, though guided, are intended to
give students some latitude in searching for mathematics and science concepts
gently tucked away in the fun at the park.
Page 2
What’s in this workbook?
Name
Rocket Research
Common Core
Virginia Standards of
Learning (SOL)
Major concept/task
6.EE.9
m4.7
Set up and test a variable
(Education Days Only)
PS.10
Rate the Ride
Watching Winners
s3.1 s4.1 s5.1
s6.1 s7.1 s8.1
LS.1
m8.17
What a Wonderful Day
m4.13 m4.14 m5.14
m7.9
s4.6
My KD Mascot
s3.4 LS.9
How High is High?
7.SP.5 7.SP.6
S.MD.5
4.MD.6
G.SRT.8
m5.11 m8.6 T.9
(Education Days Only)
Shape Search
3.G.1
Thought for Food
6.RP.1
8.F.4
7.RP.2
m3.14 m4.12 m5.13
m6.13 m7.7
m6.1 m6.2 m7.4
m8.3
5.G.1
6.NS.5
We Are Here, Where
Are You?
Coaster Quests
F.BF.1 F.LE.1
m6.11
m8.16
8.14 A.11 AFDA.2
AFDA.3 AII.4 AII.9
Page 3
Design a rating system using
qualitative data
Gathering data from
experimental probability
Use knowledge of weather to
rate the day for outdoor
activity
Apply knowledge of
environment to animal habitat
Measure angles and use a table
to find the height of an
inaccessible object
Recognize geometric shapes in
real world setting
Estimate measures and apply
ratios
See how coordinates help
communicate mathematics in a
real world application
Finding the curve of best fit
Rocket Research
At Kings Dominion, try your hand at an experiment at the Rocket Research table. With a
partner design a rocket and launch it up, up and away. It’s as easy as 3-2-1.
3. Choose your nose cone.
2. Choose your fins (number of fins and shape).
1. Design 2 identical rockets with one small change.
My Hypothesis:
Identify the following:
Independent Variable
Dependent Variable
Constants
Now test your prediction. Set up your experiment so all the variables are the same except the
one thing you and your partner switched.
What were the results?
What can you conclude about your experiment?
Do your results make sense?
Yes
or
No
Why or Why not?
Does your experiment mean those same results will happen every time?
Be prepared to explain and share your answer.
Page 4
Yes
or
No
Rate My Ride
Part of your time at Kings Dominion is seeing how many rides you can discover during your stay. It’s very
difficult to ride every ride in a single day. Choices need to be made. Designing a metric can help you
determine which rides you should tackle today.
To begin, list 5 aspects of rides that are important to you when deciding which rides you want to ride.
List them below.
Important When Choosing A Ride
Now score each one based on how important it is to you. (1 through 10 – 1 is the lowest, 10 is the
highest)
Length
of
ride
is
important to me, so I
am going to give my
favorite ride, the Rebel
Yell, a 9.
Using your system, determine which ride you should go to first. Which
one would be next? And next?
1.
2.
3.
Now look at the map of the park. Estimate how long it will take you to ride your top 3
rides including travel time to each ride. ____________
What factors did you use to help you make your estimate?
Does this affect the order? Yes or No.
Why or why not? Explain
Page 5
Watching Winners
Is there a way to increase your odds of winning a big prize without the need to spend a small fortune?
Or, at least figure out how often you have to play a game before you are fairly certain you will win a
prize?
Just as athletes and coaches watch their opponents play to figure out a way to win, so can you. Find a
game or prize that you like. Now stand back and watch to see how often someone wins a big prize.
Keep track of how often the game is played (with wins and losses too). Also note skill. Is there
something the winner did differently to help them win?
Special skill or technique needed:
Calculate the experimental probability of winning the game?
Is your ratio about what you expect to happen in the park every day?
Conclusion:
Page 6
Yes or No Explain.
What a Wonderful Day
What would be the perfect day at Kings Dominion? Using your knowledge of weather,
determine which factors mean the most to your day at the park. Is it better to be 80 degrees
and humid or 85 degrees and dry? Use your own scale to find the perfect conditions then rate
the day.
Weather includes factors such as temperature, humidity, sunniness, cloudiness, rain, and wind.
Determine the recipe for the perfect day. Place a mark in each row to help determine your perfect day.
More of
↙ This
Factor
Equal
Amounts
More of
This ↘
Factor
Cloudy
Sunny
Humid
Dry
Calm
Windy
Dry
Rain
Hot
Cold
Write a sentence or two that describes your perfect day:
Is there a different kind day that can be “equally perfect”? Yes or No (be prepared to defend your answer)
Page 7
My KD Mascot
Spend some time walking the park looking at all the things that make up the Kings Dominion
environment. Now, using your knowledge of animals (or you can search the web), pick the best
animal to be a KD mascot in the park.
