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Mathematics Tips for Parents

Boy by "My Cute Graphics"
Success in school starts and continues at home, but many parents feel inadequate when it comes to helping their children with math. While parents can usually find time to read a story to their children, thereby instilling a love for books, they are often at a loss as to how to instill a love and appreciation for mathematics.  Like reading, mathematics is a subject that is indeed necessary for functioning adequately in society.  Here are some tips to help you as you work with your child this school year.

Recognize that you make an important difference in your child's education.   Most children develop a sense of numbers way before the "regular" school years.  If you have a young child, take advantage of those early years through activities at home that teach and at the same time are enjoyable.  You might take your child on a counting walk in your neighborhood to count how many trees, shrubs, plants, houses, birds, dogs, etc. you see.  Look for twigs or pine cones or leaves, etc. and have your child count as many as s/he can. Then lay them side by side to compare the length and ask your child, "Which is the longest, which is the shortest? Are there any that are the same length?"

Provide experiences at home that help your child be successful, and seek ways to let children, even very young children, know that they are needed and important.  Cooking is a fun way to do this. Help your child follow the directions on a Kool Aid packet or frozen juice can to make refreshments for the family.  Help your child cut a fruit or vegetable into halves, fourths, thirds, etc. Let them help prepare a meal while asking, "What do you do first? Second? Third?"  or better yet, allow them to measure the ingredients for a recipe.

Children do not need a lot of motivation when it comes to recognizing and learning the value of coins.  You know they are interested when they start bugging you for money.  However, it is not sufficient for children to be able to just recognize coins, they must also know the value of these coins.  The best way to accomplish this is to use real money.  You might show your child two or more coins and have him/her tell you the total value of the coins.  Or hold up a coin.  After your child identifies it, discuss what the coin would buy at the store.  When going to the grocery store, give your child his/her own money to buy something.  Have them select an item that costs less than the money you have given them.  You can also do a similar activity by asking them to determine what are the fewest number of coins it would take to pay for the item. Give your child a practical math experience by estimating how long it takes to prepare a meal from start to finish.

Parents' attitudes toward mathematics have an impact on children's attitudes; so, be patient with your child.  A wrong answer on a math test or a homework assignment is not a time for scolding.  It tells you to look further, to ask questions, and to find out what the wrong answer is saying about your child's understanding.  Ask your child to explain how they solved the problem.  Most importantly, relax!  Know that neither you nor the teacher needs to be perfect for your child to learn math.  Remember, one bad math assignment/test will not destroy your child's ability to learn math.

But what if you need some assistance?  Luckily, in today's world, we can find mathematical help at the click of a button.  Below are some great places to go and find outside help if your child is struggling or if you need more information for yourself.

Study Shack is a great place to find or make flashcards, play hangman, do matching activities or crosswords.  It has activities for grades 1-6 as well as addition, multiplication, algebra and geometry.  Cliff's Notes for Math is site that has notes, examples and quizzes for your older children.  The subject areas include Basic Math through Calculus.  There are many on-line math dictionaries.  My favorite is A Math Dictionary for Kids because it includes animation and interactive activities.  Even You Tube is a great resource for students struggling with a concept and needing an alternative way of seeing it. 

Finally, talk about people who use math in their jobs, including builders, architects, engineers, computer professionals, and scientists.  Point out that even if your child does not plan to pursue a career in which s/he will use math, learning it is still important because math teaches you how to solve problems and how to think logically.  AND we use math everyday!

My Cute Graphics offers FREE clip art and images for teachers, classroom projects, web pages, blogs, scrapbooking, print and more. Check out the website by clicking either under the boy sitting on the equal sign at the beginning of this article or on the purple letters in this paragraph.

Parabola - The Arch Enemy?

I love to relate math to the real world with my students because that is the only way they will see the relevance.  Our family (son + his wife + three grandkids + husband) just returned from a trip to Orlando.  While driving home from Cocoa Beach, my daughter-in-law noticed a purple arch.  Being that my mind is always, always thinking about math, I informed her that it was a parabola with a negative slope.  My son, who is an engineer, starting talking about slope, and the two of us shared some equations such as the one for lines y = mx + b (much to the chagrin of the other travelers stuck in the car with us).

