Math Games and At-Risk Kids

As an elementary mathematics specialist, I work in K-6 classrooms all the time. Time after time teachers ask the same question, “How do I help floundering students who lack basic math skills?” In every class there are a handful of students who are at risk of failure in math.

What can be done for such students? How can we help children be proficient at the basic skills.

Struggling math students typically need a great deal of practice. Math games can be an effective way to stimulate student practice.

First graders and second graders need to have the addition facts to 10 in long-term memory. When they hear 6+4, they immediately know (without counting fingers) that the answer is 10. Using fingers to count is a good, early strategy but with practice, those facts should be automatic.

Family Fact Feud is a great game for achieving that goal.

What you need:
2 players
deck of cards, face cards removed

Players sit side by side (not across from each other)

Teacher/parent decides the particular fact to practice (i.e. +1, +2, +3, etc.) Once the constant addend is determined, that card is placed between the two players. Players then divide the cards evenly between themselves. Each player turns over one card and adds that card to the constant addend in the middle. The player with the highest sum collects both cards. Players must verbalize the math sentence.

Example:
Teacher/parent decides the constant addend will be +1.

Player #1 turns over a 5, and says, “5 + 1 = 6″.
Player #2 turns over an 8 and says, “8 + 1 = 9″.

Player #2 collects both cards.

In the event of a tie (both players have the same sum), each player turns over one more card and adds this card to the 1. The player with the greatest sum takes all four cards.

When the deck is finished up, players count their cards. The player with the most cards is the winner.

Third graders and fourth graders need to have all of the multiplication facts to automaticity.

Multiplication Fact Feud is great for that.

What you need:
2 players
deck of cards, face cards removed

Teacher/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:
Teacher/parent selects x5 as the constant.

Player #1 draws a 4 and says, “4 x 5 = 20″.
Player #2 draws a 7 and says “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.

Playing to Learn

Everyday Mathematics is a comprehensive Pre-K through 6th grade mathematics curriculum developed by the University of Chicago School Mathematics Project. It is currently being used in over 185,000 classrooms by almost 3,000,000 students.

The federal government’s What Works Clearinghouse gave Everyday Mathematics the highest rating of any commercially published elementary mathematics curriculum.

Here’s what they have to say about the use of math games:

“Frequent practice is necessary to attain strong mental arithmetic skills and reflexes. Although drill focused narrowly on rote practice with operations has its place, Everyday Mathematics also encourages practice through games.

Drill and games should not be viewed as competitors for class time, nor should games be thought of as time-killers or rewards. In fact, games satisfy many, if not most, standard drill objectives – and with many built-in options. Drill tends to become tedious and, therefore, gradually loses its effectiveness. Games relieve the tedium because children enjoy them. Indeed, children often wish to continue to play games during their free time, lunch, and even recess.

Using games to practice number skills also greatly reduces the need for worksheets. Because the numbers in most games are generated randomly, the games can be played over and over without repeating the same problems. Games practice, therefore, offers an almost unlimited source of problem material.”

Games can be easily linked to any mathematics textbook.

No matter which textbook your district uses, math games can easily be incorporated into instruction. Even if your textbook does not include 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 any workbook page or ditto.

Essential Elementary Math Skills

What should children be able to do in math by age 12, or by the time they leave elementary school?

Students should have math facts at their fingertips, such as addition and subtraction combinations to 20, multiplication tables to 12×12, and related division facts. Children learn some of these facts easily, but memorization is still necessary (and often painful) to learn all of the facts.

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: through the use of physical manipulatives within the context of developmentally appropriate practice – games require active involvement.

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.

Games teach or reinforce many of the skills that a formal curriculum teaches, plus a skill that formal learning sometimes, mistakenly, leaves out – the skill of having fun with math, of thinking hard and enjoying it.

Use math games to prompt interest and make the memorizing much more effective and a great deal more fun. Games help children develop mathematical concepts and reasoning and encourage a great deal of practice of these basic mathematical skills. In addition to being effective, games are also challenging, interesting, and enjoyable.

Let’s Play Math!

How we, as teachers, teach math or how we, as parents, help our children with math can make or break a child’s success in mathematics and the many subjects based on it.

A good math experience typically prepares and motivates students to excel in any future math course. A bad experience can turn that same student off to a subject that is not only the basis for well-paying, in-demand careers in science, engineering and technology, but essential for understanding the world around us.

Once a child disengages from studying math, it can be very difficult to catch up. This happens too often to students we know are capable of succeeding at math. The elementary grades are a time when kids firm up values and impressions. We want them to understand math and feel that it’s worthwhile.

We need to offer experiences that encourage elementary-aged children to explore the unknown, tinker with ideas, and satisfy an innate sense of curiosity.

Children need to be asked to understand things, not just memorize them. They need to be encouraged to explore and be curious in everyday activities so they understand that math is everywhere. This kind of teaching can provide the motivation to learn, create, and excel.

How do we help our children become creative thinkers who are capable of solving real-world problems? There are many good answers to that question. One of the simplest is math games. Math games offer children the opportunity to practice problem-solving and teamwork which are disguised as fun.

