Begin by teaching your child to count. I know
that sounds simplistic, and it is, but it is the foundation to all math. A
child who can’t count can’t do Algebra.
Have I panicked you? “Yeaghhhh! Grab
your pacifier, Junior! I have to run out and buy a text book RIGHT THIS
MINUTE!”
Hold on. It is not so bad. You begin by simply teaching your toddler
or preschooler to count to three. “Ok Jessie, how many spoons do we need on the
table for boys? Jim, Jon, Joe, Three. That is right. You count them out now;
one, two, three. Good.”
Everyday life can supply enough math for a child
at least up to six or seven and sometimes up to ten. Have them count every day,
gradually going higher.
Don’t be afraid to use manipulatives (physical objects
such as Hot Wheels, Barbies, raisins, M&Ms), even once they start doing
their math on paper. Manipulatives help children to “see” the math
concepts. They will quit using physical objects when they become proficient
enough that it is faster to do it in their head. You don’t need to discourage
them from using them.
(My favorite manipulatives are base ten blocks. Small
cubes for the “ones,” rods the size of ten cubes laid end to end for the tens,
and flats the size of one hundred cubes for the hundreds. You can make your own
version using popsicle sticks or check eclectic catalogs or Amazon. An abacus is also handy.)
I use a grid with 100 squares on it to help
teach the four and five year olds. We add one number per day, beginning at one
and filling them all in. Then we read all the numbers together. (See appendix) When
they do that well, you introduce adding, subtracting and skip counting using
the chart.
Adding “There are three boys and four girls in
our family. How many children is that all together? You have four cookies with
your lunch if I give you four more how many will you have?”
Subtracting “We have ten plates on the table.
If you put three in the sink, how many would be left? Let’s count and see.
There are four cans of green beans on the shelf. If we buy two of them how many
would be left?” (See appendix for a chart for them to fill in when they begin
to get the hang of adding and subtracting)
Skip counting” Three, six, nine…twelve, fifteen,
eighteen…twentyone, twentyfour, twentyseven…thirty.” (To the tune on the Math Rocks Video from School House Rocks. Available at most
libraries, Amazon.com and YouTube).
We practice skip counting together in “school
time.” My four year old counts to five, my six year old counts to twenty by
ones and counts by threes and tens. My seven year old counts by twos, fives, and
elevens. The ten year old counts by fours, sevens, nines, and twentyfives. My
thirteen year old does the sixes, eights and twelve’s. I do the fifteens. We
take turns and do them in order. Because everyone listens, everyone learns even
if they are not old enough to do it themselves yet.
Multiplication is easy. It is just adding fast.
Show your child how to make three stacks with two raisins in each stack. Count
them. Then explain that 3 stacks with 2 each is 6. 3 x 2 =6. Show them how to
write it down. Move your raisins around and practice. If they already know how
to skip count this will be easy to figure out. It is anyway, really.
I
introduce the concept to my children at around five. I don’t have them actually
do any multiplication work. I just teach them how to think that way. When they
are older it is no big deal because they have “always known that.”
Division is the same thing as multiplication
only backwards. Introduce it early with toys or food. “We have twelve cookies.
If we divide them up between the three of you boys, how many will each of you
get? 12 ÷ 3 = 4.”
You can gradually introduce using a paper and
pencil to figure their math. This is a pretty abstract concept, though so go
slow (1030 minutes a day. No more). Slowly work your way up to explaining long division and multiplication.
Aim for getting them working on these at around ten years old.
Some children
will “get” math very fast. You may find yourself explaining advanced concepts
to a seven year old. Others will not care about math in the least. You may have
to push an eleven year old to understand the basics. We are all different and
as long as they get it by the time they are in their teens, it doesn’t really
matter.
Cooking is a good way to introduce fractions,
even to five and six year olds. You can cut up pies and apples and let them
play in the water or sand with an old set of measuring cups and spoons (I have
a set of cups in the bath toys) to illustrate the basic principles, then bake
cookies or cakes every week to practice them. “Oh dear. We only have one measuring
cup (hide the rest). It is a ¼ cup measure. The recipe calls for 1 ½ cups of
flour. How many ¼ cups will we need?” Double, triple and half recipes to get
the hang of multiplying and dividing fractions.
3 teaspoons = 1
Tablespoon

1 Tablespoon = ½ ounce

4 Tablespoons = ¼
cup

1 cup = 8 ounces

2 cups = 1 pint

16 ounces = 1 pound

4 cups = 1 quart

2000 pounds = 1 ton

4 quart = 1 gallon

7 = 1 week

1
thumb joint = about 1 inch

12 = 1 dozen

4
inches = 1 hand (The width of a hand with fingers together)