Mathematically speaking, a parabola is a two-dimensional, symmetrical curve or simply, a special curve shaped like an arch.  All parabolas are vaguely “U” shaped, and they have a highest or lowest point called the vertex.  The vertex is the place the parabola makes it sharpest turn.  Any point on a parabola is at an equal distance from a fixed point (the focus), and a fixed straight line (the directrix). Parabolas may open up or down and may or may not have x-intercepts, but they will always have a single y-intercept. Those that open up have a positive slope (they form a smile) and those that open down have a negative slope (they form a frown).  We always get a parabola when we graph a quadratic equation, an equation that contains a variable that is squared such as y2 = 20x or x2 - 9y = 0.

Now that all of this is as clear as mud for many of you, let's look at some parabolas in real life.  Yes, they are out there!  Can you identify the ones below?

Did the last picture stump you?  Well, it would unless you were from Los Angeles.  It is the
Encounter Restaurant, atop Los Angeles International Airport’s landmark Theme Building.

Other real life examples include....

1) Throwing or Kicking a Ball - If you throw a baseball, kick a soccer ball, shoot an arrow, fire a missile, or throw a stone, it will arc up into the air and come down again following the path of a parabola! (Except for how the air affects it.) The next time you watch a football being thrown from the quarterback to a receiver, think of a parabola.

2) Roller Coasters that arc up and down and sometimes around - the one ride I avoid! When a coaster falls from the peak (vertex) of the parabola, it is rejecting air resistance, and all the bodies are falling at the same rate. The only force here is gravity. Most people (I am NOT included) enjoy or get a thrill out of parabolic-shaped coasters because of the intense pull of gravity.

3) Reflectors - Parabolas are also used in satellite dishes and flashlights. In satellite dishes it helps reflect signals that then go to a receiver, which interprets the signals and shows satellite-transmitted channels on your television. In flashlights, car headlights and spotlights, the parabolic shape helps reflect light. Notice the beam of light coming from the flashlight on your right. See how the light appears to be in the shape of a parabola?

4) Suspension Bridges such as the Golden Gate Bridge, the Brooklyn Bride, the Washington Bridge, etc.  Suspension bridges are capable of spanning long distances and actually are the only type of bridge to span the longest distances possible for a bridge. This is because the shape of the suspension bridge is actually one of the most stable structures there is. In the image of above, can you see how the cables form parabolas?

So now you know parabolas are everywhere even when you are playing ports, watching T.V., riding a roller coaster at your favorite theme park or going cross a suspension bridge.  So what kind of parabola will you display on your face today…a negative parabola (a frown?) or a positive parabola (a smile)?

Elvis and PEMDAS

Any math teacher who teaches the Order of Operations is familiar with the phrase, "Please Excuse My Dear Aunt Sally".  For the life of me, I don't know who Aunt Sally is or what she has done, but apparently we are to excuse her for the offense.  In my math classes, I use "Pale Elvis Meets Dracula After School".  Of course both of these examples are mnemonics or acronyms; so, the first letter of each word stands for something.  P = parenthesis, E = exponents, M = multiplication, D = division, A = addition, and S = subtraction

I have always taught the Order of Operations by just listing which procedures should be done first and in the order they were to be done.  But after viewing a different way on Pinterest (originally posted on Math = Love by Sara Hagen), I have changed my approach. Here is a chart with the details and the steps to "success" listed on the right.

Since multiplication and division as well as addition and subtraction equally rank in order, they are written side by side. What I like about this chart is that it clearly indicates to the student what they are to do and when.  To sum it up:

When expressions have more than one operation, follow the rules for the Order of Operations:
  1. First do all operations that lie inside parentheses.
  2. Next, do any work with exponents or radicals.
  3. Working from left to right, do all the multiplication and division.
  4. Finally, working from left to right, do all the addition and subtraction.
Failure to use the Order of Operations can result in a wrong answer to a problem.  This happened to me when I taught 3rd grade.  On the Test That Counts, the following problem was given.

The correct answer is 11 because you multiply the 4 x 2 and then add the 3, but can you guess which answer most of my students chose?  That's right - 14!  From that year on, the Order of Operations became a priority in my classroom.  Is it a priority in yours?  Should it be?


I have a new product that I recently added to my store entitled: Order of Operations - PEMDAS, A New ApproachThis ten page resource includes a lesson plan outline for introducing PEMDAS, an easy to understand chart for the students, an explanation of PEMDAS for the student as well as ten practice problems.  It is aligned with the fifth grade common core standard of 5.OA.1. Just click on the words under the cover page if it is something you might like.

