What are Percentages? You can observe percentages almost everywhere, in shops and supermarkets, advertising and even on the internet. Percentages are one of the essential concepts that form the basis of many advanced mathematical concepts. Students must have a firm grip on this concept to help them gain a better understanding of future concepts. The basic learning of percentages begins in third grade which then steadily advances in future grades. To fully grasp the concept, students should be able to understand the relationship of percentage with decimals and fractions. The term 'percent' stands for 'out of hundred'. Percentages, like decimals and fractions, are used to describe the parts of the whole. In percentage, the whole is divided into a hundred equal parts. Percentages are denoted by the symbol '%'. To help your students learn percentages easily, try using 100 small boxes. You can use the grid to represent the whole and parts of percentages. If you color the 25 boxes out of the 100 boxes, then students can visualize 15%. If you color all the 100 boxes, you can demonstrate 100% to the students. Encourage students to design their grids and compute different percentages by coloring different numbers of boxes. You will work through all kinds of conversions with percentages. I like to call them the "Math Conversion Trilogy": Decimals, Fractions, and Percentage. You will move between all three very often.
- Adding and Subtracting Percentages and Decimals - We show you how to master sums and differences between these two forms.
- Compare Percentages and Decimals - This is something, if done well, can really help you understand if you are getting a good deal.
- Conversion Between Decimals, Fractions, Percentages - We show you how to make all the transitions between these forms for the same value.
- Creating Pie or Circle Graphs From Data Charts - This helps use better understand the data and the trends that exist within.
- Find Percentages of Numbers - This is helpful when you are attempting to calculate a sale price, among other things.
- Finding Percent of Fractions Word Problem - These types of problems are a daily occurrence in jobs that exist in warehousing units of products.
- Finding Percentages By Using Decimal Method - We capitalize on the nature of decimals. Many students prefer this method to the others below.
- Finding Percentages By Using Fraction Method - This is helpful when you are transitioning values within groups or sets.
- Finding Percentages By Using Ratio Method - The value over one hundred comes in handy here.
- Finding the Percentage of a Decimal Value - You will make use of dividing and multiplying by one hundred here often.
- How Much Greater Is the Percentage Value - This type of math is very common in business transactions.
- Interpreting Pie or Circle Graphs - We show you how to read and make sense of these types of visuals.
- Markups and Markdowns Word Problems - Merchants will make use of this math every day.
- Multistep Ratio and Percent Word Problems - These problems will require you to make at least to separate calculations.
- Patterns of Association (Using Data Tables) - This will help you find trends in data and make good decisions based on it.
- Percent Error and Percent Increase - How wrong were you? How much does a value grow?
- Percent Equation - You will learn how to apply this to basic and complex situations. It has a bunch of applications.
- Percentage as a Rate per Hundred - These are common calculations that apply to many forms of science.
- Percentages and Numbers Lines - A great way to visually understand percentages.
- Percentage Decrease of Integers - These are similar to markdowns on a broader scale.
- Percentage Word Problems - Being able to perform these well is very helpful when you graduate.
- Probability of the Chance of an Event - Probability and percentages go hand in hand.
- Visual Fractions, Decimals, and Percentages - Give these values shape through the use of images.
Best Practices for Teaching Students the Concept of Percentage
The goal here is to help students understand how much of each unit in a group contributes towards a full unit. This is a fundamental concept that all students will need to understand to become productive citizens. Here is the progression of lessons we have found to really help students solidify their understanding of this concept:
One Hundred Grids - Start with a 10 x 10 (100) grid to pass this concept on to students. The 100 grid is the whole and the part represents the amount of the part that you have in hand. A good starting point is a value that is less than half, such as 35%. That value would fill the first 3 rows and half of the 4th row so as the image to the right portrays.
From here you could move on to a value that is greater than a half. This art-based approach really helps students visualize the concept of a whole and the parts that have been occupied within the whole based on the percentage that is given. We encourage you to continue on with this form until it becomes second nature for them.
Percentage of a Value - Then we move the visual to a tag diagram to best understand the progress towards a whole unit. This leads us to using a rectangular shape which we estimate a portion of the whole. If we were to find the value 35% towards a whole, it would look like what you see to the right.
This then progresses us towards the use of math. We introduce students the concept that a percentage is a decimal value based on the logic that 1 is equal to 100%. That means that 35% is equal to 0.35, when observed from a 100% view. This means that if we were asked what is 35% of 60, it would be the same as 0.35 x 60 or 21. This progression carries on to any value. Take the percentage and just divide by 100.