# SL Scheme Number & Algebra

The new Mathematics: Applications and Interpretation syllabus is out and published on the IB website. Log in to your MyIB account and head to this link . It is a new course with a new name and renewed focus on understanding the relationship between mathematics and its application and interpretation. It is still intended very much that the SL course will cater for the same group of students that might currently opt for Mathematical Studies. It is hoped that some of the current SL students will opt for the applications HL. Clearly all sorts of permutations are possible. Read more about the development of this course through the links in the New Syllabus section of the website. This page will focus on the Number and Algebra unit and evolve over time as the new applications site is built.

## An SL Scheme of work

Based on these guidelines, here is an idea about how we might spend the time. Remember that the Toolkit hours can come anywhere we want them. Clearly there are a number of ways in which this can be done, but this is just a suggestion to get us started.

I have included 5 hours of the toolkit time - That gives a total of 21 hours and creates the time to get the course of to a great conceptual start.

A note about assessment - Each week shows a suggested assignment and there are a number of ASSESSMENT points through the unit. Many teachers like to use regular quizzes and clearly, all of this can be weaved in and out as the teacher chooses.

**Week 1 - Accuracy, Estimation and standard form**

This lesson focusses on the role that estimation plays in understanding the world around us - The The 6 million question activity might be an excellent opening activity for the course and bring many of these issues into focus. This might facilitate further discussion.

Focus on calculations for percentage error, possibly involving those involving rounding - This Percentage Error is an excellent way to zoom in on the importance of these issues as well as practice the calculations. Further activity might come from this Percentage Error task.

Focus on understanding the notation and working with numbers in this form. Demonstrate the utility of this form of notation - Big & Small Numbers might be a useful catalyst for discussion.

* Assignment* - Set a practice assignment for accuracy, estimation and standard index form from the N & A Practice page.

#### Week 2 - Indices and logs

- Building on the work done with standard form and focussing on the index laws with a particular emphasis on negative indices.
- An introduction to logarithms with base '10' understanding equivalences.
- Introduction of 'e' in the context of the natural logarithm - This will involve a careful introduction of the number 'e ' and explaining the advantages of the natural logarithm.

* Assignment* - Set an assignment on the laws of indices and the understanding of logarithms

**Week 3 - Arithmetic Sequences**

- Exploring patterns in arithmetic sequences leading to generalisations about the nth term and sums of an arithmetic sequence - This topic provides an excellent opportunity to focus on the mathematics that leads to generalisation. Visual Sequences and Arithmetic Sum are great ways to do this.
- Formalising and applying the generalisations form the previous lesson - The teacher will likely demonstrate and number of examples of the formulae in action and provide practice exercises.
- This lesson will focus on arithmetic sequences in context and approximations to arithmetic sequences - This is a strong possible link with linear regression. The idea is that students would be looking at the data in terms of finding an approximation for the likely 'common difference'

* Assignment* - Set an assignment involving practice of Arithmetic sequences

**Week 4 - Geometric Sequences**

- Exploring with Geometric Sequences and focussing on the fundamental difference in their nature - Some attention to be paid to the key differences which can come out of the light hearted In The Money activity.
- Formalising and applying the generalisations related to nth term and sum of a Geometric Sequence - Formal demonstration of examples involving the application of the formulae
- Problem solving with geometric sequences including use of GDC, table function and equation solver - Based on the formulae that have been derived for Geometric Sequences, problems should include a range of unknown variables.

* Assignment* - Set an assignment involving practice of Geometric sequences

#### Week 5 - Financial applications of geometric sequences

Investigation of the concept of compound interest and its relation to Geometric Sequences. Leading to a derivation of the formula - Making a compound interest calculator using spreadsheets is a useful activity. Show students a working spreadsheet and ask them to construct their own. You might use such a spreadsheet to explore what happens on a loan repayment on 1 unit at 100% pa as the compounding period gets increasingly small. This will be a nice link with the introduction of 'e' from earlier..

Introducing annual depreciation and relating it the work done on compound interest - Extending the work from the previous lesson understand that the common ratio of a sequence will be 100 - % decrease when talking about depreciation. Lots of opportunity to start with application here.

Problem solving with compound interest and annual depreciation - This lesson will focus specifically on the different ways in which these kind of questions can be asked, setting up equations and solving for different variables. It is easy to overlook that understanding of the key ideas is not the same as the experience in solving related problems.

* Assignment* - Set an assignment involving practice of Compound interest and depreciation

#### Week 6 - Amortization

- Introducing the idea idea of amortization in the context of loan repayments
- Problem Solving with Amortization
- Review of some of the ideas in the unit in the context of solving equations - For example - when solving questions like 'what term of the geometric sequence will be equal to.... or 'After how many years will the investment have doubled' etc might efficiently be done using the equation solving tools, graphing function (x-solve, y-solve and calculate) or the table function.

* Assignment* - Set a review exercise for the whole unit working towards a unit test.

#### Week 7 - Review and Assess

1 hour devoted to helping students review the syllabus items - You might use some fill in the gap notes, or decide to go over some examples from the review exercise set as the last assignment. Organisation of files and clarity about exactly what students might expect to see in an exam

**ASSESSMENT POINT** - A 1 hour unit test on the syllabus items above