Number sense involves more than just counting. It requires understanding quantities and comparison concepts like more/less, larger/smaller. Your child only gradually acquires these skills through the preschool years. (See my article, Is Math and Number Sense a Language Skill?) But you can start very early to lay a foundation for your child developing number sense.
Lay a Foundation for Number Sense by Counting One and Two
Hands and feet lend themselves well to working with your baby on the concepts of one and two. For a fun little game, hide one hand behind your back and say, “One hand!” Then show both hands together and say, “Two hands!”
As you dress your baby, name the clothes, “Here is your shirt. Now we need your pants. Where are your shoes?” Hold up one shoe while you hide the other. “Here is one shoe. Where is the other shoe? We need two shoes! “ Then show both together and repeat, “We need two shoes.” At this point you are merely demonstrating and modeling. Your child will start imitating you when ready.
Continue with your toddler contrasting one to two in conjunction with treats such as cookies, crackers, apple slices, or small pieces of candy. Hold up one first and ask, “Do you want one,” then show one more with the other hand and continue, “or two?” Even a toddler is likely to stretch up both hands and say, “Two!”
The young child probably first perceives “two” as simply meaning more, so to teach the concept, you have to find ways to contrast “two” to “just one,” and later to “three.” Still using the treats, you could create situations in which “just one” is more appropriate, while also acceptable to the child. You may, for example, have big cookies and small cookies and allow just one of the big ones or two of the small ones.
Counting objects to Three, Four and Five
Your two-year-old might proudly hold up two fingers in answer to the question, “How old are you?” It is not likely that your child at this point understands the concepts of age and years. But it is possible that the concept of two as opposed to one or three is now making sense to your child. It is then time to start counting objects.
Start with just one, two and three. You can use any toys such as blocks, cars, animals, anything your child enjoys. Count with your child, guiding him or her to physically move each object while counting. This will help your child learn to count with one-to-one correspondence.
Only gradually expand the counting to four and five, as your child seems ready. Most children will initially have difficulties matching their counting with the objects they are attempting to count. This is why it is so important to have your child physically move the objects rather than just pointing to them.
I also believe it is best not to emphasize mere rote counting at this early stage. Instead, count with your child as he or she moves the objects one at a time. It will encourage slower counting, so that the child’s hand can keep up with the counting.
Make It a Game
When your child is able to count three objects without your help, it is time to use the counting meaningfully. Here is just one way you can do this:
In a simple back and forth game, ask each other for one, two or three of the objects. Use a short lead-in phrase such as “Give me…” or “I want…” followed by the number. Also add the name of the object if your child is ready to handle that much language. You will want your child to be able to use the phrase you are modeling while focusing on the number.
Once your child can count up to five objects, you can expand the game. If you are using blocks, you might stack them till the stack gets too tall and tumbles down. The one who gets the tallest stack without it falling down “wins” the game. If you are using cars or animals, you might simply line them up in a row. Then compare the two rows to see who has more, another important concept in acquiring number sense.
Your child will quickly realize that asking for the highest number leads to winning the game. That is okay, as long as you vary how many you ask for. You want your child to get the practice in counting all the numbers learned so far. But it is good to let the child win every time! It makes him or her want to play again. After all, you are not trying to teach the value in being a good loser at this early age!
More Ways to Make It Meaningful
By the time your child is counting to five, you can have the child count the fingers on one hand.
Continue playing games to reinforce the concepts and develop number sense. You can now also find ways to use the counting in various daily activities such as setting the table. Have your child help you count the needed plates, forks etc.
Your child can also help you sort the laundry and count the socks of a certain color, etc. When going shopping, you could have your child help you pick up two or more of a certain item. And when baking, you might have your child help count the cupfuls of sugar. I am sure you can think of more ways to have your child practice counting objects around the house.
There are various puzzles and numerous other counting-toys, all intended to help you teach your child to count. Most of these include the numbers from one to ten. As adults, we tend to think of counting to ten as a single, basic skill. After all, our entire number system is based on the number ten.
