Real world Mathematics

1. Real world Mathematics Warm-ups for Coordinate Algebra and Analytic Geometry (CCSS Aligned) (Click on the pictures for a short video)

2. Rail gun The U.S. Navy has unveiled a new secret weapon that its developers call a rail gun. Its projectile can travel at seven times the speed of sound and could potentially change the way America fights wars. How fast is that exactly and what number and units would you use for your answer? Coordinate Algebra, Unit 1, Lesson1 Units and Dimensional Analysis, N-Q.1, N-Q.2

3. Mars lander Part 1 - The distance from Earth to Mars is 140 million miles. The mars rovers capsule took 7 minutes to land on the surface. After the rover landed it took 14 minutes for the signal of the rover to reach Earth. How fast was the signal travelling? Part 2 - It took 150 days for the rover to get to Mars. How fast did it travel? Coordinate Algebra, Unit 1, Lesson 1 Units and Dimensional Analysis, N-Q.1, N-Q.2

4. Breakbone fever The AedesAegypti mosquito is just two to three millimeters long but its impact is devastating. Of the thousands of mosquito species, this one bears primary responsibility for one of the world's deadliest and fastest growing diseases. In the past 50 years, incidence of Dengue Fever has multiplied by 30 according to the WHO, spreading from nine countries in 1970 to over 100 today. There is no vaccine or cure for the painful virus known as Breakbone Fever, and of the 50-100 million people infected each year, over 20,000 die. What percentage of people die from the disease? How fast is the disease spreading? What units could you use? Coordinate Algebra, Unit 1, Lesson 1 Units and Dimensional Analysis, N-Q.1, N-Q.2

5. Deepface Facial recognition software has developed quite a bit in recent years. Facebook has developed something called DeepFace and it is almost as accurate as the human eye in recognizing familiar faces from one photo to the next. Human eye – 97.53% accurate DeepFace – 97.25% accurate DeepFace was told to analyze a picture of every person in Atlanta (~443,775). About how many faces did the DeepFace correctly identify? Coordinate Algebra, Unit 1, Lesson 2 Accuracy, N-Q.3

6. Goal linetechnology “Accuracy, speed and reliability were the main criteria which the manufacturers of goal-line technology systems have had to meet…” – Joseph Blatter, FIFA President Goal Line technology was used competitively in the 2014 FIFA World Cup for the first time. How accurate do you think the technology should be? Let’s pretend that the technology is 95% accurate. Not including the finals, 94 goals have been scored in the 2014 World Cup. Would the goal line technology successfully recognize all of them? About how many goals did the goal line technology rule on correctly? Coordinate Algebra, Unit 1, Lesson 2 Accuracy, N-Q.3

7. Solar Road The solar road is a design that serves many purposes. It’s main function is to gather electricity from the sun’s solar radiation during the day. For the first 7 hours of the day there wasn’t a cloud in the sky and the each solar panel was producing 230W an hour. The next 3 hours the sun was partially blocked so, the panel only produced on average 105W of power each hour. Write an equation for the total power a single panel produced that day. Coordinate Algebra, Unit 1, Lesson 3 Interpreting Structure, A-SSE.1a&b

8. Runningraptor robot The fastest robot, the Running Raptor Robot, tops out at 46 km/h. The designers want to test the durability of the robot. So, run it at full speed for 20 minutes to see how it holds up. After 20 minutes, they cut it down to ¾ speed for an additional 20 minutes and finally ½ speed for another 20 mintues. Write an equation for the total distance the robot ran. How far did it go? Coordinate Algebra, Unit 1, Lesson 3 Interpreting Structure, A-SSE.1a&b

9. Clash of clans Clash of Clans has become a very popular game. The possible ways to set up your base and the number of different ways to attack those bases are virtually infinite. You decide that an army of archers only is the way to get what you want. Maxed archers cost 300 elixir to recruit. You only have 58,000 elixir in storage. Write a one variable equation for the number of archers you can create. Solve for the number of archers you can build. Coordinate Algebra, Unit 1, Lesson 4 Writing Equations in One Variable, A-CED.1, A-CED.3

10. LED indoor farming A particular LED indoor farm grows 10,000 heads of lettuce a day. Now that’s a power plant! Write an equation for the number of days it takes to grow 3,365,000,000 (about how much lettuce the US consumes each year). How long would it take for the single farm to grow enough for the U.S.? How many of these indoor farms would you need to satisfy the U.S. demand for lettuce? Coordinate Algebra, Unit 1, Lesson 4 Writing One-Variable Equations, A-CED.1, A-CED.3

11. Wireless electricity Magentic field strength decreases at a rapid rate the further from the source of the field you get. The following equation models the phenomena. is the strength of the field (or the Force placed on electrons at that location) and is the distance from the source of the magnetic field. Part 1 - A cell phone charger generates a magnetic field (Teslas). This field is used to charge a cell phone with a battery that has uses magnetic fields to charge. You have a phone that is 1 foot from the charger. Another object is 3 feet from the charger. Which cell phone will charge faster? How many times faster? Part 2 - Let’s pretend that your phone must be in a magnetic field strength of at least 0.3 Teslas to charge. Write an inequality What is the maximum distance your phone can be from the charger? Coordinate Algebra, Unit 1, Lesson 5 Writing Inequalities in One Variable, A-CED.1&3

