Friday, November 16, 2012

Breaking It Down- Math

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…twenty-one, twenty-four, twenty-seven…thirty.” (To the tune on the Math Rocks Video from School House Rocks. Available at most libraries, 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 twenty-fives. 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 (10-30 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=1000th 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
Hundred Million
Ten million
Hundred Thousand.
Ten thousand
Units (ones)
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
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.”
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.
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.
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.
53 = 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
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+4+5+5=18, The perimeter of this rectangle is 18” (inches).
4x5=20 Its area is 20”.
To find the area of a triangle you multiply length by height and divide by two. For perimeter add the sides.
5” wide
6” tall

For the area of a circle you πR2 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=

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 concept-teaching 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
  • Pre-algebra, Algebra, Geometry, Advanced Algebra, Trigonometry, and Calculus are pretty self-explanatory 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 10th 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 non-consumable, 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!)


  • 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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