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.

Exploring Math with Your Child

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:

• You have a great deal of important mathematical knowledge to share.

• Children learn best from the people who most accept and respect them.

• Learning is more lasting when it takes place in the context of familiar home experiences.

• 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 one of my favorite get-the-family-involved math activities. It is an engaging learning experience and a lot of fun!!!

The Washcloth Toss

Have each member of your family estimate (make a smart guess) how far they can throw a dry washcloth. Record your estimates. Now throw the washcloth. Measure and record how far the dry washcloth really went. The person closest to their estimate wins.

Now do it again, making an estimate first. Then throw the dry washcloth again, and measure and record how far it went. Were you any closer to your estimate this time? Who won?

Wet your washcloth this time. Estimate how far you think you can throw the wet dishcloth and record your estimates. Now throw the wet washcloth. Measure and record how far the wet washcloth really went. The person who is closest to their estimate is the winner.

Now do the wet washcloth experiment again, making an estimate first. Throw the wet washcloth again, and measure and record how far it went. Were you any closer to your estimate this time?

Which washcloth went farther – the dry one or the wet one?

Why do you think that happened?

Who is the dry washcloth winner? (closest to estimate)
Wet winner? (closest to estimate)

Teaching Math at an Earlier Age

Saying students would have more success in the future, a new report (PDF) from the Aspire Institute at Wheelock College is urging schools to start teaching math and science skills as early as pre-kindergarten.

Why is it that some children seem so curious and eager to learn? How do you raise capable, confident children who seek intellectual challenges? How do you support your children’s learning so that they grow to be imaginative, creative, intuitive, capable, competent, self-motivated, persistent, and know that effort is necessary for achievement? As a parent, I’ve asked myself this question numerous times. As an elementary teacher of many years, I continue to hear parents ask those very same questions. Good! They have begun their journey!

As an educator, I also know that the role of the family in early childhood education (birth to 8 years old) is enormously significant. Research has shown decisively that children’s experiences during early childhood not only influence their later functioning in school but also can have significant lifelong implications. Experiences during the earliest years of formal schooling are also formative. Studies demonstrate that children’s success or failure during the first years of school often predicts the course of later schooling.

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 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.

• 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?

Math games are a great place for preschoolers to begin. There are many games in the Kindergarten math games manual that are appropriate for 3 to 5 year olds.

Helping Your Child Build Basic Math Skills

Here are some ways to encourage your child to develop solid math skills throughout the elementary years, suggests an article in Louisville, Kentucky’s Courier-Journal.com.

I agree with every single suggestion except for the last one – “Buy a few inexpensive, age-appropriate math workbooks for your child to use at home.”

As an elementary math specialist, 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.

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.

Games have another use, too. They offer a pleasant way for you, as parents, to get involved in your child’s mathematics education. You don’t have to be a math genius to play a game. You don’t have to worry about pushing or pressuring your child. All that you have to do is propose a game to your 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 (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?

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.

Playful Ways to Help Your Child Learn Math

A parent’s involvement in a child’s education is the single most important factor in that child’s academic success. The single most important factor. 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 I’ll describe, you’re the essence of your child’s education; you’ve got the power!

Don’t Laugh – That’s Math
by Judith A. Zaino

Many times I’ve heard a parent say,
“I can help my child in any way,
But don’t laugh –
I can’t do math”.
I think for a minute before I say,
Let’s look at this another way.
Have you ever said, “Wait a minute:
Here’s a box with four things in it,
Let’s take turns; you first then me”,
Helped your child count branches on a tree?
Then you’re on the right path.
Don’t laugh – that’s math!
Have you taught your child left and right?
Counted her toes in bed at night?
Repeated his favorite nursery rhyme?
Said good night just one more time?
Have you ever split a cookie right in half?
Formed a pattern on a snowy path?
Well, don’t laugh – that’s math!
Have you ever played a game?
Measured for a picture frame?
Have you cut chains for your Christmas tree?
Noticed a butterfly’s wings have symmetry?
Did you ever check the miles into town?
Have you counted stairs both up and down?
Did you ever measure to see how tall?
Find the weight of her favorite doll?
Well, don’t laugh – that’s math!
Math can be seen in everything,
Even in the songs we sing.
Math isn’t just adding and subtracting,
multiplying, dividing, or even protracting.
Math exists all around us;
We didn’t find it – it found us!
Now remember, when this little poem is done,
If it has given you a small fraction of fun,
Don’t laugh – that’s math!

Family involvement is an essential element for a child’s success in mathematics and school. You are one of your child’s most valuable resources.

Math is all around us. The following math games and activities are just a few of the things you can do with your children which will nurture their mathematical development while being just plain fun!

• Count, count, and count! Young children love to count and will count everything and anything. Encourage your child to count out loud the number of steps climbed, spoons in the silverware drawer, french fries in her kids’ meal, buttons on all her shirts, etc.

• Practice classifying by separating toys into sets, such as things with wheels, things that have red on them, things that have numbers or words on them, things that roll, etc. Ask questions related to size or quantity: Which is larger? Which is largest? Which is smaller? Which is smallest? Do you have more dolls or more animals? Are their fewer dogs or fewer cats?

