My youngest daughter wanted to do Singapore math. Miquon Red was her main math text at the time, but we added a bit of Singapore Primary Math 1B whenever she was in the mood.
We turned to the lesson on subtracting with numbers in the 30-somethings.
Do you enjoy math? I hope so! If not, browsing this post just may change your mind.
Welcome to the 106th edition of the Math Teachers At Play math education blog carnival — a smorgasbord of links to bloggers all around the internet who have great ideas for learning, teaching, and playing around with math from preschool to pre-college. Let the mathematical fun begin!
By tradition, we start the carnival with a puzzle in honor of our 106th edition. But if you would like to jump straight to our featured blog posts, click here to see the Table of Contents.
If you slice a pizza with a lightsaber, you’ll make straight cuts all the way across. Slice it once, and you get two pieces.
If you slice it five times, you’ll get a maximum of sixteen pieces. (And if you’re lucky you might get a star!)
A friend emailed me, frustrated with her child’s math lesson on bar diagrams: “Why do they have to make it so complicated? Why can’t we just solve the blasted problem?”
I told her bar models themselves are not the goal. The real question for parents and teachers is:
To solve word problems, students must be able to read and understand what is written. They need to visualize this information in a way that will help them translate it into a mathematical expression.
Bar model diagrams are one very useful tool to aid this visualization. These pictures model the word problem in a way that makes the solution appear almost like magic.
It is a trick well worth learning, no matter which math program you use.
https://www.youtube.com/watch?v=HKsYDzQK8Zw
“Visualization is the brain’s ability to see beyond what the eyes can see, and we can develop visualization in many ways.”
https://www.youtube.com/watch?v=I6Ipio8JntU
“A bar model is a way to represent a situation in a word problem using diagrams — in particular, using rectangles.”
https://www.youtube.com/watch?v=i7LAHc1qvig
“This is one of the ideas that children learn in mathematics: the use of diagrams to represent quantities, especially quantities which are unknown.”
I’ve written a series of blog posts that explain bar model diagrams from the most basic through to solving multistep word problems. Check them out:
I’ve started working on a book about bar model diagrams, and I’d love to hear your input. Have you tried using them? Do they help your children? What questions do you have?
You can help prevent math anxiety by giving your children the mental tools they need to conquer the toughest story problems.
Check out Word Problems from Literature: An Introduction to Bar Model Diagrams—now available at all your favorite online bookstores!
And there’s a Student Workbook, too.
CREDITS: Videos and quotations from Dr. Yeap Ban Har’s YouTube channel. “Girl doing homework” photo (top) by ND Strupler and “math notebooking equal fractions” by Jimmie via Flickr (CC BY 2.0).
It’s here! My long-awaited upper-elementary Math You Can Play games book has finally hit the online bookstores.
Multiplication & Fractions features 25 kid-tested games, offering a variety of challenges for school-age students. Children master several math models that provide a sturdy foundation for understanding multiplication and fractions. The games feature times table facts and more advanced concepts such as division, fractions, decimals, and multistep mental math.
Click here to find Multiplication & Fractions at your favorite bookstore.
Maybe you never really understood what multiplication means or what fractions are? As long as you start with an open mind and are willing to engage playfully, the activities in the book can help you as you help your kids.
Anecdotally, these two areas are the first major stumbling point for students in their math studies. The sequencing in the book will help kids develop a strong foundation.
Kids (and parents!) find these games fun. I’ve been field testing math games for the last 18 months and keep seeing how engaged kids get when playing math games.— Joshua Greene
Multiplication & Fractions Math Games from Denise Gaskins (a review)
Chapters include:
If you are a parent, these games provide opportunities to enjoy quality time with your children. If you are a classroom teacher, use the games as warm-ups and learning center activities or for a relaxing review day at the end of a term. If you are a tutor or homeschooler, make games a regular feature in your lesson plans to build your students’ mental math skills.
So what are you waiting for? Clear off a table, grab a deck of cards, and let’s play some math!
It starts with models that are visual explanations of the concepts. Gaskins also breaks learning these concepts into comfortable steps that emphasize patterns and relationships, the real ideas that are behind properly understanding multiplication and fractions (indeed, math generally).
The sequence of games in each section starts by building familiarity and then fluency (speed) to solidify all of that work.— Joshua Greene
Multiplication & Fractions Math Games from Denise Gaskins (a review)
Most of the Math You Can Play games use materials you already have around the house, such as playing cards or dice. But this book introduces multiplication and fractions with several games using two special mathematical model card decks.
Click here to download the Multiplication & Fraction Printables, featuring all the math model cards, hundred charts, and game boards you will need for any game in the book.
From Peggy Kaye’s classic book Games for Math:
“Games put children in exactly the right frame of mind for learning difficult things.
“Children relax when they play — and they concentrate. They don’t mind repeating certain facts or procedures over and over, if repetition is part of the game.
“Children throw themselves into playing games the way they never throw themselves into filling out workbook pages.
“The games solidify the achievements of children who are already good at math, and they shore up children who need shoring up. They teach or reinforce many of the skills that a formal curriculum teaches, plus one skill that formal teaching sometimes leaves out — the skill of having fun with math, of thinking hard and enjoying it.
