Sudha Aravindan has taught high school Math and professional development in Information Technology for over 10 years. Sudha has a Doctorate of Education degree in Mathematics Education from the University of Delaware, USA, a Masters degree in English Literature from the University of Kerala, India, a Bachelor of Education degree in Teaching of Math from the University of Kerala, India, and a Bachelor of Science degree in Math, Physics and Statistics from the University of Kerala, India. Sudha has a certificate in Java programming and Statistical Analysis.
Assignment Explanation and Topic Overview
This assignment for 9th grade students in Algebra I class challenges the student to solve problems involving ratio and proportions, money, percentages, distances and time. Answers and a grading rubric are provided at the end.
For help, students can review practice problems for calculating ratio and proportion.
- Ratio: A ratio is a mathematical relationship between any two things to indicate how many of one is contained in the other. For example, if there are 4 red tulip plants and 7 yellow tulip plants in a garden, the ratio 4:7 means that for every 4 red tulip plants there are 7 yellow tulip plants. In other words, out of a total of 11 tulip plants, 4 are red and 7 are yellow.
- Proportion: A proportion means that two ratios are equal. For example, if the recipe for one cake uses 2 eggs, we can say that the same recipe for two cakes would use 4 eggs. In this case, the ratio of cakes to eggs is 1/2 which is equal to 2/4. A proportion is written as an equation: 1/2 = 2/4. If one of the numbers in the proportion is unknown, it can be calculated using the cross product.
- Percentage: A percentage is one part out of a 100, represented by the symbol %. A percentage can be written as a ratio, percent or fraction. For example, you can represent the amount of pepperoni in a pizza different ways: (a) the pizza contains 25% pepperoni (b) if the pizza is divided into 100 equal parts, 25/100 is pepperoni (c) the amount of pepperoni in the pizza is 0.25 out of 1 part.
Instructions for Students
You will have five problems to solve. For each problem present your solution in ONE of the following formats: Written Response, Explanation Video, Storyboard, or Game Show format. More details are explained below.
- To make a video presentation of your solution, first write down your solution using a diagram, equation, graph or table. Use math words and symbols. Describe patterns that you discover and the steps you took to solve the problem. Explain your findings and solution in a clear and logical way.
- Create illustrations with characters and dialogue to represent the scenario presented in the question. The storyboard should follow a sequence that tells a story that the reader can follow through. The reader should understand the solution from the sequence of events you present in your storyboard. You can use a PowerPoint slide show method, white board, poster board, or any other format for your storyboard.
- Game Show
- Follow the format of Jeopardy or your popular game show. Break up your problem into a set of sub-problems. Create a set of quizzes or questions that you can ask to your friends or family. The solution to the questions will be the solution to the different steps in your problem.
Problems to Solve
- You have a cake recipe that calls for 2 eggs and 5 tablespoons of sugar to make one cake. How much sugar would you need if you are making 4 cakes with 8 eggs using the same proportion of measurements? Explain the solution in the form of the ratio of eggs to sugar. Explain in your own words why this is a proportion.
- Your family is planning on taking a road trip. You have decided on a destination that is 200 miles from home. If you plan to travel an average of 55 miles per hour, how many hours will it take for you to reach your destination? Explain the relationship between rate, distance and time.
- Your favorite jacket in the store was too expensive for you to buy at the price of $70. Today you are excited to see that the jacket is on sale for 40% off. What is the new price? Provide one other example of price and percentage with an accurate solution.
- You went for a bicycle ride in the neighborhood for 90 minutes. The speedometer on your bicycle registered an average of 10 miles per hour. What is the distance you traveled? Provide the formula that indicates the relationship between rate of speed and time with explanation.
- You finished reading 150 pages of a book in 10 days. If you continue to read the same number of pages each day, how many pages will you finish reading in 15 days? Explain how you solved this problem in terms of ratio and proportion.
Solutions to Problems
- The ratio of eggs to sugar to make 4 cakes is 8:20. This can be calculated by writing the 1st ratio eggs to sugar as 2:5 or 2/5. The 2nd ratio for 4 cakes can be written as 8:s or 8/s where s is the tablespoons of sugar and 8 is the number of eggs. Since the number of eggs 8 is found by multiplying 2 by 4, you would multiply the number of tablespoons of sugar, 5, also by 4 to get the number of tablespoons of sugar in the 2nd cake as 20.
- This is a proportion because the 2 ratios are equal. We know the ratios are equal because the original ratio 2:5 is multiplied by the same number 4 to get the new ratio 8:20.
- The number of hours it will take is 3.63 hours. We can use the formula s=d/t to calculate for t. We have s=55 and d =200, so solving for t, we have t = d/s or 200 m / 55 hr = 3.63 hr.
- The relationship between rate of speed, distance and time can be expressed using the formula speed (s) =distance (d) / time (t). Speed indicates how quickly, or the rate at which an object moves from point A to point B to complete the travel within the time taken.
- The new price is $42. The original price was $70 and the sale will reduce the price by 40%. This means that we have to pay only 100-40=60% of the original price. We can figure out 60% of the original price by calculating 70*(60/100) to arrive at the final price after the sale as $42.
- Another example of price and percentage can be: The cost of a laptop was $400. On a weekend sale, the cost was 10% less. The new price will be 90% (100-10%) of the original price. This can be calculated as 400*(90/100) = $360.
- The distance traveled is 15 miles. We arrive at this answer by using the formula s=d/t, and d = s*t. First we convert the time (t) 90 minutes to hours by dividing by 60 (90/60). Then we multiply speed (s) 10 mph by the time 90/60 hours to arrive at the distance; 10 * (90/60) = 15 miles.
- The formula used is speed (s) = distance (d) / time (t). In other words, speed is directly proportional to distance and inversely proportional to time. As speed increases, distance traveled increases for a period of time increases. And, as speed increases the time taken to travel the same distance decreases.
- The number of pages read in 15 days is 225. Expressing this as a proportion, we have 150/10 = p/15, where p is the number of pages read. Solving for p, we have p=(150*15)/10 =2225.
- The ratio of the number of pages read to the number of days taken to read can be expressed as a proportion because the same number of pages are read each day.
|Problem 1 Answer: is correct|
|Problem 1 Explanation: is logical and easy to understand|
|Problem 2 Answer: is correct|
|Problem 2 Explanation: is logical and easy to understand|
|Problem 3 Answer: is correct|
|Problem 3 Explanation: is logical and easy to understand|
|Problem 4 Answer: is correct|
|Problem 4 Explanation: is logical and easy to understand|
|Problem 5 Answer: is correct|
|Problem 5: Explanation is logical and easy to understand|
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