Middle School Workbook
Page 1 Note to the Teacher:
Our Education Days 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.
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What’s in this workbook?
Name Common Core Virginia Standards of Major concept/task Learning (SOL) Rocket Research 6.EE.9 m4.7 s3.1 s4.1 s5.1 Set up and test a variable (Education Days Only) s6.1 s7.1 s8.1 LS.1 m8.17 Rate the Ride PS.10 Design a rating system using qualitative data Watching Winners 7.SP.5 7.SP.6 m4.13 m4.14 m5.14 Gathering data from S.MD.5 m7.9 experimental probability What a Wonderful Day s4.6 Use knowledge of weather to rate the day for outdoor activity My KD Mascot s3.4 LS.9 Apply knowledge of environment to animal habitat How High is High? 4.MD.6 m5.11 m8.6 T.9 Measure angles and use a table (Education Days Only) G.SRT.8 to find the height of an inaccessible object Shape Search 3.G.1 m3.14 m4.12 m5.13 Recognize geometric shapes in m6.13 m7.7 real world setting Thought for Food 6.RP.1 7.RP.2 m6.1 m6.2 m7.4 Estimate measures and apply 8.F.4 m8.3 ratios We Are Here, Where See how coordinates help Are You? 5.G.1 6.NS.5 m6.11 m8.16 communicate mathematics in a real world application Coaster Quests 8.14 A.11 AFDA.2 Finding the curve of best fit F.BF.1 F.LE.1 AFDA.3 AII.4 AII.9
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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? Yes or No Be prepared to explain and share your answer.
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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 Using your system, determine which ride you should go to first. Which important to me, so I one would be next? And next? am going to give my favorite ride, the Rebel 1. Yell, a 9. 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
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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? Yes or No Explain.
Conclusion:
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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 Equal More of Factor Factor ↙ This Amounts This ↘
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)
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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 1. 2. 3. that matter to animals
How is your animal prepared to handle those 1. 2. 3. conditions?
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?
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How High is High? *This activity is 3 pages* Clinometer Template 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 0- line 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° .02 15° .27 29° .55 43° .93 57° 1.54 71° 2.90 2° .03 16° .29 30° .58 44° .97 58° 1.60 72° 3.08 3° .05 17° .31 31° .60 45° 1.00 59° 1.66 73° 3.27 4° .07 18° .32 32° .62 46° 1.04 60° 1.73 74° 3.49 5° .09 19° .34 33° .65 47° 1.07 61° 1.80 75° 3.73 6° .11 20° .36 34° .67 48° 1.11 62° 1.88 76° 4.01 7° .12 21° .38 35° .70 49° 1.15 63° 1.96 77° 4.33 8° .14 22° .40 36° .73 50° 1.19 64° 2.05 78° 4.70 9° .16 23° .42 37° .75 51° 1.23 65° 2.14 79° 5.14 10° .18 24° .45 38° .78 52° 1.28 66° 2.25 80° 5.67 11° .19 25° .47 39° .81 53° 1.33 67° 2.36 81° 6.31 12° .21 26° .49 40° .84 54° 1.38 68° 2.48 82° 7.12 13° .23 27° .51 41° .87 55° 1.43 69° 2.61 83° 8.14 14° .25 28° .53 42° .90 56° 1.48 70° 2.75 84° 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!
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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 matter what size! (That is some powerful Is it okay to have a ratio represented as a mathematics!) decimal? A good topic for discussion.
So, how many heights can you calculate around the park? Use the chart below to record your findings. Distance Ratio Needed Ride Angle Calculations HEIGHT from Ride
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.
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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) Location Shape Name Sketch It Base of the first hill Find a three sided shape. triangle on the Ricochet.
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!
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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.
SIZES/AMOUNT ITEM ADDITIONS AMOUNT SCALE SPECIAL NOTES AVAILABLE Water Lemon 1 wedge 1 wedge 8 oz. – 1 wedge Be sure the wedge is about Wedge 8 oz. water 12 oz. – 1.5 wedges this shape or else 24 oz. – 3 wedges the water tastes too bitter.
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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.
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We are Here, Where are You? (continued)
A B
C D E F
G H I
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
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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!
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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.
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 Math Tip 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.
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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.)
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