**Fractions, Ratios & ****Percentage **

### Foreword

Jika Communication and Training welcomes you to this course, **Fractions, Ratios and Percentage**. This course is broken up as follows:

Participants will attend 2 contact sessions (Session 1 will be 1 day and Session 2 will be 1 day, with 3 weeks of experiential on-site learning and application of what was presented in the first contact session.

**Session 1 (1 day)**

Ice breaker activity and a focus on theory which will be presented in experiential mode: in other words, participants will first engage in an activity, reflect on it and then discover the essence of the activity on their own, in pairs or in groups. Self-discovery is key to this course which not only guides learners through the content in activity-based methodologies, but also allows room for individual reflection which we feel is an invaluable dimension of embedded learning.

During day one, participants will after certain sections, complete activities in a separate workbook. The workbook will also include activities that have been planned for on-site (at school) application and reflection. These tasks performed while the participant is at work, will inform the next training session.

*EXPERIENTIAL ON-SITE LEARNING BETWEEN SESSION 1 AND 2*

### Session 2 (1 day)

The “homework tasks” are discussed and the next part of the course is completed, with participants completing their continuous assessment and reflection activities. This workbook is handed in and serves as part of the participants PDP. Within 4 weeks, workbooks are returned to us and we arrange the uploading of SACE points.

**T****ABLE OF CONTENTS**

**Background**

**Unit 1 What is a Fraction?**

- Activity 1.1 – The language of fractions
- Activity 1.2 – Introducing fractions to learners
- Activity 1.3 – Fractions are actually just division sums
- Activity 1.4 – A half is not always bigger than a quarter!
- Activity 1.5 – The answer of a division sum is not always a fraction!
- PDP Assignment 1

**Unit 2 What is a percent?**

- Activity 2.1 – Percentages

**Unit 3 What is a decimal?**

- Activity 3.1 – Fractions

**Unit 4 What is a ratio?**

- Activity 4.1 – Ratios
- PDP Assignment 2

**Annexure A**

**Annexure B**

### Background

Bradley S Witzel said: To achieve in mathematics, learners must acquire a good sense of numbers early in their academic career. This topic was addressed in the workshop on place value and number sense. Reports on ANA indicated that fractions are the next concept that posed challenges.

In his article Fractions, Decimals & Advanced Place Value: *The Three Essential Elements of **Algebra Readiness, *David Berg said the following:

How many times have I heard exasperated students exclaim, “I hate fractions!” Even students who feel math is easy often claim, “Yeah, that other stuff is pretty easy, but I’m really bad at fractions – oh, and decimals, too.” Fractions are challenging, and are estimated to have an 80% failure rate nationwide.

He then carries on to say that these challenges are equalled by the challenges math educators face in successfully teaching fractions! Fractions’ fundamental connection to place value and decimals makes it the most crucial **bridge **connecting elementary mathematics to algebra.

Teachers tend to teach fractions by using purely procedural instructional methods and this make the challenges learners face in developing effective algebra readiness even bigger.

He concluded that most learners struggle with fractions because they did not master the **m****ul****tiplication and division facts **sufficiently.

In order to understand fractions, learners need a sound knowledge of the following:

- what fractions are
- numerator/denominator relationships
- equivalence and lowest terms
- mixed fractions and improper fractions.