Simple saver
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Introduction
This set of resources provides opportunities for students to learn skills and solve problems in financial situations that involve simple interest, use associated graphs and apply linear functions to answer related questions.
By the end of Year 8, students recognise irrational numbers and terminating or recurring decimals. They apply the exponent laws to calculations with numbers involving positive integer exponents. Students solve problems involving the 4 operations with integers and positive rational numbers. They use mathematical modelling to solve practical problems involving ratios, percentages and rates in measurement and financial contexts. Students apply algebraic properties to rearrange, expand and factorise linear expressions. They graph linear relations and solve linear equations with rational solutions and one-variable inequalities, graphically and algebraically. Students use mathematical modelling to solve problems using linear relations, interpreting and reviewing the model in context. They make and test conjectures involving linear relations using digital tools.
Students use appropriate metric units when solving measurement problems involving the perimeter and area of composite shapes, and volume of right prisms. They use Pythagoras’ theorem to solve measurement problems involving unknown lengths of right-angle triangles. Students use formulas to solve problems involving the area and circumference of circles. They solve problems of duration involving 12- and 24-hour cycles across multiple time zones. Students use 3 dimensions to locate and describe position. They identify conditions for congruency and similarity in shapes and create and test algorithms designed to test for congruency and similarity. Students apply the properties of quadrilaterals to solve problems.
They conduct statistical investigations and explain the implications of obtaining data through sampling. Students analyse and describe the distribution of data. They compare the variation in distributions of random samples of the same and different size from a given population with respect to shape, measures of central tendency and range. Students represent the possible combinations of 2 events with tables and diagrams and determine related probabilities to solve practical problems. They conduct experiments and simulations using digital tools to determine related probabilities of compound events.
Content descriptions
Use mathematical modelling to solve practical problems involving rational numbers and percentages, including financial contexts; formulate problems, choosing efficient calculation strategies and using digital tools where appropriate; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model. (AC9M8N05)
Create, expand, factorise, rearrange and simplify linear expressions, applying the associative, commutative, identity, distributive and inverse properties. (AC9M8A01)
Graph linear relations on the cartesian plane using digital tools where appropriate; solve linear equations and one-variable inequalities using graphical and algebraic techniques; verify solutions by substitution. (AC9M8A02)
Use mathematical modelling to solve applied problems involving linear relations , including financial contexts; formulate problems with linear functions, choosing a representation; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model. (AC9M8A03)
Teacher resources
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Saving versus investing
Simple interest graphs
Student learning resources
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Saving versus Investing
Simple saver
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Suggested activity sequence
This sequence is intended as a framework to be modified and adapted by teachers to suit the needs of a class group.
Part A: What is the difference between saving and investing?
- Introduce the concept of saving or investing money using the explainer to clarify terms and concepts. Students could read these sections of the explainer individually or in pairs and take notes using the worksheet Part 1.
- Invite student responses and use the saving versus investing visualiser to show possible answers to the worksheet.
Part B: Calculating simple interest on savings and investments.
- Explicitly teach students how to calculate simple interest using a gradual release of responsibility model.
To calculate simple interest: Interest = Principal x Rate x Time
Where the principal is the original amount of money, and rate is converted to a decimal value.
To calculate the future value of an amount of money in a savings account: Amount = Principal + Interest
Example Problem
Calculate the interest earned on investing $2000 at 4.5%pa for 2 years. What is the final amount of money available.
Solution:
Interest = Principal x Rate x Time
= 2000 x 0.045 x 2
= $180
Amount = Principal + Interest
= $2 000 + $180
= $2 180
- Students complete Part 2 of the worksheet.
Part C: Calculating simple interest on loan accounts and determining repayment amounts.
- Explicitly teach students to calculate the repayment amount required to repay a loan in a given timeframe using the gradual release of responsibility model.
To calculate the repayment amount required to repay the loan within a given timeframe: Repayment = Amount ÷ (Time x Frequency)
Where the Amount = Principal + Interest, Time is years, and Frequency is the repayment frequency eg. weekly, monthly, etc.
Example Problem
Calculate the weekly repayments required to pay back a loan of $2000 with an interest rate of 4.5%pa taken for 2 years.
Solution:
Interest = $180, Amount = $2,180
Repayment = Amount ÷ (Time x Frequency)
$2,180 ÷ 2 x 52
= $20.96
- Students complete Part 3 of the worksheet.
Part D: Simple interest graphs and linear function applications
- Use the simple interest graphs visualiser to explicitly teach about simple interest graphs, linear functions and how to solve associated problems.
- Students complete Part 4 of the worksheet. Use your discretion on which questions different students will answer. For example, you may set question 4 as an extension activity.