• Find two and three-dimensional geometric shapes, such as circles and spheres.

• Let your child help set the table. Fold napkins as rectangles one day, then as triangles the next. Find the number of legs on the chairs and table needed for everyone to eat.

• Let your child sort the laundry. Before washing, have your child sort the piles by colors or by family members. How many zippers? How many buttons? Are there more buttons or more zippers?

• Practice counting and making change. Ask your child to help you figure out how much money you have in your pocket or purse. Sort the coins. Let your child pick out the paper money and change needed when making a purchase, and have your child tell you how much change you should get back.

• Use sharing to reinforce division concepts and fraction skills. How many cookies will each child get if two children need to share 8 cookies? How many cookies will each child get if two children share 5 cookies? How can we cut the birthday cake so we can feed at least twenty people?

• Incorporate measuring during everyday activities, such as cooking, gardening, crafts, or home-improvement projects. Practice measuring things with a ruler, yardstick, tape measure, measuring cups, and scale.

• Use the kitchen to reinforce mathematics concepts and skills. Your child can practice sorting by helping put the groceries away and can practice measuring ingredients by helping cook meals, bake cookies, etc. Measuring cups are great for the sandbox or beach, too! Older children can determine how to adjust the ingredients to halve or double the recipe. After meals, your child can practice spatial reasoning skills by determining the appropriate size of containers to use for leftovers.

• Numbers are all around us! Look for numbers in the environment (e.g., addresses, sports statistics, weather forecasts, license plates, prices), and talk about what they mean and how they are used.

• Keep charts or graphs to help your child organize information and keep track of data. A child who is saving his/her allowance to buy an item might create a chart or graph to show how much he/she can save.

• Open a savings account. Work with your child to keep track of deposits, withdrawals, and interest and to compare this record with the monthly bank statement.

• Encourage a child who is a sports enthusiast to keep track of scores and statistics.

The following are two great games for young children:

Speed!

What you need:
Each player requires their own full deck of cards.

Each player holds their deck of cards until the parent says “Go”. Each player then proceeds to sort the complete deck into piles according to the same numbers as quickly as possible.

Piles MUST be put into consecutive order from smallest to greatest value. The first player to sort all their cards accordingly wins.
Play this one over and over again!

Blast Off!
What you need:
2 players
2 dice
1 set of cards 1-10 for each player

Each player arranges their cards in front of themselves in order:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Each player must get rid of their cards in sequence starting with the 10 and going down. Players must first roll a 10, then 9, etc.

Player #1 rolls the dice. Players have two rolls per turn. If player #1 does not roll a 10 in his/her 2 rolls, he/she loses the turn.

Player #2 does the same.

The first player to eliminate their cards in sequence, and is left with only the 1 is the winner.

Fostering Your Child’s Success in Math

What does math mean to you? Do you remember math as a bunch of rules to memorize, concepts that did not make sense, and assignments unconnected with everyday life?

Regardless of your own experiences, you play an important role in your child’s attitude toward, and success with, math. A strong mathematical background is essential for every child’s future. A solid mathematics education is essential for an informed public, our national security, a strong economy, and national well-being. Mastering challenging mathematics is not just a classroom skill – it’s a life skill.

The following is a National Council of Teachers of Mathematics’ list of what families can do to help their children succeed in and enjoy math:

1. Be positive! If you have a negative attitude about math, chances are your child will, too. Help your child have a “can do” attitude by praising your child’s efforts as well as his/her accomplishments. Acknowledge the fact that math can be challenging at times and that persistence and hard work are the keys to success.

2. Link math with daily life. Every day, people face situations that involve math, such as deciding whether one has enough money to purchase a list of items at the store, reading a map to find out where one is, building a budget, deciding on the shortest route to a destination, developing a schedule, or determining the price of an item on sale. Help your child realize that math is a significant part of everyday life.

3. Make math fun. Play math games, solve puzzles, and ponder brain teasers with your child.

4. Have high expectations. You would not expect your child not to read; similarly, you should not expect your child not to do math. Your attitude and expectations are crucial to influlencing the future opportunities for your child.

5. Support homework, don’t do it! Homework is an area that can cause trouble in many households. Relax, and remember whose homework it is. If you take over doing homework for your child, you encourage him/her to easily give up or seek help when working on a challenging problem.

Teaching Young Children About Money

There are many math games and activities that help children learn about money.

Helping your child learn the value of coins is a real-life skill that can be taught and learned easily if you use the following activities which are educational and fun:

Free Exploration

Give your child a small tub of real coins and allow him/her time to explore. This might be a good time for you to watch your child and note what is happening. Does he/she already know the names of each coin? Does he/she know the values? Do they notice likenesses and differences? Do they sort the coins? Make patterns (i.e. penny, nickel, penny, nickel, or dime, dime, quarter, dime, dime, quarter)?

