mom helping daughter with math homework

A recent New York Times article made a splash when it cited research showing that math-anxious parents who try to help their kids with math homework are doing more harm than good. They are transmitting their own anxiety to their children, and the result is poor grades.

Furthermore, parents don’t even have to help with homework to cause damage. Casual comments such as “I’m not a math person” or “I’ve never been good at math” are detrimental to the education of a child who is struggling with math. These comments relay the message that math isn’t really that important. They give kids an out. Mom and Dad have good jobs and they’re not good at math, so I don’t need it either.

While the researchers cited in the NYT article believe this to be a “newly discovered factor,” ask any math tutor and she’ll shake her head and roll her eyes. The fact is, we tutors see this problem first hand, and on a regular basis. One comment I hear often is: I’m not good at math, but I want my child to be. Parents say things like this in front of their kids without realizing that it is detrimental. I wrote about this problem in my book, Math Can Be Fun. Fortunately, this part of the problem is easy to fix. Be careful how you talk about math. As simple as that.

But what else can you, the math-anxious parent, do?

Researcher Dr. Harris Cooper suggests modeling math behavior. Demonstrate to your children that you do, in fact, use math every day, while buying groceries, paying for dinner, and balancing the checkbook.

But is that enough? Sorry, but no, it isn’t. Someone has to help with homework. That someone could be a math tutor. That’s the easy solution. But that someone could also be you. The article describes a mom who took the bull by the horns and studied the math curriculum so she could help her son with his homework. That is inspiring!

And that mom is not alone. I know a mom who is doing the same thing. Actually, she is a great example of a third option for math-anxious parents: join your child in math tutoring sessions!

This mom hired me to help her son toward the end of the last school year. His skills improved quickly, but she really wanted to be the one who helps him with his homework. And she didn’t want to pass her math anxiety on to her son. So over the summer, she started attending tutoring sessions with him. She’s as busy as most moms, working full time, taking both her sons to baseball practices and games, and working on her master’s degree. Maybe she’s more busy than most moms. But she decided that math is as important as all those other things that compete for her family’s time.

In my book, she is a hero. And guess what. We all had fun!

Is tutoring the only way for parents to improve their math skills? No! If your child is doing okay in math right now, but you worry that the time is coming when you will not be able to help him, there’s a great alternative to tutoring. It’s called Khan Academy. KA is a non-profit started by Sal Khan; his objective is to level the math playing field, making quality math help available to all students. It offers a complete math curriculum that is being used by many home-schooling parents. It’s a fantastic resource for those parents who need to hone their own skills. And it’s free.

You can use the KA site in various ways, but my suggestion is to target a specific grade level. Decide where you think you fell off the math wagon when you were in school, and start at the previous level. The site will step you through the skills, offering videos with examples to teach you how to solve a given type of problem. Then you answer questions, starting with easy problems and progressing to more difficult ones. If you approach it with an open mind, you’ll actually find that it’s fun. Plus, you’ll have the satisfaction of knowing that you are taking charge of your math anxiety!

Believe it or not, I have a friend who woke up one day and decided he was tired of not being comfortable with math. His kids are grown, so there was not a pressing need for him to hone his math skills; he just wanted the knowledge. He began at the beginning, and has worked up to the 9th grade. And he’s still plugging away. His days in any math classroom ended many decades ago, so if he can do it, you can too.

So do yourself and your kids a favor. Find a tutor or sign up for Khan Academy. Maybe you can talk some other parents into joining you. You can overcome your math anxiety, and in doing so, you’ll be a great role model for your kids.

 

 

recipe for inspired learning

Remember the 3 E’s? Engagement, Enthusiasm, and Encouragement make up the base of a magic potion for inspiring a child to learn. The E’s are characteristics that parents, teachers, and tutors must bring to the table. They are our job, not the kids’. Today I’m introducing the other half of the recipe…the 3 C’s: Creativity, Choice, and Collaboration.

Over the course of the summer, I’ve had the pleasure of sharing the magic with a group of children from my area, as part of Math Games at the Library. By my definition of success—”Did every single child have fun doing math?”—the program has definitely made the grade. My biggest problem has been keeping the volume down; the kids have so much fun that they forget they’re at the library. That’s a good problem to have when you’re teaching math.

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Some people think of creativity as something that applies to art, or writing, but it is a critical part of teaching kids any subject, including—and perhaps especially—math. Why especially math? Because while children tend to approach the non-math curriculum with enthusiasm, they often think of math as something they have to do but they’ll never enjoy. One of those “Let’s get it over with” things. So getting them to open their eyes to the possibility of having fun doing, say, fractions, requires a bit more effort than enticing them with the pleasure of reading a storybook.

So how do we apply creativity to math learning? The same way we apply it to anything: we come up with activities that kids find fun to do and that happen to involve some form of mathematics. It’s possible to change almost any game to include math concepts. Here are some we played this morning:

Simon Says. We played the geometry version today. The children took turns being Simon, and instructed the group to make a specified angle or shape with their hands or arms, for example, “Simon says ‘Make an acute angle'” or “Simon says ‘Make a triangle.'” Of course they didn’t always say “Simon says” and that’s part of the fun. If a child makes the angle or shape when the leader has not said “Simon Says,” that player is caught, but he or she was never out. This is supposed to be fun; it isn’t a competition. Whenever someone is caught, everyone has a good giggle, and it’s the next person’s turn.

