Indispensable Math Facts

Louisa

 

Math facts! Those stalwart, foundational facts that carry us through our lives, making us able compute things in our head at the grocery store and figure out the cost of a tank of gas. We need them! Our kids need them! Let’s give it our best to teach them to our kids, making their experiences with math much easier.

I heard a Calculus teacher at the university explain that most of the errors he saw on his student’s test papers were not problems in forgetting a math formula. They were simple math fact mistakes that made their answers wrong! Math facts must be learned, and learned to mastery in order for math to be “fun” or “easy” for children.

When should a mom start teaching math facts? I think just as soon as children are able to grasp the concept using hands-on objects. If you set up 2 blocks and add another 2 blocks and your child can conceive of the concept of addition, it’s time!

How? I am not a flashcard fan. I don’t like drill. But I do love math games that make computation part of the play, like Sum Swamp or Muggins. I like the games that roll dice, and have the player add up the sum (or subtract or times or divide it) and use that number to advance so many spaces.  You can make your own games with just a pair of dice.

Setting the table is great for mental math practice. My kids, as they were growing, used to recite, “We have 9 in our family and Daniel is gone and that makes 8 and Mark is at work and that makes 7 and Emily’s friend is staying for dinner and that makes 8.”

As children progress in learning their math facts, you can play a fun game we made up called “Gotcha”. Each player has a stack of number cards face down in front of them. (You can use Uno cards, or write your own numbers on index cards.) Players both flip a card at the same time, and the first player to say the answer wins both cards. Once the cards are depleted, measure the stacks side by side, and the player with the highest stack wins the game. You can use this to practice addition, subtraction, multiplication or division facts. When I play with my daughter Louisa, I clap my hand down on the table 3 times softly before allowing myself to answer. This evens up our ability level and gives Louisa a chance to answer before I whip her!

Multiplication Songs

Multiplication facts are great to music!  It’s really hard to forget them once you’ve driven around town running errands with them playing on your car CD player.

When I teach times tables, I always start with the “9′s”. They are the easiest! Here are two tricks to get you started:

Hand Me the 9′s

Hold your hands out in front of you. Now look at the math problem: let’s say it is “9 x 4″. Bend your 4th finger and take a look. Starting on your left hand, how many fingers do you see before the bent finger? “3″. How many fingers remain after the bent finger? “6″. The answer to the problem “9 x 4″ is “36″. For the problem “9 x 6″, you would bend down your 6th finger, and see the answer: 5 fingers before the bent down finger, and 4 fingers after = 54. Try it with a few numbers and you’ll get actually see the answer in your fingers.

Magic Digits

Another trick for learning the “9 times facts” is the realization that all “9 times” problems have an answer in which the digits add up to 9. Look at the “9 times” answers below:

9 x 2 = 18

9 x 3 = 27

9 x 4 = 36

9 x 5 = 45

. . . and so forth. Do you see that in every answer, adding the two digits will equal “9″. In “9 x 3 = 27″, adding the digits of the answer (“2 + 7″) will equal “9″.

To get the first digit of the answer, just look at the number being multiplied by “9″. In the case of “9 x 3″, look at the “3″. Now count back by one. “3″ counts back to “2″. That is the first digit of the answer. Write down “2″. Now, to get the second digit of the answer, you just have to find the number that adds up to “9″. In this case, “2″ plus “7″ makes “9″, so you have figured out both digits of the answer!

Hoping to make math fun!

May I recommend:

Hates Math

Question:

I homeschool my three girls. My oldest is 9 and works 2 grades ahead, and works independently. My middle child, 7, is advanced and just as intelligent. She absolutely hates sitting and doing worksheets, especially in Math. I am getting extremely frustrated and this in turn frustrates her. Neither of us is happy. She loves to sing, listen to music and work on the computer. Help!

Answer:

How blessed you are to have three little girls! It must feel like Little Women at your house.

God sends these children to us with such diversity of personality. It is really up to us as mothers to study out our children’s temperaments and dispositions and figure out how to reach them individually. Each child has a natural curiosity, love of learning, inborn talents and interests. It is our joyful task to arrange their environment so they can retain that enthusiasm while learning the skills they will need to contribute as an adult. We don’t want to drum the love to learning out of them with an approach to learning that they find dull. Learning is fun! If your daughter (and you) find it tiresome, then it is time to re-evaluate your methods. Some children (not many) enjoy workbooks, and they are self-directed learners that make homeschooling very easy! Other children need time, plus the resources and supplies, to pursue what they find interesting (that is educational and wholesome), plus some directed learning by mom that makes the unpleasant subject as fun as possible.