Which animal would you choose?
What environment is
normally best suited for
your animal?
List 3 environmental
factors of Kings Dominion
that matter to animals
1.
2.
3.
How is your animal
prepared to handle those
conditions?
1.
2.
3.
Where is your animal
going to sleep?
What traits would your mascot need to develop that would make him/her better suited for life at Kings
Dominion?
Is there anything that Kings Dominion can do to help sustain the animal’s environment?
Page 8
How High is High?
Clinometer Template
*This activity is 3 pages*
TAPE WEIGHTED STRING HERE
TAPE STRAW HERE
* For best results, print on cardstock
Mathematics allows us to go places we cannot get to. Using a clinometer, you can figure out
the distance (or in this case the height) of an object using your line of sight (eye).
DIRECTIONS: Cut out the template above. Use a piece of sting or yarn a little longer than the 0line above and a weight (like a washer). Tie the washer to one end of the string and tape the
other end to the marked vertex above. Tape the straw as shown above.
USE: The easiest way to use it is look through one end while a partner
reads the angle where the string is dangling.
25˚ angle
Page 9
How High is High? (continued)
Proportions can be extremely useful when trying to calculate unknown values. The table of
values below is the ratio of legs of a right triangle listed by the angle measure of one of the
angles. Because it is a ratio, we can use it to find an unknown value – in this case the height of
an object! All we need is the distance we are from the object, and the angle from where we are
to the height of that object.
Height
Distance
Angle
Tan.
Angle
Tan.
Angle
Tan.
Angle
Tan.
Angle
Tan.
Angle
Tan.
1°
2°
3°
4°
5°
6°
7°
8°
9°
10°
11°
12°
13°
14°
.02
.03
.05
.07
.09
.11
.12
.14
.16
.18
.19
.21
.23
.25
15°
16°
17°
18°
19°
20°
21°
22°
23°
24°
25°
26°
27°
28°
.27
.29
.31
.32
.34
.36
.38
.40
.42
.45
.47
.49
.51
.53
29°
30°
31°
32°
33°
34°
35°
36°
37°
38°
39°
40°
41°
42°
.55
.58
.60
.62
.65
.67
.70
.73
.75
.78
.81
.84
.87
.90
43°
44°
45°
46°
47°
48°
49°
50°
51°
52°
53°
54°
55°
56°
.93
.97
1.00
1.04
1.07
1.11
1.15
1.19
1.23
1.28
1.33
1.38
1.43
1.48
57°
58°
59°
60°
61°
62°
63°
64°
65°
66°
67°
68°
69°
70°
1.54
1.60
1.66
1.73
1.80
1.88
1.96
2.05
2.14
2.25
2.36
2.48
2.61
2.75
71°
72°
73°
74°
75°
76°
77°
78°
79°
80°
81°
82°
83°
84°
2.90
3.08
3.27
3.49
3.73
4.01
4.33
4.70
5.14
5.67
6.31
7.12
8.14
9.51
Don’t take our word for it, try for yourself. Make 2 right triangles that
have the same angles but different lengths for its sides. Use a fraction
to compare the sides to one another, see what you discover!
Page 10
How High is High? (continued)
Luckily, at Kings Dominion has some distances marked off for you. When you find a distance
marker you can use your clinometer to find the angle from your position to the top of the
object you want to know the height of. Once you have the angle you can find the ratio for any
right triangle with that angle measure - no
Is it okay to have a ratio represented as a
matter what size! (That is some powerful
decimal? A good topic for discussion.
mathematics!)
So, how many heights can you calculate around the park?
Use the chart below to record your findings.
Ride
Angle
Distance
from Ride
Ratio Needed
Calculations
HEIGHT
BONUS QUESTION: Mark found that from where he was standing, the Eifel Tower and the
tallest hill on the Rebel Yell were the same distance to his position. He predicted that they
would be the same height since he was the same distance from the two rides. Is Mark’s
prediction correct? Explain using mathematical thinking and your knowledge of finding heights.
Page 11
Shape Search
Shapes, shapes are everywhere. Shapes are easy to find at Kings Dominion.
However, can you find specific shapes in the park? Find as many different shapes
that fit the trait(s) below as you can.
Have fun. With a partner, give yourself a set amount of time to find shapes around
the park. How many can you find in 20 minutes? Can you find more than your partner?
Use the chart below to keep track.
Trait(s)
Find a three sided shape.
Location
Base of the first hill
on the Ricochet.
