Guest Blog Post: Fractions, Decimals, and Percents--Interrelationships in Mathematics, Applied to Test-Taking Strategy

Fractions, Decimals, and Percents--Interrelationships in Mathematics, Applied to Test-Taking Strategy

By Alexandra Berube, bostontutoringservices.com

Being able to memorize the most common fractions, decimals, and percents, is key to performing well on standardized tests. I prepare students for the ISEE and SSAT tests regularly, and this is one of the most important concepts for them to mater. In many types of math, you need to be able to manipulate different forms of the same amount, such as 25% =1/4 = .25. Or, 10% =1/10=.1.

Understanding the interrelationship of these will make solving word problems so much easier. Many problems will ask them to find the percent of something, and they need to understand why the word 'of' in this case means 'times' (X). To solve 10% of 100, first I need to show them that 10% is 1/10, because a percent means the number over 100 (such as, 78% means 78/100, or 30% means 30/100)--so 10% means 10/100, which reduces to 1/10.

Then I show them why 1/10th of something means 1/10 times something. I draw a grid with 10 columns, and I show the student that 1/10 of those is one. So 1/10 of 10 is 1. I have to translate this into 1/10 times 10 is 1. I show this as: 1/10 X 10 is 1/10 X 10/1 (because any integer becomes a fraction if you put it over one--when you divide an integer by one, the result is the original number). 1/10 X 10/1= 10/10 which reduces to one. I do this in a number of ways with a number of percents that have been translated into fractions, until they understand that the percent of something means the percent times that number.

Furthermore, knowing certain concepts and the shortcuts you can use with them is crucial in test-taking strategy. Knowing that 10% of something means you are lopping off the last zero, or moving the decimal place over once to the left, such as in 10% of 80 equals eight. If they can do this in their head, they can save so much time.

In the same way, they should know that any percent of one hundred is that number (25% of 100 is 25). There are a million shortcuts like these that adults who have been using math for decades will not even think about. All adults have our own shortcuts that we apply on a daily basis, but explaining these to students is crucial, because we can never assume they will adopt these shortcuts on their own.

Yet it is extremely important to introduce the shortcuts at the appropriate times, once they already understand the longer way to solve a problem. I will show them that 25% means 25/100, which can be reduced to 1/4. 1/4 of 100 means 1/4 times 100, which is 100/4, which is 25. You can't skip any steps and assume that they will make these leaps on their own.

About Alexandra Berube
Alexandra is the Managing Director of Boston Tutoring Services, a tutoring company that offers one-to-one in-home tutoring in Massachusetts. She is also a former Kindergarten teacher who also tutors students in grades K-8, in all subject areas, including test preparation.

Math Resources to Keep on Hand When Tutoring

                                  
                                 

Math can be quite difficult to teach, especially regarding the analytical process and mental manipulation that people tend to go through with each problem they encounter. If you are tutoring Math, make sure you have the following resources that can ensure a smooth math tutorial, especially as they help maintain smooth function of the tutorial session.

Calculators

Bringing calculators is a staple in Math subjects as you can use them to countercheck answers and to simplify long processes that are preliminary to a given topic but are not required to go over once the student understands the topic at hand.

Charts

You can bring different charts to represent the topic you are discussing. For example, you can have a table of formulas of areas and volumes of planes and solids for a Geometry tutorial or perhaps a table of integrals for a Calculus one. Use charts as visual aids to guide people.

Problem Sets

Math is all about practice, so make sure you have enough problem sets for your student to try out. This is one practical way for him or her to learn Math.

Board

Math can’t be read out loud or perhaps just simply shown on a PowerPoint presentation. It must be applied manually through the solving process, and that is what a board is for. Bringing a whiteboard and showing how the equation is solved can allow your student to grasp the material easily.

Teaching Math can be quite tough without the right materials. With these Math resources to consider, you can perform your tutoring session smoothly as you are allowed to optimize the resources you bring for that session.

Tackling Math Subjects--Tutoring Tips to Consider

Math isn’t easy, and it becomes a growing subject children need to be tutored in. Let’s face it, Algebra or Geometry aren’t easy to learn and even more difficult to teach. If you really want to help children out with the math subjects, then here’s what you need to do, here are some considerations you should check out before starting the tutorial session.

Read Over the Material

Learn how the book approaches the material. Math is cumulative, so you should ask yourself: is there need to review a previous concept? This will allow you to modify your approach in order to allow the child being tutored to learn the material and even more future topics using the same strategy. If they introduce calculations before concepts, then try to work around that by formulating that session by writing it down for reference later.

Work Away From the Material

Once you’ve read it, it’s time to add some unique flavor to the teaching style. Math can be boring for those that aren’t interested, so spice things up. Add a little game to the tutoring session to keep children interested. Don’t stick to book-bound concepts because it tends to tire them out. Math can be a very tiring subject to learn, so keep in mind the short attention span most children have.

Explanation before Application

Kids want to know why something happens before they can see it for themselves. It gives them that expectation when they solve a problem or do an operation. Explain why the process goes that way in order to give the child the perspective of how math really works. After that, give them a problem to do, and once they get the process right, the answer comes smoothly.

Math is a difficult subject to teach, especially when the child isn’t interested. Understand the focus and scope of the lesson beforehand and work from there to make math a fun subject to teach. Always remember to give an overview of the process by showing him or her how it’s done so they learn actively.