To Mom and Dad
Math is a Wonderful Gift

 

[Math Matters Home] [To Mom and Dad] [Math Rhymes & Raps]
[Great Math Books] [Algebra Connections] [For Kids] [For Parents] [For Teachers]
[Why Math] [What Skills and When] [A Head Start] [You Can Teach Math!]

Why Math?

Most want their children to use and enjoy math.  Young children learn math enthusiastically, counting games can provide endless hours of fun.  Math is more than counting -- a child is playing with math when they arrange blocks in patterns.  Perhaps our challenge is to nurture that excitement.  Perhaps some of us are uncomfortable because somehow, we have lost that enthusiasm about math that most had when we were young.

Math is all about patterns and using those patters to solve problems.  It is a language.  It is a journey that can branch in many paths.  Understanding and appreciating math takes more than ability and knowledge of facts.  It requires a positive attitude, a willingness to share and work with others.  After all, few of us will just discover math by ourselves.

Adding, subtracting, multiplying, and dividing represent the basic mathematical operations, but math is not all about "number crunching."  It is about making sense of the world around us -- it is about discovering patterns and truths.  Think about it, "4 equals 4" is a statement that people across the world will agree on.  Are there really other fields of study where people will universally agree on truth? 

In many ways, math is how we learn to structure and present all kinds of ideas.  We may not think of writing a term-paper as an adventure in math, but organizing and structuring ideas requires many of the same skills that are taught when we learn the fundamentals of math.  Its more than numbers, its about how to present the concepts behind the numbers.

Those that do not understand mathematics can struggle when making decisions or can be more easily fooled or mislead.  There are many ways that math is mistakenly used.  The result is that people can accept as "true" something should be looked at more skeptically.  Perhaps just as importantly, those that do not understand math can become unwilling to accept anything that relates to numbers is true.  Yes, some statistics are not accurate or do not apply to a given situation; that does not mean that ALL statistics are bad and meaningless.  Like it or not, it is up to each of us to decide for ourselves.

A technological society demands literacy and numeracy.  Math skills are important in our personal lives, relationships with our family and others, education and career paths, and roles as a citizen.  Technology allows us to use calculators and computers to "crunch numbers," performing calculations we prefer not to manually compute.  That does not mean that these machines actually "do the math."   Math skills are more important today than ever. 

Most parents want their children to get a good education.  Most want to see their children appreciate and develop math skills.  We know that success in school demands math skills.  We want our children to have choices.  Helping a child prepare for success in math is an important way to more fully ensure that they complete high school with a meaningful diploma and skill set.  That, in turn, will be what gives them real choices after graduation.  Giving a child a "head start" in math is one of the most important gifts anyone can give.  It is a gift that keeps on giving.

By Bill Breitsprecher
2006, Breitlinks
All Rights Reserved

[Math Matters Home] [To Mom and Dad] [Math Rhymes & Raps]
[Great Math Books] [Algebra Connections] [For Kids] [For Parents] [For Teachers]

[Why Math] [What Skills and When] [A Head Start] [You Can Teach Math!]
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What Skills and When

A good question many ask is, "What skills should children be learning and when should they learn them?"  Reasonable people can disagree on the "best answer" here, but this is clearly a question that shows people care.  Children develop differently, no one can "prove" that "one size fits all."

It is also important to recognize that we cannot research these types of education issues with tests or "double-blind", scientific studies.  We must actually work with each child to study how they learn.  We cannot perform "empirical" studies that would "force" some children to "not learn" so that we can structure research about those that are learning.  Saying how children should learn cannot be a precise science.  Fortunately, many years of experience, both within and outside of America, does provide guides to help us better understand how children learn.

The National Council of Teachers of Mathematics has developed NCTM standards and expectations to describe how they work to teach children mathematics from pre-kindergarten to high school.  Wisconsin Department of Public Instruction has also developed Wisconsin 's Model Academic Standards for Mathematics to provide direction for Wisconsin's schools.  It is not our purpose to restate these objectives.  Parents are encouraged to review those links if they want to review how math skills are typically taught in today's schools. 

We would like to present how math skills have been traditionally taught.  After all, while Mom and Dad can help a child with their math homework, they can also supplement school-based instruction by sharing a variety of math skills. 