Fractions are fun with the Pizza Fractions Fun gamePizza Fractions. I’ve discussed this game before. It is as fun as any board game I’ve ever played, and it’s a great way to learn the basic concepts of fractions. We play one of two different versions. In one, we make “pizza sandwiches,” which comprises two layers of pizza slices of any flavor. The trick is that the bottom layer can have only one piece, e.g. a slice that is 1/4 of a whole, while the top layer must have at least two pieces, e.g. two slices that are each 1/8 of a whole, so the two layers represent the same amount of pizza. In the second version, which we played this morning, the goal is to make as many whole pizzas as possible, and each pizza can include only one flavor. The kids like this version best, especially when we play “beat the clock,” which I’ll discuss in a bit.

Buzz. In this game, I choose a number, say, 3, and we go around the table counting by 1s, starting at 1. When we get to a number that is a multiple of 3 or that has a 3 in it, the player is supposed to say “buzz” instead of the number. If she doesn’t say buzz when she should, or she says buzz when she shouldn’t, she sits down until her turn comes around again. It’s important to choose the number such that a different player or players say buzz in each go round. For example, if there are 6 kids, don’t choose 3; use 4 or 5 instead. The game goes like this (for our example using 3): 1, 2, buzz, 4, 5, buzz, 7, 8, buzz, 10, 11, buzz, buzz, 14, buzz, 16, 17, buzz, and so on. If the kids are up on their skip counting, they do great until they get to the first number with a 3 in it that is not a multiple of 3, which in our example is 13. That gets them almost every time. It’s really fun once it gets going, and it’s a wonderful way to teach skip counting in preparation for learning multiplication.

If you need more ideas for creating fun math activities, please have a look at my book on Amazon.

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this way to fun with mathLet’s talk about choice. I don’t know about you, but when I was young, there was no choice, either at school or at home. The teacher told us, or my mom told me, what we were going to do next, and that’s what we did, like it or not. I’ve never understood that approach. We are all happier doing something when we feel we have some say in the planning of it, and every kid I know learns better when he doesn’t feel like he’s being forced into it.

I’m not saying he would choose to work on fractions over playing ball outside, but his mind will be a lot more open to learning fractions if he’s given choices. For example, at the library this morning, I asked each of the kids which activity they’d like to do today. Then we voted on which one we’d do next and next and so on. The same principle can be applied in the classroom and at home. If you need to cover equivalent fractions and decimal multiplication, you can let the kids choose the one they’d rather do first. Then, if possible, let them choose the specific activity for that topic. If your child must complete homework, offer an incentive in the form of a math game following homework. And be sure to let her choose the game.

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teamThe final ingredient is collaboration. This is a topic that has been getting a lot of press, and many schools are going all out to introduce group projects in many subjects. That what I call progress. In my engineering career, I worked with lots of very smart people, some of whom had the skills to work as an effective member of a team, and some of whom did not. In case you haven’t heard, today’s business environment demands teamwork. The brilliant guy at the end of the hall who keeps his door closed most of the time is fast becoming a dinosaur, and he’ll be an easy target when it comes time for layoffs. Why? Because today’s systems are complex, and designing and implementing them requires many different skill sets. The people who have those skills have to be able to share information (not protect it), participate in brainstorming as an equal with others on the team (no prima donnas allowed), and communicate their ideas to people who have different skills and communication styles.

How do we teach teamwork skills to children? We look for every opportunity to let them learn and practice as part of a collaborative group. At the library, the kids don’t compete against each other. In pizza fractions they work together to make as many pizzas as possible in 15 minutes, so they’re racing the clock, not each other. In multiplication bingo, we keep going until everyone has bingo, and the kids are encouraged to ask each other for help if they need it. So in addition to learning math, they are learning to be good team members.

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I hope you find ways to mix up your own magic potion. Your kids will thank you for it!

students working together

I am currently enrolled in an on-line certificate program called Developmental Therapy-Teaching (DTT). The course was created by Dr. Mary Wood of the University of Georgia, and it is based on her book, Teaching Responsible Behavior. I have to admit that I don’t love the title of the textbook – I get a little hung up on the word “responsible” – but I think the content is wonderful.

No, fantastic. I highly recommend it to anyone and everyone who lives or works with children. It doesn’t matter whether your job title is “teacher.” If you interact with kids, please read on.

Before I attempt to describe DTT, I want to emphasize that I am just learning; I am by no means an expert in this area. With that said, here is my take on it.

Developmental Therapy offers a structured approach for parents and teachers, or anyone who deals with children, to understand the sequence in which children learn specific skills in four areas: Doing, Saying, Relating, and Thinking. DTT divides a child’s development into five stages. Each stage is defined by an overall goal for development as well as specific competencies in each of the four areas. With this understanding, adults can begin to recognize gaps in a child’s development and help the child to fill in those gaps using positive, nurturing approaches. They can also tailor activities, at school and at home, to promote development without pushing a child to jump ahead before he or she is ready.

