The activities in Math Behind the Market are organized into four main mathematic strands:

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2 Dear Teacher, Thank you for considering Math Behind the Market for use with The Stock Market Game (SMG) program in your classroom. Fully sponsored by the McGraw-Hill Companies, Math Behind the Market provides you with activities that promote a deeper understanding of complex numbers, quantitative relationships, statistical analysis, and algebraic representation among your students. The activities in Math Behind the Market are organized into four main mathematic strands: 1. Thinking Algebraically Recognizing patterns, developing formulae, and executing algorithms efficiently. 2. Interpreting Statistics Reading and interpreting statistical information quickly and accurately. 3. Communicating Quantitatively Representing information through the creation of graphs, charts, and tables as well as speaking clearly about mathematics. 4. Tackling Complex Problems - Honing critical thinking skills through multi-step computations and word problems. The activities in Math Behind the Market are correlated to the National Council of Teachers of Mathematics (NCTM) Principles and Standards in School Mathematics. They are organized around lessons addressing twelve core investment topics identified by the SMG program as essential to a fundamental understanding of saving and investing. We recommend that the activities in this book be used in conjunction with the core topic lessons. However, we understand that students and teachers approach The Stock Market Game and the Math Behind the Market activities from abroad range of prior knowledge and class schedules. We rely on your judgment as teacher to determine the most effective use of this book. For information about The Stock Market Game program near you, please visit Thank you again for choosing The Stock Market Game program as a part of your daily instruction. Sincerely, Vincent Young Director of Curriculum Initiatives The Stock Market Game SIFMA Foundation for Investor Education

3 Lesson Summary What is a Stock? What is a Stock? discusses the many facets of stock in detail and uses two leading chocolate companies to explain the difference between a public and private company. Lesson Objectives Define the terms: stock, investor, public company, private company, earnings, and dividends. Make group decisions on the benefits and risks of investing in stocks. Calculate gains and losses of sample stock sales. NCTM Standards 1A - Understand numbers, ways of representing numbers, relationships among numbers, and number systems. 1B - Understand meanings of operations and how they relate to one another. 1C - Compute fluently and make reasonable estimates. 5A - Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them. 5C - Develop and evaluate inferences and predictions that are based on data. 6A - Build new mathematical knowledge through problem solving. 6B - Solve problems that arise in mathematics and in other contexts. 6C - Apply and adapt a variety of appropriate strategies to solve problems. 7B - Make and investigate mathematical conjectures. 7C Develop and evaluate mathematical arguments and proofs. 8A - Organize and consolidate mathematical thinking through communication. 8B - Communicate mathematical thinking coherently and clearly to peers, teachers, and others. 9A - Recognize and use connections among mathematical ideas. 9C - Recognize and apply mathematics in contexts outside of mathematics. 10A Create and use representations to organize, record, and communicate mathematical ideas. 10B Select, apply, and translate among mathematical representations to solve problems. 10C Use representations to model and interpret physical, social, and mathematical phenomena. Mathematical Strands Thinking Algebraically Interpreting Statistics Communicating Quantitative Information Tackling Complex Problems Students will work with integers by calculating the profit or loss of investments. Students will practice calculating the value of a portfolio, given the changing prices of its stock. Students will practice graphing the value of a portfolio over time. Students use percentages and fractions to solve problems and make investment decisions. Math Behind the Market Beginner Sample 1

4 THINKING ALGEBRAICALLY Calculate the gain or loss for each stock and record your answer in the third column under Change in Price. In the fourth column, write whether the change in price is a gain or loss. Price Bought Price Sold Change in Price Gain or Loss $36.13 $37.01 $12.42 $12.27 $58.43 $53.48 $ 5.39 $ 6.02 $44.95 $45.99 $29.83 $28.75 $ 9.48 $15.02 $22.58 $22.59 How do you know when the change in price is a gain or loss? Multiply the Number of Shares by the Price Per Share to calculate the Total Cost of Shares. Example: 500 shares x $22.40 per share = $11, Number of Shares Price Per Share Total Cost of Shares 500 $ $ $ $ $ $34.00 What is a Stock? 2

