**Mathematics Badge**

(Discover Science & Technology)

*By Elizabeth Simmons and Margaret Chind, Pioneer Troop #100 Mama Leader
(Margaret's website: www.CreativeMadnessMama.com)
*

*The purpose of this badge is to show that math is much more than a bunch of numbers and equations. We use math everyday in a variety of ways and believe or not, it can even be fun!*

**Penguin (Do 3 requirements including the two starred)**

________1.* Learn to count from 1-20 vocally.

________2.* Be able to identify numbers 1-10 and 0 (zero).

________3. Learn to count to 100 or more.

________4. Learn how to write numbers 1-10.

________5. Discuss how math is used everyday. Take a day, and whenever you use math, (with a delighted squeal) point out, “I used math!” to your parent or caregiver.

________6. Learn how to skip count by 2’s and/or … by 5’s… by 10’s.

________7. Measure yourself in 3 ways - height, speed, weight, arm length, etc.

________8. Go on a shape scavenger hunt. Look at home and around town and find the following shapes: Square, Rectangle, Triangle, Circle and Star.

**Otter (Do 4 requirements including the two starred)**

________1.* Set a timer for 2 minutes. How many different ways can you name where you use math everyday? Examples may include measurements for recipes, grocery bills to add, dividing a sandwich in half, etc.

________2.* Measure yourself in 5 different ways. How tall are you? How much do you weigh? What size clothing do you where? How fast can your run? How long is your stride? These are just a few examples of the ways you can measure *You! *Be creative and come up with your own *You* things to measure.

________3. Go on shape scavenger hunt. Look at home and around town and find the following shapes:

Square

Rectangle

Triangle

Circle

Oval

Hexagon

Pentagon

________4. Make a prediction about whether most people wear shoes with shoelaces or without. Now, make a chart with shoelaces written on one side, and no shoelaces written on the other with a line in between. Pick somewhere to sit where you can see a lot of people’s feet. Try the mall, a park bench, maybe a restaurant. Using tally marks, spend 10 minutes noting who is wearing shoelaces and who is not on your chart. Was your prediction right? Would it be the same if you only counted men’s shoes? Or just women’s? Would it be different at a different time of year?

________5. Learn to play “Pyramid Solitaire.” Using a deck of cards, shuffle and deal the cards on the table face up in the shape of a pyramid. On top should be one card, then the next two should slightly overlap the first, then three, four, five, six and seven. Once your pyramid is seven layers you are ready to play.

The object is to remove pairs from your pyramid that equal 13 when added together. Only cards that are exposed (no card is still covering any portion of it) can be removed. So when you start, you can only remove cards from the lowest level of your pyramid. As you remove cards, you will expose cards higher up that you may then use to make pairs. A Jack is worth 11, a Queen 12, and a King is 13. Therefore any exposed King may be immediately removed as it does not need a match. A Jack would pair with a 2, a Queen with an Ace, an 8 with a 5, etc.

If there are no pairs exposed, flip over the first card in your remaining deck and try to match it with an exposed card. If no match can be made, flip over the next card, etc. The object is to remove your entire pyramid before you run out of cards in the deck.

________6. Learn a math magic trick. Cut out a piece of paper about 3” x 3”. Trace a dime in the center of the paper and cut out the circle you traced. Ask your audience, “Which of you can push a quarter through the hole without tearing the paper?” Unless they have seen the trick before, they will probably not be able to do it. When they give up, fold the paper in half and place the quarter inside the fold so that it sticks out slightly through the hole. Hold the folded corners of the paper and raise them up slightly. The hole will widen and the quarter will fall through. Diameters are not always what you think!

_______ 7. Read 3 math books such as the Anno books, The Doorbell Rang, Math Curse, One Hundred Hungry Ants, How Much is a Million? Find one you really like and either give an oral report to your troop or do an extra book report on it to show your teacher.

_______ 8. Play at least 4 board games that use math. Make a chart to show which games help people practice which skills. Determine which game covers the most math. Which one is the most fun?

_______ 9. Practice your math facts while jumping rope, dancing, dribbling a ball and singing a math song. Which way do you like best?

_______ 10. Watch a math video or TV show such as PBS’s Cyber Chase.

**Dolphin (Do 5 requirements)**

________1. Set a timer for 2 minutes. How many different ways can you name where you use math everyday? Examples may include measurements for recipes, grocery bills to add, dividing a sandwich in half, etc. If you did this as an Otter, see what new things you can come up with.

