## 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.

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.

## Mathematics and Young Children

As an elementary mathematics specialist, I have always listened carefully to what the NAEYC has to say. They are an authority that I greatly respect.

The National Association for the Education of Young Children (NAEYC) is dedicated to improving the well-being of all young children, with particular focus on the quality of educational services for all children from birth through age 8.

I regularly refer to their Mathematics in the Early Years. In it, early childhood specialists, mathematics professors, educational researchers, classroom teachers, nursery school directors, sociologists, and psychologists combine their individual perspectives to explain what mathematics in the early years should look like. This book is a gold mine for parents and teachers!

The following are their guidelines for parents who are eager to get their children started on a sound mathematical footing:

1. Use everyday situations to create purposeful, in-context learning.
Everyday family activities such as storytelling, playing games, shopping, distributing items (e.g., candles, playing cards, silverware), preparing for a birthday party, noting the number of days until a special event, or cooking present numerous opportunities to learn, apply, and practice mathematics.

2. Encourage children’s exploration of mathematics in the world around them.
Welcome their questions. Be willing to discuss mathematical ideas they encounter in their activities, and help them find answers to problems.

3. Use games to prompt interest and development.
Play is one of the most important ways children learn about their world and master skills for coping with it. Games are a particularly useful form of play that help children develop mathematical concepts and reasoning and practice basic mathematical skills. In addition to being challenging, interesting, and enjoyable for children, games provide a means for structuring experiences to meet children’s developmental needs. Games can also serve as an invaluable diagnostic tool. By observing a child playing a particular game, parents and teachers can detect specific strengths and weaknesses in mathematical concepts, reasoning, and skills.

4. Serve as a “guide on the side versus sage on the stage”. Because meaningful knowledge and a number sense must be actively constructed by children, imposing knowledge on them is far less effective than creating opportunities for them to discover patterns and relationships and to invent their own strategies and solutions. Moreover, drilling young children on mathematical facts will not promote mathematical understanding or thinking and may create a negative disposition toward mathematics. To foster autonomy and confidence, generally allow children to try out and self-correct their own strategies and solutions instead of simply telling them answers or correcting them.

5. Use children’s natural interest about counting, numbers, and arithmetic in deciding what materials and experiences to provide for them.
Children’s questions are a strong indication of what is appropriate and when guidance is needed. Note, however, that their individual interests may vary greatly.

6. Promote social interaction.
Children learn from other children. The mathematical knowledge that young children have varies. Play with other children can provide a natural opportunity for correction and guidance. Encourage small-group play and discussion.

7. Encourage children’s use of verbal, object, and finger counting to represent numbers.
Give them opportunitities to use finger or object counting to solve simple problems, such as, “How much is three candies and one more?” When possible, make counting fun for children by playing mathematics games.

8. Foster the development of children’s number sense.
Give children lots of opportunities to estimate the size of collections and then let them count. The more estimating and counting they do, the better they will become.

## Math Games and Math Anxiety

Parenting is arguably the biggest thing you can do in your life, and guess what? No manual. Everything else has a manual. I just brought home a plant, and it had instructions pasted on the side. I purchased a bookshelf, and there was an entire pamphlet of detailed instructions and pictures on how to put it together – in three different languages!

As a veteran elementary teacher, I have found that many parents are eager to help their children with their school work, but don’t always know what is best or where to begin. What I, also, know is that a parent’s involvement in a child’s education is the single most important factor in that child’s academic success.

Decades of educational research tells us that an involved parent contributes overwhelmingly to his/her child’s grades and test scores, school attendance and quality of homework, positive attitudes and behavior at school, likelihood of graduation, and desire to enroll in higher education.

I bet you’ll never guess which subject raises the greatest consternation in parents – you’re right, math! Math anxiety is rampant in the world, and yet no one comes out of the womb with a stamp on their head that says, “I am math-anxious”.

Many parents don’t feel comfortable with math, or they assume it takes special expertise to teach it. Remarks like “I never was any good at math” or “How can I help my child with math? I can’t even balance my checkbook!” are common. However, even parents who feel this way use mathematics all the time. They hand out lunch money, cut sandwiches into quarters, calculate how much paint or wall paper they need to buy, estimate how much a trip will cost, read and interpret graphs, talk about the probability of rain, and decide that it’s time to fill the gas tank. Some of them knit, piece quilts, measure wood for cutting, decide how many cups of spaghetti sauce they need to make for 6 people, and use metric tools to work on their cars. The list goes on and on.

Many adults also feel they aren’t doing things the right way, that they aren’t really using mathematics, because their approaches, even though they work, are not the methods they learned in school. There are, in fact, many ways to do mathematics, and more than one can be right. People who devise their own strategies for finding answers to mathematical questions, far from being mathematically incompetent, are often excellent independent problem solvers. They are using mathematics creatively.