5 THINKING ALGEBRAICALLY Enrichment Find the cost of the following: A. 90 shares at $45.00 per share B. 90 shares at $12.40 per share C. 750 shares at $36.00 per share Find the cost of a, b, and c above including commission. To calculate the 2% commission, use the formula: (Cost of Shares) x.02 = Commission (2% =.02) Total Cost = Cost of Shares + 2% Commission Cost of Shares 2% Commission Total Cost A. B. C. What is a Stock? 3

6 INTERPRETING STATISTICS 1. If you know the number of shares you bought and the price per share, how would you calculate the total cost of your investment? 2. If you bought 40 shares of DreamWorks Animation SKG, Inc. (DWA), in March for $26.00 per share, how much did you invest initially? 3. This is a table of closing prices from March to September for DWA stock. Month Price March $26.00 April $27.00 May $26.00 June $23.00 July $21.00 August $21.00 September $25.00 Make a table that shows how much your investment is worth during each of the months listed in the table. Month Price Investment Value What is a Stock? 4

7 COMMUNICATING QUANTITATIVE INFORMATION Below is a table of a group s SMG portfolio value over the course of 10 days. First, round each value in the table to the nearest thousandth. Then, use the graph below to create a line graph of the rounded values over time. Group A Date Value Rounded Value 4/3/2007 $100,000 4/4/2007 $102,430 4/5/2007 $101,021 4/6/2007 $99,321 4/9/2007 $97,230 4/10/2007 $98,933 4/11/2007 $99,982 4/12/2007 $101,222 4/13/2007 $102,000 $105,000 $104,000 $103,000 $102,000 Portfolio Value (in dollars) $101,000 $100,000 $99,000 $98,000 $97,000 $96,000 $95,000 4/3/07 4/4/07 4/5/07 4/6/07 4/7/07 4/8/07 4/9/07 4/10/07 4/11/07 4/12/07 4/13/07 What is a Stock? 5

8 TACKLING COMPLEX PROBLEMS For each scenario, you are presented with problems that involve investing in companies. Show mathematically how you solve each problem and be prepared to explain your work and your thinking. You own 1,000 shares of a company at $42 per share. You own 10,000 shares of a company at $12 per share. In which company is the total value of your shares greater? Explain how you know which is greater. Your team wants to invest $4,000 of its portfolio in companies that develop recycling facilities. The team wants to split the $4,000 equally among five companies. One team member wants to buy Casella Waste Systems (CWST). The company is selling its stock at $16 per share. How many shares can your team afford to purchase? What is a Stock? 6

9 TACKLING COMPLEX PROBLEMS Enrichment Company A Company B 10% % % 90% The two graphs represent your ownership in two companies (Company A and Company B). Which graph represents the company that has 20 shares in which you own 5 shares? Which graph represents the company that has 1,000 shares in which you own 100 shares? What is a Stock? 7

10 Lesson Summary Dividends and Earnings Dividends and Earnings examines the ways investors may receive earnings on their investments through dividends and by selling stocks for a profit. Lesson Objectives Draw conclusions as to how to examine a company before making investments. Describe the factors that influence investment decisions. Calculate dividends paid out to stockholders. Calculate net gain/loss for an investor. Explain the difference between earnings and dividends. NCTM Standards 1A - Understand numbers, ways of representing numbers, relationships among numbers, and number systems. 1B - Understand meanings of operations and how they relate to one another. 1C - Compute fluently and make reasonable estimates. 2A - Understand patterns, relations, and functions. 5C - Develop and evaluate inferences and predictions that are based on data. 6A - Build new mathematical knowledge through problem solving. 6B - Solve problems that arise in mathematics and in other contexts. 6C Apply and adapt a variety of appropriate strategies to solve problems. 7C - Develop and evaluate mathematical arguments and proofs. 8A - Organize and consolidate mathematical thinking through communication. 8B - Communicate mathematical thinking coherently and clearly to peers, teachers, and others. 9B - Understand how mathematical ideas interconnect and build on one another to produce a coherent whole. 9C - Recognize and apply mathematics in contexts outside of mathematics. 10B Select, apply, and translate among mathematical representations to solve problems. Mathematical Strands Thinking Algebraically Interpreting Statistics Communicating Quantitative Information Tackling Complex Problems Students use a simple formula for calculating dividend payments to investors. Students use information presented in a chart to answer questions. Students explain dividends and possible gains from investing in stocks paying out dividends. Students apply their knowledge of dividends to accurately compute the value of investments over time. Math Behind the Market Beginner Sample 8