I find this focus on the number ten for our young children to be unfortunate. Learning to accurately recite all the numbers to ten and beyond will eventually be important for your child. However, working on this before your child can count objects at least to five is putting the cart before the horse.
Learning the concepts by accurately counting objects in a variety of tasks will help your child develop number sense. Few children are ready to count objects beyond five before they are five years old. I therefore recommend working on the numbers one through five till the child has fully acquired these concepts.
It takes some searching but is possible to find good counting toys appropriately geared to this stage. Some only go to four, but I prefer a focus on the number five, as with the one in this picture:
I also question the wisdom in including number symbols on these early counting toys. I suppose the idea is to expose the children to the numbers early. But I am not sure of the value in this. Even five-year-olds tend to have difficulty recognizing and remembering abstract symbols. The girl in this picture looks to be about four years old. You might notice that she holds the puzzle so she sees the numbers backwards.
Most preschool children enjoy playing store. You can use this to practice number sets in a fun way. If your child has a toy cash register, great–kids love them! But you do not need to go out and spend money on one. A child size table where you can line up the merchandize and a box for the “money” will do.
At this stage, you are going to set aside any play money your child might have. Most toy cash registers now come with play money. This is fine for pretend play, but your child is not yet ready to understand and convert the different values. Exchanging money is a complex math skill only gradually learned from first through third grade. However, as I will explain, you can soon set the stage for learning about relative values.
Any token of uniform size will work fine as “money.” If you do not have appropriate tokens, you can buy a checkers replacement set. These will make great tokens, easy for small hands to handle. I suggest you call your tokens “quarters.” Don’ label them “pennies.” You just wouldn’t want your child to get the idea that a few real pennies will actually buy you something!
By calling your tokens quarters, you can soon take a first step toward helping your child understand money values. When you believe your child is ready, you can introduce the idea that four quarters make up a dollar. That is a good reason not to call the tokens “dollars,” which otherwise might seem natural.
There are lots of toy foods available to purchase in various sizes and price ranges. But you don’t necessarily need them. You can simply use toys your child already has, such as little cars, animals etc.
Assign a value to each item of one, two, three, four, or five “quarters.”. This gives you a great opportunity to practice the concept of more as it pertains to value. Unless both words are already in your child’s vocabulary, I suggest you do not yet also use the word less. Contrary to what we as adults tend to think, children do not generally learn early opposites together. (See my article on Learning Words)
Make “price tags” by drawing one to five large dots on sticker notes or little cards. Make sure the dots are far enough apart for your child to be able to count them by pointing. For the four and five, you might want to place the dots in a pattern like on a die.
You could now also start to introduce the number symbols. One way is to superimpose the dots right on the number. Simply place large dots in a contrasting color at appropriate spots on the numbers.
There is a program called TouchMath, which has put this idea into a whole system. I find their system a bit overworked and awkward for numbers above five. If you do decide to use this system, you will want to follow their pattern from the start.
I prefer to place the dots somewhat differently on the numbers 1, 2 and 3. I would place a dot right in the middle of the line on 1. The 2 would get one dot on the top of the curve and the other at the sharp turning point. That would make sense since the numbers 4 and 5 use each sharp turn. On 3, I would place one on each of the top and bottom curves along with the one at the sharp turning point. This places the three dots above each other, so your child can count them in a straight line.
Playing the Game
There are obviously two roles to play, the store owner/clerk and the customer. Each customer gets a certain number of “quarters,” perhaps eight or twelve.
The customer has to choose something to buy, read the price tag and count up the tokens. The storeowner then has to look at the price tag and check the money by also counting it. Thus, no matter the role your child is playing he or she gets plenty of practice counting.
At first, let each customer buy just one item at a time. Customers then come back to buy something more. They now have to count their money to see if there is enough left for what they want to buy. This gently leads into understanding the principal of subtraction.
Have fun playing store with your child!
Your child soon reaches Kindergarten age. It is now time to teach the connections between the number concepts and their visual symbols in a structured way. See my Tools post Use Number Charts to Teach Early Number Awareness.
For great information on number sense, see the website understood.org.