• You have a great deal of important mathematical knowledge to share.
• Children learn best from the people who most accept and respect them.
• Learning is more lasting when it takes place in the context of familiar home experiences.
• Children must see that math is not just a subject studied in school but is used constantly in everyday family life.
• The home is an ideal place in which to learn mathematics because the problems encountered there are real, not just paragraphs in textbooks.
How can parents foster math skills and mind-sets so that their children are confident mathematicians? Make math games a family ritual!

Games offer a pleasant way for you, as parents, to get involved in your child’s mathematics education. You don’t have to be a math genius to play a game. You don’t have to worry about pushing or pressuring your child. All that you have to do is propose a game to your child and start to play.

## Number of the Day

One of my favorite math activities for any age child is Number of the Day.

This is a great activity for anyplace you happen to be! It will give your child lots of computation practice, be a good deal of fun, and everyone (even you) will be forced to “prove” that they are correct!

Let’s say that our “number of the day” is 6. Everyone has to think up one way to make 6. Young children will probably begin with simple addition.

Example: 4 + 2 = 6

Ask your child to “convince you” (prove) that 4 + 2 = 6.

Everyone has to come up with an equation that equals 6, and each one has to be different.

After gaining in confidence, encourage your child to think of 2 different things that equal 6.
Example: 3 + 3 and 5 + 1

Then ask them to find 3 things that equal 6
Example: 1 + 2 + 3 = 6

See how many different ways everyone can find to make the number of the day. Write it all down if pencil and paper are handy.

Depending on your child’s age begin to encourage the use of other operations such as:
• subtraction 9 – 3 = 6
• addition & subtraction 8 – 4 + 2 = 6
• multiplication 3 x 2 = 6
• multiplication & addition 2×2+2 = 6
• division 24 ÷ 4 = 6
• all 4 operations in one equation
(50 ÷ 2) x 3 – 70 + 1 = 6
• coin values – 1 nickel and 1 penny =
6 cents
• fractions 4 ½ + 1 ½ + 6
• decimals 2.4 + 3.6 = 6 or 12 x .5 = 6
• integers – positive 10+negative 4 = 6

Family members can take turns choosing the number of the day. What about the day of the month, someone’s age or weight, number of windows in your home, the sum of your telephone number, etc. Try a variety of numbers, including large ones (such as 555 or 62,437) and small ones (they can be just as challenging as large ones).

Well, you get the idea! Dad might be coming up with 4 x 25 – 80 – 14 = 6!!
Does he have to prove it??!! Absolutely!

## Helping Children Learn Mathematics – Count Collections!

As a veteran elementary teacher, I have found that most kindergarten children and many first graders come to school able to rote count to ten, or twenty, or higher. Even though the counting sequence seems to be in place, these children often have difficulty counting objects accurately past five or ten.

After more than 20 years of being an elementary math specialist, I have found that the most important thing parents can do to support their children’s mathematical growth at this age is to count things.

Experiences with counting provides a solid foundation for future experiences with addition, subtraction, multiplication, and division.

The following counting and comparing activity is one that I always sent home as homework:

Counting and Comparing Collections

The concepts of more than, less than, and equal to are important in your child’s development as a mathematician.

We use the following symbols:
= to mean “is equal to”
< to mean “is less than” > to mean “is more than”

For example, 7<18, which means 7 is less than 18 (small, closed end points toward the smaller number) Count the following things around your house and record how many and then put in the appropriate symbol.

_________ ________

__________, _________
ceiling lights, lamps

_______, _______
chairs, tables

______, ______
people, pets

_____, ______
girls, boys

_____, _____
doors, windows

________, _______
bedrooms , bathrooms

_______, ________
forks, knives

_______, _______
cups, glasses

_______, ______
books, TV’s

_______, ______
shoes, socks

________, _______
watches, clocks

What are some other things you could count and compare at your house? Do it!

## Math Games and Computation

In their theoretical classroom, children would spend a short period of time each day practicing computation — adding, subtracting, multiplying and dividing.

As a veteran elementary teacher, I have found that math games are an effective and useful way to practice that computation.

Math games put children in exactly the right frame of mind for learning. Children are normally very eager to play games. They relax when they play, and they concentrate. They don’t mind repeating certain facts or procedures over and over. Games incorporate the ways children best learn mathematics – games require active involvement. Actively engaged children learn more quickly.

Children throw themselves into playing games the way they never throw themselves into filling out workbook pages or dittos. And games can, if you select the right ones, help children learn almost everything they need to master in elementary math. Good, child-centered games are designed to take the boredom and frustration out of the repetitive practice necessary for children to master important math skills and concepts.

