## 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.

## A Math Game for Fourth Graders

By the time students reach 4th grade, they should be getting fairly good at multiplication. Students need dozens of repetitions of each multiplication fact before it is solidly in long-term memory. The following math game is appropriate for fourth graders. It helps them practice their multiplication skills and extends their knowledge into exponents.

Exponent War

What you need:
2 players
deck of cards 1 – 5, or 1 – 9 (for advanced players)
paper and pencils

Shuffle cards. Players divide cards evenly between themselves. Players turn over two cards each. The first card turned up is the base card and the second card is the exponent.

Example: Player #1 turns up a 3 then a 4. His/her total is 3 x 3 x 3 x 3 = 81.

The player with the highest total wins all four cards. Play continues until one all the cards are gone. The player with the most cards is the winner.

In the event of a tie, each player get two more cards. In the same manner, the player with the highest total wins all 8 cards.

## 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.

## 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!

## 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?
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

_______________________ ______________________

## 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?

## Teachers Search for Ways to Energize Math

As an independent, elementary mathematics consultant, I work with elementary teachers all the time as they search for ways to motivate and energize their students in math. I just read the following article about Indiana elementary teachers on that very quest. Take a look at how a grant brought together ISU professors and Vincennes teachers.

One of the instructional strategies they are trying are math games, an effective, hands-on way to teach math concepts. 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 skill 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 for you of what your students know and can do than a workbook page.

Here are some of the many benefits of using math games in the classroom:

• Meets your state’s elementary mathematics standards
• Easily linked to any mathematics textbook
• Offers multiple assessment opportunities
• Meets the needs of diverse learners
• 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

## Parents and Math Games

Parents often ask for suggestions about activities to do with their children 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.