The course comprises four modules, as follows.

  • Module 1: A Developmental Approach to Classroom Teaching
  • Module 2: Developmental Assessment for Curriculum Planning and Instruction
  • Module 3: Emotions and Behavior in the Classroom
  • Module 4: Getting Started in Your Own Classroom

I’m about two-thirds of the way through the first module, and I’ve learned quite a bit. Keep in mind that my background is engineering, not teaching, so most of this is new to me. Even so, I have the sense that the approaches taught in this course will be new to some teachers and many parents.

One idea that I’ve found practical application for already is that children are generally not ready for competition until Stage 4, which starts at about age 9 for typically developing children. So for some of my tutoring students, and in the Math Games program that I host at the local library, I am finding ways to reduce emphasis on competition and increase emphasis on teamwork. Here are a couple of examples.

I often play checkers with my individual students. Each square contains a math problem that can involve anything from fractions to division. When a player lands on a square, he or she must solve that problem. What I’ve changed is that we no longer play until one of us wins; we stop at some other predefined point, such as whenever someone gets “king”-ed. This may sound like a subtle difference, but it’s not. One student, in particular, used to have hurt feelings whenever he lost. Before studying DTT, I thought I was helping him by teaching him to be a “good loser.” I was wrong! This student is 10 years old, but he has developmental challenges, and he is not ready for competition. Now there is no loser. Someone gets “king”-ed and we move on to another activity.

Fractions are fun with the Pizza Fractions Fun gameI have made similar changes for the Math Games group. When we play Buzz, instead of having a student who says a wrong answer sit out the remainder of the game, he or she gets to stand back up when his or her turn comes around again. We just play until we get to 50. When we play Pizza Fractions, we play until a certain number of pizza sandwiches have been created, independent of how many sandwiches any individual has made. Again, this takes the emphasis away from winning or losing, and keeps the focus on learning. Next week I’m going to change this one again by challenging the students to see how many pizza sandwiches they can make as a group in 10 minutes.

I realize that some readers may believe in the importance of individual competition at a young age. After all, it’s a tough world out there, right? My response to this is that DTT does not intend to eliminate competition; it just presents it when each student is ready. Before kids are ready for individual competition, they need to learn to interact successfully in a group. One way to introduce competition is to have a team of students compete against their own team record. This presents the same kind of challenge as other competitive activities, without resulting in a “winner” and a “loser.”

I am only focusing on the competition aspect of DTT because it has directly influenced my tutoring approach when it comes to games. There are many, many competencies in each of the four areas (Doing, Saying, Relating, Thinking) and each of the five stages of development.

At this point, I can highly recommend Module 1 for all parents, and you can sign up for just one module if you choose. I’ll let you know about the others as I progress. If you are interested in learning more about DTT, please visit the University of Georgia web site.

Math Night Redux

Math NightAbout a month ago I wrote about my plans for organizing a math night at a local elementary school. The event was SO much fun that I decided to share some photos. Thanks to the school staff, the parents, and the students for making it a great success!

These photos represent only a small subset of the activities. Please refer to the previous math night post for a complete list. I’ve added captions to explain what’s happening. Maybe this will give you the incentive you need to start a math play group this summer!

counting activity

K-1 kids counted by 2’s and 4’s using the legs on farm animals

human number line

K-1 kids solved addition problems by stepping them out on the number line

Grades 2 & 3 created shapes by answering riddles about the attributes

Grades 2 & 3 created shapes by answering riddles about the attributes

Grades 2 & 3 used the hopscotch game to practice skip counting

Grades 2 & 3 used the hopscotch game to practice skip counting

Grades 4 & 5 used play money to answer a series of riddles

Grades 4 & 5 used play money to answer a series of riddles

dominoes fractions

Grades 4 & 5 used dominoes to compare fractions. The Fraction Tower was a big help. This student had fun lining up the dominoes after he finished the problems.

multiplication twister

Grades 4 & 5 had a blast playing multiplication twister

child swinging

 

No More Summer Backslide

boy on slideAre you worried that your kids’ (or grandkids’) math abilities are going to slide backward over the summer? It is a common, but preventable, problem. There are lots of ways to reinforce math skills during the school break. A quick internet search, or a search on this blog, will bring up ideas for using math at home, outside, and in the car. My book, Math Can Be Fun, is full of creative approaches as well.

And here’s another idea. Start a math play group for your neighborhood, or even for your community.

I know. It sounds like a lot of work. You’re thinking, “I don’t have time to do that.” But it’s not and you do. I’ll show you how.

The Benefits of a Math Play Group

two kids happyFirst, let’s talk about the benefits. Obviously, it will help the kids to exercise their math skills. And while your kids are having fun playing math games, they’ll be strengthening their social skills, especially if you include some cooperative activities. And, I promise, you’ll get enjoyment from seeing children helping each other with math. Look at it as a way to give back to your community while also benefiting your family.