144 (12x12) = 1 gross

9
inches = 1 span (The width of a man’s hand with the fingers apart)

20 = 1 score

12
inches = 1 foot

144 square inches=1
square foot

18
inches = 1 cubit (from middle finger tip to elbow)

9 square feet=1 square
yard

3
feet = 1 yard (from the chin to the outstretched finger)

30 ¼ square yards=1
square rod

6
feet = 1 fathom

160 square rods=1 square
acre

5
½ yards = 1 rod

1728 cubic inches=1 cubic
foot

320
rods = 1 mile

27 cubic feet = 1 cubic
yard

3
miles = 1 league

128 cubic feet (8ft long
x 4 ft wide x 4 ft high)=1 cord

Mil=1000
(Latin)

Millimeter=1/1000 of a
meter =About the thickness of a dime

Cent=100
(Latin)

Centimeter=1/100 of a
meter =the width of a pinky

Deci=10
(Latin)

Decimeter=1/10 of a meter

Meter=measure
(Greek)

A little less than a
yard.

Deca=10
(Greek)

Decameter=10 meters

Hecta=100
(Greek)

Hectometer=100 meters

Kilo=1000
(Greek)

Kilometer=1000 meters=^{5}/_{6}
of a mile

Gram=the
weight of water contained in one cubic centimeter.

1000
grams = 1 liter
Milligram=1000^{th}
of a gram

Measure things from one centimeter to one mile. Measure
your rooms, you cars, your toys, and yourselves. Look at maps and plan pretend
trips figuring how far you would go how much it would cost and what you would
need to take. Include a shopping list for your meals.
Learning to change numbers from digits to words
and back is also an important skill
Billion
Hundred Million
Ten million
Million
Hundred Thousand.
Ten thousand
Thousand
Hundred
Tens
Units (ones)
Tenths
Hundredths
Thousandths

1 , 2 3 4 ,5 6 7 , 8 9 1 . 2 3 4
This would be read one billion, two hundred thirty four million, five
hundred sixty seven thousand, eight hundred ninety one and two hundred thirty
four thousandths. You say a unit of measure (thousand, million) at each
comma)

Use money to teach decimals. Take ads from the
paper or catalogs and make pretend shopping lists. You can add up your “order,”
subtract items from the list, buy multiple items, etc. Use your imagination.
If
you have older children that think they should have more money to spend, tell
them your income and list your bills and let them figure it out. The worst
thing that could happen is they find a way to make things work better than you
do! They will definitely get a jump on learning money management.
Teach them to read a clock (a regular one as
well as digital). Start with the hours, then minutes, then seconds.
Pretend to remodel the house or build a new one.
Figure how much material you would need and what it would cost. (Look in the
Sunday ads from hardware stores or take a field trip to Home Depot)
Design a farm that would grow all your family’s
food for a year and figure out how much that would be.
Some
Rules To Give You Ideas Of What To Teach


“Times” can be written X
(2 x 3 = 6), · (2 ·
3 = 6), or by a number next to a parenthesis ( 2(3) = 6) .


To multiply by 10 just add
0 (10x 96=960). To multiply by 100 add two 0’s (52x100=5200). To multiply by
1000, add three 0’s, etc. (If you are doing decimals you multiply by moving
the decimal point as many places to the right as you have 0’s, adding 0’s if
need be (100x3.5=350.))


To
divide by ten move the decimal to the left one place (300÷10=30). To divide
by 100 move the decimal to the left 2 places (24.56÷100=.2456)
etc.


All numbers have a
decimal. You just can’t always see it if it is on the right.

(396 = 396.)


When adding or subtracting, always keep the decimal
points aligned in a column: Then add straight down

12.34
546.478
266.4
825.218


To multiply, multiply like normal multiplication,
count the digits to the right of decimals in the problem, count that many
digits in the answer and “ping.”

12.5
24.3
375
500x
250xx
303.75


To divide, move the decimal in the divisor (first
number) to the right until it is at the end. Move the decimal in the dividend
to the right the same number of spaces (adding 0’s if you run out of digits)
then move the decimal straight up.



To change a
fraction into a decimal, divide the bottom number into the top number.



To change a
decimal into a fraction, put the decimal over a 1 with as many zeros as you
have places to the right of the decimal. Reduce.