Not on the Test

Not on the Test
While watching my granddaughter at her tennis lesson, I was visiting with two teachers.  One was a retired fourth grade teacher and the other currently taught Algebra in middle school.  Both we decrying the fact that each year the students come with knowledge that is more narrow than broad.  They both felt this was because more and more time is now spent on testing or getting ready for testing.  As I stated in my January 25, 2012 posting entitled The Pros and Cons of Testing, "High stakes tests have become the “Big Brother” of education, always there watching, waiting, and demanding our time. As preparing for tests, taking pre-tests, reliably filling in bubbles, and then taking the actual assessments skulk into our classroom, something else of value is replaced since there are only so many hours in a day.  In my opinion, tests are replacing high quality teaching and much needed programs such as music and art."

A long time ago, a friend sent me a song written by Tom Chapin with John Forster called Not on the Test. I saved it, and I listen to it often, especially when I am having a "down" day.  Tom and John wrote the song to express their disappointment in the lack of arts education in many public schools.  Even though the song refers to No Child Left Behind, with Common Core approaching with its own set of tests, I think you might get a much needed laugh from the song.  Just click on the link under the picture, and let me know what you think!

Math or Maths?

I keep seeing the word "maths" on Pinterest. hmm   To me it is confusing and puzzling in addition to being a misspelling or misuse of the word "math".  Where in the world did this word come from, who created it, and why?

Math can be used in the singular form ("math") or in the collective form ("math") without distinction. Math is a field of study which is divided into specific multiple disciplines such as algebra, geometry, etc. which then are again divided into mathematical subgroups.

Likewise, "physics" is single word for a particular field of study, even though it ends in "s". You don't study "a physic"; you study "physics". Just like physics, mathematics is considered singular, but maths? Isn't that like saying deers for deer or sheeps for sheep?

Well, here is the mathematical truth.  Maths is the term commonly used in England, Australia, New Zealand, etc.  It is a shortened form of mathematics.  They pluralize the word, and refer to studying "maths" because mathematics has an "s" on the end.  So the answer to this "maths" question is that it depends on where you live as to what word you use.  Therefore be aware of the geographical differences so you can use the correct form of the word in your writing or speaking.  And when you see the word "maths", don't jump to the conclusion it is a misspelling or a misuse.  Recognize that the writer most likely lives outside of the United States.

Interested in "Math" stuff?  There are 51 resources in my store just for math.  Just go to the category of Math Stuff.

Is zero even? What an "odd" question!

My daughter and her husband are heading to Las Vegas with his family to celebrate his parent's 50th wedding anniversary.  I guess when you are at the roulette table, (never been there or done that) and you bet "even" and the little ball lands on 0 or 00, you lose. Yep, it's true; zero is not considered an even number on the roulette wheel, something you better know before you bet.  This example is a non-mathematical, real-life situation where zero is neither odd or even.  But in mathematics, by definition, zero is an even number. (An even number is any number that can be exactly divided by 2 with no remainder.)  In other words, an odd number leaves a remainder of 1 when divided by 2 whereas an even number has nothing left over.  Under this definition, zero is definitely an even number since 0 ÷ 2 = 0  has no remainder. 

Zero also fits the pattern when you count which is the same as alternating even (E) and odd (O) numbers.
Most math books include zero as an even number; however, under special circumstances zero may be excluded.  (For example, when defining even numbers to mean even NATURAL numbers.)  Natural numbers are the set of counting numbers beginning with 1 {1, 2, 3, 4, 5....}; so, zero is not included. 
Consider the following simple illustrations.  Let's put some numbers in groups of two and see what happens.

As you can see, even numbers such as 4 have no "odd man out" whereas odd numbers such as 3 always have one left over.  Similarly, when zero is split into two groups, there is not a single star that does not fit into one of the two groups.  Each group contains no stars or exactly the same amount.  Consequently, zero is even.

Algebraically, we can write even numbers as 2n where n is an integer while odd numbers are written as 2n + 1 where "n" is an integer.  If n = 0, then 2n = 2 x 0 = 0 (even) and 2n + 1 = 2 x 0 + 1 = 1 (odd).  All integers are either even or odd. (This is a theorem).  Zero is not odd because it cannot fit the form 2n + 1 where "n" is an integer. Therefore, since it is not odd, it must be even.

I know this seems much ado about nothing, but a great deal of discussion has surrounded this very fact on the college level.  Some instructors feel zero is neither odd or even.  (Yes, we like to debate things that seem obvious to others.)

