Wise Investments

Purpose

The purpose of this unit is to engage students in applying their understanding of decimals and percentages to problems within the context of financial literacy. This develops an appreciation of the calculations necessary to make informed decisions when investing.

Achievement Objectives
NA5-1: Reason with linear proportions.
AO elaboration and other teaching resources
NA5-3: Understand operations on fractions, decimals, percentages, and integers.
AO elaboration and other teaching resources
NA5-5: Know commonly used fraction, decimal, and percentage conversions.
AO elaboration and other teaching resources
Specific Learning Outcomes
  • Apply understanding of currency and percentages to problem solving contexts. 
  • Use spreadsheets to display balance, interest, and deposit data. 
  • Apply numerical reasoning involving decimals, currency, and percentages.
Description of Mathematics

In this unit, students apply their understanding of percentages, decimals and currency, and develop their ability to solve problems in an integrated mathematics and social sciences: financial literacy and investment context. To ensure engagement and participation in this unit, you should consider your students' prior knowledge of percentages, decimals and currency.

Opportunities for Adaptation and Differentiation

This cross-curricular, context-based unit aims to deliver mathematics learning, whilst encouraging differentiated, student-centred learning. 

The learning opportunities in this unit can be further differentiated by providing or removing support to students, and by varying the task requirements. Ways to differentiate include:

  • roaming and supporting students in a variety of groupings to ensure they understand the task at hand, the skills needed to succeed, and can apply these skills in a suitable process
  • varying the amount of structured scaffolding and guided teaching you provide to students when investigating new tasks
  • providing opportunities for students to create their own problems related to a relevant financial context
  • providing extended opportunities for students to revise and apply learning from throughout the unit
  • modelling the application of ideas at every stage of the unit
  • strategically organising students into pairs and small groups in order to encourage peer learning, scaffolding, and extension
  • allowing access to calculators to decrease the cognitive load required in each stage of the unit
  • working alongside individual students (or groups of students) who require further support with specific areas of knowledge or activities (e.g. creating a spreadsheet).

With student interest engaged, mathematical challenges often seem more approachable than when presented in isolation. Therefore, you might find it appropriate to adapt the context presented in this unit. For example, you might investigate finances that are relevant to your class (e.g. the use, saving, and investment of funds for a shared goal, such as the price of new sports gear, a new school van, new laptops for students etc.). Consider how the relevance of each of the contexts presented in the unit might be enhanced for your students, and how links might be made to students' cultural backgrounds, interests, and learning from other curriculum areas.

Structure

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.

Following the introductory session, each subsequent session in the unit is composed of four sections: Introducing Ideas, Building Ideas, Reinforcing Ideas, and Extending Ideas. Note that sessions one, two, and three have the same focus (on students applying their understandings of currency and percentages to problem solving), as do sessions four and five (on students applying numerical reasoning involving decimals, currency, and percentages).

Introducing Ideas: It is recommended that you allow approximately 10 minutes for students to work on these problems, either as a whole class, in groups, pairs, or as individuals. Following this, 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.

Building Ideas, Reinforcing Ideas, and Extending Ideas: Exploration of these stages can be differentiated on the basis of individual learning needs, as demonstrated in the previous stage of each session. 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 building, reinforcing and extending activities, the teacher is freed up to check back with the ‘early peelers’ and to circulate as needed.

Importantly, students should have multiple opportunities to, throughout and at the conclusion of each session, compare, check, and discuss their ideas with peers and the teacher, and to reflect upon their ideas and developed understandings. These reflections can be demonstrated using a variety of means (e.g. written, digital note, survey, sticky notes, diagrams, marked work, videoed demonstration) and can be used to inform your planning for subsequent sessions.

The relevance of this learning can also be enhanced with the inclusion of key vocabulary from your students' home languages. For example, te reo Māori kupu such as ōrau (percent), tau ā-ira (decimal number), and moni (cash, money, currency) might be introduced in this unit and then used throughout other mathematical learning.

Required Resource Materials
  • Calculators
  • Spreadsheet software
Activity

Introductory Activity

  1. Introduce the following problem to students: 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!)

As students work, observe their capacity working percentages, and finding and expressing ratios. Use these observations to assess students' progress on the Multiplicative Thinking learning progression.

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

 
Introducing Ideas

  1. Introduce the following context to students: 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.

DateParticularsBalance
30 SeptemberOpening Balance   $25.00
30 OctoberInterest25.15
31 OctoberDeposit50.15
30 NovemberInterest50.45
 Deposit75.45
30 DecemberInterest75.90
31 DecemberDeposit100.90 

  1. Discuss, drawing attention to the following points:

  • How much has Josie deposited into her account in the 3 months this statement covers?
  • Josie earns interest on her savings. What is the total of the interest she has earned?
  • 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?
  • 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

  1. Provide time for students to work through the following tasks:

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

Reinforcing Ideas

  1. Explain to students: Josie’s bank advertises 7.2% per annum paid monthly. 

  2. Provide time for students to work through the following tasks:

  • What is the rate of interest per month?
  • 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

  1. Introduce the following context to students: 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

Introducing Ideas

  1. Introduce the following context to students: 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? 

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

Building Ideas

  1. Provide time for students to work through the following tasks:

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

Reinforcing Ideas

  1. Pose the following task to students: Josie’s account pays interest monthly. How much more interest has she earned over two years of savings than if her bank paid annually? What if her bank paid quarterly?  

Extending Ideas

  1. Explain to students: At this stage in Josie's savings, the interest earned in her account is much smaller than her monthly contributions. 

  2. Provide time for students to work through the following tasks:

  • Build a spreadsheet to answer the following questions.
  • When will her balance be when her monthly interest earned is the same as her monthly deposit?
  • 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. 
  1. Discuss whether either of these situations are realistic within Jose’s lifetime. 

Session Three

Introducing Ideas

  1. Introduce the following context to students: 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)?

  1. Discuss, drawing attention to the following points:

  • 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?  
  • 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?
     
  1. 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

  1. Introduce the following problem to students: 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 $500 per year, $2000 per year, or $1000 every second year?

Reinforcing Ideas

  1. Introduce the following problem to students: 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

  1. Introduce the following problem to students: 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

Introducing Ideas

  1. Introduce the following context to students: 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?

  1. Discuss, drawing attention to the following points:

  • 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

  1. Explain: 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.
  2. Have students find Jared's net profit after deducting the stockbrokers charge 1% trading fees for when he bought and again when he sold his shares. 

Reinforcing Ideas

  1. Explain: 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

  1. Explain: 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

Introducing Ideas

  1. Introduce the following context to students: 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?

  1. Discuss, drawing attention to the following points:

  • 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

  1. Explain: A laptop 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

  1. Explain: A laptop 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

  1. Explain: A laptop 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.
Home Link

Dear parents and whānau,

We have been applying our understanding of currency, percentages, and numerical reasoning to problems in the context of money and investments. Ask your child to share their learning with you.

Printed from https://nzmaths.co.nz/resource/wise-investments at 8:27pm on the 19th April 2024