Traditional Approach to Teaching Math in Elementary Schools.  Many parents want to help their children with math, but when they look at their children's textbook, they see "new math."  The textbooks that are used in schools change; the fundamentals of math do not.  Clearly, calculators have forced math instruction to change -- the use of calculators in school is still "controversial" among many math teachers.  Studies also show that high school teachers and college math professors disagree on what skills are fundamental. 

Math instruction changes.  Here is a "checklist" of how math has traditionally been taught in American elementary schools.  We don't present this as the "best" instruction.  Our goal is to share with parents and families how many generations of Americans have mastered mathematics.

bulletKindergarten.  Counting is an important start.  Young children can learn to count, to at least as high as 10.  Kindergarteners may not be able to count accurately, but they enjoy doing it.  These children can also start to develop an understanding that numbers are just a part of mathematics.  Kindergarteners can learn to recognize squares, rectangles, triangles, and circles; being able to compare and contrast how they are similar and different.  They can also learn patterns by stacking blocks -- shapes of blocks will stand and shapes of blocks that will fall.  Young children love to sing, chant, clap their hands, and stomp their feet.  The more you get a kindergartener involved, the better.  Having fun is more important than being accurate.
bulletFirst Grade.  Addition is emphasized.  As children learn to add, it becomes possible to start collecting data as a group.   Each child can be responsible for counting a particular object.  The class adds each student's data to gain a better understanding of applying math to solve problems and work with larger numbers in a "real-world" situation.  As students master counting, they learn, "skip counting" -- counting by 2's (2, 4, 6, 8) and then 3's, etc.  Students also start recognizing and counting dots in patters, squares, rectangles, and triangles.  This, in turn, prepares then to learn multiplication.  Simple multiplication may even be presented.  Puzzles, riddles, and games become an important instructional tool.  Students are also introduced to the concept of "half" and "one third."
bulletSecond Grade.  Students learn to add and subtract, using numbers up to at least 18.  Some teachers believe that now is when to teach "place values", others find that children this age "don't quite get it yet."  Others start to teach multiplication.  If children have learned to count dots in rectangles earlier, this provides the foundation to start teaching multiplication.  Second grade is when students are taught to think about "negative numbers."  This is an abstract concept, we don't actually use negative numbers when counting.  This prepares them to work with number lines and more fully see the value of "0."  Once children start working with number lines, they are ready to start looking at subdivisions along the number line (i.e. 1/2, 2/3, etc.).  The concepts of symmetry and number lines prepares students to work with fractions as they get older.  This is also a good time to introduce children to currency -- counting pennies, nickels, dimes, quarters, and dollars reinforces the concept of "parts" and prepares them to work with decimals and fractions.  Experimenting with weights can also be valuable.  Working with money and weights helps keep math in a fun, useful, "real-world" context.
bulletThird Grade.  This is when student have traditionally been taught multiplication tables.  Students are also expected to have basic addition and subtraction tables memorized.  By the end of the year, students should be able to multiply, without the aid of a calculator, up to "10 times 10."  As students get comfortable working with the larger numbers that this multiplication produces, it is time to introduce addition and subtraction of 2, 3, and 4 digit numbers.  These large numbers tend to fascinate children, especially when they have dollar signs in front of them.  They can be taught the concept of tens; hundreds; thousands; ten-thousand; hundred-thousand; and then a thousand thousands, which is a million.  Traditionally, the third grade is when fractions are formally taught, though basic concepts that underlie fractions have been introduced since first or second grade.  When students begin to learn fractions, they are developing the foundation to learn division -- all fractions indicate division.
bulletFourth Grade.  Students continue to work with fractions and division is formally introduced.  Fractions prepare students to divide sets or objects into even parts, work with proportions, ratios, and division tables -- how many times does 10 go into 40?  As students learn the basics of fractions, decimals, multiplication, and division; all kinds of problem solving and related topics are possible.  At all grade-levels, math instruction needs to be more than "drill and practice" of basic math operations.
bulletFifth Grade.  Fractions are a fairly complex subject, encompassing many different types of skills.  In the fifth grade, students continue to explore fractions.  Adding, subtracting, multiplying, and dividing fractions is beyond some elementary school students -- be understanding and sympathetic.  Try to remember that operations with fractions and simplifying the results involves an understanding of prime numbers and factoring.  These are topics that are typically considered beyond young children, but realize that some children are ready to master them.  It is common to work with students on these skills and then take a "break", introducing elementary algebra, averages, probability, geometry, graphs, or functions.  Each of these topics can be used to create an opportunity to "revisit" math skills with fractions.  The fifth grade has traditionally been used to review and reinforce math skills and continue to extend that understanding.

