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
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.
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
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
By Bill Breitsprecher
All Rights Reserved
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.
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
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
|Kindergarten. 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
|First 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
|Second 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"
|Third 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
|Fourth 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.|
|Fifth 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
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
All Rights Reserved
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
for counting and number themes.
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
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
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
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.
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.
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”
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:
- 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!
- 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.
- 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
All Rights Reserved
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
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
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.
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
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.
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
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."
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.
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
|Difference. When on person has 5 cookies and another
has 2 cookies, the difference between them is 3 (5 cookies - 2
cookies = 3 cookies. |
|Find 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).|
|Distance. 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
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."
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!
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: Probabilities. RELAX!!! 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
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.
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.
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
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
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
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
All Rights Reserved
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.
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.
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:
|What words in the problem look helpful and what do they
|What should be our first strategy?|
|Will ( suggest a strategy ) help us get started?|
|What resources or tools will be helpful?|
|Can we record our thinking?|
|Are we making progress? Is our strategy working?|
|Have we answered the question or found all the possible solutions?|
|Are there patterns in what we have done?|
|Have 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
By Bill Breitsprecher
All Rights Reserved