COUNTING
Before a child can understand addition, they need to know how to count. The following checklist will help you determine if your child is ready to learn how to add:
1. Count forward from 1 to 100.
2. Count from any number to 100.
3. Count backwards from any number to zero.
4. Given two numbers between 0 and 100, recognize which one is larger.
Understanding Quantity
As with all learning, we believe understanding how and why something works is more important than rote memorization. Being able to sing the alphabet song does not mean your child is learning reading skills; being able to rattle off a sequence of numbers does not mean your child understands counting, either. Memorization of basic facts is important in developing arithmetic skills, but rote memorization without understanding causes problems later. Memorizing should come incidentally, from lots of practice figuring out answers to arithmetic equations.
The following games and activities can be used to make sure your student really understands quantity.
NUMBER RECOGNITION
Flash Cards -
You will need a set of basic flash cards for this activity. As with our phonics program, we believe cute, decorative cards with lots of pictures distract the child from the learning. It is easiest to make your own cards with some poster board and inexpensive markers. Simply cut the poster board into rectangles. We recommend 2" x 3" so you can make equations with them later.
On each card write one number on one side. The only thing on the card should be a single number. Leave the other side blank. Do not decorate the cards with pictures, stickers, or other art work. We recommend you start with 20 cards, with the numbers 1 - 20 written on them. Notice we do not include the zero; the concept of representing "nothing" with "something" can actually be very confusing to young children.
We recommend you leave out the zero for preschoolers
Number Line -
Since you already have poster board to make flash cards with, now would be a good time to make a number line. The old fashioned railroad track style is good for older students. For younger children we like to use a number line that looks more like a game board. Our number lines at the tutor center are 36" long and 2" wide. Lines are drawn on the strip to make 1"-wide rectangles. The first space has the word "Start" in it, just like a child's game board. For older children you may want to put a zero in the first square instead. The rest of the squares contain the numbers 1 through 35.
Game Pieces -
Any game piece from an old game or even a favorite small toy can be used on the number line. Miniature cars and trucks are fun to "drive" up and down the number line.
Manipulatives -
When learning to count, add, subtract, multiply and divide, we strongly recommend using manipulatives, no matter how old the child is. Remember, numbers and all applicable theory is strictly abstract; using manipulatives gives your student something tangible to make sense out of. It is, in our opinion, an imperative.
Your choice of manipulatives is important. Flat objects are difficult for little hands to pick up and move around. We recommend a collection of toys. Small building blocks or miniature toy cars work great. Our favorite manipulatives are Lego blocks. The uniform shape and size plus the ability to link them, make them perfect for teaching all four operations, grouping and much more. We use nothing else at the tutor center.
Naming the Number
This can be done with toys (manipulatives) and flash cards (or magnetic numbers), or in worksheet format. The purpose of the activity is to help a child learn to count, recognize the symbol that represents the quantity counted, and match the number to the quantity of objects.
We will describe how to do the activities with toys, but worksheets can easily be made to simulate the games.
Recognizing numbers: First, say the number "one" and have your student repeat the word. Place a single toy on the play surface, pointing to it, explain that there is "one" toy. Now show the flash card with the number one on it, and explain that this is a picture of "one". Add 2 or 3 other flash cards with numbers on them, and mix them up with the "one" card. Ask your child to find the number one. Now ask you student to pick up "one" toy (or whatever manipulative you are using).
Now repeat the process with 2 toys, counting to two as you point to each. Ask your child to repeat what you did, counting the "two" toys. Now show the number two, explaining that it is a picture of "2". Mix the one and two flash cards with a couple others and have your student find the picture of the one, then find the picture of the two. Now have your child pick up two toys.
Simply repeat this process with each number. You can play until your child gets confused or bored, or you run out of time (whichever comes first). Always review previously learned numbers with the above activities before moving on to the next one.
Once your student gets the hang of this, you may find yourself counting everything. Have fun, but be sure they are actually counting and not just naming things.