Shape Name
triangle
Find a shape with 3 equal sides
Find a shape with only 1 pair of
parallel sides
Find a shape with 4 equal sides
but at least two different angle
measures
Find a shape with 5 sides
Find a shape with 8 sides
Find a shape with 4 equal sides
and no right angles
Find a shape with more than 2
sets of parallel sides
BONUS: Find 2 shapes that are
congruent
BONUS: Find 2 shapes that are
similar but not congruent
Number of different shapes: 1 to 3 Amateur Sleuth
4 to 6 A Searching Professional
7 or more The Great Finder! Look out Euclid!
Page 12
Sketch It
Thought for Food
You are the newest food critic for Kings Dominion. However, unlike most food critics that just say food is
good or bad, you get to put your mark on the park! Do you like fries? Then like a good chef you find a
way to make the fries taste zee best! Maybe it’s hotdogs. A plain hotdog is okay but with the right
amount of relish and mustard, it becomes your masterpiece.
So what is your perfect recipe? Find you favorite food in the park and explain how you perfect it. Once
you have your perfect recipe scale it for all to enjoy.
ITEM
Water
ADDITIONS
Lemon
Wedge
AMOUNT
1 wedge
SCALE
1 wedge
8 oz. water
SIZES/AMOUNT
AVAILABLE
8 oz. – 1 wedge
Be sure the wedge is about
12 oz. – 1.5 wedges
this shape or else
24 oz. – 3 wedges
Page 13
SPECIAL NOTES
the water tastes
too bitter.
We are Here, Where are You?
How do we describe things? There are many ways. One way is to use mathematics to describe
a person, place or thing. Let’s look at an example. Below is a group of points. Pick one. Now
describe which point it is so you’re certain a person can locate your specific point.
Was it easy? Are some points easier than others? Mathematics can help us describe the
location of something easily.
Wikipedia.com
On the next page locate a point. Describe which point it is so you’re certain a person can locate
your specific point.
Page 14
We are Here, Where are You? (continued)
A
F
C
B
D
E
G
I
H
J
Was that easier? Labels make describing a location much easier. What happens when you have too
many objects to label them all? One way is to create a locating system for the object. If you have ever
looked at an atlas or played battleship, then you have seen a grid system which allows each and every
point on a piece of paper to have a specific, named location. You can create your own system to locate
rides, people, food, etc.
And, like the dots above, labels make a big difference.
Wikipedia.com
Page 15
We are Here, Where are You? (continued)
** Remember to make 2 identical maps for you and your partner **
You and a friend can text coordinates and find each other easily. Try it!
Page 16
Coaster Quests
How do you make a coaster? Roller Coaster Mania® is a game you can use to design coasters, but how
do you know which ones will work in real life? One way is to see the coasters that are at Kings Dominion
right now and see if you can find a mathematical model to describe the coaster. Then you can use that
model to create one of your own.
The process of curve fitting allows you to create a mathematical function that can best fit a data set. In
this case, we are using the data from a picture. If you have a TI-nSpire® calculator you can upload the
picture and find the curve of best fit.
A few questions that may need to be answered as you attempt to find a function for your curve.
1. Where does the curve start and end?
2. Does this curve have a name (e.g. parabola)?
3. How can you tell which curve (of fit) is the correct curve?
4. Should I have ketchup with my boardwalk fries or vinegar?
Use your smart phone to take a picture of a curve on any of the coasters in the park. You can
upload that picture to some graphing calculators and find the curve of best fit. Texas
Instruments makes software that links your calculator right to your computer. Check out
www.education.ti.com for more information.
Math Tip
Remember, a mathematical function will “fit itself” to any data set – it’s your job to see if
that curve is the right one. Regression is a statistical method that can assist in finding the
uncertainty of your fit. That is what r and r2 values are for -- to help you determine if the
model fit the data well. Using a graphing calculator you can find if a curve fits a specific set
of data, but you also need to know how well your model fit the data.
Is there a specific model used on the first hill of all coasters? Explore and find out.
Page 17
Coaster Quests (continued)
Try this!
Hold this piece of paper up and find a curve on a coaster. Plot at least 10 points for the curve for which
you want to find the function. Now find the coordinates of those points. This data can now be
transferred to a graphing calculator.
Now Plot your points.
(
(
(
(
(
(
,
,
,
,
,
,
)
)
)
)
)
)
(
(
(
(
(
(
,
,
,
,
,
,
)
)
)
)
)
)
Not sure how to enter points into a graphing calculator? Check out:
http://mathinscience.info/public/0%20how%20to/83_how_to/graph_interp.pdf (This activity also has
information on linear regression – in case you need it.)
Page 18