As an adult, student, or parent, it is common to experience a lack of confidence in dealing with numbers. This common problem many times gets blown out of proportion and can sometimes be a roadblock to success in school, work, or helping your children become more confident in their abilities. In this article, I outline five skill areas to improve in order to increase your own skill, speed of calculations, and self-confidence when thinking mathematically.
These skill areas are exactly that: things to practice repeatedly until you can do them quickly and with confidence. In school, beware of things being taught but with inadequate time given to practice. Think of these ideas as homework assignments for you or your children. If given enough time, these building blocks can tremendously help a student get through mathematical situations in school or life with ease!
Math Skill Building Block #1: Basic Math Facts
This step is very common sense, but extremely important, and is sometimes not practiced enough in elementary school before students are allowed to move on. Everybody MUST know addition and subtraction facts of at least two-digit numbers. We have to combine or take away quantities like this every day, and we don’t need a calculator! Push the calculator away; practice adding or subtracting two-digit numbers comfortably until you can do this quickly without your fingers.
Learning the multiplication facts up to at least 12 is also a must. When you really know these, you should be able to list the multiples of 12 easily, or count backwards from 100 by 7’s, etc. If you are working with your child, try these multiple lists or counting backwards subtract exercises.
TIP: Break numbers apart in order to add or subtract. Instead of 12 + 39, think of it as 10 plus 39 equals 49, but add two more to get 51. OR 12 plus 40 is 52, take away one more is 51. This is an excellent mental math exercise.
Math Skill Building Block #2: Working with Percents
Knowing how to take a percent of a number is really just taking a part of a whole amount. We know how important this is when we work with money, finance, buying & selling, investment, and other parts of our lives.
Students must be able to work with percent concepts. To practice, find 10% of any number. Of course, this is just moving the decimal point over one place to the left. For example, 10% of 55 is 5.5, 10% of 39.6 is 3.96, and 10% of 442 is 44.2.
Likewise, people need to find 1% of a number (move the decimal 2 places to the left), 5% (half of the 10% amount), 20% (one-fifth of something), 50% (half of something), 75% (half of the number, then add half of that). The understanding of percents and their fractional equivalents is HUGE! And, it takes a lot of practice and repetition.
TIP: A magical way of finding the percent of a number is to take advantage of the fact that, mathematically, 15% of 50 is the same thing as 50% of 15 (7.5). Just switch the percent number with the other number to find an easier calculation. Try it!
Math Skill Building Block #3: Using Estimation and Rounding
The ability to estimate how much something will cost, how much paint needs to be purchased, how much space is required, etc., is a critical skill for students to master. With repetitive practice, all of us need to be able to improve our speed of rounding numbers before a calculation, or rounding the result of our calculations. Most of the time, we don’t need the exact answer. Knowing how much to round and estimate our numbers is tested all of the time in our math and science classes at school.
Look for opportunities to find estimates: cost of a home improvement project, money earned over time, time it takes to accomplish a task, or increase and decrease of temperature over time. After estimating, challenge yourself or your children to use a calculator or paper to test out how close you are to the actual answer. If students can quickly estimate an answer, even for a complicated calculation or problem solving exercise, their confidence will skyrocket!
TIP: Practice estimation skills when grocery shopping. You or your children can call out the price of an object before putting it in the cart, and keep track of the estimated total. Whoever is closest to the actual total is the winner! If the grocery list is huge, just round each amount to the nearest $5 or $10, or whatever might be appropriate.
Math Skill Building Block #4: Creating Your Own Word Problems
This skill is the reverse of the dreaded task of reading a word problem from your math textbook and solving it. In this case, parents or students should think of a situation in terms of how it could be written in a math textbook. I encourage my students to put a problem in their own words (aloud), then write it out on paper (they can be really creative at this point), then do the next critical step: look for mathematical operations clues. These “clue words” force the solver to think about how the quantities are related or how they interact in the problem. If students can’t put the situation into mathematical language, then they don’t really understand what is being asked.
TIP: Mathematical “clue word” to look for, after you write out the problem on paper ---
Addition: sum, total, together, combined, given to, put in the pile, money earned
Subtraction: take away, withdrawn, money paid, amounts lost, less
Multiplication: multiple groups, piles with the same amount, repeated addition, “of”
Division: split into groups, how many in each group, part of, “part”
Math Skill Building Block #5: Understanding Basic Geometric Concepts
The geometric concepts of area, perimeter, and volume are ideas that can be directly relevant to students as they study them in school. A simple connection could be the task of building a house or constructing anything. Other ideas to include are properties of squares, rectangles, and the sides of special right triangles. Building block #3 (Estimating) ties in to this idea, also.
Have yourself (or your children/students) estimate the volume of water that a certain container will hold. Use simple block shapes at first to reinforce the volume formula of three-dimensional objects (area of base X height, OR length X width X height). Then pour water into the container that has measurements on the side to check the estimate.
Another idea is to measure the two legs of an object that is in a right triangle shape. Then estimate the hypotenuse (diagonal distance). An example would be to find out how high a set of stairs is, how far out horizontally they reach, then measure the distance along the top of each stair down to the lower level. For older students studying the Pythagorean Theorem (for right triangles) this is a great application of the idea. For younger students, ask them how far it looks from one corner to the other of a rectangle or square on a piece of paper. Then measure to see who is closest.
TIP: Geometric ideas relate directly to objects found in our everyday lives. Take advantage of this and practice applying what you know about squares, rectangles, and diagonals to estimate square roots without the calculator. Then check your calculations. You will feel or see increased confidence after several successful tries.
These building blocks are taught in the early days of everyone’s education, but sometimes are not practiced enough to be effective tools in your mental toolbox. Whether you are a student, parent, or someone who feels a lack of math confidence, keep these tips in mind. It doesn’t have to be dull; just increase your speed with basic math facts and estimation, then learn to work with percent concepts. Look for “clue words” in problem solving situations, and check things out later with a calculator. With these tips, anyone can again rediscover their “math brain”!