_______2. Measure yourself in 5 different ways. How tall are you? How much do you weigh? What size clothing do you where? How fast can your run? How long is your stride? These are just a few examples of the ways you can measure *You! *Be creative and come up with your own *You* things to measure. If you did this as an Otter, come up with 5 new ways to measure yourself.

________3. Draw a square on a piece of paper. Now draw one straight line anywhere across the square. How many pieces do you have? Can ever get more than 2 pieces by cutting the square with only one straight line? Now try two lines. How many pieces did you get? Number each piece to help you keep track. Now try it again and try to get different number of pieces with only two lines. An example is shown below. Continue this exercise with 3 lines. How many different number of pieces can you divide the square into? Now try 4 lines….5 lines…up to 10 lines. What do you notice?

1 line = 2 pieces 2 lines = 3 pieces 2 lines - 4 pieces

________4. Make a prediction about which takes more steps, to not step on any crack in a sidewalk, or to try to step on every crack. What happens if you just walk regularly? How many cracks do you think you will step on? Now, test your prediction. Choose a section of sidewalk 1 block long with regular sidewalk cracks.

First, walk the whole block regularly and count how many steps it takes. Write it down.

Then walk back regularly again and count how many cracks you stepped on. Write it down.

Now walk back again making sure to step on every crack. Count your steps and write them down. Last, walk back one more time, this time avoid every crack. Change the length of your stride only to avoid cracks. Count your steps and write them down. What conclusion can you draw?

________5. Go on shape scavenger hunt. Look at home and around town and find the following shapes:

Square Cube

Rectangle Rectangular Prism

Triangle Pyramid

Circle Sphere

Oval Cylinder

Hexagon Cone

Pentagon triangular prism

________ 6. Visit your local ice cream parlor and figure out how many combinations you could choose from if you wanted a 2 scoop cone. For example, if the ice cream parlor carries 3 flavors, chocolate, vanilla, and strawberry, you would have 6 different combinations to choose from. Chocolate with Chocolate, Chocolate with Vanilla, Chocolate with Strawberry, Vanilla with Vanilla, Vanilla with Strawberry, or Strawberry with Strawberry.

________ 7. Learn about exponential growth and maybe even earn some money at the same time. Offer to do the dishes every night (or some other chore that is not part of your daily routine). Tell your parent that you will charge 1 cent for the first day and each day you will charge twice as much as the day before. This may not sound like such a great deal for you, but look how the numbers grow if they are doubled each day. 1, 2, 4, 8, 16, 32, 64, 128, 254, 508, 1016, 2032, 4064, 8128. If you start with 1 cent on day one, you will be earning $81.28 to do the dishes by the end of two weeks. See how long it takes before your parents catch on decide they can no longer afford you.

________ 8. Memorize at least five math riddles, jokes or story puzzles. Present them to an audience of at least six people.

_______ 9. Play at least 6 board games that use math. Make a chart to show which games help people practice which skills. Determine which game covers the most math. Which one is the most fun?

_______ 10. Practice your math facts while jumping rope, dancing, dribbling a ball and singing a math song. Which way do you like best?

**Butterfly (Do 6 requirements )**

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_______ 1. Play a game of Poison. You will need a friend to play against and 12 small items that are the same such as rocks, bottle caps, beans, or toothpicks and one thing that is different. The different item is the poison. Put all items in a pile between you. Take turns removing either 1 or 2 things until only the poison is left. Whoever takes the poison loses. Can you figure out how to win every time? Is it better to go 1^{st} or 2^{nd}? What would happen if there were a different number of things? How would it be if you could take away 1, 2, or 3 things? Keep playing until you figure it out.

_______ 2. Make “kaleidoscope” designs with a compass (and ruler). Color them with beautiful colors. Give some away as small posters or the front of stationery. Use the compass to make a variety of sizes from small (about 2” diameter) to large (as wide as your compass can go)

_______ 3. If you toss a penny, the probability that it will land heads up is ½ , or 1 out of 2, but a penny does not always come up heads exactly ½ the time you toss it. That is what probability is all about. It is probable that it will land heads up ½ the time, but not guaranteed.

Toss a penny and a nickel in the air. What is the chance they will both land heads up? Since there are 4 ways the coins can land (HH, HT, TT, TH) there is a ¼ chance, or 1 out of 4, that both will land heads up. Toss your coins 10 times Make a chart to keep track of your tosses. How close to the theory do your tosses come? Toss the coins 20 times. Now how close did you come to your theory? Try 30 tosses. The more tosses you make, the closer you should come to a ¼ outcome.