In general, endless drill-and-practice will not move students to master subjects that they are not ready to conceptualize, no matter what grade they are in.  Different children have different needs.  When a student is having trouble with a given topic or "underachieves" when tests is compared to another student, perhaps they are not being challenged. 

Most "experts" believe that improving math skills across diverse populations does not mean slowing instruction down or providing remedial instruction.  There are any number of cases where "underachieving students" dramatically improved their skills when they are introduced to increasingly more advanced topics and innovative ideas to teach math.

By Bill Breitsprecher
2006, Breitlinks
All Rights Reserved

[Math Matters Home] [To Mom and Dad] [Math Rhymes & Raps]
[Great Math Books] [Algebra Connections] [For Kids] [For Parents] [For Teachers]

[Why Math] [What Skills and When] [A Head Start] [You Can Teach Math!]
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Giving Your Children
a "Head Start" in Math

We all want our children to do well in school.  Do you want to give your child a "head start" in math?   There are many ways you can start.  One does not need to be an "expert."   Math is all around us.  Think about the things you do regularly that involve math.  When shopping, writing a check and balancing a checkbook, measuring distance, telling time, using a calendar, cooking or baking, play games, or just watching sports on TV, you are using math. 

Showing comfort and confidence when using the math we encounter daily helps children build a positive attitude about math.  Perhaps the most important thing we can share with children is excitement about learning and enthusiasm about math.  Children are naturally curious, they love to count.  We don't  need to teach children to enjoy math; we want to encourage them to keep enjoying discovery and the many ways math is all around us.

Simple things make a big difference.  Count things they enjoy.  Let them count with you.  Don't worry if they make mistakes -- this is part of learning.  Children love songs and rhymes -- there are lots of rhymes for counting and number themes.

Talk about shapes -- help them recognize circles, squares, triangles, and rectangles.  Math is more than numbers, its about patterns.  When children start to recognize shapes, ask them how squares and rectangles are alike, then ask them how they are different.  This is also a great time to talk about colors. 

When children start to learn colors and shapes, now there more things to count!  Start a collection -- it doesn't have to be anything expensive.  Kids love interesting looking rocks (free) or inexpensive toys just as much as the fashionable "collectibles."  Count the collection regularly until the child can remember how many items they have.  Adding new items to the collection introduces addition. 

Keep in mind that subtraction is not always about "taking something away," though that is one way teach children to subtract.  We can also use subtraction when we determine that we have 3 bears and need 2 more to have 5.  A child that starts kindergarten with an ability to recognize numbers, count to 10, and recognize basic shapes and colors has a HUGE head start.  It doesn't matter if they get it right all the time.  Looking at these tasks with some excitement and enthusiasm is more important.  What we are really building are positive attitudes and a willingness to learn. 

Talk about the size of things, a cup, a quart, a half-gallon of milk.  Better yet, show them by filling containers with water or sand.  Let them do it themselves.  Ask them to predict if the contents of one container will fit in another.  Let them watch you cook or bake.  When they are old enough to help, get them involved.  A good way to experience math is to measure the ingredients of a recipe.  A batch of cookies contains lots of fun math, especially if you double the recipe.  Kids will have fun while the cookies are being made and they will enjoy results too.

There is lots of fun math in preparing for a shopping trip.  Make a list, count the items, and decide how much money to take.  Look at ads and find the "best" price.  At the store, ask them to look at prices.  Ask "Which one is a better buy?"  or "How much will 2 boxes of cereal cost."  Don't be afraid to bring a calculator and put them "in charge." 

Let them buy something -- ask them how much money they will need and how much change they should get back.  Today's cash registers are computers that calculate change due -- you can still teach your children to count change.  "Fifty-two cents out of one dollar?  Three pennies make 53, 54, 55.  Two dimes make 65, 75.  Adding a quarter makes 1 dollar." 

