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Fun and (Math) Games!

Saturday School A Success At Lincoln Elementary reads the headline from Madison, Wisconsin. Even on a Saturday, and even on a day that felt like summer, dozens of students at one elementary school spent the morning in class.

Every Saturday since the end of January, about 100 students have gathered for about two hours a week to get a little extra work done and to do so while having a little bit of fun. It is easy to assume that kids would want to be anywhere but school on a weekend morning, but this program is proving to be different. Instead of traditional instruction, students learn through playing games.

It seems somehow sad to me that kids are allowed to have fun with math only on Saturdays. Why isn’t math engaging, challenging, and fun all the time? As a veteran elementary teacher, I do understand that teachers feel like they don’t have enough time to teach all of the content within the course of a school year. Why on earth would they ever want to add more material in the form of math games when they can’t seem to finish the assigned math textbook? Turns out that making time to incorporate math games in the classroom can lead to rich results. I’ve been using games to teach mathematics for many years, and here are some of the significant benefits of doing so:

Benefits of Using Math Games in the Classroom

• 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

Pick a skill that your students need to practice. One of the big ones is subtraction at any level. Kindergarteners through 6th graders find subtraction to be a challenge. Here’s a great double-digit subtraction game:

500 Shakedown

What you need:
2 players
2 dice
paper and pencil for each

Each player starts with 500 points.

Player #1 rolls the dice and makes the biggest two-digit number he/she can. Now he/she subtracts this number from 500.

Example: Player #1 rolls a 2 and a 4 and makes 42. Now he/she subtracts 42 from 500.

Player #2 rolls the dice and does the same. Players continue to alternate turns. The first person to reach 0 wins.

There’s only one complication! When you throw a 1, the rules change. You don’t subtract. Instead you make the smallest two-digit number you can and add.

Example: If the player throws a 1 and a 5, the smallest two-digit number is 15. So he/she adds 15 to the total.

Variation: Start with 5,000 points and use three dice or start with 50,000 and use 4 dice.

In Terms of Decimals, Math Is the Best Game in Town!

Ask fourth, fifth, and sixth grade teachers about decimals and the question is followed by groans of dissatisfaction. Basically, the groans stem from the lack of success that teachers have in teaching this concept. As one student put it, a decimal is “a thing that makes numbers even more confusing”.

Teachers can get some help in this area by playing decimal math games with their students. A math game has advantages over the traditional approach. Playing a game increases the excitement of any mathematics lesson, and games are engaging and give students the chance to cooperate and communicate with their peers. The following decimal games are two student favorites:

Decimal Dice

What you need:
2 players
two dice
paper and pencil.

Player #1 rolls the dice one at a time. The first number rolled is the whole number and the second number rolled is the decimal.

Example: Player #1 rolls a two and then a 6 – the score is 2.6

Player #1 records this decimal at the top of his/her paper.

Player #2 rolls the dice, one at a time, and records his/her score.

Players continue to alternate turns until each player has 10 decimals.

Player #1 adds his/her 10 decimals together. Player #2 does the same. Players exchange papers and check each other’s addition.

For each double rolled (2.2, 3.3, 6.6, etc.) you add 10 bonus points to your final score.

The player with the highest sum wins the game.

Variation: This game can also be played with subtraction. Begin with a score of 100. Roll the dice in the same manner and subtract your decimal from your score. If you roll doubles, subtract 10 bonus points. The person with the LOWEST score wins!

Decimal Dice 2

What you need:
2 players
two dice
paper and pencils

In this game, each player will roll the two dice exactly three times. At the end of three rounds, the player closest to 10 wins the game.

Player #1 rolls both dice. Player #1 must decide which of the numbers is the whole number and which is the decimal.

Example: Player #1 rolls a two and a 6 – he/she decides whether to
make 2.6 or 6.2

Player #1 records this decimal on his/her recording sheet.

Player #2 rolls both dice. Player #2 must decide which of the numbers is the whole number and which is the decimal and record this on his/her recording sheet.

Players continue to alternate turns until each player has thrown the dice three times.

Players add their decimals. Players exchange papers and check each other’s addition.

The player with the sum closest to 10 wins the game.

