History

The idea of decimals has been around for over three thousand years! Although the origin of them is relatively unknown there is evidence that they were utilised in the ancient civilisations of Greece and Rome. Furthermore, just to outline an example, in 2500BC the ancient Indus Valley Civilisation, who existed geographically on modern day Pakistan and northern India, used decimals in their weighing system. So that is how important decimals have been to various human societies over the past centuries and now it is your turn to expand your knowledge in regards to them!

Why should you learn decimals?

Well they are important to learn because they simply appear regularly throughout life. Having a good understanding of the concept is ideal as there are many times when they are needed for referral in everyday situations . Decimals, like fractions, are in the essence also just another way of expressing part of a whole. They could therefore emerge quite often in everyday life. An example includes dealing with money and having amounts rounded off to the nearest cent. Another is measuring weight on a scale.

Syllabus Outcomes Covered

A student:

• communicates and connects mathematical ideas using appropriate terminology, diagrams and symbols MA4-1WM
• applies appropriate mathematical techniques to solve problems MA4-2WM
• recognises and explains mathematical relationships using reasoning MA4-3WM
• operates with fractions, decimals and percentages MA4-5NA

My Plan

My plan is to break up the syllabus dot points required to obtain a good understanding of decimals, into eight lessons. Gradually new content will be introduced as we progress through the lessons but by the end all the major dot points will be covered. It is also worth noting that some lessons will repeat content that was introduced in the lesson before. This is just to ensure that the 'heavier' dot points will be given the attention that they require so that students will be able to understand each concept and ideas better!

So firstly in the website for lesson one we will look at the role of place value in decimals and then move onto ordering decimals. Following on from this next lesson we will look into the idea of rounding off decimals to a certain number of decimal places. This will then lead us onto the following lesson which deals with terminating, recurring decimals and rational numbers. In the next lesson after this we will look into connecting decimals with fractions and percentages and stressing the idea that all of these concepts are just different ways of representing a whole. We will also be converting fractions to decimals and terminating decimals to fractions. The next three consecutive lessons after this will deal with operations involving decimals. Firstly addition and subtraction will be touched upon and then we will move into multiplying and dividing decimals. We will then conclude the unit by calculating decimals of quantities. This is a good way to end as it is the perfect lesson to relate decimals to real life situations and scenarios to stress their relevance to students.

Link to NESA: https://educationstandards.nsw.edu.au/wps/portal/nesa/k-10/learning-areas/mathematics/mathematics-k-10/content/1137

Approximation: A value of quantity that is nearly but not exactly correct. For example 100 is the approximated version of 120 rounded off to the nearest hundred.

Convert: To change the form of something

Notation: Written symbols used to represent numbers

Operators: A symbol or function denoting an operation

Order: To arrange things in relation to each other according to a particular method. For example 1,2,3,4,5,6 are arranged in chronological order.

Quantity: Something that can be measured. For example time, mass, length, volume, temperature etc

Recurring: Occurring again repeatedly.

Terminating: Something that is brought to an end.

Very useful page for teaching decimals with some interesting ideas:

https://extranet.education.unimelb.edu.au/SME/TNMY/Decimals/Decimals/index.htm

This could be useful for obtaining ideas on the teaching of place value for decimals

https://files.eric.ed.gov/fulltext/EJ891799.pdf

Another video which helps with explaining why the rule for multiplying decimal numbers works

https://www.homeschoolmath.net/teaching/d/multiply_decimals_by_decimals.php