**Scenario information**

**Subject:** Mathematics

**Grade:** 2nd grade, high school

**Level of implementation complexity:** medium

**Correlations and interdisciplinarity:**

- ICT
- Entrepreneurship
- Personal and social development
- Civil education

Find tips and instructions for using digital teaching tools at e-Laboratory. (in Croatian language)

**Key Words:** exponential function, loan, logarithmic function, compound interest calculation, savings

**Learning outcomes:**

- determine the final and initial value of a deposit with compound interest (A, B)
- explain the relationship between the initial and the final savings amount depending on the term of savings and the interest rate (A, C)
- apply an exponential and logarithmic function on a complex interest calculation (A, B, C, D)
- associate the understanding of interest calculation with real life situations (C, D)

**In parentheses, there are letters indicating the teaching scenario activities, and their implementation contributes to achieving the respective outcomes.*

**Activity description**

**A Linked cards**

In this activity, students practice compound interest calculation – the calculation of one of the four variables. Before doing exercises, have the students remember what compound interest calculation is, what is its basic principle and how it is calculated. Talk about the variables which appear in the formula, and what values these variables usually take in reality. Talk to students about the use of compound interest calculation in everyday life situations and about the importance of knowing how to calculate it. After the discussion, encourage the students to practice by doing exercises in pairs.

Give each pair eight cards (in Croatian) with exercises. You can create the exercise cards yourself by using a word processor, for example Word. The pairs should complete all the exercises given in the cards. The cards are linked – the result of one card is the default data in another exercise. Students will notice that they cannot complete the exercises in a random order and that they are expected to combine the exercises in order to complete them in the fastest and most productive way possible. Hand out cards with the QR code revealing the answers (in Croatian) to each student pair after completing all the given exercises. You can create a QR code by using the QR Stuff generator.

Follow the students’ work and offer them help. At the end of the activity, discuss the exercises, their answers, the most common mistakes and the best solving strategies, in the online tool Tricider.

**Support procedures**

Given the complexity of the problem solved in this activity, it is very important to provide students with disabilities with simple, brief and clear instructions related to the exercises, and to check their understanding. If necessary, split the exercises into smaller stages, and give the students instructions in each stage. For students with specific learning disabilities (dyscalculia, dyslexia, dyspraxia), it is necessary to adjust the number and the difficulty of the exercises and give them enough time to complete them. Students with attention-deficit/hyperactivity disorder need to be introduced to the planned exercises in advance, and the exercises must be structured so that students can successfully complete them. Generally, it is useful to provide most students with disabilities with a completed exercise to serve as an example when doing similar exercises.

**B Which interest rate is the right one?**

By doing this activity, have students establish what interest rate and how long of an interest period is more favorable for a saver, and how can the exponential function be associated with everyday life.

Apply the exponential function to compound interest calculation, and find out how much do students know about calculating interest by using the Desmos activity entitled Interest Rate (example of activity in the Desmos tool in Croatian). Have students access activities by entering the class code which you can generate by logging into Desmos, where you can monitor the activity of each student. By filling in the table, the student will find that it is more favourable for the saver to have as short of an interest period as possible (including the same interest rate). They are introduced to the concepts of a nominal, relative and conforming interest rate. After the activity, discuss their use together so that students can think critically about the conditions provided by banks.

**Support procedures**

To a large extent, this activity is related to the everyday, and especially to the future life of students, and it develops the foundations of financial literacy. Therefore, it is important for students with specific learning disabilities and attention-deficit/hyperactivity disorder to be provided support in various ways to gain the knowledge which will be of utmost importance for them. The terminology should be further explained (nominal, relative and conforming interest rate) so students can understand them well. It is advisable to explain them firstly by using small numbers to allow the students to learn the stages of the procedure. Students can have a glossary in their notebook so that they can always recall what each term means. Instructions for tool use, support and step-by-step explanation of exercises and additional clarifications are only some of the possible support procedures, which are described in more detail in the Didactic-Methodical Guidelines for Natural Sciences and Mathematics for Students with Disabilities. (in Croatian language)

**C I choose to save**

Ask students whether they save money and what do they know about savings. What conditions are offered by banks? Is it worth to save at a bank?