How to Make It Happen

Setting up a math play group is really quite easy. You need: 1) a venue; 2) math activities; and 3) an adult who is enthusiastic about math. Let’s take these one at a time.

Venue

boy in libraryThe most important aspect of the venue is its location. It must be convenient for parents to get their kids there. I learned this part the hard way. Earlier this year I set up a math play group in a church that is centrally located between two communities. The location was inconvenient for people in both areas so hardly anyone showed up. It is much better to serve a smaller area from a location that is convenient to the people who live there. If you are serving your neighborhood, you could try rotating to a different house each week.

For a community-wide play group, your best bet is a public library. Everyone knows where the library is, and parents will have something to do while their kids are involved with the group. Also, most, if not all, public libraries have a kids’ area equipped with tables and chairs. My guess is that the staff will be thrilled at the idea of adding math play time to their programming—I know my library is. I’ll be shocked to hear back from anyone that their library does not embrace the idea, but if that is your experience, try another library.

Get recommendations from the staff on the best day and time to host the group, but Saturday is generally the best choice since more parents will be off work.

If, for some reason, a library is not an option for you, approach the leaders of your church or any church that is centrally located within your community. Most churches have gathering rooms and church leaders are always looking for ways to support the local community. Some may require the adults involved in the program to have a basic background check done. I got mine here for $19.95.

Materials

whiteboardThe materials you’ll need will depend on the age range you want to target and how creative you want to get. I chose to focus on kids in 2nd through 5th grade. I find that many kids in this age range have already developed a fear and/or dislike of math, but they are still young enough to change this mindset. But choose the age range that works best for your neighborhood or your community.

There are many, many activities that you can do with no materials at all, or with just a white board. The most comprehensive list of activities I’ve found is washmath.org (link downloads GamesAndActivities.pdf file). You can also find a list of activities that I used for an elementary school math night here.

You may be able to borrow a white board from the library, if that is your venue. Otherwise, you can pick one up for very little money. Be sure it is at least 3 feet wide, and don’t forget dry erase markers and a felt eraser.

You can also assemble a basic “math kit.” You’ll find some great math teaching aids in your own home. Some basic items include: playing cards, measuring cups, a checkers game, dominoes, and rulers or measuring tapes. I use “wet erase” markers to write math problems on the checkers squares, and I use playing cards and dominoes for addition, subtraction, multiplication, division, and fractions activities. Look for the book Mega-Fun Card-Game Math in your library (or purchase it on Amazon) for ideas for math card games. As a variation, dominoes can be substituted for cards in many of the games. Also, kids love measuring things, and they can use their measurements to make line and bar graphs.

You can also start networking with family, friends, and teachers to gather commercial math manipulatives and games. Or you can buy them. Two of my favorites are the Fraction Tower (about $14) and Pizza Fractions (about $15). You don’t have to have these kinds of items, but they are wonderful teaching aids.

Leader

woman thoughtThis could be you! And if it’s not, there is surely at least one adult in your circles who is enthusiastic about math. If you know two or three adults who could be co-leaders, even better. It may take a bit of convincing, though. Here are some points you could make.

It will only take an hour of their time each week, plus travel time.

They will be doing a community service.

They will get that joyful feeling that only comes from helping others.

They will have fun.

Let’s Go!

What are you waiting for? Call a few friends today to let them know what you’re planning. Head to the library after work today. Start thinking about the age range you want to include. And get excited! This could be the most fun you and your kids will have this summer.

I’d be glad to share my play group flyer with you. You can just write your specific information into the blank boxes. Send me a quick note and I’ll send it right over.

Don’t hesitate to ask if you have any questions, and please let me know how it goes!

The Specter of the EOG

standardized testing

One Test Could Be the Deciding Factor

eog specterMy heart goes out to young students at this time of year, especially this year. They are living with the specter of one all-important standardized test and the possible implications of their performance on that test. I’m talking about the end-of-grade (EOG) test that is required in North Carolina. Even as “the state considers eliminating EOG testing” (TWC News), in favor of a series of four tests given through the school year, students are facing a single test that could determine whether they will be promoted at the end of this school year.

Last week one my students informed me that “This year the test counts.” Mark is a 7th grader whose math grade has risen steadily from a very low C to a solid B since we began working together last fall. Still he’s worried because he failed the EOG last year, when the results “didn’t count.” Mark is unclear about whether he will be retained if he fails the test again this year. So are his parents. I think he’s going to pass, both the test and 7th grade, but he is unsure, and his past performance on the EOG looms large.

When I asked one of the girls in my free “math play” group what she had learned in math class this week, she responded, “How to take the EOG.” She didn’t seem to be too worried about the test, even though she’s not at all confident that she’s going to pass. I wonder whether she understands the potential implications.

I just began working with another 4th grade student whose mother has been told he will very likely be retained if he doesn’t pass the EOG. He has ADD. That means he can have trouble focusing in class and on tests. He is allowed extra time to take tests, but it isn’t clear to me how that might help his focus. And even though his performance is improving, if he fails the EOG there is a good possibility he will have to repeat 4th grade. Summer school is not being offered in our area this year, so that one test score could be the determining factor. What’s most disturbing to me is that this little boy is actually pretty good at math. He’s just not very good at taking tests. Yet.