Playing math games is even more beneficial than spending the same amount of time drilling basic facts using flash cards. Not only are games a lot more fun, but the potential for learning and reasoning about mathematics is much greater, as well. Games require a variety of problem-solving skills, such as making and testing hypotheses, creating strategies (thinking and planning ahead), and organizing information. Plus, as children play, they further their development of hand-eye coordination, concentration levels, visual discrimination, memory, and their ability to communicate and use mathematical language.

## Yes, It’s Possible to Have Fun Doing Math!

Parents are always looking for activities and games to challenge their child’s mind while having fun together. My goal is to help parents and their children enjoy mathematics. When children play with mathematics in their everyday lives, they can grow up loving it.

Children must see that math is not just a subject studied in school but is used constantly in everyday family life. The home is an ideal place in which to learn mathematics because the problems encountered there are real, not just paragraphs in textbooks.

How you encourage and promote your child’s math learning, from preschool to high school, can be pivotal to their attitude toward math and their achievement in this subject area. Children are taught math in school, but research shows that families are an essential part of this learning process. In other words, by doing math with your child and supporting math learning at home, you can make a great difference.

The following is just one of many activities that can help you make math a natural part of your family’s everyday work and play.

Alike and Different (Comparisons)

Pick two objects.

For example: apple and orange

Possible responses:

They are alike because they both are food, fruit, have seeds, make juice, come from trees.

They are different because one is orange and the other is red; one has wrinkles and the other is smooth; one has black seeds and the other white; we eat apple peels but not orange peels.

Make a list of what you compared and how they were alike and different.

Play the game over and over, using a different set of objects each time.

Now give one of my math games a try and continue the learning and the fun!

## Math Games Can Motivate Students

“Games can motivate students, capture their interest, and are a great way to get that paper and pencil practice”, says Marilyn Burns, world-renowned mathematics expert.

Games offer teachers a way of practicing and reinforcing arithmetic and other math skills, as well as supplementing a sole diet of drills and practice-problems with workbook pages or dittos.

Not only do games engage students, they also present the opportunity to present “high level” math concepts in a colorful and simple way.

In my experience, students are more engaged when we connect the mathematics they are going to learn with something that excites them (e.g., games).

Despite those benefits, some teachers and parents are reluctant to use board games and similar activities. Those critics tend to regard them as activities that cut into time spent on practicing problems, when in fact games should be used as another form of math practice.

Research on the link between games and math learning has implications not just for educators, but also for parents.

Turning off the television and engaging children in a simple card or dice math game just a few times a week can greatly improve their comfort in math.

There’s a huge amount of math in card and dice games that is not on television and video games.

## Using Math Games at Home

Games offer a pleasant way for parents to get involved in their children’s education. Parents don’t have to be math geniuses to play a game. They don’t have to worry about pushing or pressuring their children. All that parents have to do is propose a game to their child and start to play.

Math games for kids and families are the perfect way to reinforce and extend the skills children learn at school. They are one of the most effective ways that parents can develop their child’s math skills without lecturing or applying pressure. When studying math, there’s an element of repetition that’s an important part of learning new concepts and developing automatic recall of math facts. Number facts can be boring and tedious to learn and practice. A game can generate an enormous amount of practice – practice that does not have kids complaining about how much work they are having to do. What better way can there be than an interesting game as a way of mastering them?

All right, you’ve chosen a math game to play with your child. Now what? How can parents effectively help their child while playing a game?

Parent Responsibilities

Too often the parent is willing to give the child the answer, thus making it possible for him/her to do no thinking whatsoever. Not good! Your primary responsibility is to ask your child questions – questions that will force him/her to think and verbalize what he/she is doing and why.

Sometimes children don’t know what to do. Here are a few good questions to help them begin to help themselves, not just rely on you, the parent, to give them the answer:

• Use your fingers to count?
• Count the dots on the dice or cards?
• Use counters (such as beans, paper clips, pennies, etc.) to figure
it out?
• Draw a picture?
Example 1: If you know that 5+5 =10, how can that help
you know what 5+6 equals?

Example 2: If you know that 5×6 = 30, how can that help you
know what 6×6 equals?

The power of questioning is in the answering. As parents, 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.

Here are a few more great questions to ask your child when playing a game:
• 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 the right answer?
• Will this work with every number? Every similar situation?
• When will this strategy not work? Can you give a counter-example?
• Convince me that you are right.

Parents who observe and interact with their child while they are playing math games can find out a great deal about what their child knows and can do in math. While playing a game, what do you notice – what are your child’s strengths and weaknesses?

Finally, games provide children with a powerful way of assessing their own mathematical abilities. The immediate feedback children receive from their parents while playing games can help them evaluate their mathematical concepts. Good games evaluate children’s progress. They provide feedback so that parents, and the child know what they have done well and what they need to practice.