.25 = ^{25}/_{100}
= ^{1}/_{4}


To add fractions with the same denominator (bottom
number) just add the Numerators (top numbers): ^{1}/_{4}+^{1}/_{4}+^{1}/_{4}=^{3}/_{4}


To make the Denominators match, find the smallest
number they both go into and multiply the top by the same as the bottom: ^{1}/_{2}+^{1}/_{3}=
(2 and 3 both go into 6 evenly, so) [1 x 3=3, 2 x 3=6] ^{3}/_{6}
+ [1 x 2 = 2, 3 x 2 = 6] ^{2}/_{6 }= ^{5}/_{6} (^{3}/_{6} +^{2}/_{6}=
^{5}/_{6})


To subtract fractions, do the same as above except
wherever I said add you subtract. (^{3}/_{4}  ^{1}/_{4}
= ^{2}/_{4}, ^{5}/_{6}
 ^{3}/_{6} = ^{2}/_{6})


To multiply fractions, just times it straight
across: ¾ x ¾ =^{9}/_{16}


To divide fractions, flip the second fraction, then
multiply: ^{4}/_{5} ÷ ^{1}/_{2}
=^{4}/_{5} X ^{2}/_{1} = ^{8}/_{5}


To fix an improper fraction (the top number is
bigger than the bottom) divide the bottom into the top (that gives you your
whole number) and make the rest a fraction: ^{14}/_{4} = 14÷4
= 3 remainder 2= 3 ^{2}/_{4} (this is called a mixed number)


To change a mixed number into an improper fraction,
multiply the bottom number (denominator) by the whole number and add the top
number (numerator). 3 ^{2}/_{4} = 4 x 3 + 2 = ^{14}/_{4}


To reduce a fraction, divide the top and the bottom
by the same number (you can only do this if they come out even, no
remainders): ^{4}/_{8} ÷^{4}/_{4} =^{1}/_{2}


PERCENTAGES
Percent means part of a hundred, (cent is Latin for hundred).

The percent sign (%) is a 1 with two zeros
(00). This will help you remember that percent is part of 100.


To change a
decimal into a percent, move the decimal two places to the right.

.56=56%


To change a
percent into a decimal, move the decimal two places to the left (if there is
no visible decimal, put one to the right of the last number.

30% = .30


To change a
fraction to percent, first convert the fraction into a decimal and then a
percent.

.25=25%


To change a
percent into a fraction, put the percent over 100 and reduce.

25% = ^{25}/_{100}
= ¼


To find the amount
of simple interest multiply the principle (beginning amount) by the percent,
then by the time.

$100.00 principle
x 5% (.05) = $5.00 per year x 3 years = $15.00 (interest mailed to you after
three years)


Exponents (the
little number to the upper right) mean to multiply a number by itself that
many times.

5^{3} =
5x5x5 = 25x5 = 125


Do whatever is in
the ( ) first.

2(3+4) = 2x7 = 14


To find compound
interest multiply the principle by (1+ interest)^{time} or P(1+R)^{T}

$1000 loan at 12%
annual interest compounded monthly (1% added per month) for five months would
be 1000(1+.01)^{5} or 1000(1.01x1.01x1.01x1.01x1.01)=
1000x1.0510100501 or
1051.0100501
At the end of five
months you would have $1,051.01


To round off, you
go up for five or more and down for four or less.

764 rounded to the
nearest hundred is 800 (6 is higher than 5 so you go up)
924 rounded to the
nearest ten is 920 (4 is lower than 5 so you go down)


To average, add
all the numbers and divide by how many numbers you have.

Joy has 3 hats
Jim has 3 hats
Jon has 6 hats
Joe has 4 hats
16÷4 kids=an average of 4 hats per kid.


The < or >
sign points to the smaller number.

3
>
2
The hungry little bird
eats the bigger number.


< means is less than;

2
is less than 3; 2 < 3


> means “is greater than”

3
is greater than 2; 3 >2


To find the perimeter of
a rectangle, you measure the distance around. To find the area (space inside)
you multiply the length by the width.

4”
5”


To
find the area of a triangle you multiply length by height and divide by two.
For perimeter add the sides.

6x5=30÷2=15”
6.5+6.5+5=18”


For
the area of a circle you πR^{2} In other words you multiply the
radius of the circle by itself then by 3.41.