Alike and Different with a Magnifying Lens

Children need to be able to identify coins before they can learn their values. This activity gives children the opportunity to examine pennies, nickels, dimes, and quarters closely and think about what things are the same and different among them. Noticing likenesses and differences is important in math and reading for young learners.

You will need a magnifying lens and 1 penny, 1 nickel, 1 dime, and 1 quarter.

Allow your child to experiment with the magnifying lens first.

Begin with the penny. Have your child look at it closely and tell you what he/she notices. I usually start with the heads side. Identify the year and place the coin was minted, the other words on the coin, and so on. Then look at the tails side. Don’t forget to examine the edges. You might want to have them cut out a large circle and draw pictures of both sides of the penny.

Look closely at each coin in turn, noting how they are alike and different. You might take a blank piece of paper and draw a vertical line down the center, dividing the paper into two columns. List Alike at the top of the first column and Different at the top of the second column. Begin to write about what you discover. Some things appear on every coin; some do not.

Talk about size and value. This can be confusing for young children because the nickel is larger than the dime but worth less.

What Are the Coins?

You’ll need some coins for your child to use to solve the problems.

Ask your child the following questions:

I have three coins in my pocket. They are worth 7 cents. What do I have? (a nickel and 2 pennies)

I have three coins in my pocket. They are worth 16 cents. What do I have? (a dime, a nickel, a penny)

I have three coins in my pocket. They are worth 11 cents. What do I have? (2 nickels and 1 penny)

I have three coins in my pockets. They are worth 30 cents. What do I have? (3 dimes)

I have six coins in my pocket. They are worth 30 cents. What could I have? (1 quarter and 5 pennies or 6 nickels). This problem has more than one answer. It is challenging for children to experience problems like this.

I have coins in my pocket, which have a value of 11 cents. How many coins could I have?

Teachers – these activities can be used successfully in the classroom, and I think the secret to their success is using real coins.

A Math Activity for Anytime and Anywhere

The following is a math activity that can be done anytime – I call it a “waiting” activity. It can be done while waiting for dinner to arrive at your favorite restaurant, waiting to get someplace in the car, waiting for the car to be serviced, waiting in the doctor’s office, waiting for the rain to stop, etc. Basically, you can do it anytime and anywhere.

It is called Guess If You Can and is appropriate for children of all ages, depending on the numbers you use. The following is a sample conversation.

Parent: I am thinking of a number between 1 and 100.
Child: Is it more than 50?
Parent: No.
Child: Is it an even number?
Parent: No.
Child: Is it more than 20 but less than 40?
Parent: Yes.
Child: Can you reach it by starting at zero and counting by 3’s?
Parent: Yes.
(At this stage, the parent could be thinking of 21, 27, 33, or 39.)

After your child has guessed your number, let your child think up a number for you to guess by asking similar questions.

Parent Pointer
It is important to help children develop an understanding of the characteristics and meanings of numbers. Doing this kind of math activity over and over helps your child develop number sense – hugely important for future success in mathematics.

Getting Ready for Kindergarten Math

People have this conception of kindergarten as children playing, getting cookies and milk, and taking a nap. As any kindergarten teacher will tell you, that isn’t the reality anymore. The focus on academics has been pushed downward.

In my many years teaching kindergarten through third grade, I watched unstructured playtime shrink, replaced by worksheets and nightly homework. The shift started in the 1990s, when studies ranked students in the United States well below those in other developed nations like Japan in math and reading. There was a push to close that gap, and one solution was to start emphasizing academic subjects at a younger age.

When kindergarten was less academic, it was an easier transition from home to school for most children. Now seat work starts in kindergarten, which means the transition is difficult for many children. Many kids aren’t so eager to make the jump into the world of worksheets and seat work.

It’s normal for students to be all over the map developmentally at this age. Each child’s brain develops differently, and their level of exposure to different experiences as they enter kindergarten varies widely. That’s why students attend preschool and kindergarten programs instead of just jumping straight into primary school – to get everyone on the same page before barreling full tilt into the world of letter grades and federal testing.

There are many things parents of young children can do to help their children be ready for kindergarten. See “Success in School Begins with Involved Parents”.

Playing math games is one of the most effective things parents can do to help their child make an easier transition into kindergarten math.

The following game is one of my favorites for young children:

Counters in a Cup

What you need:
2 players
5-10 counters (buttons, pennies, paper clips, etc.)
paper cup
paper and pencils

The object of this game is to figure out how many counters are hidden.

Decide how many counters you will use. Write this total number on the paper. With very young children, begin with a small number, such as 4.

Player #1 closes his/her eyes. Player #2 hides some of the counters under the cup and leaves the rest out for all to see.

Player #1 opens his/her eyes and figures out how many counters are hidden under the cup. Lift the cup to check. On the paper, write the hidden number in the cup and the number left out. For example, 3 left out, 1 under the cup = 4.

Player #2 hides his/her eyes and Player #1 hides some of the counters under the cup.

Players continue to alternate turns.

Your paper will reflect different ways to break the total number into two parts: 4=3+1, 4=2+2, 4=4+0
Can you find a way that is not shown?

Now pick a different amount of counters and continue to play.