Counting money and change is a great way to introduce decimals and fractions.  If a child is becoming comfortable with decimals, use that to introduce fractions -- fifty cents (.50) is one-half of a dollar.  If a child had become comfortable with fractions, use this to introduce decimals -- one-half of a dollar is 50 cents (.50).  Many math topics are related --  children learn best when they are introduced to new ideas that build on what they already know.

You don't have to do this at the store -- kids will find it just as much fun doing it at home.  They will enjoy holding the money, even if it is just "play money" that you make together.  Math teachers call the items that children hold and move while learning "manipulatives."  Virtually anything works -- older people remember playing "Jacks," a manipulative counting game.  While most of us think of an abacus as being "old-fashion" and technologically obsolete, it is still a great way to introduce children to concepts of counting and numbers.

"Dominoes" and "Checkers" are also fun and feature numbers and counting.  Lots of games function as manipulatives -- computer games can feature "virtual" manipulatives.   The Math Matters Links for Kids page features online games and resources that children will enjoy. Introduce children to fun ways to use math. 

"Tick Tack Toe" introduces shapes, counting, and strategy.  "Connect the Dots" is a simple counting game that only needs paper and pencils   This game not only looks at squares and rectangles, it introduces strategies and counting.  It can be made simple with a few dots or advanced with more dots.

As children learn fractions and/or decimals, they are ready to be introduced to percents.  A percentage is the top part of a fraction whose bottom part is 100 -- 50% means 'half of" and 25% means "a quarter of'."  One hundred percent means the complete quantity.  Ask children to compare things using percentages.  Ask children to figure out a sale price if it is 10% "off."

Show them the "pattern" when working with "tens" -- 10% is as simple as moving a decimal place to the left one place.  Ten percent of 100 is 10, ten percent of 1.25 is .125.  Working with money is a great opportunity to talk about decimals and "rounding."  There is no coin that represents half-a-penny, we will have to call 12.5 cents 13 pennies.

Working with 10's creates "short-cuts" and allows us to do math without a calculator.  When children are ready to work with 10's and percents; show them a "trick" for calculating “tips” for waitresses, hairdressers, and other “personal service” providers.

Explain that it is a common courtesy to tip 15% of the total bill. When service is great, some tip more; when service is poor, some tip less. Let’s assume a dinner tab of $44.38. Our 15% tip can be determined in 3 steps:
 

  1. We can identify 1/10th (or 10%) of any number by simply moving the decimal 1 place to the left. Therefore, 10% of $44.38 is $4.438 -- for our purpose, we can make our math easier by rounding to the nearest dime. In this case, $4.40 – we don’t need to be precise when tipping!
  2. Because a 15% tip equals 10% of the total plus an additional 5% of the total, we can determine the remaining 5% by taking our answer from step 1 and dividing by 2. ($4.40)/2 = $2.20.
  3. Finally, add the values that were determined in step 1 and step 2. THIS IS YOUR TIP! $4.40+$2.20 = $6.60 tip.

Don't forget that math is related to all kinds of learning.  We can count words in a list, sentence, story or poem.  We can count letters of the alphabet or letters in words.  There are many wonderful children's books that feature math.  Some are picture and chapter books that introduce numbers or pattern into their story.  Others are specifically written to teach math concepts.  Be sure to look at Math Matter's Great Math Books page for sum suggested books to read and share with a child.

The suggestions presented here do not require "big" math skills -- they are just about sharing ways we use math in our lives.  Please don't be afraid to share math with children.  While some of us are comfortable and capable of introducing our children to higher levels of math, algebra, geometry, trigonometry, calculus or statistics, that isn't necessary to give our children a "head start."

The beauty of sharing math with our children is that we can choose the areas that we are comfortable with -- what we teach them is less important than how we do it.  Kids enjoy sharing anything with mom, dad, other family members, and family friends.  The key is to be encouraging and enthusiastic.  People that have had bad experiences in higher-level math classes have nothing to fear.  We can help our children and promote positive attitudes by getting them involved with areas of math that we are confident with. 

