# Wise Investments

Purpose

The purpose of this unit is to engage the student in applying their knowledge and skills of decimals and percentages to solve problems within the context of financial literacy, in order to gain an appreciation of the calculations necessary to make informed decisions when investing.

Achievement Objectives
NA5-1: Reason with linear proportions.
NA5-3: Understand operations on fractions, decimals, percentages, and integers.
NA5-5: Know commonly used fraction, decimal, and percentage conversions.
Specific Learning Outcomes

Students develop their skills and knowledge on the mathematics learning progression Multiplicative Thinking, in the context of financial literacy and investment.

Description of Mathematics

Students will apply their understanding of percentages, decimals and currency, developing their ability to solve problems in the context of financial literacy and investment.

Activity

### Structure

This cross-curricular, context based unit has been built within a framework that has been developed with input from teachers across the curriculum to deliver the mathematics learning area, while meeting the demands of differentiated student-centred learning. The unit has been designed around a six session focus on an aspect of mathematics that is relevant to the integrating curriculum area concerned. For successful delivery of mathematics across the curriculum, the context should be meaningful for the students. With student interest engaged, the mathematical challenges often seem more approachable than when presented in isolation.

The first session is an introductory activity that is aimed to spark the imagination of students, to introduce the need for a particular idea or technique in mathematics that would enable them to explore deeper into that context. It is expected that rich discussion may be had around the context and around the nature of the mathematics involved.

The following five sessions are each based around a model of student-centred differentiated learning.

• There is a starting problem to allow students to settle into the session and to focus on the mathematics within the chosen context. These starting problems might take students around ten minutes to attempt and/or to solve, in groups, pairs or individually.
• It is then expected that the teacher will gather the students together to review the problem and to discuss ideas, issues and mathematical techniques that they noticed during the process. It may be helpful to summarise key outcomes of the discussion at this point.
• The remaining group of activities are designed for differentiating on the basis of individual learning needs. Some students may have managed the focus activity easily and be ready to attempt the reinforcing ideas or even the extending ideas activity straight away. These could be attempted individually or in groups or pairs, depending on students’ readiness for the activity concerned. The students remaining with the teacher could begin to work through the building ideas activity together, peeling off to complete this activity and/or to attempt the reinforcing ideas activity when they feel they have ‘got it’.
• It is expected that once all the students have peeled off into independent or group work of the appropriate selection of buildingreinforcing and extending activities, the teacher is freed up to check back with the ‘early peelers’ and to circulate as needed.

### Introductory activity

(to motivate students towards the context/integrated learning area and to inform teachers of each student’s location on the learning progressions):

John earns \$12 a day for babysitting his siblings after school each weekday. He likes to have a small amount of money to spend on treats at the school canteen that his parents refuse to buy, but he also wants to build up some savings. John decides to put a fraction of his earnings into a jar straight away. He spends all the rest on canteen treats. After a 9-week term, John has \$382.50 in his jar. What fraction of the \$12 does he save? (nb – There were no days off school during those 9 weeks!)

In this activity, the teacher(s) will be able to locate their students on the Multiplicative Thinking learning progression by observing how students manage percentages and how they find and express a ratio. This activity integrates mathematical skills and knowledge with the social sciences learning area.

Mathematical discussion that should follow this activity involve:

• This problem can be broken into parts, i.e. several smaller problems. What are those parts?
• If this problem is broken into parts, does the order in which each part is solved and applied matter? Explain in terms of the properties of the operations involved.

### Session One

Focusing on problem solving involving currency and percentages.

Focus activity

Josie has started a savings account. She saves exactly half of her pocket money and puts this into the bank each month. Look at the statement of her account below to answer the following questions.

 Date Particulars Balance 30 September Opening Balance \$25.00 30 October Interest 25.15 31 October Deposit 50.15 30 November Interest 50.45 Deposit 75.45 30 December Interest 75.90 31 December Deposit 100.90

1. How much has Josie deposited into her account in the 3 months this statement covers?
2. Josie earns interest on her savings. What is the total of the interest she has earned?
3. Josie’s bank advertises a fixed annual interest paid monthly into their savings accounts. What is the advertised annual interest rate for Josie’s savings account?
Discussion arising from activity:
• Josie’s account pays interest monthly, is this better for her than one big annual payment?
• Discuss the advantages/disadvantages of saving regularly over a long period of time.

Building ideas

Continuing with Josie’s savings plan:

1. Continue the statement of Josie’s account to show one full year of her saving in this way.
2. Find the total interest paid in monthly, over the year of Josie’s saving in this account.

Reinforcing ideas

Continuing with Josie’s savings plan:  Josie’s bank advertises 7.2% per annum paid monthly.

1. What is the rate of interest per month?
2. How much interest would Josie have earned if 7.2% of interest was paid on the average balance over the year, at the end of the year?

Extending ideas

Josie could put her money into a savings scheme that pays 7.5% interest per annum on the average yearly balance at the end of each year. Which savings scheme would pay the most interest to Josie after one year of savings?

### Session Two

Focusing on problem solving involving currency and percentages.

Focus activity

Josie has been saving \$25 per month in an account that gives 7.2% interest paid monthly. If she continues this savings plan to bring it to two full years of savings, what will her final balance be?

Discussion arising from activity:

• Discuss the advantages/disadvantages of saving regularly over a long period of time.

Building ideas

Continuing with Josie’s savings plan:

1. What will Josie’s balance be after three full years of savings?
2. How much has Josie deposited over three full years of savings?
3. What is the total interest that Josie has earned over three full years of saving?