_______ 4. You can buy insurance for just about anything. Lets suppose that someone wanted to buy insurance that it would not rain on their birthday, and if it did they would collect $100. Insurance companies rely on the theory of probability to decide how much to charge. If you are going to offer insurance on a no-rain birthday, the first thing you need to know is how many days does it rain each year? When are those days most likely to be? Should clients with birthdays in February pay more than clients with birthdays in July? Check an almanac for weather information. How much would you charge? How many people would need to buy your no-rain insurance to make sure that you would not lose money?

_______ 5. A palindrome is a number that looks the same both forward and backward such as 3223. You can find palindromes by using addition. Take any number and add it to the number that is made when you reverse the number. For example, 137 would be added to 731. The answer, 868 is a palindrome. Some numbers take longer before you reach a palindrome, but the method is the same. Take the number 68 and add it to its reverse, 86. You get 154 (which is not a palindrome), so add 154 to its reverse, 451, to get 605. Since 605 is not a palindrome, continue on and add 605 to its reverse, 506, to get 1111, a palindrome! Try to reach palindromes using at least 3 different numbers. Try 89 (just make sure you have a LOT of paper).

_______ 6. Using your favorite cookie recipe, triple the recipe and donate the cookies to a local shelter, fire station, police station, or shut ins. Now take another recipe and cut it in half. Use these cookies as dessert for your family.

_______ 7. Play a “tycoon” style computer game such as Chocolatier, Monopoly Tycoon, Zoo Tycoon, Lemonade Stand, or Roller Coaster Tycoon. Play the game as though it were real life and try to build the most successful business that you can.

_______ 8. Help a younger child with their math homework or play a game with them that helps to teach math skills.

_______ 9. What is the difference between plane figures and solid figures? Take a minimum of six of the shapes in Dolphin #5 and make them into a sculpture. At least one needs to be a plane figure and at least one has to be a solid figure. You may have as many of the same shape as you want. You may make your own shapes or use ready-made shapes, but they need to be precise. Also make sure you know what a polygon, trapezoid, parallelogram, and right triangle are.

_______ 10. Find a source of math quizzes on 100 multiplication facts or 100 division facts. You will need several versions of the quiz(zes) so that when you retake them you can’t just memorize the order of the answers. On the first day, time yourself (be sure to use a timer that records seconds) and convert your total time to seconds. Figure out what ten percent of your time is. Take either the multiplication or division quiz over again each day until you are ten percent faster, making sure your accuracy remains the same or improves.

_______ 11. Play at least 8 board games that use math. Make a chart to show which games help people practice which skills. Determine which game covers the most math. Which one is the most fun?

_______ 12. Help some adults plan a meal for a large group such as a rescue mission dinner or church banquet. Offer to convert the measurements for one dish into the large quantity (at least eight times the original). Then figure out how much it will cost *per person *to serve that dish to the larger group. Is an individual serving cheaper or more expensive when you serve a larger group?

_______ 13. Help plan the food for a campout for your troop. You will need to do this way in advance. Take the grocery list to at least three different stores to compare prices and then do the purchasing from at least two locations. Figure out how much you saved on groceries over the most expensive store for each item. Figure out how much gas it took to go to the different stores. You will need your parent’s prior permission and try to plan your stops in between other errands to reduce fuel usage. If you made your stops while doing other errands in the same parking lot, do not add in any fuel cost for that stop.

**Eagle (Do 7 requirements)**

_______ 1. What does math have to do with home decorating? Most home decorators need to work within a budget. But in order to figure out what you'll spend, you first have to know what you need. How will you know how many rolls of wallpaper to buy if you don't calculate how much wall space you have to cover? Understanding some basic geometry can help you stick to your budget.

Imagine you're planning to buy new carpeting for your home. You're going to put down carpeting in the living room, bedroom, and hallway, but not in the bathroom. You could try to guess at how much carpet you might need to cover these rooms, but you're better off figuring out exactly what you need. First, figure out the total area of your floor plan. Then subtract the area of the bathroom since you don’t plan to carpet that. This will tell you the total number of square feet you will need to carpet. What if the carpet only comes in rolls 10’ wide? How many linear feet of carpet will you need? If your ceilings are 10’ high, how much wall paper would you need for each room?

