In this recent article from the New York Times, two New Jersey elementary schools use math games to connect parents, students, and their math curriculum.
Here’s what happened:
1. Math skills were strengthened.
2. Parents became involved in their school’s math program.
3. Parents and their kids had a lot of fun doing math together.
4. They realized that everyone can be good at math!
Much of the math we do as adults involves making estimates. We are not born with the ability to make fairly accurate and reasonable estimates. Children need to have lots of experiences with making estimates.
Find a small box with a lid. Ask your child to guess how many pennies, cheerios, paperclips, etc. the box will hold. Whatever the guess, be it reasonable or not, have the child write the estimate down. Never comment negatively or positively on the estimate. I usually respond, “Okay”. A negative response to their estimate will lead to an unwillingness on the part of the child to make any more estimates.
Then fill the box and count to find out how many it did hold. Next time keep the same box but fill it with something different. Will this change the estimate? For instance, if you used Cheerios the first time you filled the box, and this time you are using marbles, will the estimate and count change? Can you get as many marbles in the box as you did Cheerios? Why or why not?
Do this many times and record your estimates and actual counts. The more your child does it, the better their estimates will become. He/she will probably also begin to notice that the smaller the objects, the more will fit in; the bigger the objects, the fewer that will fit in. Use all shapes and sizes of boxes and continue to make estimates and count.
When the french fries arrive from McDonald’s, have your child make an estimate and then count and eat to find out. Estimate coins in Dad’s pockets (number and value), houses on the block, days till the next birthday, meals you eat in a month, etc.
Here’s one of my favorite estimating activities:
How Many Shoes?
Make an estimate (smart guess) of how many shoes you think you will find in your home. ________________
Count the shoes in your home.
Your shoes _______________
Your Mom’s shoes ______________
Your Dad’s shoes _______________
Your brothers’ shoes ____________
Your sisters’ shoes ______________
Other shoes _________________
Total number of shoes _______________
How many pairs of shoes are in your home? ____________________
Are there more shoes or more pairs of shoes? ___________________
How many shoes do not have a matching one? _________________
How many shoes are in your closet? ___________________
Arrange your shoes in pairs. How many pairs? __________________
Are there more shoes or more feet in your home? ___________________
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 math 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. Quality mathematics throughout early childhood does not involve pushing elementary arithmetic onto younger children. Dittos or workbook pages are not appropriate if you want your young child to be excited about math. Quality mathematics allows children to experience mathematics as they play in and explore their world. Children’s interests and play should be the source of their first mathematical experiences.
• 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?
Play math games with your children. Take a look at my grade-level specific math games.
Learning to count correctly is a process that can take a long time. Enjoy your child’s progress, however slow it may seem and accept their emerging ability to count the way you accepted their ability to walk and to talk. It doesn’t pay to be in a hurry. With lots of practice and encouragement, children will learn to count with confidence and enjoyment.
Research around the country is showing that students need many, many experiences counting. Preschool and young primary students need to count objects of all sorts by ones. Primary students start counting by ones and find ways to organize their counting using more efficient strategies such as counting by 2s, 5s, 10s or 100s.
Counting Activities
Put out a collection of items. You choose the number based on the needs of your child. Use beans, cubes, counters, stones, or crayons –whatever you have a bunch of and vary the items on different days.
Ask your child, “how many “cubes” do you think are in this pile?” Accept all answers (even if you think it is an outrageous guess). Count them and check. (note how they organize their counting.)
Look for:
1. How they use the counting words.
2. Whether they organize the objects in order to keep track. Do they move them as they count? Do they put them in groupings of 5 or 10 or some other number?
3. Whether they recognize that they get a different number than their estimate.
4. Whether they adjust their estimate.
Try re-counting the same group of objects, only this time, count them a different way – by 2s, or 5s, or 10s. Did they get the same answer? Does this surprise them? What would happen if you added 10? Took 10 away?
Look for opportunities to count informally. How many steps do you think it will take to get from here to the (bus, door, corner)? How many windows do you see from the backyard?
For example, your child’s room is a mess! Lots of stuff on the floor! Make the chore of uncluttering the floor a little more fun. Have your child estimate (make a smart guess) how many things are scattered on the floor. Then they count the things as they put them away!
While in the car, invite your child to choose something fun to look for and count. Stop signs, fire hydrants, baby strollers, bikes, red cars, dogs, trucks, cows, etc. might be a few examples.
Provide a notepad and pencil. Help your child think of a simple way to make a mark on a piece of paper (such as an X, a circle or slash or line) every time the item is spotted. Each mark will be equal to one item seen.
So, start counting! Everything! Count things by ones. Count things by twos. Count things by fives. And then, start counting things by tens.
Give a counting game a try. Here’s one of my favorites!
Counting Cheerios
What you need:
2 players
1 die
bowl of Cheerios for each team
paper plate (cheap) for each player
pencil for each player
Player #1 rolls the die and takes that number of Cheerios from the bowl.