I understand the need for assessment, but I don’t believe that a single test should ever be the deciding factor for the retention decision. It’s seems to me that the state is trying to apply a cookie cutter approach to gauging the abilities of children whose learning styles and test-taking proficiencies are unique to each individual.

Focus on Word Problems

math word problemBut the system is what it is, at least for now, and it will certainly change, for better or for worse. Anyway, it isn’t my job to worry about the politics of education; it is my job to teach math to my students. And at this time of year, it is my job to help prepare them for the EOG.

I’m not saying that I “teach to the test.” I couldn’t do that even if I wanted to, given that I work outside the system. I only have access to the materials that the state makes available to the public on the internet. Still, I am not completely in the dark about what will be tested. I am very familiar with the curriculum standards for every grade, and I’ve downloaded the most recent sample tests that have been posted to the state’s “Accountability Services Division.” One think I am sure of is that a significant percentage of the questions will be in the form of word problems.

So here’s my approach to working with students at this time of year. To the extent possible, I incorporate the required skills into word problems that I make up. I teach my students to read the problem twice, to circle important information, to box the question, to consider drawing a picture, to think about whether the problem involves just one computation step or more, and to use key words to decide which operation is appropriate in each step.

I even use word problems for part of our geometry work. I ask questions like, “What shape has four equal angles and four sides, two of one length and two of another length?” The process of interpreting a description like this results in a deeper understanding of geometrical attributes than a statement like, “Draw a rectangle.”

Sure, I also include examples in which the student has to interpret numerical expressions and figures, but in my experience these kinds of problems are easier for most kids than are word problems.

Using word problems, rather than simple numerical expressions, allows students to develop a sense of how math applies to the real world while also reinforcing specific skills such as adding, subtracting, multiplying, dividing, and working with fractions and percentages. And because I make up the problems, I have the latitude to create problems that involve the specific interests of each of my students. So even though we’re preparing for the EOG, the work is interesting for the kids.

Let’s Not Forget the Fun

smiley faceWhile I’m working with my students, I am careful not to add to the worry that they are already experiencing. I don’t talk about “the test” too much. And we take breaks from word problems to play multiplication hopscotch, draw glyphs, and compete in pizza fractions and addition war. The winner gets Skittles. So does the loser.

With the specter of the EOG looming over them, students are under a lot of stress. So there is no more important time to help them have fun while learning math.

Math Night!

mathnight

Now’s the Time!

If you’ve ever wanted to have a math night at your child’s school or homeschool group, now’s the time. This event makes a great stress reliever for students, either before or after state testing. And I don’t know of any better way to get parents involved in their children’s math education.

The hardest part is getting on the calendar, so take care of that first. Putting together the activities is easy, especially if you have a few other enthusiastic parents and/or teachers to help. Even if you’re planning it by yourself, it’s very doable. I’ve read about schools forming committees and meeting several times before the event. But I happily left committees and meetings behind when I retired from engineering, so my approach was to just dive in. I did it by myself, and I had fun in the process. You, or you and a couple of other parents and/or teachers, can do this with ease. The only requirement is that you are enthusiastic about promoting the idea of having fun with math.

Here’s What I Did

I’m organizing a math night at a local elementary school at the end of the month. The activities I chose are mostly from my regular tutoring practice, but I included a few that I found on the internet. I divided the activities into three levels: K-1, 2-3, and 4-5.

I created an Excel spreadsheet with columns for Level, Curriculum Standard (not required, but helpful), Activity Name, Description, Number of Players, Number of Stations, Materials Needed, and Forms to create and print. I also created a “to do” list and a shopping list. It turned out that I only had to buy a small set of plastic farm animals and a couple of boxes of crayons.

Here’s a complete list of activities, by level, along with a brief description.

For Kindergarten and Grade 1:

cow mathHow many legs? Draw a plastic farm animal from the bag, count the legs, and add them to your current total. Keep going as far as you can.

Combinations. Using a printed page containing pictures of groups of items, find as many ways as you can to make a specified total by adding up items in selected groups.

Glyphs. Answer questions and create a drawing with characteristics that correlate to your selected answers. This is a data representation activity. I have a two-sided chalkboard table easel that will be perfect for the little ones who want to pair up for glyphs. (I blogged about how to make and use glyphs several weeks ago.)

Shapes. Draw a card containing the name of a shape and create that shape using Play-Doh and craft sticks.

Abacus. Count the beads on the top row, one by one. Then skip count by twos on the second row. For a bonus, try skip counting by threes, fours, and fives on subsequent rows.

Line Jumping. Draw a card, then start by standing on the specified number on the life-size number line on the floor, and move the required number of spaces to find the specified sum or difference. (Thanks to Lakeshore Learning for the idea!)

Storytime. Listen while a parent reads one of the available math storybooks out loud. (This is intended to accommodate the sleepyheads near the end of the evening.)

