Teaching Young Children About Money

There are many math games and activities that help children learn about money.

Helping your child learn the value of coins is a real-life skill that can be taught and learned easily if you use the following activities which are educational and fun:

Free Exploration

Give your child a small tub of real coins and allow him/her time to explore. This might be a good time for you to watch your child and note what is happening. Does he/she already know the names of each coin? Does he/she know the values? Do they notice likenesses and differences? Do they sort the coins? Make patterns (i.e. penny, nickel, penny, nickel, or dime, dime, quarter, dime, dime, quarter)?

Alike and Different with a Magnifying Lens

Children need to be able to identify coins before they can learn their values. This activity gives children the opportunity to examine pennies, nickels, dimes, and quarters closely and think about what things are the same and different among them. Noticing likenesses and differences is important in math and reading for young learners.

You will need a magnifying lens and 1 penny, 1 nickel, 1 dime, and 1 quarter.

Allow your child to experiment with the magnifying lens first.

Begin with the penny. Have your child look at it closely and tell you what he/she notices. I usually start with the heads side. Identify the year and place the coin was minted, the other words on the coin, and so on. Then look at the tails side. Don’t forget to examine the edges. You might want to have them cut out a large circle and draw pictures of both sides of the penny.

Look closely at each coin in turn, noting how they are alike and different. You might take a blank piece of paper and draw a vertical line down the center, dividing the paper into two columns. List Alike at the top of the first column and Different at the top of the second column. Begin to write about what you discover. Some things appear on every coin; some do not.

Talk about size and value. This can be confusing for young children because the nickel is larger than the dime but worth less.

What Are the Coins?

You’ll need some coins for your child to use to solve the problems.

Ask your child the following questions:

I have three coins in my pocket. They are worth 7 cents. What do I have? (a nickel and 2 pennies)

I have three coins in my pocket. They are worth 16 cents. What do I have? (a dime, a nickel, a penny)

I have three coins in my pocket. They are worth 11 cents. What do I have? (2 nickels and 1 penny)

I have three coins in my pockets. They are worth 30 cents. What do I have? (3 dimes)

I have six coins in my pocket. They are worth 30 cents. What could I have? (1 quarter and 5 pennies or 6 nickels). This problem has more than one answer. It is challenging for children to experience problems like this.

I have coins in my pocket, which have a value of 11 cents. How many coins could I have?

Teachers – these activities can be used successfully in the classroom, and I think the secret to their success is using real coins.

A Math Activity for Anytime and Anywhere

The following is a math activity that can be done anytime – I call it a “waiting” activity. It can be done while waiting for dinner to arrive at your favorite restaurant, waiting to get someplace in the car, waiting for the car to be serviced, waiting in the doctor’s office, waiting for the rain to stop, etc. Basically, you can do it anytime and anywhere.

It is called Guess If You Can and is appropriate for children of all ages, depending on the numbers you use. The following is a sample conversation.

Parent: I am thinking of a number between 1 and 100.
Child: Is it more than 50?
Parent: No.
Child: Is it an even number?
Parent: No.
Child: Is it more than 20 but less than 40?
Parent: Yes.
Child: Can you reach it by starting at zero and counting by 3’s?
Parent: Yes.
(At this stage, the parent could be thinking of 21, 27, 33, or 39.)

After your child has guessed your number, let your child think up a number for you to guess by asking similar questions.

Parent Pointer
It is important to help children develop an understanding of the characteristics and meanings of numbers. Doing this kind of math activity over and over helps your child develop number sense – hugely important for future success in mathematics.

Teaching Math with Games

Do your students like to play math games? If so, do you think of games as time fillers or part of your educational program?

In my classroom, teaching math with games was a serious educational activity. The value of math games can be enhanced or decreased depending on what teachers/adults do. The following are three of the most important principles of teaching that I followed while students were playing games:

• Do not show students how to play at a higher level; instead, encourage them to do their own thinking.
• Do not reinforce “correct” behaviors or correct “wrong” ones.
• Play with individual children whenever possible.

Most of us have been taught that the way to teach mathematics is by showing children what to do. Extensive research into how children learn mathematics shows that children construct mathematical knowledge by doing their own thinking. Therefore, we must encourage them to figure things out rather than obeying and mimicking their teachers.

Also, most of us were told that the role of the teacher is to reinforce “right” behaviors and correct “wrong” ones. A teacher’s occasional expression of pleasure is not harmful, but when the teacher says that an answer is correct, all thinking stops! I know this is a radical thought, but I truly believe that students should be encouraged to come to their own conclusions based on debate among themselves. The nature of mathematical knowledge is such that if children argue long enough, they will agree on the correct answer (unless the question is too hard for everybody in the group).