Consider this multiple choice question.  (It might just appear on some important standardized test.)Which answer would you choose and why?

             Zero is…
                      a.) even
                      b.) odd
                      c.) all of the above
                      d.) none of the above

Mathematically, I see zero as the count of no objects, or in more formal terms, it is the number of objects in the empty set.  Also, since zero is defined as an even number in most math textbooks, and is divisible by 2 with no remainder, then "a" is my answer.

Odd Man Out!

Sometimes we think everyone knows the difference between an odd and even number.  When I was teaching my remedial math college class, we were learning the divisibility rules, the first of which is that every even number is divided by two.  I wrote the number "546" on the board and asked the class if this was an odd or even number.  I had one student who disagreed with the group answer of even.  I asked him why he thought the number was odd, and he replied, "Because it has a "5" in it. " It was obvious this student got all the way through high school without a clear understanding of odd and even numbers.  So the moral to this story is to be sure to discuss the difference between an even and an odd number with your students. 
A good definition for an even number is that it can be put into groups of two without any left over, like giving each person a partner.  But when you have an odd number of things and put them into groups of two, one will always be left out.
Try this approach.  Make your hands into fists and place them side by side as seen in the illustration.  Say  a number.  Now count, and as you count, put up one finger for each number said, alternating between hands, with fingers touching. 
For instance, if you said “4”, you would count one, (left pointer finger up) two, (right pointer finger up and touching the other pointer finger) three, (left middle finger up), four (right middle finger up, touching the other middle finger).  Four is even because each finger has a partner to touch.   
Repeat this several times, giving the students odd as well as even numbers.  By always having a concrete visual (their fingers) will help the kinesthetic and visual learner to "see" the odds and evens.   
Activities such as this can be found in a 24 page booklet entitled Number Tiles for The Primary Grades.   It contains 17 different math problem solving activities that extend from simple counting, to even and odd numbers, to greater than or less than to solving addition and subtraction problems.  
OR.....Check out the ten page free version by clicking here...FREE Version                     

Are Trapezoids "Trapping" Your Students?

In a previous posting (Aliens and Trapezoids, July 7, 2011) I shared with you how I taught my students to remember the word trapezoid.  Today, I would like to talk about the characteristics of a trapezoid. 

As I search on Pinterest, I find quadrilaterals that look like the one on the right classified as "trapezoids".  Indeed they are, but this is a special kind of trapezoid because it has one set of equal sides, one line of symmetry and one set of parallel sides.  It is called an isosceles trapezoid.  Isosceles means "having two equal sides" just as an isosceles triangle has.
BUT to be a trapezoid, the only characteristic needed is one set of parallel sides.  Look at the red quadrilateral on the left.  It is a trapezoid because it has one set of parallel sides.  YET, students rarely see this kind except on those math tests that COUNT!  Why?  Because those trapezoids (and test writers) are out to "get" your students.  So think about it.  Are the trapezoids in your classroom trying to "trap" your students or can your students recognize a trapezoid even if it doesn't have symmetry? 


I love teaching geometry, and therefore I have several geometry products for sale in my Teachers Pay Teachers Store.

Geometry Parodies - The four page handout includes 20 unusual definitions of geometric terms such as “A place where people are sent for committing crimes.” Each definition is a play on words or a parody.

Plane Geometry Test - This 100 point assessment is over
plain geometry concepts and focuses on using and applying geometry. Measuring and categorizing angles, identifying lines, angles, quadrilaterals, etc., solving for circumference, using formulas, recognizing symmetry, and comparing using and applying geometry. Measuring and categorizing angles, identifying lines, angles, quadrilaterals, etc., solving for circumference, using formulas, recognizing symmetry, and comparing two quadrilaterals are included.

Plane Geometry Vocabulary Crossword - This puzzle is designed so that the student will practice and use geometric vocabulary. It is a free form crossword puzzle that features 25 different geometry terms. The 25 clues are in the form of definitions which emphasize points, lines, and angles.

Solid Geometry Test - This 100 point test is a summative assessment given at the end of the solids unit in our math book. It highlights using and applying formulas to find area, perimeter, circumference, surface area, and volume.

Solid Geometry Vocabulary Crossword - This crossword puzzle is designed to practice geometric vocabulary and recognize formulas. It is a free form crossword puzzle that features 23 different geometric terms or formulas. The 23 clues are in the form of definitions or a formula format which give emphasis to polyhedrons, circles, and formulas for area, surface area, and volume.