Caution With Fingers
We have noticed that very young children seem to be able to count on their fingers, but get confused when translating this to other objects (even toes!) It seems that some children, especially very young ones, are not actually counting their fingers, but have learned to associate a particular name, such as "one" or "two", to each finger. If a child counts their own fingers, it is best to use the index finger of one hand to count the fingers of the other hand, as opposed to raising the fingers as they recite the numbers. You should also have them count from thumb to pinky one time, then from pinky to thumb another, so they understand that the words "one, two, three", etc. are not names for the fingers but represent the order and collection of objects.
You won't have to explain this directly, simply having your child count lots of different things is enough; their little minds are miraculously quick and the average child will pick up on this naturally; it is only you, the teacher, who needs to understand what it is they learning so you can guide the learning process for them.
We recommend you use this acitivity at least through the number 20. How much time you spend on this activity depends entirely on the age and ability of your child. Don't rush! Young children can "count" long before they can understand addition and subtraction. You may find your child learns to count at the age of two, but may not be ready for addition until the age of 5 or 6. You will just have to wait until your student is ready; it will happen soon enough.
Children's Board Games
Any simple board games for children are excellent incidental learning tools. In learning to move a game piece along a board, a little at a time, without starting over, is teaching the child to start counting from somewhere other than one, and will help them when learning to add.
As with most early learning, you don't have to explain this to your child,
but knowing it helps you utilize the games to guide the child's learning
experiences.
Our system of teaching arithmetic is based on a few basic observations about the human brain and how people learn. It is generally known that people tend to remember the first and last things they see or hear, and forget what is in the middle. Given a normal amount of intelligence, it seems that the average person can, with some concentration, remember the first twoand last two things seen or heard. Keeping with this idea, if you cut out all "middle" fluff, we can safely assume a person can accurately remember 3 or 4 things, or processes, with little difficulty.
With this in mind, it would logically follow that any calculation or sequence of calculations can take up to 4 steps, and this includes addition by counting. Our arithmetic is designed around our basic philosophy which incorporates these theories, creating logic patterning that follows with the child from basic addition on up through subtraction, multiplication and division, leading them naturally into the upper level theoretical mathematics.
If you are working hard, you are doing it wrong!
Lesson 1: ADDING ONE, TWO AND THREE...
Teaching a child to add 1, 2 or 3 to another number is simply the process of showing them how to "count up" from any number other than 0. For young children, we strongly recommend the following order:
1. Manipulatives: Always teach arithmetic in order, from 1 up. Therefore, put one toy on the play surface to count, then add "one more" and count from one to two.
2. Number Line: Have your student put the game piece on the number one, and ask him to count "one more" space, then read the number landed on (2).
3. Writing: On paper, write out the equation, 1 + 1 = 2. Explain that the plus sign means add, or count up. The equal sign means "is". When reading equations, it is a good idea to read the symbols correctly, explaining their meaning when necessary. For example, 1 + 1 = 2 is read, "One plus one equals two". It is NOT read "One and one is two". Math is a foreign language, and using the proper terms will help your child develop a natural understanding for the language and enhance further development in the future. One of the most common problems students have in math is solving word problems. In a nutshell, they don't know the language of math and therefore cannot translate from English to Math and back again.
Repeat these 3 steps to introduce the idea and teach the skill of adding one to each number, through 12. Most children 5 years old and older can learn these equations in just a couple short lessons. If your student wishes or needs to take longer, go slowly and continue to practice and review until you are sure they are completely comfortable with the concept and the equations.
Finally, pick numbers larger than 12 that they are comfortable counting (remember
your student should be able to count to 100 with ease). Have them "count up"
one from that number. Try several different numbers, out of order, and have
them add one. Make sure they can answer easily.
Remember, if your child becomes upset, confused or forgets, slow down or stop and take a break altogether. It is much better to move slowly at first, with complete confidence and understanding, than to rush ahead into compounded confusion!
As always, if you have any questions, or if we can help you in any way, please feel free to email us. Just click at the bottom of the page.
Lesson 2: Doubles
THIS IS THE MOST IMPORTANT LESSON IN ALL OF ARITHMETIC!!!
DOUBLES