I have always believed that assessment is much easier to accomplish when using a math game, rather than a workbook page. Teachers find out much more about children’s thinking by playing with individual children or a small group than by merely observing them. Therefore, playing with them whenever possible is desirable.

Getting Ready for Kindergarten Math

People have this conception of kindergarten as children playing, getting cookies and milk, and taking a nap. As any kindergarten teacher will tell you, that isn’t the reality anymore. The focus on academics has been pushed downward.

In my many years teaching kindergarten through third grade, I watched unstructured playtime shrink, replaced by worksheets and nightly homework. The shift started in the 1990s, when studies ranked students in the United States well below those in other developed nations like Japan in math and reading. There was a push to close that gap, and one solution was to start emphasizing academic subjects at a younger age.

When kindergarten was less academic, it was an easier transition from home to school for most children. Now seat work starts in kindergarten, which means the transition is difficult for many children. Many kids aren’t so eager to make the jump into the world of worksheets and seat work.

It’s normal for students to be all over the map developmentally at this age. Each child’s brain develops differently, and their level of exposure to different experiences as they enter kindergarten varies widely. That’s why students attend preschool and kindergarten programs instead of just jumping straight into primary school – to get everyone on the same page before barreling full tilt into the world of letter grades and federal testing.

There are many things parents of young children can do to help their children be ready for kindergarten. See “Success in School Begins with Involved Parents”.

Playing math games is one of the most effective things parents can do to help their child make an easier transition into kindergarten math.

The following game is one of my favorites for young children:

Counters in a Cup

What you need:
2 players
5-10 counters (buttons, pennies, paper clips, etc.)
paper cup
paper and pencils

The object of this game is to figure out how many counters are hidden.

Decide how many counters you will use. Write this total number on the paper. With very young children, begin with a small number, such as 4.

Player #1 closes his/her eyes. Player #2 hides some of the counters under the cup and leaves the rest out for all to see.

Player #1 opens his/her eyes and figures out how many counters are hidden under the cup. Lift the cup to check. On the paper, write the hidden number in the cup and the number left out. For example, 3 left out, 1 under the cup = 4.

Player #2 hides his/her eyes and Player #1 hides some of the counters under the cup.

Players continue to alternate turns.

Your paper will reflect different ways to break the total number into two parts: 4=3+1, 4=2+2, 4=4+0
Can you find a way that is not shown?

Now pick a different amount of counters and continue to play.

Math Games and Effective Teaching

I have spent many years of my elementary teaching career building a community of learners who approach math with eagerness. I’ve learned that students need to be mentally engaged in a challenging and worthwhile mathematical task that emphasizes the conceptual aspects of the mathematical topic and promotes the formation of mathematical connections if they are to learn skills with meaning and be able to use those skills to solve problems.

It is not so critical whether students “discover” everything for themselves but it is critical that students are allowed to do some genuine mathematical work on their own. If teachers do all the work and students are left only to copy and imitate and practice what the teacher has done, they are less likely to make sense of the material, remember it later, transfer it to new situations, or do well on standardized tests.

The most important thing with respect to student learning is the nature of the learning task students engage in. Students need to be encouraged to think and persist with respect to the mathematical task, and the teacher should refrain from stepping in too early to provide students with answers or tell them exactly what steps they should use. Rather, the teacher can support students by asking them questions that guide them toward mathematical learning. This can be effectively done in a range of instructional settings from the most student-centered to the most teacher-centered.

Reform-minded teachers pose problems and encourage students to think deeply about possible solutions. They promote making connections to other ideas within mathematics and other disciplines. They ask students to furnish proof or explanations for their work. They use different representations of mathematical ideas to foster students’ greater understanding. These teachers ask students to explain the mathematics.

I have found that math games are an engaging and mathematically challenging task that can effectively offer students the opportunity to be engaged and talking with one another, and where they are encouraged to question and think about the mathematics and mathematical relationships. Have you ever used a ditto or workbook page that could make that claim?

Of course, it is not enough to teach students the game and let them play it. It is the teacher’s responsibility to move from group to group, listen to the conversations, and ask probing questions. My most-used question is, “Can you convince your partner and me that you are correct?” After hearing the question several times, the students usually begin to ask the question of their partners without my prompting.

Other questions that are well worth asking are:
• What card do you need?
• Which cards would not be helpful?
• Prove to me that a ____ is what you need.
• Why do you think that?
• How did you know to try that strategy?
• How do you know you have an answer?
• Will this work with every number? Every similar situation?
• When will this strategy not work? Can you give a counterexample?
• Who has a different strategy?
• How is your answer like or different from another student’s?
• Can you repeat your classmate’s ideas in your own words?
• Do you agree or disagree with your classmate’s idea? Why?