For Grades 2 and 3:

hopscotchHopscotch. Throw a pebble on a square and then hop up and back, skip counting by the number specified on the square where the pebble landed.

Dominoes. Pick a tile from the bag and add (2nd grade) or multiply (3rd grade) the two numbers.

Glyphs. Answer questions and create a drawing with characteristics that correlate to your selected answers. This is a data representation activity.

Shapes. Draw a card containing characteristics, but not names, of shapes and create that shape using Play-Doh and craft sticks.

Length. Choose an object from the basket and measure its longest dimension in both inches and centimeters, to the nearest whole unit (2nd grade) or half unit (3rd grade). Third graders are also invited to create a line plot of their data.
Money Riddles. Choose a card and use the play coins to figure out the answer to the riddle.

For Grades 4 and 5:

dominoDominoes. Draw two tiles at a time. Place them in front of you so that each tile represents a proper fraction. Then figure out which fraction is larger. (I’ll have a Fractions Tower there to help them figure it out if they need it.)

Multiplication War. Each player draws a playing card. The first player to correctly name the product of the two numbers wins the round.

Symmetry. Separate a basket of objects according to symmetry.
Factors. Draw two playing cards. Multiply the two numbers and then find all other factor pairs for the product.

Glyphs. Answer questions and create a drawing with characteristics that correlate to your selected answers. This is a data representation activity.

PEMDAS. Use your knowledge of the order of operations to place parentheses in an equation to make the result equal to a specified number. (Thanks to my friend Mary for this one!)

Magical 1s. Study the 1s Pyramid to find the number pattern, then fill in the remainder of the pyramid.

Twister GameMultiplication Twister. Spin the dial and place the specified appendage on the answer to the multiplication problem indicated.

I’m planning to save the movement activities for the last rotation of the evening so kids won’t be tempted to play Multiplication Twister all night!

Maximize Participation

Now, about incentives. “My” particular elementary school is offering two. First, each family will receive a copy of my book, Math Can Be Fun. And even better, every child who attends will get a 100 on a virtual math test! I’m expecting a very good turnout. Not all schools can be that generous. I’ve heard of schools giving a choice between a very long homework assignment and attending Math Night.

Let Me Know If I Can Help

If you have any questions about hosting a Math Night at your school, please contact me. If you’re in western North Carolina, I can even organize it for you!

And remember, this is supposed to be fun … it is not a test! So be sure to have teachers available to help students if they need it.

Let me know how it goes!

Spring Into Math Fun!

child enjoying nature

Math in Nature

It’s April, and spring has finally come to the North Carolina mountains, where I live. And spring always makes me think of math.

colored pencilsNature is the original mathematician, and she offers lots of fun activities you can do with your child to reinforce math skills and introduce new math concepts. Here are some of my favorite outdoor math activities. So take a walk in the woods, along a stream, or in the park. Take along a notepad, a pencil (or, better yet, a few colored pencils), a marker, a ruler, a tape measure, and a small basket with a handle.

As you try different activities, make a mental note of the ones that capture your child’s attention the most. Also, don’t spend more than a few minutes on any one activity. This should be fun and exciting, not rote or boring.

Counting

leaves
pebblesAsk young children to gather a handful of small rocks, sticks, flowers, or leaves, and then count them. Little ones just love to collect things, even pebbles! Also help them to count the birds or butterflies they see on the way, and count the petals on a single flower. Let her draw some of the objects or critters in her notepad to make it even more fun.

Addition and Subtraction

Use the collected objects to practice adding and subtracting. Quiz your child by making up problems to solve using the objects, or ask her to quiz you. (Kids love being the teacher!)

Skip Counting

Begin by separating the objects into groups of 2, and practice counting by twos. Then move on to 3s, 4s, and so on.

Fractions

Start by setting up a group of 4 objects. Then divide them into 2 groups of 2. Talk about the fraction of objects that are in each group (both 1/2). Do the same with groups of 3 and 1 (3/4 and 1/4). Then move on to fractions related to a total of 5, or 6, or 8. This is also great for explaining equivalent fractions, e.g. 2/4 = 1/2.

Multiplication and Division

Start with 2 groups of objects with 2 in each group. Show that 2×2 = 4, and that it is equivalent to 2+2 = 4. Then move on to 2 groups of 3 objects each, and show that 2×3 = 6 is the same as 3+3 = 6.

Then turn it around, starting with a group of 4 and dividing them into 2 groups to talk about dividing 4 by 2. Move on to higher numbers.

Patterns

swallowtail
spider webAsk your kids to find as many examples of symmetry as they can. The most common type is reflection (or planar) symmetry, as you see in leaves, birds, butterflies, frogs, spiders, and humans. In reflection symmetry, each half of an object is the mirror image of the other.

Then look for rotational symmetry, in which a part of an object is repeated a number of times as you go around in a circle. Examples include flowers and spider webs.

Some flowers, such as the passion flower, have both rotational and reflection symmetry!

pine coneIf you can find a pine cone, you’ll see that it exhibits rotational symmetry in two directions … clockwise and counterclockwise. Let your child use her marker to draw the spirals on the pine cone.