11 THINKING ALGEBRAICALLY Use the formula below to determine the answer to each question. Unless stated otherwise, the dividends are paid annually. The first question is done for you. Show all work in the space provided. Dividend Payment = (Dividend Per Share) x (Number of Shares) 1. Jonathan has 50 shares of a stock that is paying $0.12 in dividends per share annually. What will his total dividend payment be? Example: 50 x $0.12 = $ Cecilia owns 85 shares of a stock that is paying a $0.30 dividend annually. What will her total dividend payment be? 3. Darius has learned that his 120 shares of stock will be paying a $0.27 annual dividend. How much money should Darius expect to receive in a dividend payment? 4. Deondra owns shares of a company that will pay $0.33 per share in dividends. If Deondra owns 350 shares, how much will her dividend payment be? Dividends and Earnings 9

12 THINKING ALGEBRAICALLY 5. Christopher owns 430 shares of a stock that will pay a $0.22 dividend this year. His brother, Wayne, owns 510 shares. How much more money in dividend payments will Wayne receive than Christopher? 6. Tiffany bought 3,400 shares of a stock that will pay $0.18 per share in dividends. She wants to use her money to purchase a new computer for $620. Will she have enough money? (You can ignore commission.) 7. Jarren received a total dividend payment of $ for the 80 shares of stock he owned. How much was the dividend per share? Dividends and Earnings 10

13 INTERPRETING STATISTICS Below is a chart that shows the earnings per share for three different companies. Use the information provided in the chart to answer the questions below. Earnings Per Share $32 $30 $28 $26 $24 $22 $20 $18 $16 $14 $12 $10 $8 $6 $4 $2 $0 Company A Company B Company C 1. What is the earnings per share for Company A? 2. What is the earnings per share for Company C? 3. Which company shows the greatest earnings per share? Dividends and Earnings 11

14 4. Which company shows the least earnings per share? INTERPRETING STATISTICS 5. What is the difference between the company with the greatest earnings per share and the company with the least earnings per share? 6. Based on the information above, which stock would you prefer to buy? Why? Dividends and Earnings 12

15 COMMUNICATING QUANTITATIVE INFORMATION You are a financial advisor and your client has come to you confused about which of two stocks to buy with $900. Stock A is a stock in the consumer goods industry. It costs $45 per share. Stock B is a stock in the consumer goods industry. It costs $45 per share. Stock B also awards quarterly dividends of $1.25. Your client is confused because he has never heard of a dividend. Answer the questions below. 1. In what ways are the two stocks similar? 2. In what ways are the two stocks different? 3. Write a short letter to your client explaining how dividends work, and what it would mean if he invested all his money in either stock A or stock B. 4. Do you know for sure which stock is a better investment? Why or why not? Dividends and Earnings 13

16 TACKLING COMPLEX PROBLEMS Read the scenarios below and answer the questions that follow. Remember to show your work in the space provided. 1. On November 30, 2005, Susan bought 300 shares of Walt Disney Company (DIS) stock for $31.89 per share. On December 13, 2006, Disney paid a $0.31 dividend per share, and on February 12, 2007, she sold the stock for $33.89 per share. Did Susan gain or lose on this investment? How much money did she gain or lose on this investment? 2. On January 23, 2007, Jovian bought 400 shares of Intel Corporation (INTC) at $20.00 per share. He sold half his shares on February 6, 2007 at a price of $21.00 per share. Ignoring any broker s fees, how much money did he gain or lose on this investment? Dividends and Earnings 14