My daughter Louisa (at age 12) did not like doing math in a textbook format either. In fact, as long as I try to make her learn math through her textbook, she “hates math”. So, I studied out what she enjoys and tried to apply her interests. She enjoys art a lot, and interaction with me, rather than quiet sitting studying. So, here is how we do her math facts practice: I sit at the table and she stands (her enthusiasm makes sitting impossible!)  We play a math game called “Got It” . We turn over two cards with single digit numbers on them, and we race to multiply the numbers on the cards and say the answer. To make the game more fair, I tap my hand down on the table twice before I shout the answer, to give her some thinking time. (She may shout it out just as soon as she is able!) She loves the suspense and delights when she can beat me to the answer! This takes us about 10 minutes every morning. Louisa would be glad if I would play it with her for an hour (!) and she is quickly getting quite proficient on her times tables. We used to do multiplication facts worksheets, which were dreary to her. We are reaching the same goal, getting the same results–the multiplication facts learned. The method, though, makes the difference between a happy encounter between us, or a dull exercise.

To teach the math lesson, I use either a chalkboard and colored chalk, or a stack of scratch paper and some colorful markers. I scan the concept in the Saxon book and draw out as much as I can in picture form. If I can use real objects to teach the lesson, I do it. I have her draw out as much as possible to help her visualize the problem. I teach the concept, talking it through with pictures and then we do just one problem on each piece of scratch paper, drawing the numbers colorfully and big. When the lesson is on something concrete, such as weight measurements, I get out a food scale and some different items to weigh and we just do a hands-on lesson. (Did you know that 1 grape weighs 10 grams?)  I learn something too! I pose all sorts of questions (how much do you think a dollar bill would weigh: an ounce or a gram) and she does the hands-on work to find the answers. Once I feel sure she has mastered the concept, I review a few concepts from the previous lessons, and feel confident that we have done enough math. And she does retain those concepts so much better than if she had done the whole Saxon lesson!

You will be surprised to find that your other daughters pick up on the concepts too, even if they are not the “right age” for the lesson!

If your daughter enjoys singing, music and computer; teaching math could be really fun! I can think right off of several math resources that would be delightful: math facts set to music as  Multiplication Songs CD, computer games such as Quarter Mile Math that drill math facts, and other computer games that teach math lessons. Math Wrap-ups are a creative way to practice math facts. There is also a great series of math books for the creative child, called Life of Fred.  Try a few ideas, and see which she takes to the best. I do think it is necessary to ensure children learn math skills, but please do all you possibly can to make it fun.

Think of Mary Poppins! A spoonful of sugar does make the medicine go down!

Opposite Math

 

Hot . . . Cold

Wet . . . Dry

New . . . Old

Open . . . Shut

Children can grasp the idea of opposites at a young age. If you take advantage of this concept when teaching math, it cuts your work in half!

Instead of teaching subtraction, teach “opposite addition”. If you know that 3 + 5 = 8, then you can do the opposite. When you see this problem: 8 – 5 =___, just make it into a backwards addition problem. Start at the opposite end (the back) and add this way: what number plus 5 equals 8 ?

This works for multiplication too. Once you know your times tables*, then division is a snap! If you know that 4 x 6 = 24, then “opposite multiplication” will solve 24 divided by 6 = ___ . Start at the opposite end (back) of the problem to read it: what number times 6 equals 24?

The most fun application of opposite math is in dividing fractions. This may look like a formidable problem to kids:

(I know that it stumps me briefly when I cook and have to divide a recipe.) But if you teach them that division is just “opposite multiplication”, then you can turn the second fraction upside down (into its reciprocal), and make this into an easy multiplication problem:

Now it’s easy to divide fractions. Just let opposites do the work!

Have a good math day!

 

*If you want some excellent help teaching math facts, take a look at Math It, my very favorite “math facts” product. It gives children a reason and memory clues, rather than just requiring rote memorization of the addition and multiplication facts. Great stuff!

Keep on Schedule or Let 'em Fly?

Question:

I just started homeschooling my 5 year old boy who loves math. I bought the Calvert Kindergarten curriculum because I had no idea what I was doing and thought I needed a lot of structure (which is what I got). It seems to be too slow for him and sometimes boring. He already knows how to do simple addition, subtraction, and multiplication in his head because he is always asking us math questions (especially related to money). He carries around a calculator all day and comes to tell me what 572 plus 12 is. He wants to know about millions and billions and beyond. We have never done addition or beyond on paper but it seems he is ready for that. Should I continue on with these lesson plans as they are outlined or let him go on ahead as he wants to do?