_______ 2. Play a “tycoon” style computer game such as Chocolatier, Monopoly Tycoon, Zoo Tycoon, Lemonade Stand, or Roller Coaster Tycoon. Play the game as though it were real life and try to build the most successful business that you can.

_______ 3. Help a younger child with their math homework or play a game with them that helps to teach math skills.

_______ 4. Research careers that require a strong math background. Examples may be engineers, financial advisors, accountants, or construction. Find out what type of math classes are required for these careers. Shadow someone with a math oriented career for a day.

_______ 5. What is the value of the dollar. Find out what the value of a dollar is compared 12 different world currencies such as the Japanese Yen, the EU Euro, the United Arab Emirates Dirham, the Swiss Franc, or the Mexican New Peso. Look up the currencies you have chosen on the internet and see if you can find pictures of what they look like.

_______ 6. Americans love their cars. We drive to school, to work, and on trips. Math can help us with our cars and in our driving in many different ways. For example, we can save money by using math in choosing limited or unlimited mileage in car rentals, determining the best routes for trips, analyzing the cost trade off of driving various size cars, and deciding just how much you can afford to spend on a car.

Figure out what the average gas mileage is for your family car. The next time you fill up the car with a full tank write down the number on the odometer. On the following trip to the gas station write down the new number on the odometer and fill up your tank. Subtract the first odometer reading from the second to get how many miles you drove. Then divide that number by the number of gallons it took to fill the car (this is the number of gallons you used since your last fill up) to get your gas mileage. For example if the odometer read 78274 on your first fill up and 78578 on your second, you drove 304 miles. If it took 16 gallons to fill your tank, you get 19 miles to the gallon. Keep in mind that you will get less miles to the gallon if you did mostly city driving than you will if you did most of your driving on the highway.

_______ 7. Math and investing go hand in hand. In simple interest, you earn interest payments from the principal only. In compound interest, you reinvest the interest payments and earn interest on interest. This is the equation for finding compound interest:

A = P (1 + r / k) ^{k * n}

Where

A = amount in account at end of the period

P = principal

r = rate (usually, an annual rate)

k = number of compounding times per year

n = number of years

Using this equation, if you are 15 years old and you want to retire at age 65 with a million dollars in the bank and you can invest your money to earn 10% compound interest per year, how much do you have to invest each year? Divide this amount by 12 to find out how much you would have to invest each month. Can you fit this into your family budget?

_______ 8. Math and music have always been considered closely connected in many ways. It is widely believed that students who do well in music also excel in math. Some research shows that starting music lessons at a young age enhances math ability . One theory is that music strengthens the neural chords that transmit information between the two hemispheres of the brains.

Take a look at some of the basic components of music such as rhythm, tone and pitch, and see what math has to do with them.

_______ 9. Math started around 2,000 B.C. Many great mathematicians developed key concepts such as algebra, geometry, trigonometry, and calculus. You will find names like Euclid, Pascal, Newton, and Gauss in your textbooks. Most of these mathematicians were scientists too. Choose a famous mathematician and create a booklet to teach younger girls what their contribution was to our current understanding of math.

_______ 10. What is the difference between plane figures and solid figures? Take a minimum of six of the shapes in Dolphin #5 and make them into a sculpture. At least one needs to be a plane figure and at least one has to be a solid figure. You may have as many of the same shape as you want. You may make your own shapes or use ready-made shapes, but they need to be precise. Also make sure you know what a polygon, trapezoid, parallelogram, and right triangle are.

_______ 11. Play at least ten board games that use math. Make a chart to show which games help people practice which skills. Determine which game covers the most math. Which one is the most fun?

______ 12. Find someone who buys most of her groceries at a discount store or through a food co-op. Ask her for one week’s worth of her grocery list and her cash register receipt or invoice. Go to a regular grocery store or a health food store and compare the cost for that week of food.

_______ 13. Help plan the food for a campout for your troop. You will need to do this way in advance. Take the grocery list to at least three different stores to compare prices and then do the purchasing from at least two locations. Figure out how much you saved on groceries over the most expensive store for each item. Figure out how much gas it took to go to the different stores. You will need your parent’s prior permission and try to plan your stops in between other errands to reduce fuel usage. If you made your stops while doing other errands in the same parking lot, do not add in any fuel cost for that stop.

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**World Currencies**

http://www.thereareplaces.com/infgdes/money/currnames.htm

**Math in Real Life**