If a child asks a question that we don't have an answer for, that creates a "teachable moment."  We can tell children that they have asked a great question and that we want them to have a "great answer."  Celebrate and nurture this curiosity and model positive attitudes about learning.  Think about who you know that might be able to explain the answer to both or you.  Take them to a library and ask a librarian to find a book or website that will help.  Remember, the process of learning is more important than the facts and figures.

By Bill Breitsprecher
2006, Breitlinks
All Rights Reserved

[Math Matters Home] [To Mom and Dad] [Math Rhymes & Raps]
[Great Math Books] [Algebra Connections] [For Kids] [For Parents] [For Teachers]

[Why Math] [What Skills and When] [A Head Start] [You Can Teach Math!]
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You Can Teach Your Child Math!

Do you feel ready to teach your child math?  Don't worry, we are not talking about finite math, calculus, or even algebra.  We are talking about fundamental concepts that prepare your child for success..  Most schools have qualified teachers and follow carefully created math instruction that moves a child towards mastery of higher level math.

Mom and dad can help children develop positive attitudes, enthusiasm and confidence with basic math skills.  At all levels, math is a subject that builds on prior learning.  By helping a child develop an appreciation of fundamental math skills, you are more fully ensuring that they have the tools they need to succeed in school.  Often when students struggle with math, the real problem is a concept or procedure that underlies the topic that seems to cause the trouble.  This can feel overwhelming and prevents a child of proceeding with confidence and comfort. 

As good as most school-based math instruction is, you can help your child by teaching ideas and concepts that may not be fully part of a given math book or class.  One-size does not always fit all.  Building and reinforcing math at home gives a child other ways to learn.  Here are some suggestions about helping children with math that may or may not be part of how math skills are taught in school.  Helping your child with these concepts will prepare them to excel in math classes.

What is a Number.  Most of us learn numbers by counting.  This is a fun way to learn, although it is helpful to realize that each number is a concept in and of itself.  Getting kids comfortable with small numbers, so that they do not have to count to understand them is good.  Dice and dominoes have small numbers of dots arranged in patterns.  Playing games with these patterns helps children understand small numbers.  As they play dice and dominoes, children learn to recognize their values without having to count each dot. 

When in a situation where there are small numbers of people or objects present, ask children how many there are.  "How many wheels on the car?"  "How many leaves on this flower's stem?"  "How many plates should we set at the table?" are good ways to help a child become comfortable with small numbers.  When there are a few people in a room, ask, "How many people are here?"  Eventually, children will start seeing numbers without having to count each preceding value.

Try arranging groups of dots on a piece of paper, 2 dots to a group and 2 groups of dots.  At first, a child may need to count each dot - 4, but with practice, they will find "shortcuts" to "see" how many dots there are without counting each one.  As a child is comfortable with this, show them larger groupings and, when they are getting good at it, use mixed groupings.  Try arrange dots uniformly in circles, squares, and rectangles. 

Zero, its Nothing.  Most children learn numbers by counting.  We don't actually count the number 0 -- there is nothing to count.  It is an important concept.  When something is gone, there is no more cookies, it is a great time to show a child the concept of 0.  Baseball fans see a lot of zeros -- it is common for games to have scoreless innings. 

When rockets are being sent into space, we count down ...5, 4, 3, 2, 1, BLAST OFF!   "Blast-off" represents zero.  Its a point that separates time BEFORE a rocket is launched and the time AFTER a rocket is launched.  Thermometers use 0's.  Celsius temperatures use 0 in a useful way -- it is when water freezes.  Above zero, water is a liquid.  At 0 and below, it is ice, a solid.  

Zero is also used as a placeholder.  When we write 9, the next number is 10.  The 0 "holds the place" of the 1's and we put a "1" in the placeholder for 10's.  The number 130 has no 1's, three 10's, and one 100.  Its actually a pretty sophisticated concept, but once we understand it, we think "nothing" of it!  Zero is an important number to talk to children about because it is not a "counting number."