Players alternate rolling the die. Play continues until all players have had 10 rolls. They will need to keep tallies on their paper plates.
Children count their Cheerios. The player who has the most Cheerios is the winner. Players may eat their Cheerios!
Variation 1: The winner could be the player with the least
number of Cheerios.
Variation 2: Use two dice and add them together.
Variation 3: Put 50 (or any number you choose) Cheerios on a
plate, roll the die, and subtract Cheerios from the
plate. The first player to reach 0 is the winner.
Now take a look at all the counting games in my grade level math games manuals.
Parents are always looking for activities and games to challenge their child’s mind while having fun together. My goal is to help parents and their children enjoy mathematics. When children play with mathematics in their everyday lives, they can grow up loving it.
Children must see that math is not just a subject studied in school but is used constantly in everyday family life. The home is an ideal place in which to learn mathematics because the problems encountered there are real, not just paragraphs in textbooks.
How you encourage and promote your child’s math learning, from preschool to high school, can be pivotal to their attitude toward math and their achievement in this subject area. Children are taught math in school, but research shows that families are an essential part of this learning process. In other words, by doing math with your child and supporting math learning at home, you can make a great difference.
The following is just one of many activities that can help you make math a natural part of your family’s everyday work and play.
Alike and Different (Comparisons)
Pick two objects.
Ask your child what makes them alike. Next, ask your child what makes them different.
For example: apple and orange
Possible responses:
They are alike because they both are food, fruit, have seeds, make juice, come from trees.
They are different because one is orange and the other is red; one has wrinkles and the other is smooth; one has black seeds and the other white; we eat apple peels but not orange peels.
Make a list of what you compared and how they were alike and different.
Play the game over and over, using a different set of objects each time.
Don’t forget to ask your child what’s alike and different about the two of you.
Now give one of my math games a try and continue the learning and the fun!
A parent’s involvement in a child’s education is the single most important factor in that child’s academic success.
Decades of educational research tells us that an involved parent contributes overwhelmingly to his/her child’s grades and test scores, school attendance and quality of homework, positive attitudes and behavior at school, likelihood of graduation, and desire to enroll in higher education. In many ways, as we’ll describe, you’re the essence of your child’s education; you’ve got the power!
It’s true that many other important factors, including school funding, teacher qualification, student resources, child nutrition, and a host of others can swamp our considerations of what affects academic success. These factors do matter. A lot. But research about the family’s role, a parent’s influence, and the relationship between school and home has produced clear-as-a-bell results: nothing affects the academic outcome for a child as much as the involvement of a parent or other adult caregiver in that child’s education. This is true no matter what personal factors are at work: the number of parents raising a child; the family’s economic situation; the parent’s familiarity with English; the size of the family; the parent’s education; or a child’s own interests, talents, and abilities. The bottom line is that whatever your academic or cultural background, your family situation, or the many pulls on your time, you are in the most influential position to shape your child’s future.
Parents and other adult caregivers are their children’s first and most enduring teachers. Even the best teacher your child encounters in school will only be with your child for a year, or perhaps two; even after children enter school, they spend seventy percent of their waking hours outside of the school setting. As a parent, you have greater opportunity to make a difference, to teach, model, and guide your child’s learning, than anyone else. You have a more intimate knowledge of your child’s needs and talents. You have a keener interest in your child’s schooling and future, and deeper motivation to help your child succeed. No one is better placed or more qualified than you to make a difference in your child’s academic and lifelong education.”
“Games can motivate students, capture their interest, and are a great way to get that paper and pencil practice”, says Marilyn Burns, world-renowned mathematics expert.
Games offer teachers a way of practicing and reinforcing arithmetic and other math skills, as well as supplementing a sole diet of drills and practice-problems with workbook pages or dittos.
Not only do games engage students, they also present the opportunity to present “high level” math concepts in a colorful and simple way.
In my experience, students are more engaged when we connect the mathematics they are going to learn with something that excites them (e.g., games).
Despite those benefits, some teachers and parents are reluctant to use board games and similar activities. Those critics tend to regard them as activities that cut into time spent on practicing problems, when in fact games should be used as another form of math practice.
Research on the link between games and math learning has implications not just for educators, but also for parents.
Turning off the television and engaging children in a simple card or dice math game just a few times a week can greatly improve their comfort in math.
There’s a huge amount of math in card and dice games that is not on television and video games.
As a veteran teacher of grades K-3, I have been using math games to motivate and energize my mathematics curriculum for many years. I am not alone in this endeavor. The following newspaper article gives credence to this fact:
The research concludes that playing a board game with numbers helped children improve on four kinds of numerical tasks. Those gains were still evident nine weeks later.
So, get out those cards and dice or buy a board game that involves numbers, and be ready to watch your child learn and have fun!
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!!!!!
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
_______________________ ______________________