Integer Addition Games

There are several highly effective math games which can deepen children’s understanding of integer computation and help them make sense of the concepts underlying the addition of integers. These three games would be appropriate for fourth graders, fifth graders, and sixth graders.

Integer Addition Match

What you need:
2 or more players of equal skill level
regular deck of cards (Jack = 11, Queen = 12, King = 0)
(red cards are negative numbers, black cards are positive numbers)

Players divide the cards evenly between themselves and place them in a pile face down in front of themselves. Each player then turns over one card at the same time. Players must add the two numbers. The first player who says the correct sum out loud collects both cards.

Example:
Player #1 turns over a red 8.
Player #2 turns over a black 3.
-8 + 3 = -5

When the piles are used up, players count their cards. The player with the most cards wins.

In the event of a tie, both players turn over one more card. The first player who says the correct sum out loud collects all 4 cards.

Integer Addition War

What you need:
2 players
regular deck of cards – remove Jacks, Queens, and Kings
(red cards are negative numbers, black cards are positive numbers)

Players divide the cards evenly between themselves and place them in a pile face down in front of themselves. Players turn over two cards each and add them.

Example:
Player #1 turns over a red 5 and a red 2 (-5 + -2 = -7) Player #2 turns over a black 3 and a red 4 (3 + -4 = -1)

The player with the greatest sum collects the four cards. In the event of a tie (i.e. both have the same sum), each player lays down two more cards and adds them together. The player with the largest sum takes all 8 cards.

When the piles are used up, players count their cards. The player with the most cards wins.

Variation: Play 3 addend addition with cards still holding positive and negative values.

Salute Integers Addition

What you need:
2 players or 2 teams of two
standard deck of cards – face cards removed
Red is negative. Black is positive.

Shuffle deck and place face down in center of table.

Player #1 turns over the top card and places it face up on the table.

Player #2 draws a card and does not look at it. Player 2 holds the card above his or her eyes so that player #1 can see it.

Player #1 combines the 2 cards mentally and says the sum out loud.

Player #2 listens and decides what his or her card must be and says that number out loud.

Esample:
Player #1 turns over a red 8 and both players see it.
Player #2 picks up a card and, without looking at it, puts it on his head so that only player #1 can see it. It is a black 4.
Player #1 says, “-8 + your number equals -4”.

Both players decide if the response is correct. If it is, player #1 gets 1 point.

Players reverse roles and play continues until one player or team has 10 points.

The Perfect Math Game!

Are you looking for creative and engaging ways to help your students/children learn basic math concepts and skills?

Teachers and parents often ask for suggestions about activities to do with their children at school and at home to help further their mathematical understanding. I’ve been teaching math to children for many years, and I’ve found that math games are, from a teacher’s and a parent’s point of view, wonderfully useful. 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.

Children throw themselves into playing games the way they never throw themselves into filling out workbook pages or dittos. And games can 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. In a non-threatening game format, children will be more focused and retention will be greater.

Math games are the perfect way to develop, reinforce, and extend children’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 (remember those times tables?) 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?

One of the most effective and engaging math games is War. It has many variations. Give one or more of the following a try:

More or Less

Many of you may know this game as “War”. For mathematical purposes, I think it is more appropriate to call it “More” or “Less”.

What you need:
2 players
1 deck of cards

Shuffle cards well and deal them face-down equally to all players. Players do not look at their cards. All players turn over their top card at the same time. The player with the greatest number (More) collects all the cards. In the event of a tie, players turn over one more card and put it on top of their first card. The player with the biggest number takes all four cards.

Each player might add the two cards together and the player with the biggest total would take all four cards. Or the biggest number on the second card turned over could be the winner. You decide what is most appropriate.

You follow the same rules to play “Less”. The player with the smallest number wins the cards.

Variations:

Addition War – Each player turns over two cards and adds them together. The player with the greatest sum or the smallest sum (you decide which) wins all four cards.

Addition War (3, 4, 5, etc. addends) – Each player turns over three cards and adds them together.

Subtraction War – Each player turns over two cards and subtracts the smaller number from the larger number. The player with the smallest or greatest difference (you decide which) wins.

Addition and Subtraction War – Each player turns over two cards and adds them together. Then each player turns over one more card and subtracts it from their sum. The player with the greatest or smallest difference wins. I like this game because it involves the use of two operations.