How Big.  Measuring is a great way to get children interested in numbers and extend their understanding beyond counting.  Kids love to see how they are growing, so get them involved with keeping track of their height.  Teach children to use a ruler -- you can measure one side of a piece of paper and then help them measure the other side.  Baking has all kinds of measurements, its a fun way to learn.  It is much easier to learn metric units than traditional U.S. units.  Start with whatever you and your child are comfortable with.  Measuring is a great way to introduce children to the concept of a fraction, but don't be concerned if they don't understand numerators (top number) and denominators (bottom).  Remember, the goal is not to "test" them; there is no reason to consider answers "wrong."  You can always "double check" a child's measurement and show them how to correctly find the value.  We want to share and help the learn what they are developmentally ready for.  If a child is really confused, it is best to simply change the subject and talk about something else.  We don't even need to tell them that they have made an error in their math.

"Subtraction" is Not Always About Taking Something Away.  Many math books describe addition as putting parts together (3 apples + 3 apples = 6 apples).  Likewise, many books define subtraction as starting with a number and taking some away (5 apples - 2 apples = 3 apples).  Often, these images are a great way to get children started.  Subtraction, however, mean more than "taking away."  While we use subtraction to "take way," show children that we also use subtraction for:

bulletDifference.  When on person has 5 cookies and another has 2 cookies, the difference between them is 3 (5 cookies - 2 cookies = 3 cookies. 
bulletFind Missing Numbers.  We use subtraction to solve equations, finding a value for a missing number.  If we have 4 cookies and daddy gets 1 cookie, how many are left for everyone else?  (4 cookies -1 cookie = 3 cookies).
bulletDistance. Subtraction can also used to calculate distance.  For example, if we walk 5 city blocks forward and then three city blocs back, how many blocks are we from where we started (5 blocks - 3 blocks = 2 blocks) 

You can help children see the four ways we use subtraction: "take away," difference, finding missing number, and determining distance.  This will help them as they learn math in schools and are required to learn different ways to think of subtraction. 

Multiplication and Area.  Teaching children to measure the length of an object is important.  Likewise, children can learn to find out how much something weighs and determine temperature.  Each of these measurements is 1 dimensional.  Mathematically, it is important to be able to determine area -- 2 dimensional measurements.  Area is based on length and width. 

While this may sound confusing to a child, it is easy to show them by using a square.  If the sides are both 1 inch, then the area is one square inch.  The concept is easy to see by drawing shapes on graph paper.  This allows children to count the square units.  The concept is easiest to see with squares, but works for rectangles too.  Being able to work with area prepares students for multiplication.

Fractions:  Parts of a Whole.  Most of us think of pieces when we think of fractions -- they consist of a numerator over a denominator (n/d).  A fraction has different meanings and uses.  When a child understands small numbers, they are ready to be introduced to fractions.  Teaching children the concept of fractions as parts is probably the easiest way to introduce them to children.  When making a child a sandwich, ask how many pieces they want it cut in -- if the child says 2, cut the sandwich in two.  Give the pieces to the child one at a time, stating, "here is one half a sandwich."

As discussed earlier, many recipes have fractions in units.  Measuring cups for 1/8, 1/4, 1/3,  1/2, and 1 cup make wonderful toys too.  Let children practice with sand or water.  As they get comfortable with the idea, talk about fractions when it seems appropriate.  Don't worry if a child makes a mistake -- we don't have to grade children at home!

When a child gets something wrong, you can just ignore it and talk about something else.  Keep things positive.  Sometimes a child just isn't ready to do what we expect of them, that is OK.  If a child makes an error with math, you can change the subject to a math area they understand.  They don't even need to know they made a mistake.  Birthday cake, pies, and pizza are great for getting children involved with fractions.  Sharing a cookie or candy bar also presents a great opportunity to talk about fractions.

Fractions:  Points on a Number Line.  Showing children how numbers are ordered on a number line is easy.  Draw a line and label the left endpoint zero.  Write counting numbers to the right: 1, 2, 3, 4, 5, 6...  Point out that we have a "number line" not "numberdots."  The line has to include points BETWEEN the values that we have indicated.  Half-way between zero and 1 is 1/2. 

Half-way between 1 and 2 is 2 and one-half.  Together you can fill in these "dots".  As children get comfortable with this, you can point out that between ANY 2 points, is another midpoint -- there are fractions between each of the fractions you can identify.  In theories, you can identify fractions on the number line forever!  How's that for some meaningful conversation with your child!

