“Why do we have to learn this?”
“Why do we have to show our work?”
“When are we ever going to use this in real life?”
Math teachers endure a barrage of these questions on a daily basis. And sometimes, students can seem justified in their protests. (When is the last time you solved for the derivative? Or figured out the cosine of an angle?)
More often, however, students are not challenged to apply their skills in a real world environment. Skills that, if nothing else, are essential for success in the classroom and on standardized tests such as the SAT and the ACT.
From my extensive experience as a test prep tutor, I have noticed certain areas of math that students should have already mastered back in middle school, but still cannot completely grasp as juniors and seniors. Here are some of those areas, and some tips on how you can have your sons and daughters practice in “real life.”
Percentages
Leaving the Tip: Parents who make their children figure out how much tip to leave on the bill at a restaurant usually teach easy shortcuts: Find 10 percent then double it for a 20 percent tip, or find 10 percent, then 5 percent for a 15 percent tip. And while these tricks usually work, children do not understand why they work. Ask them to leave an 18 percent tip and watch them falter helplessly. Challenge your kids to leave 17 percent and 22 percent tips. Anything that is an unordinary number to force them to use actual math skills.
Additionally, have them solve for the total bill amount. High school students struggle with the idea of increasing a value by a certain percentage. Present the restaurant bill in this light: If you leave a 21 percent tip, the final amount is a 21 percent increase from the total charged for food and taxes.
Shopping for discounts: While tips represent a percent increase, shopping for sales requires students to solve for a percent decrease. Take your kids shopping, with one rule: For any item on sale, if they cannot solve for the discounted price, they are not allowed to buy it. If the price tag shows the already discounted price, do not let them peek—just tell them the original price and the discount percentage. And even when sales are over, keep the game going. Make up discounted rates and if your kids cannot solve the problems you create for them, they cannot purchase that item.
Averages
Sports statistics: Let’s make the assumption that your son or daughter either plays sports or watches sports. If they play a sport, pick two or three statistical categories and have them figure out their average per game over the span of a season. The quantity and quality of the statistic does not matter. Whether they are solving for large numbers (points per game in basketball), small numbers (goals per game in soccer), good statistics (race times in track or swimming), or bad statistics (double faults in tennis), the process of problem-solving is the same. And if they religiously watch a certain team play, have them act as the team statistician. Maybe they can figure out the Phillies average runs scored in a game, or the Eagles average points given up per game.
Class Grades: Every student waits for their report card to learn their GPA, but why should they have to wait that long? Have them figure out their GPA throughout the semester. If a student knows their average grade in each class, have them calculate their GPA for that quarter or trimester. Then, as the year goes on, they can figure out their GPA in each class to date, and combine those calculations together to get their cumulative GPA.
And most significantly, later on in a quarter, challenge them to figure out what test score they will need to achieve or maintain the grade they want in a class. If they know their test average in world history is an 87, but they want at least an A- for the quarter, have them figure out the minimum score they need on the last exam to achieve their goal.
More to come at a later date, but this is a good place to start! The more students use these math skills beyond class and homework, the more fluent they will become in problem solving for percentages and averages.
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