The radius (the distance from
From the middle to the edge)
Is
5” so 3.41x5x5=3.41x25=
82.25”

All of these things can keep you busy for a
number of years, if you are creative enough, until they graduate (very few are that creative, though you can find resources on the internet).
I, personally, prefer something more formal,
though.
I like to use the Calculaddar drills. They go from 1+1 to Geometry. The
child does each drill until he can pass it then he moves on to the next level.
These are simple for us to use. They put each drill in a plastic page protector
and use a dry erase marker, or just photocopy it.
My oldest ones correct their
own. I have explained to each of them that cheating would just make things
harder on them later on (“If you don‘t know it well enough to pass and you go
on anyway, the next level will just be that much harder.”) I know they really
understand the work because they did it fast enough and accurate enough to
pass.
You could make your own drills by writing up a page of problems (20 for a
six year old, 100 for a thirteen year old) and photo copying them. Just make
them gradually harder. Or you can buy or make flash cards and go through them every
day.
I discovered a book at a library sale
called “All the Math You Will Ever Need.” It gives the basic
instructions on how to do any common everyday math problems; interest,
percentages, geometry, sales tax, etc. It doesn’t have nearly enough practice
problems, but it should not be much trouble to make some up based on the
information given. I am sure it will be a well used reference tool in our home.
For a conceptteaching text, I used Math U See for many years.
It was written by a professional tutor. While most math texts teach a little of
everything, spiraling up harder and harder in each area, MUS teaches counting
and place value until the child really understands it. Then it teaches addition
in every form (1+1 to several, long numbers in a column). Only then does it
address subtraction. This “Sequential Method” is the way math is taught in
every country that skunks us in international test.
Each lesson contains three lesson pages and
three review pages. I have each child watch the video of the author teaching
the lesson, then do a lesson page. If they get them all right, they do the
review page the next day. If they get that all right, they obviously understand
the concept and just go on to the next lesson. If they miss any on the lesson
page, they do the second lesson page the next day. They do the third if they
still don’t “get it.” Same for review pages.
This is like having a math tutor come to my
house every day to teach my children. If they don’t understand the video, I
explain it better to them, but most of the time they just don’t need my help.
MUS levels don’t have grade numbers. Each book
covers a specific subject:
 Primer=counting, number recognition, place value
 Alpha=Addition
 Beta= Subtraction
 Gamma=Multiplication
 Delta= Division
 Epsilon=Fractions
 Zeta=Decimals
 Prealgebra, Algebra, Geometry, Advanced Algebra, Trigonometry, and Calculus are pretty selfexplanatory names.
 Stewardship teaches money management skills for life from a very biblical viewpoint. I require it after Algebra. My children must either do math through 10^{th} grade or Stewardship, whichever is later.
I find MUS compliments Calculaddars quite well.
They help each other teach the child.
From a teacher’s point of view, I liked Saxon
math also. They were nonconsumable, very easy to use and came with everything
you needed. My oldest daughter, however, found them boring in the extreme. They move
at teeny tiny steps, reviewing everything every day. She could not see herself
progress. When she cried because she KNEW the answers…”Why do I have to do
this? I know it?”… I knew it was time for a change. This is an example of a bad
curriculum fit. Saxon is the most recommended math text on the market, but for
us it was not a good match. Other things have been. Every family is different.
We switched a year ago to CTC math. Written by a professional math teacher in Australia (and homeschool dad to 10), this curriculum is entirely contained on the internet. No workbooks to buy or keep track of. No teacher's guides or keys to keep up to date. No new videos to purchase every time technology changes. It even does the grading and keeps the records. And the cost is about what I was spending on MUS each year.
Each child logs onto their own page each day, and does a certain number of lessons (or the same lesson a certain number of times. They can do each lesson as many times as they need to to "get it.") Doing a lesson includes watching a video teaching the concept and then doing the work on the computer (later grades need to print pages out). They get immediate feedback on how they did, earning badges along the way.
Then each afternoon, I log into my parent account and see how long each child worked, what lessons they did, and how they scored. If I want to I can make assignment or log into their account and see their view (which I actually often find more helpful.) I am keeping better track of what they are accomplishing and they are learning more.
CTC is more spiral than I like (repeating each concept each year), but it isn't as bad as Saxon.
The price includes 5 student accounts, all lessons, all grades, available to all students.
Honestly, the goal of most math instruction is
to have adults that can function in the real world: balance a check book, find
deals at the store, figure how much paint and carpet they need to remodel the
house, bake from scratch, etc. Any adult that can do these things can learn the
formal, upper maths if they need them (or just want them. I find math fun
myself. Like a secret code you have to break!)
Summary:
 Teach your child to count.
 …Place values.
 …Add and subtract.
 …Multiply and divide.
 …Change numbers to words and back.
 …Use fractions.
 …Use decimals.
 …Use percents.
 ... Measure everything in standard and metric.
 …Find area and perimeter. (all of which MUS, CTC, and Saxon do cover)
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