Games teach or reinforce many of the skills that a formal curriculum teaches, plus a skill that formal learning sometimes, mistakenly, leaves out – the skill of having fun with math, of thinking hard and enjoying it.

Games can provide an atmosphere where children are encouraged to:
• share their ideas with other children and adults
• be alert and curious
• come up with interesting ideas, problems, and questions
• have confidence in their abilities to figure out things for themselves
• speak their minds with confidence

In the process of playing the game, students may develop initiative, interest, curiosity, resourcefulness, independence, and responsibility. Our future needs this kind of creative thinker.

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 for Preschoolers

Many parents of preschoolers show a great interest in helping their children become ready for starting school and often ask what they can do at home to help foster their children’s mathematical learning.

Among other activities, I believe that math games can effectively engage young children in meaningful mathematics learning. The Kindergarten Math Games Manual has many games that are appropriate for 3-5 year olds.

Math games for three-,four-, and five-year-olds? Is this a developmentally appropriate way to get young children interested in math and ready for school?

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 to get ready for the elementary school years. 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.

At the very simplest level, give the following two games a try:

Cover Up!

What you need:
2 players
1 die
paper and pencils
number line for each player (write the numbers 1,2,3,4,5,&6 horizontally and fairly large on a piece of paper)
6 counters (M&Ms, paperclips, tiles, beans, pennies, etc.) for each player

The winner of Cover Up is the first person to put a marker on all six numbers.

Players take turns rolling the die and putting a marker on the corresponding number on his/her number line. If a number already has a marker on it, that player loses his/her turn.

Variation: Roll two dice and add them together. Each child will need a
2-12 number line.

This game seems simple, but it really helps young children recognize the dots on the dice. When they begin, they may need to count the dots each time, but soon they ought to learn what number the dots represent without counting them.

Roll Them Out

What you need:
2 – 4 players
1 die
deck of cards – 7’s – 10’s + face cards removed

Shuffle cards. Each player gets 5 cards. The remaining cards are placed face down in a pile.

Player #1 rolls the die. The number shown on the die is the number the players look for in their hands. If they have that number, they must give the card(s) to the die thrower. If no one has that number, no cards are given to the die thrower.

Players alternate turns. After each turn, each player makes sure they have at least 5 cards in their hand. If they don’t, they draw from the pile to bring them up to 5 cards.

When all the cards in the pile are gone, the player with the most cards is the winner.

Actively Learning Math

Is it any wonder that Pine Street Elementary was the only school in the tricounty area of South Carolina to earn “excellent” in both absolute and growth ratings?

The picture shows a classroom of children studying math through activities that get them out of their seats. Active (as opposed to passive) learning is always a more effective teaching and learning strategy.

Research has demonstrated that students learn more if they are actively engaged with the math they are studying. Constance Kamii, a world renowned expert on how children learn math puts it this way, “Children who are mentally active develop faster than those who are passive.”

Active learning is, in short, anything that students do in a classroom other than merely listen to a teacher’s lecture. There are several ways of doing this. Playing math games is a particularly useful one.

Math games:
• provoke students into discussing, explaining, and thinking
• challenge and interest students
• get students actively involved in their learning
• result in learning
• provide some immediate assessment

In the process of playing the game, students may develop initiative, interest, curiosity, resourcefulness, independence, and responsibility. Would that happen with a ditto or workbook page?

Children learn math best when they participate in games that are relevant to them, hold their attention, and require them to “make meaning” for themselves.

Teaching methods that stress rote memorization of basic number facts or algorithmic procedures are usually boring and do not require learners to participate actively in thought and reflection.

Multiplication Games and Activities

Traditionally, instruction in multiplication has focused on learning the multiplication facts using flash cards, dittos, workbook pages, and timed tests. However, it is becoming apparent to many that these methods are woefully ineffective, and children continue to struggle to memorize their multiplication tables.

So what can parents and teachers do to help their children/students learn these multiplication facts? The following are some very effective math games and activities that not only work, but are lots of fun! When was the last time you or your children said that about multiplication?!

1. 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.

The following are just a few of the situations we used:
• 3 weeks – how many days?
• 9 cans – how many round bottoms?
• 12 noses, how many people?
• 5 cows, how many legs?
• 8 sleeves, how many shirts?

2. Play “What Am I?” Say to children “Seven is one of my factors. The sum of my digits is 6. What am I?” (42). Repeat this activity with other numbers.

3. Use a blank multiplication chart. Ask the children to enter the multiplication facts that they are sure of. Then have pairs of students exchange charts and quiz each other on the facts that are on the chart. If a child misses a fact, ask the partner to make a small mark by the fact to indicate that they need to practice it further. Marking missed problems with a highlighter is a strategy that may benefit some students. Keep these multiplication charts around and continue to add to them and test each other.