Product War – Turn up two cards and multiply.

Product War II– Turn up three (or more) cards and multiply.

Product War (advanced) – Each player turns up three cards and moves them around and arranges them in a problem where two-digit number is multiplied by a one-digit number. The player with the greatest or least product (you decide) wins.

Division War – Each player turns up three cards and moves them around and arranges them in a problem where two-digit number is divided by a one-digit number. The player with the least or greatest quotient (you decide) wins.

Fraction War – Each player turns up two cards and use the larger card as the numerator and the smaller card as the denominator (or vice versa, whichever you choose). The player with the greatest or least fraction (you choose) wins.

Integer Addition War – Each player takes two cards and adds them together. Red cards are negative (I’m in the red), and black cards are positive. The greatest sum wins.

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.

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:

What can you do to help yourself?
• 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?
• Start with something you already know?
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

_______________________ ______________________

Having Fun with Math Games

The old-fashioned method of solving problems from a textbook was not getting the job done at Hanover-Horton Elementary School.

So the school took a new approach to math education Wednesday – games.

Take a look at how Hanover-Horton Elementary School students are using board game to improve math skills.

This Michigan school is typical of most elementary schools – they are looking for ways to energize their math curriculum and engage their students. Math games are an enormously effective way of doing both.

Multiplication Games

More and more in my teaching career, I see that children struggle to memorize their multiplication tables. I’ve even worked in many 6th grade classrooms where it was perfectly evident that a majority of the 6th graders had not yet fully memorized their multiplication tables.

Simple multiplication is usually introduced into the math curriculum in 2nd grade, so it is important that 2nd and 3rd graders begin to get a strong handle on their multiplication facts. If they don’t, understanding division becomes ever more difficult.

I’ve found that multiplication games are wonderfully useful. Multiplication 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 the multiplication facts over and over.

Teachers and parents are partners in this process, and both can offer greater opportunities for their students/child to succeed in memorizing the multiplication tables. Multiplication games fit the bill wonderfully!

One of my favorite multiplication games is Multiplication Fact Feud. It’s a great way target and practice certain facts.

Multiplication Fact Feud

What you need:
2 players
deck of cards

Teacher or parent decides the particular multiplication fact to practice
(i.e. x7, x4, x8, etc.) Once the constant factor is determined, that card is placed between the two players. Players then divide the remaining cards evenly between themselves.

Each player turns over one card and multiplies that card by the constant in the middle. Players must verbalize their math sentence. The player with the highest product collects both cards.

Example: Player #1 Player #2
4 5 7
“4 x 5 = 20” “7 x 5 = 35”

Player #2 would collect both cards.

In the event of a tie (i.e. both players have the same product), each player turns over one more card and multiplies that by the constant factor. The player with the highest product wins all four cards.

When the cards are all used up, the player with the most cards wins the game.

Teaching Math at Home

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 what you need to help your child with math because:

1. You have a great deal of important mathematical knowledge to share.
2. Children learn best from the people who most accept and respect them.
3. Learning is more lasting when it takes place in the context of familiar home experiences.
4. 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.

Making Math Part of Your Family’s Life

It’s common knowledge that young children whose parents read to them have a tremendous advantage in school. But did you know that you can also help your child learn mathematics by doing and supporting math at home?

Today mathematics is more critical to school success than ever before. Modern occupations now require a firm foundation in mathematics – and that’s true for almost any type of job your child will consider in the future.

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.

There are many ways to make math part of your family’s life. Consider the following checklist of key ideas:

• Always talk about math in positive ways. Regardless of your own math background, let your child know that learning math is very important. Communicating a positive, can-do attitude about math is the single most important way for you to ensure that your child is successful in math. Never tell your child that math is too hard or that you hated it or weren’t good at it when you were in school.

• Make math an everyday part of your family. Find math at home. Spend time with your child on simple board games, puzzles, and activities that involve math. Involve your child in activities like shopping, cooking, and home fix-it projects to show them that math is practical and useful.

• Notice math in the world. You can help your child see the usefulness of math by pointing it out wherever you see it – not just in your home. What shape is that building? How many more miles before we get there? How many glasses of milk are in a carton? How much will you save if you buy a combo meal at McDonald’s?

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