Answer:

What a wonderful situation you are in! You have a 5 year old who wants to fly—so let him!

Your question brings back memories of my own son, Mark (who graduated from a university in Political Science), when he was just a little boy attending kindergarten public school (back in the days before I homeschooled!) A few weeks after school began, I got a phone call from the teacher. Mark was in trouble! It turned out that he was guilty of “sneaking ahead” in his math book. I had to stifle a chuckle as the teacher explained his crime! He was so interested in math that he couldn’t stay with the slow-moving class, going laboriously over things that he already had figured out. He wanted to fly! I solved the problem my taking him out of school and bringing him and his math book home, where I told him to do all the pages he wanted! It only took him a week to finish the book and beg for more. I bought math manipulatives, math games, math toys and he soared! He loved math and loved the freedom to satiate his curiosity!

I can think of no quicker way to kill a natural love of learning that to enforce a slow-moving schedule on an interested learner. Think about how it feels to us adults to sit in a class where the teacher answers your eager, pertinent questions with: “we’ll get to that later in the course.” It doesn’t take long before apathy sets in, simply out of frustration.

There are so many wonderful math resources to satisfy your son’s anxious desire to learn. If you choose to use a different textbook, I highly recommend Singapore Math. It moves quickly and caters to children with its bright pictures and visual representations of the math formulas. You can give him a free placement test (online) to see where he needs to start.

A good place to learn about big, big numbers is this website: http://www.mathcats.com/explore/reallybignumbers.html . In fact, the whole website, www.mathcats.com, is excellent for young ones yearning to learn more and more about math. Here are my favorite math resources too—you can find them in my store:

Quarter Mile Math Sum Swamp Clock-o-Dial

Multiplication Songs Addition & Subtraction Game Pack

Family Math

What could be more fun than a child who is eager, eager to learn?!  Have fun together!

Messed up in Math

Question:

Our granddaughter goes to public school and she is struggling so hard with math. The school has really messed her up and is teaching her things backwards. When we try to help her it confuses her. They are teaching her to do math problems from left to right, to do all of her borrowing before she even starts to subtract right to left. She hates math because of it and it is so hard to get to work on her math homework. We tell her how important math is and how she will use it the rest of her life. Do you have any suggestions that would help us?

Answer:

It depends on how much time you can commit to this, but if you are able, the ideal would be to take her out of school during math period. Usually math comes first in the school day, so working with her first thing in the morning, and then taking her to school might be a good option.

Math is a basic skill that must be mastered in order to move on with her education. If they are “messing her up” in math, it is pretty important to get her out of that situation, if you cannot work with the teacher to make a change. If not, tell the school you will be taking her out for private instruction in math, and get the textbook they are using and the schedule they are on, so that you keep her up to date. If the math book is faulty, then you’ll want to use Singapore or Saxon instead. Test her—both companies have free placement tests online—and find out just where she needs to start. If you can work with the math book, and it is just the teacher that is doing things confusingly, then using the math book will help her transition back into her school class eventually. Focus 10 min. daily on doing math facts, if your granddaughter is not proficient in the basic facts. If you work with her daily on math, you will be very surprised how much more you can accomplish with one-on-one tutoring in the same amount of time the school takes!

If she is feeling resistant, do things to make it fun and help renew her attitude. Math is truly fun, and she needs to feel that enjoyment again.

Here are a few ideas to motivate her:

*Make a chart with bubbles (dime size) that represent a goal (15 min. steady work, 10 problems completed, math facts done for the day, or whatever goal is appropriate) and stick a dime on each bubble when it is earned.

*Let her choose to do evens or odds (problems) for the day, if it feels like she has too many math problems to do.

*Use hands-on items to illustrated the problems, such as Legos, beans, coins, etc. (I taught my daughter to subtract using shampoo bottles while I was taking a shower!)

*Work on the chalkboard. It is easier to do math when it is big-sized and involves the fun of writing with chalk, too. You can hastily illustrate story problems to make it even more fun!

*Give her “points” for right answers, with a goal in mind. For example, if she wants a certain item or privilege, she could earn it by diligent effort.

*Use real life math to help her see how useful math skills are. Use receipts to practice rounding off numbers and adding a column, keeping the total hidden to self-check.