Fractions:  ProbabilitiesRELAX!!!  We are just talking about another way to think of fractions.  Our goal is just to get children thinking so that they are ready to learn more later -- positive attitudes are more important than math theorems and proofs.  If you flip a "fair" (balance) coin -- it either comes up heads or tails and it will do so with equal probability. 

There are 2 possible outcomes -- when we right the probability of heads or tails, 2 is the denominator (bottom number).  For each flip of the coin we expect 1 of 2 possible outcomes --  1 head or 1 tail.  This is our numerator (top number).  The probability of a coin coming up heads is 1/2.  The probability of coming up tails is 1/2.  If we flip a coin a large number of times, we will expect heads half the time and tails the half the time.  This makes a great, fun "experiment" to share with a child. 

If you roll a die (singular of dice), you have six total outcomes -- that is the denominator (bottom).  The chances of rolling a 1, 2, 3, 4, 5, 6 are all equal -- you might roll any of these on any roll.  Each of six possible outcomes are equally likely.  The probability for a each number is 1/6 (specific outcome/total outcomes).

If we want to know the probability of rolling a number that is an even number, we still have 6 possible outcomes -- 3 or which are even, 3 of which are odd.  We could express this probability as 3/6 (specific outcome/total outcomes).  Note that this fraction is not in "lowest form," 3/6 = 1/2.  Teaching children to reduce fractions requires an understanding of multiplication and factoring.  Remember, our purpose is not to make children mathematicians, it is to get them thinking about different ways they will use math. 

Fractions as Ratios.  When we compare one number to another, we form a ratio.  The fraction 1/4 can be used to indicate a ratio of one part to four parts.  Recipes often have ratios.  The traditional recipe for pound cakes is a ratio of 1 (1/1 or one-to-one).  We can make a pound cake with1 pound flour, 1 pound butter, 1 pound eggs (8 eggs), and 1 pound sugar.

If a recipe calls for 1 egg and 2 cups of flour, the relationship of eggs to cups of flour is 1 to 2. We can represent this as a ratio of 1/2.  Maintaining the proper ratios of ingredients is important when baking.  To make cookies that both look and taste good, you need to make sure to use the right amount of each ingredient and maintain the ratios in the recipe.  Add too much flour and cookies will be solid as rocks. Add too much salt, they'll taste awful.

Ratios get us ready to understand percentages.  A fraction with a denominator of 100 can easily be expressed as a percentage, for example,  9/100 = 9%.  Understanding fractions as ratios prepares children to learn proportions (comparing two equal ratios).

Fractions as Division.  An important concept in mathematics is that we can use fractions to represent parts of a whole, probabilities, and ratios; but they ALWAYS represent division.  We can always take our fraction, 1/2, divide the numerator (1) by the denominator (2) and get .5 as the answer.  Performing the indicated division of a fraction results in its decimal equivalent. 

Performing the indicated division of a probability or ratio and multiplying by 100 results in a percentage (1/2 = .5; multiply by one hundred = 50%).  In algebra, division is almost always written as a fraction -- this more clearly lets us see common factors and simplify.  To prepare children for algebra, they need to be comfortable with fractions. 

Tying it All Together.  We do not need to teach our children all of their math at home -- likewise, schools may not teach children all of the different ways that they can learn math.  If you help your children understand the concepts presented here, you are getting them ready to do well in math class.  Math topics are related.  Do you see how all of the topics presented here are related? 

Understanding numbers without having to count gets us started.  Adding the concept of zero gets us to measure things, our measuring scale starts at zero.  Measuring in one dimension prepared us to work in 2 dimensions, the concept of "area".  This introduces multiplication (length times width). 

Most of us think of fractions as a piece of something -- children will learn to understand half a sandwich, half a cookie, and one piece of pie or cake that is cut into a given number of slices.  This gets us started with fractions.  Our understanding of numbers, zero, and measurements prepares us to look at number lines; which will lead to a more meaningful discussion of fractions.  It is a natural way to show children how a fraction can be written as a decimal.

While most think of fractions as part of something larger, fractions can be used to represent probabilities, ratios, percentages, and proportions.  Fractions give us a starting point to look at division. Working with fractions and understanding how they represent division is a fundamental skill in algebra. 