Divide students into groups and assign a bank to each group. Give them an assignment:

*Find the annual interest rate on fixed-term savings in Croatian kuna for the selected bank. Determine the amount you want to place on time deposit (joint savings) until the 21st birthday of the youngest member of the group. How much interest would you receive if the interest is imputed a) annually, b) quarterly, c) monthly?*

*Choose the most favourable option from the available imputing interest options offered by the selected bank, and answer the questions: a) How much would you have to wait for the fixed-term deposit amount to double? b) How much would you have to wait to be able to withdraw HRK 20,000?*

Have groups find the required information on the web pages of the selected bank. Help them choose interest that matches the assignment requirements.

Have them make an infographic using the results of their research in Piktochart, and have them present the infographics to the rest of the class.

After the presentations, discuss the conditions offered by different banks and ask again if it is worth to save money at a bank.

Are the results what the students expected? Comment on why the period required for the fixed-term deposit amount to double does not depend on the deposit amount.

**Support procedures**

In this activity, most of the support to students with disabilities can be provided by students within the group, e.g. in reading data from the bank’s web pages to students with visual impairment and dyslexic students. If necessary, the text can be read several times, and students may write down important data in an appropriate way to create a personal problem-solving chart. It is also important to provide step-by-step guidance, more specifically clear instructions before each new stage in completing the exercises. Assess whether the student with disabilities is to complete all the proposed exercises or just those related to basic knowledge (e.g. calculating the annual interest and attributing it to the principal) according to the prior knowledge and abilities of the students with disabilities.

**D Repayment**

Talk to students about loans. What loan terms do students know? Does anyone close to them pay a loan? Why do people take out loans? Is it better to plan a loan or savings in the long run?

Explain to the students that annuity (periodic payment amount) consists of a repayment quota (the loan payment part) and an interest (the part paying the fee for using the funds transferred). The interest is calculated on the remainder of the debt. After each payment, the debt is reduced in the amount of the repayment quota.

The most common ways of repaying loans relate to equal annuities or equal payment quotas. An overview of loan repayment is given in the repayment table (in Croatian).

Have some students find someone in their surroundings who pays a loan. Have them collect information about the loan amount, interest rate and repayment time. Have them work in pairs and use Excel Online, a table calculation programme, to develop repayment tables for the two repayment methods – in equal annuities and in equal repayment quotas. To calculate an annuity in case of a loan repayment in equal annuities, use the Excel function called PMT (you can show advanced students how the amount is determined mathematically; knowledge involving the sum of a geometric series required). Other data in the tables is calculated simply from the default data. After developing the repayment table, have the students determine the total amount of interest to be paid in both cases.

Looking at the tables, have them consider which method is better and why. Have them share their thoughts via Edmodo. Have the students comment on their findings with the person who gave them the information about their loan.

**Support procedures**

By encouraging their participation in the introductory discussion, students with disabilities will be motivated for further work. After explaining the concepts of annuity, repayment quota and interest, it is necessary to check whether the students understand them, and if they do not, the concepts should be explained again by using simple language and small numbers. If the tables or their content are too challenging for some students with disadvantages (students with specific learning disabilities), they can be summarized and given to the students as a template and a reminder. Only after you are sure the students understand the basic concepts, you can involve them in further independent activities and activities in pairs. To use digital tools, you need to give them detailed instructions and check whether the students understand them. Adjust the method of loan repayment calculation to the students’ prior knowledge. Have visually impaired students who are not able to use digital tools, work calculations with a calculator and a custom result record.

**For students who want to know more**

Encourage students to find the following by browsing web pages: (in Croatian)

- what is the difference between the decursive and the anticipatory interest calculation
- what are prenumerando and postnumerando periodic payments (payoffs).

Then have them visit several banks and ask which method is used more often, in which cases and why. Have them shape their knowledge into a web page by using Tackk, where they can easily add different content (text, images, videos, links, location on the map etc.). Have them share their work with the rest of the class and then comment on it.

**Additional literature, content and links**

You can find additional clarification of terms on relevant web pages

- Google Scholar
- Struna (Croatian vocational terminology)
- Croatian Encyclopedia etc

Note: All network links were last validated on 10th March 2017

Did you apply this scenario in teaching? Tell us your opinion by filling out the questionnaire on this link. (in Croatian)

This text is licensed under Creative Commons Attribution 4.0 International. When using this text, you need to designate the authorship of the work in the following manner: CARNet (2017) e-Schools Teaching Scenario ˝ (enter the title of the teaching scenario) ˝, https://scenariji-poucavanja.e-skole.hr/.