*Let her correct her own work using the answer key herself (with you nearby observing). Often this grown-up thing to do will make a child more careful with their work.

*Time her math facts practice with a stopwatch. Saxon has this built into their program and it is truly motivational to keep a graph recording the times, seeing progress more visibly.

*Use math facts games to make it more fun. I recommend Sum Swamp, Math Wrap-Ups, Multiplication Songs, Quarter Mile Math and others.

*Work math problems on a big sized scribble pad with colorful markers.

Best success!

Mastering “Greater Than” and “Less Than”

Here is an easy way to teach your children how to remember the “greater than” and “less than” symbols in their Math lesson!

 

First, draw one of the symbols,  like this:

mastering greater than

 

Now, make that symbol into a big fish’s mouth like this:
mastering greater than

 

The fish has a BIG mouth that loves to eat the most he can get:  the largest numbers.  So the big, open part of the mouth always faces the largest number.
mastering greater than

 

If a child can remember to have the fish’s mouth face the direction of the larger number, so he can gobble it up, he’ll never get confused again with “greater than” and “less than” problems again.

Long Division Troubles?

Some children are stumped by long division. They can be progressing along just fine, learning their times tables and doing well on their math lessons, when suddenly long division enters the picture and math becomes a tearful subject. When I taught Emily (9) how to do long division, we encountered some problems. In explaining it to her, I realized that I was using an old tried-and-true, failproof method that I’d learned somewhere that seems to help every child along in learning long division. Here it is, just in case you ever need it!

Before learning long division, a child must have mastered his multiplication facts. He must also be able to do short division, one step answers such as: 45 divided by 9 = 5, 15 divided by 3 = 5, etc. To begin your long division lesson, prepare stacks of ten- and one-dollar bills. You can use real or play money. (I like real.) Draw this on a piece of paper: a column for tens and a column for ones, labeled. Have the child count the money and lay it in stacks under the tens place and the ones place (A). long division

Draw three little children, boys and girls, depending on your family configuration (B). Now, say this:

Emily, Ammon and Louisa (use your children’s names) are going to share 47 dollars.  Count out the bills (set the rest aside) and help your children stack the ten dollar bills in the tens column and the one dollar bills go in the ones column on your paper.

Look at the first number in the division box (C). It is a 4 in the tens place. That means 4 ten-dollar bills. Ask your children to pick up the ten dollar bills in the tens place and pass them out to the three kids in the drawing.  How many ten-dollar bills can each child have to share it fairly?  (one ten-dollar bill, with one ten dollar bill left over.)

On the division problem (D), write a dark 1 in the ten’s place and a light tracing of an 0 in the ones place. Explain that this means each of the 3 children (point to the divisor “3″) gets one ten-dollar bill (point to the quotient 10, in figure D).

long division

How much money did you spend?
(3 x $10 bill = $30.) Write 30 below the 47. (figure D)
How many ten dollar bills do you have leftover now?

Point to the stack of ten-dollar bills in the ten’s place (figure A).
(one ten-dollar bill and seven ones)
Perform the subtraction to show how much money is leftover.

Ask: Can 3 children evenly share one ten-dollar bill that is left in
our tens column without cutting it in pieces?
(No)

Can they trade it into the bank for 10 one-dollar bills?
(Yes)

If they trade in their $10 bill for one-dollar bills, how many
one-dollar bills will they have altogether? (10 ones plus 7 ones = 17
ones.) Put the ten ones into the ones stack with the seven ones.

Can 3 children share 17 one-dollar bills evenly?
(Encourage your child to deal out the dollar bills evenly to each
drawing of a child.) Now count up the dollar bills. How much does each
child get? What number times the 3 children is close to 17?
(five one dollar bills)

Write the number five in the ones place. (figure F)
How much money did you spend to divide the one dollars evenly?
(15 one dollar bills)

How many one dollar bills are leftover?
(2 one dollar bills).
Since the children can’t share these evenly, there are leftovers. We
call them “remainders,” and we write them after our answer like this:
r. 2. The “r” stands for remainder (see figure G).

Go through this process several times, using different numbers but the
same story of children sharing ten- and one-dollar bills. Begin by
asking, “How can ___children share ___dollars?” Here are some good
problems to do:

43 divided by 2
85 divided by 3
74 divided by 5

After your child has learned how to do long division using the $10 and
$1 bills, you can introduce harder problems by adding $100 dollar
bills to your game.