MAE3270 Module 4 - Lecture 3: Decimals and percentages

Strategies to correct decimal misconceptions:
- Using concrete materials such as base 10 blocks
- Using number lines
- Having students predict the next number in a sequence and show them on a number line
- Checking with a calculator
Introduction to percentages:
- Introduced in the upper years
- Utilize percent bars, number lines, and 10 by 10 grids
- Help students connect fractions, decimals, and percentages
Writing a percentage as a fraction:
- Write the percentage as the numerator
- Write the number 100 as the denominator
Converting percentages into decimals:
- Divide by 100
- Example: 75% becomes 0.75
Models for understanding percentages:
- 100 discs on a rope in multiples of 10
- Rectangular grids
- Percentage bars
- 100 grids

Converting fractions to decimals:
- Make the denominator one of the decimal place values
- Example: 1/200 can be converted to 5 thousandths
Converting percentages to decimals:
- Divide by 100
- Example: 234% becomes 2.34

Ratios:
- Sets of numbers separated by a colon
- Describe a relationship between 2 or more groups
Examples of ratios:
- 1 part cordial to 4 parts water
- Ratio of cordial to water is 1:4
- Ratio of water to cordial is 4:1
- Total amount is 5 parts
Simplifying ratios:
- Divide by common factors
- Example: 4:12 can be simplified to 1:3

4 goes into 4 once, and 4 goes into 12 3 times.
Ratio can only be directly converted to a fraction when the two numbers are related in a part to whole relationship.
- You add each together to get the whole.
Useful online resources for teaching decimals and percentages:
- https://www.topmarks.co.uk/
- https://au.splashlearn.com/decimal-games
- https://extranet.education.unimelb.edu.au/SME/TNMY/Decimals/teaching/models/nexpand.htm#decimal