Math Games Develop Strategic Thinking

Strategic thinking is one of the most important skills for children to develop. It requires the ability to observe, take in different pieces of information, analyze information, plan and analyze possible solutions, and choose the appropriate action.

Strategic thinking is a way to solve problems. Every day we have to solve the problems. Every day, we need solutions. Problem solving is an essential skill in our professional, family, and social lives.

Games like bridge, chess, and backgammon are ideal for teaching strategic thinking. But learning bridge is more than fun and games; students who play, practice math and reasoning skills and show improvements on standardized tests.

However, games such as bridge have complex rules that can take time to learn and master. Instead of using complicated games, there are many math games at every grade level that are much easier for children to learn and play. All of the math games are focused on providing engaging activities to entertain strategic mathematical thinking both inside and outside of the classroom.

If you are a teacher or parent, I encourage you to have a look at the assortment of games. You will find many that will pique your interest and and help you develop strategic thinking and problem solving abilities in your students/children while having fun!

Math Games and the Last Few Weeks of School

The Big Test is over. Yeah! The long Memorial Day weekend is past, or soon will be. Sigh! You’re way beyond burned out and thinking mostly about summer. You can’t figure out how you’re going to get through the next few weeks.

I have a great idea! Give a math game a try! Games can help children learn important mathematical skills and processes with understanding.

Besides that they:

• support concept development in math
• meet math standards
• offer multiple assessment opportunities which will help with report cards
• are great for diverse learners such as English-language learners
• encourage mathematical reasoning
• are easy to prepare
• are easy to vary for extended use and differentiated instruction
• improve basic skills
• enhance basic number and operation sense
• encourage strategic thinking
• promote mathematical communication
• promote positive attitudes towards math

Pick a skill set you know your students need to practice, and then find the right game that will offer practice with that skill set. The students will be engaged and quite willing to involve themselves in the repetitive practice needed to hone their skills.

Helping Your Child with (Mental) Math

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 are some important things you should know and do:

1. Problems can be solved in different ways. While some problems in math may have only one solution, there may be many ways to get the right answer. And remember, the way you solve a problem may not be the way your child solves the very same problem. Learning math is not only finding the correct answer, it’s also a process of solving problems and applying what you have learned to new problems. If their way of solving the problem gets the job done, let them give it a try.

2. Wrong answers can help! While accuracy is always important, a wrong answer could help you and your child discover what your child may not understand. The wrong answer tells you to look further, to ask questions, and to see what the wrong answer is saying about the child’s understanding. It is highly likely that when you studied math, you were expected to complete lots of problems using one, memorized method to do them quickly. Today, the focus is less on the quantity of memorized problems and memorized methods and more on understanding the concepts and applying thinking skills to arrive at an answer.

3. Doing math in your head is important. Have you ever noticed that today very few people take their pencil and paper out to solve problems in the grocery store, restaurant, department store, or in the office? Instead, most people estimate in their heads, or use calculators or computers. Using calculators and computers demands that people put in the correct information and that they know if the answers are reasonable. Usually people look at the answer to determine if it makes sense, applying the math in their head (mental math) to the problem. This, then, is the reason mental math is so important to our children as they enter the 21st century. Using mental math can make children become stronger in everyday math skills.

In terms of mental math, here are some questions you might ask your 3rd through 6th graders (no pencils and paper allowed):

Start off easy with –

98 + 47

51 + 99

146 – 101

5 x 99

150 + 199

137 – 99

99 + 49

4 x 24

58 + 16

65 – 19

Then increase the level of difficulty with –

You buy an $80. dress which has been reduced 20%. How much did it cost?

What is 3/8’s of 40?

6 ½ – 2 ¼ =

What is 75% of 32?

What is 10 squared divided by 5?

You get the idea. Now think of real-life questions that you face every day.

Teachers Taking Time for Math Games

As an elementary school teacher, you probably feel like you don’t have enough time to teach all of your content within the course of a school year. Why on earth would you ever want to add more material in the form of math games when you can’t seem to finish your assigned math textbook? Turns out that making time to incorporate math games in your classroom can lead to rich results.

One of the most immediate benefits of using math games is increasing student engagement. Games are engaging and maintain interest. Dittos or workbook pages rarely are. 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. Research has demonstrated that students learn more if they are actively engaged with the math they are studying.

Contrast this with the reaction that many students have toward the textbook: either a lack of interest or an assumption that the assigned math/problems will be too difficult.

Incorporating math games also allows you to differentiate instruction. Using math games which better match students’ abilities can help them build content knowledge and interact more successfully with the required text.

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

Your state’s mathematics standards are intended as a statement of what students should learn, or what they should have accomplished, at particular stages of their schooling. The goal of every state’s math standards is to engage students in meaningful mathematical problem-solving experiences, build math knowledge and skills, increase students’ ability to communicate mathematically, and increase their desire to learn mathematics. Those are the goals for math games, too!