Older children will (hopefully) be interested to learn that the number of spirals in one direction and the number in the other are adjacent numbers in the Fibonacci sequence. In this example, there are 8 and 13. The Fibonacci sequence is an infinite set of numbers in which each number is the sum of the preceding two numbers, as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …

Look for other spirals, such as snail shells.

Shapes

oak gallLook for circles (e.g. the base of an acorn cap), cylinders (e.g., branches and trees), and spheres (e.g., the sun or an oak gall). Let your child use the marker to outline the base of the acorn cap or other shapes she finds. Talk about approximating in the context of the shape of a nut being almost a sphere. Many nuts are better described as spheroids (a sphere that is elongated or flattened). That’s a big word but kids get a kick out of showing off their prowess with unusual words, so give it a try.

Also try to find geometrical shapes in the clouds. After a few minutes of looking at clouds, your creative mind will kick in and you’ll start to see all kinds of shapes.

Measurement

Use a ruler to practice measuring lengths and perimeters of objects. Use a tape measure to practice measuring circumference (e.g. the distance around the trunk of a tree).

Start a Math Journal

math journalIf your child enjoys these activities, think about making or purchasing a dedicated journal in which she can record her discoveries over time. Try to remember to take it with you whenever you go outside. It will highlight the importance of using math in everyday life, and it’ll make her feel special.

See you out there!
 
 
 

word problem joke

The Problem with Word Problems

Word problems are hard. Word problems are confusing. Kids hate word problems.

Why?

A student’s first experience with word problems is often overwhelming. They are used to seeing straightforward problems such as “3 + 8 = ?” or “121 ÷ 11 = ?”. Then we throw long-winded sentences at them and ask them to make equations from them. No wonder kids hate them!

What can you do?

Start Early

math on whiteboardIt is best to introduce math words and word problems at a young age. And there should be a smooth transition from simple equations to multi-step word problems.

As soon as you begin asking your child to add two numbers, get in the habit of writing down and saying out loud both the numerical expression, e.g. “2 + 2 = ?”, and the verbal equivalent, e.g., “What is two plus two?”. It is very important to write and say the words, then have your child repeat them. Use the same approach as you transition to subtraction, multiplication, and division.

In doing this, you are training his brain to be as comfortable with math words as it is with numbers. Then when he encounters his first word problems as part of his regular school work, he will understand the meaning of the statements, and it’ll be much easier for him to solve them. And since he has never developed a fear of word problems, he’ll have no issues with learning increasingly complex solution processes as he progresses through school.

He will be comfortable with word problems, and it will show in his math grades.

It’s Not Too Late

But what if your child is already afraid of word problems? Not to worry. It will take a little time and effort, but you can help him get past this barrier.

Start by stepping backwards. Choose numerical problems that your child finds easy, and write one or more verbal equivalents next to them on a whiteboard. The more variations you come up with, the better. (I’ve included a section at the end of this post to help you with the most common keywords associated with the four basic operations.)

Here are a couple of examples:

    8 x 6 = ?        What is 8 times 6? What do I get if I multiply 8 times 6? What is the total if I have 8 groups with 6 things in each group?
    50 ÷ 5 = ?     What is 50 divided by 5? What is the result if I divide 50 by 5? If I divide 50 things into 5 equal groups, how many things are in each group?

Next, begin asking your child to come up with the questions.

toy race carWhen he is comfortable with that, start making up simple word problems to go along with some of the examples you’ve been using, like this:

    8 x 6 = ?      Mary’s mom buys eggs in half-dozen cartons. If she purchased 8 cartons, how many eggs did she buy?
    50 ÷ 5 = ?    Tom has 50 toy race cars. He wants to share them with his four best friends so that everyone has the same number of cars. How many cars will each of the 5 boys have?

Finally, begin asking your child to make up his own word problems to go with numerical and verbal expressions. After he creates his first word problem, he’ll start to see that they are nothing to be afraid of.

By following this process, you are building on your child’s knowledge and approaching word problems from a comfortable place, rather than jumping into strings of sentences that look complex and confusing. Just take it a step at a time, and you’ll get there.

Common Math Words

add subtract multiply divideWord problems use a variety of terms for the four basic operations. I’ve listed some of the most common terms below.

Addition Words: add, plus, sum, combine, all together, increase by, total, gain, raise

Subtraction Words: subtract, difference, minus, take away, fewer, less, (are) left, remain, how much more, how many fewer, words ending in “er” such as “How much tallER is Cathy than Karen?”

Multiplication Words: multiply, times, product, double, triple

Division Words: divide, quotient, shared evenly, half, group

You will encounter other words, too. But these are the most commonly used terms for elementary school students.

Don’t Forget to Make It Fun!

smiley faceWhile you’re writing, or asking your child to write, equations and sentences on the whiteboard, don’t forget to draw pictures to go along with the problems. And definitely throw in a smiley face every now and then.

