## 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!

## Children Love Math Games

Another elementary school (this one is in Knoxville) has joined the ranks and begun to use math games in the classroom to motivate and engage students in meaningful mathematics.

“Often times, mathematics is viewed by our society as cruel and unusual punishment. That makes it very difficult for teachers to teach math and for students to invest the time and energy it takes to learn math. Through games, you have the motivational factor that helps move learning along.”

Classic games are finding their way into classrooms as educators creatively use the games to reinforce math, language and critical thinking skills.

I have found that games have a multitude of benefits:
• Meets Mathematics Standards
• Easily Linked to Any Mathematics Textbook
• Offers Multiple Assessment Opportunities
• Meets the Needs of Diverse Learners (UA)
• Supports Concept Development in Math
• Encourages Mathematical Reasoning
• Engaging (maintains interest)
• Repeatable (reuse often & sustain involvement
• Open-Ended (allows for multiple approaches & solutions)
• Easy to Prepare
• Easy to Vary for Extended Use & Differentiated Instruction
• Improves Basic Skills
• Enhances Number and Operation Sense
• Encourages Strategic Thinking
• Promotes Mathematical Communication
• Promotes Positive Attitudes Toward Math
• Encourages Parent Involvement

Whichever grade level you teach, there are many games that your students can play which will be effective, useful, and fun!

## 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.

## Making Estimates (Smart Guesses) with Children

Much of the math we do as adults involves making estimates. We are not born with the ability to make fairly accurate and reasonable estimates. Children need to have lots of experiences with making estimates.

Find a small box with a lid. Ask your child to guess how many pennies, cheerios, paperclips, etc. the box will hold. Whatever the guess, be it reasonable or not, have the child write the estimate down. Never comment negatively or positively on the estimate. I usually respond, “Okay”. A negative response to their estimate will lead to an unwillingness on the part of the child to make any more estimates.

Then fill the box and count to find out how many it did hold. Next time keep the same box but fill it with something different. Will this change the estimate? For instance, if you used Cheerios the first time you filled the box, and this time you are using marbles, will the estimate and count change? Can you get as many marbles in the box as you did Cheerios? Why or why not?

Do this many times and record your estimates and actual counts. The more your child does it, the better their estimates will become. He/she will probably also begin to notice that the smaller the objects, the more will fit in; the bigger the objects, the fewer that will fit in. Use all shapes and sizes of boxes and continue to make estimates and count.

When the french fries arrive from McDonald’s, have your child make an estimate and then count and eat to find out. Estimate coins in Dad’s pockets (number and value), houses on the block, days till the next birthday, meals you eat in a month, etc.

Here’s one of my favorite estimating activities:

How Many Shoes?

Make an estimate (smart guess) of how many shoes you think you will find in your home. ________________
Count the shoes in your home.

Other shoes _________________

Total number of shoes _______________

How many pairs of shoes are in your home? ____________________

Are there more shoes or more pairs of shoes? ___________________

How many shoes do not have a matching one? _________________

How many shoes are in your closet? ___________________

Arrange your shoes in pairs. How many pairs? __________________

Are there more shoes or more feet in your home? ___________________

## 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.

## Experts Recommend Math Games

As a veteran teacher of grades K-3, I have been using math games to motivate and energize my mathematics curriculum for many years. I am not alone in this endeavor. The following newspaper article gives credence to this fact:

Experts are recommending that parents can really help their children in math by playing games with them.

The research concludes that playing a board game with numbers helped children improve on four kinds of numerical tasks. Those gains were still evident nine weeks later.

So, get out those cards and dice or buy a board game that involves numbers, and be ready to watch your child learn and have fun!

## 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

_______________________ ______________________