Too often the teacher or the partner is willing to give the other player the answer, thus making it possible for that player to do no thinking whatsoever. The teacher’s or partner’s questions to that player should be:
• What can you do to help yourself? Use your fingers to count? Count the dots on the dice or cards? Use manipulatives to figure it out? Draw a picture? Start with something you already know?

The power of questioning is in the answering. As teachers, we not only need to ask good questions to get good answers but need to ask good questions to promote the thinking required to give good answers.

Math Games and Understanding Equality

I contend that one of the big reasons why U.S. students lag behind their peers in many European and Asian countries in mathematics is because we are lax in helping children develop critical thinking skills.

Critical thinking skills that require students to apply content knowledge to real-world problems is of great importance. It’s very clear that if students can recall discrete content knowledge but cannot apply it, they’re going to be in trouble.

Here’s an example. By the time students have mastered rudimentary math, elementary-school pupils should understand that the numbers on either side of the equal sign are equivalents. Many students drilled in rote memorization don’t always grasp the concept of equivalency. I’ve frequently seen sixth graders who still believe that the equal sign means “the answer goes here”.

Equivalence/equality is undoubtedly one of the most important, connecting ideas in school mathematics. Developing this concept of equivalence calls for lots of experiences with materials as students are developing their conceptual understanding of numbers and operations. More important, it calls for teachers to help students connect their experiences with the mathematical idea(s) they are developing, in this case, equivalence or equality.

One of the experiences elementary teachers can use to help develop this understanding of equivalency is math games. The following is one of my favorites, and I use it with first through sixth graders.

Balancing Act

What you need:
2 players
deck of cards, face cards removed
cut a 3×5 card in thirds. On two of the thirds write a + sign. On the last third write an = sign.

Shuffle the cards and deal six cards to each player. Stack the rest of the cards facedown in a pile.

Each player chooses four cards from his/her hand. The object is to balance the equation by arranging the cards into two addition problems with equal sums. A player earns one point for balancing the equation.

Example: a player could place a 7 and a 1 on one side of the equation and a 3 and a 5 on the other (7+1 = 3+5)

A player can also place two cards of the same value on the equation to balance it (4+0 = 0+4).

At the end of a round, the cards played are placed at the bottom of the deck. The dealer shuffles the cards and gives six more to each player. Play continues in the same way.

The game ends when one player reaches ten points.

Variation: Children can play a similar game using subtraction or addition and subtraction. Change your “operation cards” so that children can create various balancing equations.

Math Games and English Language Learners

As an elementary math specialist, I talk about math all the time. The moment I begin a conversation, a wall comes down, and so many children (and adults) quickly blurt out that they dread math and say they have never been good at it.

To be perfectly honest, as a student, I struggled with math. I didn’t understand why it came so naturally to some students, but not to me. Looking back, however, I realize that I had an advantage that I wasn’t even aware of — I understood the language in which the problems were written, even if I didn’t understand how to solve them!

I can imagine what it must be like for English language learners (ELLs). Although it is easy to assume that many ELLs will excel in math because math is a “universal language”, and students may have had prior educational experience that included mathematical instruction, that assumption can lead educators astray.

Young children, whether ELLs or native English speakers, need to work with more than just worksheets to learn and understand math concepts. Utilizing multiple learning modalities will help all students to develop a deeper understanding of number concepts and relationships, but is especially helpful for English language learners.

If your goal is an excellent mathematics program for every child, then for these students, successful teachers need to find ways to make math understandable, relevant, and familiar. It is imperative that teachers utilize multiple instructional approaches.

The use of pairs or small groups is an instructional strategy that can be very effective for ELL students. By grouping students, you can encourage communication and interaction in a non-threatening and more relaxed setting.

Because math games require active involvement, use concrete objects and manipulatives, and are hands-on, they are ideal for all learners. Games provide opportunities for children to work in small groups, practice teamwork, cooperation, and effective communication. Children learn from each other as they talk, share, and reflect throughout game times. Language acquisition is meaningful and understandable.

Math Games and Your Mathematics Textbook

Using math games is one of several effective strategies used in the Washinton, D.C. schools’ mathematics curriculum where dramatic improvement has been seen in mathematics achievement in standardized tests. From 2005 to 2009, D.C. public schools increased NAEP scores in math by 4.5 times the national average for fourth graders.

“Since 2005, the D.C. public schools have used McGraw-Hill’s Everyday Mathematics, a structured, rigorous and research-based Pre-K–6 curriculum developed by the University of Chicago School Mathematics Project that helps students learn mathematical reasoning and develop strong math skills. The program’s hands-on approach, which focuses on using a student’s own experiences, real-life examples and games, teaches basic skills as well as conceptual thinking. It is the nation’s most popular elementary math program, used by more than 4 million students nationwide.”