A little fun and encouragement will go a long way in your efforts to help your child become comfortable with word problems.

turn fractions fear to fractions fun

Fractions Often Elicit Fear

Ask a random adult what area of math they find most difficult, and they are very likely to say, “fractions.” They were never comfortable with fractions as kids, and this discomfort followed them into adulthood. The pattern continues with many of today’s kids. I’ll never forget the day that my (then) new student, Emmaline, a 5th grader, looked me in the eye and said, “I can’t do fractions.”

fractions calculatorFractions are hard. Fractions are scary. Fractions are to be avoided at all costs. And they can be avoided … at least if you are an adult. All you need is a handy fractions calculator, and the work is done for you.

Unlike adults, kids encounter fractions every day, throughout their school years, and in spite of the near ubiquity of calculators, students are required to perform some exams, or parts of exams, sans electronics. So before you hop over to Amazon to buy a fractions calculator, please read on.

Fractions Can Be Fun

With a little creativity and effort, you can change your child’s mindset about fractions. Yes, you can. The best way to overcome fear is to replace it with fun. Thanks to many of the activities you’ll read about in this post, I’m happy to report that Emmaline now says, “Fractions are fun!” and she means it. Yes, it is possible.

Here are my favorite fun fractions tips.

pie for fractionsbrownies for fractions1) Ditch the pie. Drawing a pie to represent fractions is okay when you’re breaking a whole into halves or fourths, or even eighths. But dividing it into equal thirds is difficult (today’s kids did not grow up with peace signs), and it just gets harder for fifths, etc.

For teaching the parts of a whole, replace the pie sketch with a drawing of a brownie. Rectangles are much better than circles for explaining the idea of dividing a whole into parts. If you want to make it really interesting for your kids, use real brownies.

Healthier option: granola bars (go for soft, not crunchy). Some people like to use apples or other fruit, but it is difficult to cut them into equally sized pieces.

M&M Fractions Games2) Use candy. M&Ms and Skittles are fantastic for learning about parts of a whole group. I covered this in a previous post.

Healthier options: grapes, raisins, and nuts.

Brownies are also great for comparing the concept of the parts of a whole with that of the parts of a whole group. Divide brownies into pieces for parts of a whole. Divide a group of whole brownies into smaller groups for parts of a group. Kids need to understand both ways of thinking about fractions.

 

fraction tower3) Use manipulatives. Kids learn better when you combine multiple sensory inputs. So while visuals are great, visuals that they can touch and hold are better. Brownies are a manipulative of sorts, but they can get messy. One really great non-edible manipulative for learning fractions is the Fractions Tower, by Learning Resources. It comes with a hollow bar with “1” stamped on it, and a bunch of smaller bars with fractions from 1/2 to 1/12 stamped on them. Two “1/2″ pieces are as long as the “1” piece. Three “1/3″ pieces are the same length as the “1” piece. You get the picture.

I like to choose a set of pieces appropriate for a given student, say, the 1s, the 1/2s, the 1/4s, and the 1/8s. Then I challenge him to make a whole (equal in length to the “1” bar) in as many ways as he can. I know he is really getting it when he comes up with: 1/2 + 1/4 + 1/4 to make 1. Big high 5!

By the way, the Fractions Tower has fractions on only 1 side of all the bars. One side has the equivalent decimal number, and one side has the corresponding percentage. This is a tool that your child can use through middle school. Oh, and don’t be confused by the packaging. It says both “Fraction Tower” and “Fraction Cubes.” The word “cubes” is used very loosely, given that most of the pieces do not have equal sides in all dimensions. But I digress.

4) Create games with manipulatives. Combine visuals with touch, add a little friendly competition, and you have fun! Here are some ideas:

dominoes for fractionsDominoes Fractions

Give each player an even number of tiles, face down. On each turn, the player must turn over two tiles, and orient them so that they represent “proper” fractions. That is, the upper number (numerator) must be less than the bottom number (denominator). If the top and bottom have the same number of dots, so the fraction equals 1, that’s okay too. Then the player must decide which fraction is the smaller of the two. You can sort out the dominoes before starting, to limit the fractions to values that are appropriate for your child’s level. Also, remember, this is a learning game, and your child may not know the answer right away. Have a whiteboard and marker handy so you can draw brownies to help her figure out which fraction is smaller.

playing cards for fractionsCard Fractions

This version of card fractions is similar to the dominoes game described above. Deal cards to each player, in multiples of 4. (Remove the jokers and face cards first.) Then, on each turn, the player turns up 4 cards and makes 2 proper fractions with them. Then he decides which is smaller.

 

 

Fractions are fun with the Pizza Fractions Fun gamePizza Fractions, by Learning Resources

This is my all-time favorite way of teaching fractions. It costs between $15 and $20, but it makes learning sooooo much fun! It comes with several different spinners and instructions for several different games, and you can customize them to accommodate your child’s skill level. For younger students I start with 1/2, 1/4, and 1/8. Once they begin to understand that 2/4 is the same as 1/2, I bring in the 1/3 and 1/6 pieces. There is no end to the fun, or the learning, that is possible with this game.

 

Have fun!