Reinforcing ideas

Continuing with Josie’s savings plan: Josie’s account pays interest monthly, how much more interest has she earned over two years of savings than if her bank paid

1. Annually?
2. Quarterly?

Extending ideas

Continuing with Josie’s savings plan: At this stage in her savings, the interest earned in her account is much smaller than her monthly contributions. Build a spreadsheet to answer the following questions.

1. When will her balance be when her monthly interest earned is the same as her monthly deposit?
2. When will her balance be when her annual interest earned is the same as her monthly deposit?

Give your answers in terms of years and months after the account was opened with a balance of \$25. Discuss whether either of these situations are realistic within Jose’s lifetime.

### Session Three

Focusing on problem solving involving currency and percentages.

Focus activity

Jim’s parents have been saving in a fund for his university studies. The account pays 7.5% interest per annum. They have put \$1000 into a special savings account on each of his birthdays, starting the day he was born. What will the balance of this account be when Jim starts university (shortly after his 18th birthday)?

Discussion arising from activity:

• How much money have Jim’s parents paid into this account in total?
• How did/can you work out the interest paid each year? Can you describe this process in words or algebraically?
• What is the total interest earned in Jim’s university fund?

Discussion arising from activity:

• How does this compound interest compare with one lump sum (simple interest) of 18 x 7.5% at the end of 18 years of savings?
• Would that simple interest be calculated on the opening, closing or average balance over the 18 years?
• Discuss the advantages of regular savings over a long period against other methods of saving (occasional, or larger amounts in a shorter time, etc).

Building ideas

Jim’s parents have been putting \$1000 per year into a university fund that pays 7.5% interest annually. After 18 years, the balance is \$39 000.  What would the balance be if instead of depositing \$1000 per year, they contributed:

1. \$500 per year?
2. \$2000 per year?
3. \$1000 every second year?

Reinforcing ideas

Jim’s parents have been putting \$1000 per year into a university fund that pays 7.5% interest annually. How much would they need to deposit on opening the fund if they wanted to achieve the same savings goal for Jim’s 18th birthday, with just that one big deposit on his birth.

Extending ideas

Jim’s parents have been putting \$1000 per year into a university fund that pays 7.5% interest annually. They have found it increasingly difficult to find the spare money to save for his university fund. If they wanted to achieve the same sized fund after 18 years, by contributing equal amounts every year for only the first ten years of Jim’s life, how much should each of those contributions be?

### Session Four

Focusing on numerical reasoning involving decimals, currency and percentages.

Focus activity

Jared has inherited a large sum of money which he will use to by shares on the stock market. He buys 250 shares of company X at \$21.40 each and 3000 shares of company Y at \$6.30 each. The stock broker charges a trading fee of 1% of the value of each purchase. What is the value of Jared’s inheritance?

Discussion arising from activity:

• What are the risks of this type of investment?
• Why might someone risk investing their money in shares?
• Any profit made on the sale of shares is taxable. Is this fair?

Building ideas

Jared sells his 250 shares of company X bought at \$21.40 each for \$25.00 each. He sells his 3000 shares of company Y bought at \$6.30 each, for \$9.50 each. Find his net profit after deducting the stockbrokers charge 1% trading fees for when he bought and again when he sold his shares.

Reinforcing ideas

Jared sells his 250 shares of company X bought at \$21.40 each and 3000 shares of company Y bought at \$6.30 each, making a 7.5% net profit, after deducting the stockbrokers charge 1% trading fees for when he bought and again when he sold his shares. The shares of both companies, X and Y, had the same percentage increase in value. What were the share prices of each type of share?

Extending ideas

Jared sells his 250 shares of company X bought at \$21.40 each and 3000 shares of company Y bought at \$6.30 each, making a 7.5% net profit, after deducting the stockbrokers charge 1% trading fees for when he bought and again when he sold his  shares. Company X’s shares increased by twice as much as Y’s shares. What were the share prices of each type of share?

### Session Five

Focusing on numerical reasoning involving currency and percentages.

Focus activity

Jess wants to buy a new laptop that costs \$1300. She could buy it on HP (hire purchase) with 24 monthly payments of \$70 each which includes interest, insurance and other fees, or she could put it on a credit card that charges 15% interest p.a charged monthly. If she pays the credit card off at a rate of \$70 per month would she have paid the laptop off earlier or later than the HP option?

Discussion arising from activity:

• Which option is the better option for Jess to take?
• Would Jess have been better to save her money first and then purchase a lap top? Why/why not.

Building ideas

A lap top used at school has an average life expectancy of three years. Jess works out that is costs the same to rent a laptop for three years as it does to buy a laptop on HP with 24 monthly payments of \$70 each. What is the monthly rental on a laptop?

Reinforcing ideas

A lap top used at school has an average life expectancy of three years. Jess needs a laptop for five years at high school. It costs the same to rent a laptop for three years, as it does to buy it on HP with 24 monthly payments of \$70 each. However, if she has bought her own laptop, she could sell it after two years for 35% of her purchase price. What is the cheapest option for Jess to have a laptop for each of her five years at high school?

Extending ideas

A lap top used at school has an average life expectancy of between two and four years.  Jess needs a laptop for five years at high school. It costs the same to rent a laptop for three years, as it does to buy it on HP with 24 monthly payments of \$70 each. However, if she has bought her own laptop, she could sell it after two years for 35% of her purchase price. Find the range of the cost estimates for the different purchase options that would allow Jess to have five years of laptop use for high school.

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