There are different ways that these topics can be "connected" to move students through a math class.  A textbook or class may direct students to learn math in a certain way.  Giving your children a basic understanding of the concepts presented here will more fully ensure that they have the fundamental skills they need to succeed in math class with a minimal amount of frustration.  Why not give your children more "tools" to start with.

In many ways, that is the key -- help your children prepare for math classes so that they start the class with positive attitudes and core skills.  They will maintain that enthusiasm and build on it.  We don't all need to be mathematicians, but we can do well in math class, if we get the fundamentals.

By Bill Breitsprecher
2006, Breitlinks
All Rights Reserved

[Math Matters Home] [To Mom and Dad] [Math Rhymes & Raps]
[Great Math Books] [Algebra Connections] [For Kids] [For Parents] [For Teachers]

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Helping With Homework

Most parents want to help their children do well in school.   For some, finding the time is the challenge.  Others are not confident or comfortable with certain subject areas.  Helping with homework is a great way to spend some "quality time" with a child and develop a meaningful dialog.

The good news is that the most important help we can give is encouragement and support.  We can emphasize that learning is fun.  We don't need to be "content experts."  Parents are a child's first and most important teaacher.  Sometimes, parents are ready to play a "leading role" and other times, parents can help their children work with their teachers, textbooks, or homework lessons.  Here are some things to remember when helping your child with math.

Positive Attitudes Promote Learning.  Show that you are confident your child will succeed.  It helps if you have confidence in your abilities, but be sure you have confidence in their abilities.  When a child has a questions, tell that "that's a great question."  If they make an error, that's OK, be sure to let them know this.  Treat mistakes as opportunities for learning.  Talk about positive experiences you have had in math -- don't share negative stories, that won't help.  Maybe we are not all "experts" in math, but we can show interest.  Regardless of what you feel about your math skills, be sure your children see that learning math can be fun.

Keep Yourself Informed.  Get to know your child's teachers and what they expect of your child.  It helps to look at the material your child is learning too.  Textbooks and lessons are designed to "lead" students through learning.  Don't wait until your child is "lost" to look at their lessons.  Starting in the middle of a math book can confuse even those that are confident with math.  Try to see what concepts are being presented, the sequence of the presentation, and how one topic leads to another. 

Support Good Study Habits.  Encourage students to set aside a specific period of time each day for homework.  It helps to have a desk or "work area" for homework.  Getting children to study regularly with a positive attitude is important.  Try to minimize distractions. 

Emphasize Strategies.  While "doing the numbers" is important, it is more important to determine the answer in an organized manner.  The process is often more important than any given problem.  Encourage your child to make lists, draw diagrams,  make models, guess (estimate) and check, look for different combinations, and simplify problems.  Modeling these strategies is helpful.  So is encouraging your child to talk these strategies through as they apply them.

Guide Learing With Questions.  Don't show your child how to do it, ask them questions so that they are involved.  Try to help them reach that moment when they say, "EUREKA -- I have it!"  Some good questions to ask include:

bulletWhat words in the problem look helpful and what do they mean?
bulletWhat should be our first strategy?
bulletWill (  suggest a strategy  ) help us get started?
bulletWhat resources or tools will be helpful?
bulletCan we record our thinking?
bulletAre we making progress?  Is our strategy working?
bulletHave we answered the question or found all the possible solutions?
bulletAre there patterns in what we have done?
bulletHave we clearly shown how we solved the problem?

Notice how these suggestions are all student-centered and not math-centered.  That is the key, we are actually talking about how we learn instead of just doing math.  Assume that your child will get all the "math help" they need at school.  If needed, discuss this with teachers.

Parents can develop a meaningful dialog with their children about the process of learning.  This is where you have the greatest advantage -- you know your child better than educators.  One of the greatest gifts we can give our children is an understanding of how they learn.  Helping a child with homework is really all about nurturing an excitement about learning, positive attitudes about school, self-confidence, effective study habits, and strategies for problem solving and learning. 

By Bill Breitsprecher
2006, Breitlinks
All Rights Reserved

[Math Matters Home] [To Mom and Dad] [Math Rhymes & Raps]
[Great Math Books] [Algebra Connections] [For Kids] [For Parents] [For Teachers]

[Why Math] [What Skills and When] [A Head Start] [You Can Teach Math!]
[ Top ]