4. Most children struggle with multiplying by 6, 7, 8, and 9. These are the ones that need the most practice. The following is a way to work on these factors:

Provide students with paper and crayons and ask them to draw six blue vertical lines on the paper. Now ask them to draw four red horizontal lines intersecting the vertical lines. Ask them to circle in purple each place there is an intersection and count the number of intersections. Challenge them to identify what multiplication fact they have just demonstrated. Tell them that in this model, the number of rows is given first. [4 ×6 = 24.] Ask them to turn their papers a quarter turn and name the multiplication fact now modeled. [6 ×4 = 24.]

Encourage them to generate other facts where one factor is 6, including 6 × 0 and 6 × 1.

Repeat with 7 as a factor.

It may be helpful for students to visualize the vertical lines as city streets, the horizontal lines as roads, and the intersections as marking where a stoplight is needed.

5. Distribute index cards to each pair and ask each student to make a set of 10 cards numbered 0 to 9, one to a card. When they have finished, ask them to shuffle the two decks together and stack them face down. Tell them to take turns turning over the top card, multiplying the number drawn by 6 and then saying the product. As each card is used, it should be returned to the bottom of the deck. Give students time to play, and then ask the class to skip count in unison by 6. Encourage them to do so without looking at the game board.

Repeat for 7 as a factor.

6. Number Drawings – great for helping to memorize skip counting!

What you need:
paper, pencil, and crayons

Give each child a blank piece of white paper. Tell the children that today they are going to be skip counting by 4’s to 40 and each of them would be making their own unique drawing.

Tell them they are going to start by putting the number 4 anywhere on their paper and putting a little dot beside it. The object is to scatter the numbers all over the page. Now what number comes next if we are skipcounting by 4’s? Keep going until you reach 40.

Now connect the dots starting at 4, going to 8, and so on. When you reach 40, connect it back to 4.

Now color the inside of your drawing.

Make a Number drawing for 2’s, 3’s, 4’s, 5’s, 6’s, 7’s, 8’s, 9’s, 10’s, 11’s, 12’s and so on.

7. Play a game.

Rectangles

What you need:
2 players
2 dice
12×12 grid or graph paper for each player
pencils and crayons

During a series of rounds, players toss the two dice that determine the length and width of rectangles that are constructed on 12×12 grid or graph paper. Points are scored by finding the areas of the rectangles.

Players take turns. During a turn, a player tosses the dice and constructs a rectangle by making its length on a horizontal line on the graph paper according to the number thrown on one die, and marking its height according to the number thrown on the other die. The player then outlines the entire rectangle, writes the equation within the rectangle, lightly colors it in, and calculates his score by determining the number of squares within the rectangle.

The rules for placing rectangles are as follows:
• All rectangles must be placed entirely within the graph.
• The edges of rectangles may touch (but do not have to).
• Rectangles may not overlap each other.
• No rectangle may be placed within another rectangle.

Players drop out of the game and calculate their cumulative score when their throw of the dice gives them a rectangle that will not fit on their graph. The game ends when all players have dropped out. The player with the highest score wins.

Kids Who Love Math Homework!

This school year Faleycia Moore is spending more time on her math homework than her teacher demands. Sound unbelievable? Does this ever happen at your house? What’s going on?
Her assignment is: Spend at least half-hour playing math games on an iPod Touch.

Searching for a way to help students who scored below grade level on the math portion of the Florida Comprehensive Assessment Test last year, Faleycia’s school in Clearwater decided to experiment with the iPod Touch.

Is it working? There has been a noticeable improvement in such things as students’ comprehension of multiplication tables. Kids are willingly spending two hours a night on math homework.

Is it the use of technology or the use of math games that is making the difference? Undoubtedly it is some of both.

There is no doubt in my mind that, as the Internet continues to play a larger role in education, a growing number of online sites will host free math games, most of which are challenging, exciting, fun, and age-appropriate. That’s all well and good.

But above all else, children crave time spent with their parents. Because learning is a social process, children learn best through fun games and activities that involve interaction with other people.

Stanley Greenspan, M.D., a clinical professor of pediatrics and psychiatry at George Washington University School of Medicine and author of many influential parenting books, says playing games with parents helps children develop the social skills necessary for getting along with others and is core to their healthy development.

“When you play games with your children”, Greenspan says, “you’re not only connecting and engaging, you’re exchanging back- and-forth emotional signals, which are helping the child regulate mood and behavior, learning to read social signals and learning to communicate. Each of these abilities contributes to a child’s sense of security.”

Seize this opportunity to teach them your values, and indulge them with your own undivided attention. Try a math game with your kids. A price cannot be put on the quality of the time you will have spent with your children. They will have fun while learning, and they will remember those times with greater fondness than the times they spent playing the educational computer game.

And lastly but of great importance, among the obvious benefits of sitting down and playing a good game with your children is the opportunity that games provide to apply and solidify the mathematical reasoning and calculating skills your children are learning in school. When children play on-line or video games, parents may know how the child scores, but do they know where they made mistakes and why? Playing games with your child offers you, as a parent, a greater opportunity to know what your child’s strengths and weaknesses in mathematics are.