12. What areyou eating? For all those who have wondered about the ingredients in their lunchtime burrito, Consumer Physics is gearing up to release a handheld device designed to provide the answer. Dubbed "SCiO," the device is a tiny spectrometer that can scan food, medicines and plants to determine their molecular composition. There are 70 calories and 17 grams of sugar in 100 grams of a red apple. There are 60 calories and 13.5 grams of sugar in 100 grams of a yellow apple. Part 1 - Write an inequality for someone who wants to gets at least 300 calories by eating apples. Part 2 - Write a second inequality for someone who doesn’t want to ingest more than 75 grams of sugar. Coordinate Algebra, Unit 1, Lesson 5 Writing Inequalities in One Variable, A-CED.1&3

13. Newton’s universallaw of gravitation This is one of the most important equations in recent history that has changed the way we view the universe. This equation calculates the force of gravity () between two objects. is the gravitational constant. and are the mass of the two objects. is the distance between the objects. Rewrite the equation to solve for . Rewrite the equation to solve for . Coordinate Algebra, Unit 1, Lesson 6 Writing Equivalent Equations, A-CED.4

14. Euler’s formulafor polyhedra This formula is the foundation of Topography, which extends geometry to any continuous surface, and Topology, used to understand the behavior and function of DNA, in facial recognition and even computer graphic animations. The number of faces () minus the number of edges () plus the number of vertices () equals 2 for every polyhedron. Rewrite the equation to solve for . Rewrite the equation to solve for . Coordinate Algebra, Unit 1, Lesson 6 Writing Equivalent Equations, A-CED.4

15. Relativity& radiation The energy () contained in any object is equal to its mass () times the speed of light () squared. Part 1 - This equation is actually a linear equation. Why? Part 2 - Every second, the Earth is hit by 4.5 lbs. of sunlight. 1 lb= 0.4536 kg How much of the sun’s energy (Joules, ) is the Earth absorbing every second? Part 3 - How much of the sun’s energy () is the Earth absorbing every year? Coordinate Algebra, Unit 1, Lesson 7 Writing Linear Equations in Two Variables, A-CED.2&3

16. Aquaporins & biomimicry Coordinate Algebra, Unit 1, Lesson 7 Writing Linear Equations in Two Variables, A-CED.2&3 Introduction: A thin membrane lined with Aquaporin Inside technologycould turn seawater into drinking water and let dirty water run clean. It's based on the water-transporting proteins found in all organisms. Aquaporins allow only water through hourglass-shaped channels into and out of an organism's cells. Part 1 - An 8 square inch membrane of Aquaporins can filter about 4 gallons of water in 30 seconds. You started with 10 gallons of filtered water. Create a linear equation that has the variables V, for the volume of filtered water, and t, for time in minutes. Part 2 – We increased the size of the membrane to 48 square inches. The relationship is linear. Write an equation for the new membrane. Part 3 - How much water can be filtered in 24 hours with the new membrane?

17. Bacteria, Good or Bad?You decide! You took some antibiotics the doctor gave you to fight an infection. The problem is, it wiped out the good bacteria in your digestive track and you are having digestive issues as a result. The good bacteria in your digestive track doubles every 20 minutes. There was about 100 left alive after you took the antibiotics. Your digestive track needs about 200 million to function normally. Part 1 - Write an equation that compares the number of good bacteria in your digestive system to the amount of time (hours) after the antibiotics passed through your system. Part 2 - How long will it take for your digestive system to return to normal? Coordinate Algebra, Unit 1, Lesson 8 Writing Exponential Equations in Two Variables, A-CED.2

18. Radioactive decay& half-life Half-life: the amount of time it takes for radioactive material to return to a stable form. The Chernobyl disaster released isotopes of radioactive plutonium (Pu), iodine (I), strontium (Sr) and caesium (Cs) into area surrounding the nuclear reactor site. Pu-239’s half-life is 24,000 years Pu-241’s half-life is 14.4 years Pu-233’s half-life is 20 seconds I-129’s half-life is 15.7 million years I-131’s half-life is about 8 days Sr-90’s half-life is about 28.8 years Cs-137’s half-life is about 30 years Part 1 - Which isotope is really problematic? Part 2 - You have 100 grams of the radioactive material from Chernobyl sealed in radiation proof containers for study. Write an exponential equation for one of the elements above using R for the amount of radioactive material after a certain period of elapsed time. Part 3 - How long will it take for your sample to only to contain only 12.5 grams of radioactive material? Coordinate Algebra, Unit 1, Lesson 8 Writing Exponential Equations in Two Variables, A-CED.2