Parent Response to Game

As you play a game with your child, ask yourself the following questions:

• What did I think of this game? Did I like it? Why or why not?

• Was this game too easy, too hard, or just right? How did I change it to meet the needs of my child?
• What do I think my child learned from playing this game?

• What did I learn about my child while playing this game? What are his/her strengths? What does he/she need to practice?

Keep in Mind While Playing Math Games…

Inventing, Creating, and Changing the Games

Give your child opportunities to invent and create. The rules and instructions for all games are meant to be flexible. Allow your child to think of ways to change the equipment or rules. Encourage them to make a game easier or harder or to invent new games.

You can easily vary the games within this CD to suit the needs of your child. Some variations have been described within many of the games:

• The operations used within the games can be changed. If it’s an addition game, it might also make a great subtraction or multiplication game.
• The types of numbers used with the games can be smaller or bigger. If it’s a two-digit addition game, can it be made into a three-digit game?
• The rules of the games can be altered.

Please be creative in transforming the games into new forms, and please allow your child to do likewise.

Play the games many times. Children begin to build and practice strategies (plan their moves in advance) only when the game is repeated often. Playing it just once or twice is not very helpful, unless the game is too easy for your child.

Provide repeated opportunities for your child to play the game, and let the mathematical ideas emerge as they notice new patterns, relationships, and strategies. Allow the mathematical ideas to develop over time. This empowers children to independently explore mathematical ideas and create conceptual understanding that they will not forget.

Don’t hesitate to go back to a skill and play a game if you know your child needs to practice it.

Have FUN together!!!!!

## Fractions Activity and Game

In 2006, the National Math Panel reported that knowledge of fractions is the most important foundational skill for algebra that is not developed among American students.

Research shows that fractions are one of the most difficult topics for students to understand in elementary school. I think the problem lies in the fact that children are expected to be passive receivers of information rather than be actively involved with the subject matter.

CGI (Cognitively Guided Instruction) has been stressing for many years that the best way to help children really understand fractions is to begin with “fair shares”.

Start with situations of 2 or 4 children, as children’s earliest partitions are based on halving:
4 children share 4 cookies so that each child gets the same amount.
4 children want to share 10 brownies so that each child gets the
same amount.
4 child want to share 22 apples so that each child gets the same
amount.

Move to situations with more sharers:
3 children want to share 7 candy bars.
6 children have ordered blueberry pancakes at a restaurant. The
waiter brings 8 pancakes to their table. If the children share the
pancakes evenly, how much can each child have?
Matthew has 13 licorice sticks. He wants to share them with 8
friends.
20 friends are sharing eight cakes.

Ask your child or your students to solve the problems using a strategy that makes sense to them. Strategy is the primary dimension of development because student-generated strategies can (and I believe should) serve as the foundation for mathematics instruction. A focus on student-generated strategies allows a teacher or a parent to begin with, and build on, what children already know, and it allows children to participate in instruction by making contributions that are personally meaningful.

Give children pencils and paper and access to any kind of manipulative they find helpful and allow them to work out the problem by themselves.

Once the task is completed, children need to be able to demonstrate to each other what they did and the answer that was found. The more students are encouraged to contribute the intact products of their own thinking to class discussions, the more likely they are to identify themselves as understanding math – no matter the level of the thinking.

The key in fraction instruction is to pose tasks that will elicit a variety of strategies and representations. Equal-sharing tasks are not the only problems that can do that, but many teachers, like myself, have found them to be a definite source of variety in thinking. Children learn from each other, and the teacher begins to get a picture of what each child knows.

Another great way to help your child or your students to understand fractions is to play a fraction game. I have found that Fraction War can be highly effective. The first level begins simply, and it is probably best to start here, even with older children. Once you are sure they understand this concept, move to the next concept level.

Fraction War

Materials:
 One deck of cards
 Fraction War Game Board (following)

Game:
Players draw cards and create a fraction. The player with the fraction with the greatest value wins a point for that round. The player with the most points when all the cards have been used is the winner.

Variations:

Concept 1:
Each player finds and places a one in the numerator position on his/her game board. This card remains in place until the end of the game. Each player draws a card and places it in the denominator position. The player with the greatest fraction wins the point. Play continues until all cards have been used.

Concept 2:
Place a one in the denominator position and play as above.

Concept 3:
Decide on a number between 2 and 10. Each player places that number in the denominator position. Play as above.

Concept 4:
Place the same number in the numerator position. Play as above.

Concept 5:
Each player draws 2 cards. The first is the denominator, the second is the numerator. Play as above.

Fraction War Game Board
Player #1 Player #2

_______________________ ______________________