Money, the Logical Hands-on Teaching Tool

Having taught at the same private school for many years, it only follows that I have taught several brothers and sisters of many families. I've never expected younger brothers and sisters to mirror their older siblings, but I've also noticed that they often do because of the parents' expectations. Parents who expect diligence and responsibility from their children usually have an entire household of diligent and responsible children.

One such case that puzzled me for several years was the inability of children from one particular family to count money, to make money exchanges accurately, to make change involving bills and coins, and to solve general word problems involving money. This was especially baffling considering I teach 5th grade and it is unusual to have one child, let alone several, who can't make small change accurately and easily.

And then I figured it out. These children apparently were never required to be responsible for the money they were given by their parents or for bringing accurate change back home. If one of them needed money for something, the student would be given a $20 bill with no thought for what he/she was expected to bring back home. In this one case, the lunch cost $4.50, and the student had no idea what change to expect. I discussed it with her and she wouldn't even try to reason through it. All she did was just shrug and say "I have no idea" or "I don't know" to every query I made.

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So begin early and teach your children how to exchange 5 pennies for 1 nickel, etc. Have them count money (and remember to start at zero when counting). Give them small amounts of money to purchase something and discuss ahead of time overpaying and expecting change from the clerk.


Do you save pennies in a jar? This is a good way to involve your child in a family project. Count the money by the week or month, depending on the child's age. Have the child help you swap nickels for the pennies. Then later swap dimes for nickels, etc. This helps teach your child equivalent amounts.

One game that is fun for children can be played in the car as easily as it can at the breakfast table with coins. Say to the children, "How much money do I have? I have 1 quarter and 1 dime." As children learn to solve these problems, ratchet the game up a notch to this next level: "How much money do I have if I have 2 less than 3 quarters, 1 dime and 1 nickel?" Children in second and third grade can get these problems. Then try going past the dollar, but do not mention dollar bills. "How much money do I have if I have 3 more than 6 quarters, 2 dimes and a nickel?"

Give students reasoning problems, but call them "riddles". "Here's a riddle for you. Bill has 5 coins. What five coins did he have if he has 38 cents?" At first, this can be done with coins in hand, but as children get older, they need to be able to solve this type of problem mentally.

Use money to begin teaching tally marks. More on tally marks in another post, but money is an easy way to get your children to think of counting by sets of numbers. And remember counting is the beginning of solving abstract concepts in numbers. Make sure you do a lot of counting.

Have a pretend store at home. Tell your young children that you are practicing what to do at a real store. Teach them to make change. However, the true goal should be more. You want your children to recognize incorrect change. Explain to them that this is "Wrong Change" day at the store. Tell them you are going give incorrect change for a pretend purchase, and have your child figure out what is incorrect.

Expect your child to be responsible and accountable with any money, even his own. Do not pass it out to him/her like it was candy. Children will value its importance if you value it, and will learn to value it enough to want to know how to use it wisely.

Laying the Foundation for the Abstract Concept of Numbers

Learning the abstract concept of numbers starts long before the usual introduction of pre-algebra and algebra. It begins when your child is first introduced to the meaning of numbers by counting. Yes, counting is where the development of number sense all begins.

I remember when our son was two and I was participating in an exercise class. We all took our children along and they played next to us while we exercised. Our son, interested in numbers from early on, was fascinated by the class leader's counting out loud, "One, two, three, four; two, two, three, four; three, two, three, four; four, two, three, four; ("again") one, two, three, four; two, two, three, four; three, two, three, four; four, two, three, four . . ." And our son was fascinated by the words. We adults understood that there were two sets of counting patterns being used at once, but to our son, these were just words, recited along in a pattern, with a nice rhythm, and he was intrigued, taking it all in.

A few days later, I heard him repeating the number words, in random order. He had no sense of counting; to him the words were meaningless. Ooops!

Children love counting. Counting games, counting songs, and counting rhymes all serve to draw our children's interest to the fun of counting, and at an early age.

Counting is where the understanding of the concepts and the meaning of a number begins. And it is important to know that there is much more to counting than merely calling out the numbers.

Here are a few ways to properly start your child counting so that early on, he/she will not only begin to grasp the meaning of numbers and will also apply "counting" to objects around him

Assemble a set of objects in a plastic bowl or tub. They may be pennies, blocks, craft sticks, toys, anything. You also need a second empty container. Have your child pick up an object, place it in the empty bin, while saying its number, beginning with "one". (Demonstrate this yourself. Children love to copy.) It is important that your child actually picks up the object and moves it, rather than sliding it across to another pile. Begin with 10 objects or less. Be sure that your child only picks up one object at a time.

After your child has moved the last object to the other bowl, ask, "How may trucks are in your other tub?" Your child should learn to properly say the last number he counted. Vary the number of objects in the tub. It is also important to vary the objects you use so that he/she understands that numbers are used to refer to different types of objects.

This early activity of counting, using concrete objects, though simple, is part of the learning of the abstract number concepts to come later.

And this is important: have one tub on one side of his body and the other on the other side. We want his/her hand to cross the midline of the body with each motion. We know that the brain cells fire away each time an arm or leg crosses that midline.


As your child gets older, and after he/she masters this first counting activity, there is something else very important that you must do. You must develop a sense of "zero". So this is the next step in the counting exercise: Teach your child to start counting with "zero". Before any objects are moved, teach your child that there are "zero" objects in the second tub. Teach him to say "zero" before he begins, followed by "one" as the counting and moving of objects begins.

Next, using blocks that are numbered, or making your own on pieces of paper of cardboard, teach your child the symbols (digits, numerals) that stand for each number from 0 to 20. Line them up in order and point to them as you recite the numbers. Have your child recite them with you as you point to the symbols. Then have your child recite them alone.

Later on, with the blocks still in proper order, point to the symbols in random order and have your child name them.

Much later, mix them up and have your child find them in order and say them as you and he line them up in order.

As your child learns, you can gradually increase the number set up to 20.

Books that have counting pictures can be useful. Point to the symbol and ask your child what it is. Sing counting songs with him/her. Avoid songs that count backwards at first.

Count the silverware as you place it by his plate, or as you remove it from the dishwasher, remembering to begin with "zero". Count his/her socks as you place them into his drawer. For an older child who has mastered the counting of single objects, count the socks in groups of two: "one, two," "three, four", etc., which will lead to counting by multiples of two.