Specific content knowledge will vary according to the game students play and the connection to school-day learning and the state standards. A major goal for students in the elementary grades is to develop an understanding of the properties of and the relationships among numbers. One of the very effective ways teachers can reinforce the development and practice of number concepts, logical reasoning, and mathematical communication is by using math games. They are great for targeted practice on whatever standard the children need to meet.

You will meet significantly more of your state’s grade- level mathematics standards by having your children play a game than will have been met by having them complete a ditto or a workbook page.

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

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

Making Math a Challenge and Fun

Why do so many children feel like math is a chore? I believe that it’s not the math that turns kids off. It’s the way mathematics is taught. Standardized instruction and memorization of details, which moves at a plodding pace, leave some students bored and many frustrated.

We know a lot about how children learn mathematics, but rarely use that information to inform our teaching. Here are some ways to teach math that reflects the research on how children learn mathematics:

• By confronting tasks and problems that offer a variety of solution strategies
• By engaging in meaningful conversation with partners and small groups about the tasks and problems: describing, explaining, deciding, and considering
• By encountering the mathematics in familiar, real-life situations, stories, songs, and games

I’ve been teaching math to children for many years, and I’ve found that math games are, from a teacher’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, 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.

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?

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.

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.

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.

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.

A Math Game for Third Graders

Math games are a highly effective and engaging way to get students involved in practicing basic math skills. The following double-digit addition math game is great for second graders, third graders, and fourth graders. It not only addresses addition but forces students to look at the importance of place value.

Get Close to 100

What you need:
2 – 4 players
deck of cards, 10s and face cards removed
paper and pencils for each player

The object of the game is to make a two-digit addition problem that comes as close to 100 as possible.

Shuffle cards and place them face down in a pile.

Player #1 turns over 4 cards and moves the cards around until he/she has created a problem whose sum will be as close to 100 as he/she can make it. Player #1 records this problem on his/her paper.

Player #2 checks for addition accuracy.

Example: Player #1 draws a 4, a 7, a 2, and a 5. He/she moves the cards around until she/he decides that 47 + 52 = 99 is the closest that he/she can get.

Player # 2 draws four cards and does the same.

The points for each round are the difference between their sum and 100.
Example: A sum of 95 scores 5 points and so does a sum of 105.

Players compare scores at the end of this first round. They put their four cards in a discard pile and player #2 begins first and turns over four more cards for the second round.

After six rounds, players total their points and the player with the lowest score wins.

Variation: Make this a triple-digit addition game called Get Close to 1000! by drawing 6 cards and creating two triple-digit numbers which when added together, get as close to 1000 as possible.

Real-Life Math in Elementary School and Beyond

Elementary school students in three of Kingsport, Tennessee’s four high school zones took some weekend time this school year to learn practical, hands-on applications of math in the “real world”.

My question is, why isn’t their regular, everyday math curriculum talking about math in the “real world”?

Many educators contend that children must go beyond memorizing rules—they need to know when and how to apply the rules in real-world situations. Many also argue that realistic problems can serve as a powerful motivator in the mathematics classroom. They go on to conclude that the curriculum should consist of real-world problems because students will naturally learn mathematics by solving such problems.

The basics are changing. Arithmetic skills, although important, are no longer enough. To succeed in tomorrow’s world, students must understand algebra, geometry, statistics, and probability. Business and industry demand workers who can-

solve real world problems

explain their thinking to others

identify and analyze trends from data, and

use modern technology.

The mathematics students do in school should prepare them for the new basic skills necessary for their futures.

Instead of problems done with no context using worksheets, dittos, and workbook pages, students should be working on problems to investigate that are related to real life, such as investigating salaries, life expectancy, and fair decisions, for example.

Giving students opportunities to learn real math maximizes their future options.

Using money, counting change, etc. is a real-life skill that children need to learn. Play the following game with your second graders, third graders, and fourth graders.

Money Race

What you need:
2 players
1 die
pennies, nickels, dimes, and quarters
sturdy paper plate for “bank”

The following coins (which equal $1.00) are placed in the “Bank” between the two players. A paper plate makes a great bank.

10 pennies, 5 nickels, 4 dimes, and 1 quarter

Each player also takes the same combination of coins for a total of $1.00.

Money Legend:
1 – subtract a penny and put it in the bank
2 – subtract a nickel or 5 pennies and put it in the bank
3 – subtract a dime or a combination of coins that equals 10 cents
and put it in the bank
4 – subtract a quarter or a combination of coins that equals
25 cents and put it in the bank
5 & 6 – choose any one coin from the bank

Player #1 rolls the die and either adds or subtracts the appropriate coins.

Player #2 does the same.

Play continues in this manner until both players have completed 10 rolls. Players total their own coins. The player with the greatest amount wins.

Teaching Math with Games

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

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

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

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

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

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