Games can be easily linked to any mathematics textbook.

No matter which textbook your district uses, games can easily be incorporated into instruction. As you see with Everyday Mathematics, some textbook companies are “seeing the light” and have begun to implement games as a part of each unit.

Even if your textbook does not incorporate games, identify a skills need almost all your students have, and give a game a try. I guarantee it will be more of a learning experience for the students and more informative to you of what your students know and can do than a workbook page.

Understanding and Mastering Multiplication

Many children struggle to memorize their multiplication tables, and many adults have bad memories of trying to learn them.

Why should children learn the multiplication facts? Because children without either sound knowledge of their facts or a way of figuring them out are at a profound disadvantage in their subsequent mathematics achievement. Students without multiplication-fact fluency spend more time determining routine answers and less time on more meaningful applications. Students who know their facts build on these fundamental concepts which ultimately benefits their later mathematical development.

For years, learning to compute has been viewed as a matter of following the teacher’s directions and practicing until speedy execution is achieved. There has been little or no emphasis on understanding the concept. Memorize 7×6=42, and so on.

When skills such as multiplication facts are taught for conceptual understanding and connected to other mathematics concepts and real-world meaning, however, students actually perform better on standardized tests and in more complex mathematics applications.

Numbers and equations are far more interesting when they represent real-life specifics. For example, the problem “What is 3 x 4?” can be posed as “If there are 3 pods with 4 whales in each, how many whales are there altogether?” As kids begin to visualize whales swimming through the ocean, the math becomes much more specific, rich, and understandable.

When my granddaughter was in the 3rd grade, we would use travel time in the car to practice our multiplication facts. First, I would make up a problem (7 tricycles, how many wheels?), and she would have to give me the complete equation (7×3=21). And then I would ask, “Why isn’t this a 3×7 problem?” Too many times all we say is 7×3 is the same as 3×7. That can be very confusing.

Then it would be her turn to make up a question (5 cars, how many rear-view mirrors?), and I would have to come up with the entire equation, plus justify why it wasn’t a 3×5 question.

Sometimes we would discuss what might make a good 4×7 question, or a 9×6 question, etc.

Keeping with the idea of making multiplication facts understandable, you might try a math game such as Bubbles and Stars.

Bubbles and Stars (Beginning Multiplication)

What you need:
2 players
1 die
paper and a pencil for each player (fold it in quarters)

Player #1 rolls the die and draws that many bubbles (as big as he/she can in one of the quarters).
Example: Player #1 rolls a 5 and draws 5 bubbles.

Player #2 rolls the die and draws that many bubbles.
Example: Player #2 rolls a 1 and draws 1 bubble.

Player #1 rolls the die and puts that many stars inside each bubble.
Example: Player #1 rolls a 3 and draws 3 stars inside each of his/her 5 bubbles

Player #2 rolls the die and puts that many stars inside each bubble.
Example: Player #2 rolls a 6 and draws 6 stars inside his/her 1 bubble.

Both players record how many bubbles and stars they drew and then record how many stars they have altogether.
Example: Player #1 – 5 bubbles x 3 stars = 15 stars
Player #2 – 1 bubble x 6 stars = 6 stars

Player #1 rolls the die one last time.
If the roll is odd – 1,3,5 the player with the most stars wins.
If the roll is even – 2,4,6 the player with the least stars wins.

Parents and teachers who use these kinds of activities with their children, will help them master their multiplication facts. Resultingly, these students will have a more positive attitude about their mathematics abilities and further mathematics experiences. Teaching for understanding equals a formula for success.

Making Math Add Up

Many times math doesn’t add up for students. In fact, many adults have bad memories of trying to learn the multiplication tables or figuring out the square root of a number.

How do we foster a love for learning? When we teach children to read we share colorful picture books filled with exciting stories. In science, we do lively and engaging hands-on experiments, using fun props such as soda bottles and bouncing balls. Yet how do we teach math? Often, intimidating numbers and symbols cover the board. Kids break out in a sweat trying to memorize formulas and multiplication tables. Is this encouraging a love for the process of solving problems and seeking solutions?

One way to deal with math-phobia is to get to kids while they are young and teach them about the fun side of math.

Math as fun? No problem. Experts now agree that children learn far more readily when they are having fun. So what is the simplest way to have fun with math?

Years ago I started playing fun math games in my classroom, and I soon realized that playing games is the best way to get kids motivated and enthusiastic about math. Over the years I have collected many, many classroom math games that I know kids love to play. Finally I have put them together by grade level.