I was hoping some Math Teachers can share with me how to teach percents, proportions, and ratios? Since these problems can be set up so many different ways, where do you start? - Jinx
I can not stress this enough: use real world examples that show a clear need for the student to know how to work with fractions, decimals, percents, ratios, etc. There is a satisfying reward attached to math when it results in real world problem solving.
When I was teaching at an electronics college, I was given the challenge of teaching a class for adults who failed the basic entrance math exam. The school’s motivation was financial, of course: offer a free basic math course and get the potential customer to the point where they can pass the entrance exam and be able to qualify for financial aid, but I digress.
These were all people who couldn’t calculate percentages or convert decimal numbers to fractions. But once I showed them how math was simply a tool that comes in handy to solve real world problems, nealry everybody caught on and most even seemed throroughly pleased with themselves that they had “mastered” something that had probably stumped them for so long.
To find out which real world examples are going to make the biggest impact on your student, you have to know a little something about them. If there are any cooks in the class, ask them how they’d triple a recipe that calls for 1 and one-third cups of water, 2 and one-eighth sticks of butter and seven-eighths teaspoons of flour. And tell them that measuring the ingredients three times is not an option.
The worst thing you could to is teach basic math as a set of axioms or a purely conceptual thing and expect the student to master is without a good reason. And a failing grade is often not a good reason, it just creates an adversarial relationship and sets the student against you from the start.
Math is for total nerds… So naturally, wise teachers try to fill their classes with nerds.
I’m not officially a teacher, but we homeschool and it falls to me to teach many of the sciences because that is my strong suit. So, here’s my advice, it’s worth what it costs 
Do some more reasearch on what you’re trying to teach them. Learn its history, why these concepts were developed. They weren’t developed in a vacuum, they had real-world applications for the most part. Re-create history for your students. At the moment they don’t have these concepts in their heads, so re-create the physical world from history which made these concepts necessary.
Percents. Percents were developed as a way to normalize, or shift into a common reference frame, various sizes of data sets. It’s a way to map subsets of these various sizes of sets onto a common framework, base 100. 90% of something is nine-tenths of something. We know how much 9/10 is, we can visualize a pair of hands with nine of the ten fingers up. We know that this is an overwhelming majority and it lends meaning to a statement that otherwise, while logically equivelant, might not have the same impact. Imagine saying nine hundred thousand dollars were spent on XXX out of a million dollars the person had. Well, a person may know that a million dollars is a LOT of money. And they may know that nine hundred thousand is a lot of money as well, but when you say that ninety percent of a persons money was spent on XXX, then it really hits home as to exactly how much, relatively, was spent.
Work on percentages like this. Just use fingers. All ten fingers up is 100% Ask your students to show you twenty percent of their fingers. Play around like that, maybe a half-raised finger can count as 5%. Tell your students that percentages are just a handy way of making the relationship between some subset of something(fingers up out of fingers total) easier to understand. Maybe later move on to other numbers. Give them fifty pennies and ask for 10% of their money. Or say you’ll give them 26 percent of their current total if they can tell you how many pennies that would be. Once they realize that each penny represents 2% they can easily count by twos and then find out how many pennies would be 26%. Lots of ways to get them to work with it and understand that it is just a convenient mapping to a base of numbers that they can work with easily.
Proportions are fairly easy too. Get a tape measure and build a house of cards. Measure the card-house and talk to them about if they’d like to live in a house like this. Take them to the local hardware store and measure plywood. Pretend each sheet of plywood is a card and then show them how large the real house would be if they used sheets of plywood instead of playing cards. Figure out what the scale between the cards and the plywood was.
Tons of fun, engaging ways to teach this kind of stuff. Just remember to think outside the box. For thousands of years people have learned by doing, figured out things through necessity. We don’t have to confine todays children to classrooms and teach them without the benefit of hands-on experiences or real-world applications.
Enjoy,
Steven
Don’t use pie charts. Use actual pie. You can demonstrate multiplication of fractions, such as how much pie you get when you take 1/4 of 1/3. Then everyone gets to eat some pie. Mmmmm, pie.
When teach math, bring pie.
Pi good.