“If you play these games and your child learns only that hard mental effort can be fun, you will have taught something invaluable.”
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This blog is reader-supported.
If you’d like to help fund the blog on an on-going basis, then please join me on Patreon for mathy inspiration, tips, and an ever-growing archive of printable activities.
If you liked this post, and want to show your one-time appreciation, the place to do that is PayPal: paypal.me/DeniseGaskinsMath. If you go that route, please include your email address in the notes section, so I can say thank you.
Which I am going to say right now. Thank you!
“The Value of Math Games” copyright © 2016 by Denise Gaskins.
One step closer to getting my long-awaited Multiplication & Fraction Games book out — I finished the printables file! At least, I hope I’ve finished. Sometimes it seems like whack-a-typo never ends…
Click here to download the Multiplication & Fraction Printables, featuring mathematical model cards, hundred charts, and game boards to accompany the upcoming Math You Can Play: Multiplication & Fractions book.
The Multiplication & Fractions ebook will come out sometime in November, and the paperback should follow in time for Christmas. If you’re interested, my newsletter subscribers will get a special introductory sale price whenever the book is published. Join now!
You may also want to check out:
Click here to download the Number Game Printables Pack, featuring hundred charts, graph paper, and game boards from the first two Math You Can Play books.
Also, 0–99 charts, and bottoms-up versions, too. (See my blog post Math Debates with a Hundred Chart.) And a fun cut-and-fold game board for playing Shut the Box.
You have permission to copy and use these game boards and worksheets in your own local classroom, home school, math circle, co-op class, etc. But you may not post them on your own website (though you can link to this post, if you like) or sell them. If you’re not sure how copyright works on the Internet, check out Daniel Scocco’s Copyright Law: 12 Dos and Don’ts.
Homeschoolers have an advantage in teaching math: As our students grow, our own understanding of math grows with them because we see how the ideas build on each other.
This is especially true for those of us with large families. We pass through the progression of concepts with each student, and every pass lays down another layer in our own minds.
If you’d like to short-cut that process, check out Graham Fletcher’s Making Sense of Elementary Math video series. He’ll walk you through the topics, showing how manipulatives help build early concepts and gradually give way to abstract calculations.
“Understanding the vertical progression of mathematics is really important in the conceptual development of everyone’s understanding. This whole Making Sense Series has truly forced me to be a better teacher.”
— Graham Fletcher
“I can’t find a home school math program my son likes. We’ve tried Singapore Math, Right Start, Saxon, and Math Mammoth. We subscribed to a month of IXL Math to keep him in practice, but he hates that, too. I know I shouldn’t have changed so many times, but this was our first year of homeschooling, and I was trying to please him. But I’m running out of things to try. Do you think Life of Fred might work?”
You’ve tried all those math programs in one year? Many people recommend that new homeschoolers take a few months off to “detox” from the classroom setting, to relax and enjoy the freedom of making their own choices. But your son might want a few months to detox from his homeschool experience.
I suggest you set aside all those books and focus on games and informal math. Try to avoid schoolish lessons until your son starts to enjoy learning for its own sake.
Continue reading FAQ: Trouble Finding the Right Math Program
“My oldest son has somehow developed the horrid habit of counting on his fingers. We worked on the math facts all summer. He knows the answers in simple form, such as 9 + 4, but if it’s in a bigger problem like 249 + 54, he counts up to add or counts down to subtract, all using fingers. My younger children have no problem with mental math, but he can’t seem to get it. Are there any tips or tricks to stop this?”
Counting on fingers is not a horrid habit, it is a crutch. Please think for a moment about the purpose of crutches. The blasted things are an uncomfortable nuisance, but there are times when you can’t get anywhere without them. And if you need them, it does you no good for a friend to insist you should crawl along on your own.
That is how your son feels right now about his fingers. He is struggling with something his younger siblings find easy, and he can tell that you are frustrated. His confidence is broken, in a cast, and needs time for healing. So he falls back on what he knows he can do, counting up the answer.
Think positive: this means he still believes that math ought to make sense — that to understand what he is doing is more important than to guess at an answer. You want him to value sense-making, because otherwise he will try to memorize his way through middle school and high school math. That is the road to disaster.
I love it when a plan — or rather, a series of math thoughts — comes together.
On Monday, Emily Grosvenor (author of the Tessalation! picture book) asked me how parents who are insecure in math could help their children learn through play, and I responded with this quote from my Let’s Play Math book:
If you are intimidated by numbers, you can look for patterns of shape and color. Pay attention to how they grow. Talk about what your children notice.
But I wasn’t entirely satisfied with that answer. So many adults have come away from their own school experience thinking math is only numbers. Even with shapes, isn’t it the numbers about them — how many sides, what size of angles, calculate the the area or perimeter — that are important? That’s what school math tends to focus on.
Those of us who are comfortable with math know that there are many more things to notice and think about than just numbers. We know that it’s this noticing, thinking, and wondering that is at the heart of math. And that just playing with shapes can build a powerful foundation for future math learning.
And then yesterday, Malke Rosenfeld posted a beautiful article about a paper manipulative created by Paula Krieg. Which included this video:
The ability to create, and maintain, and manipulate shapes mentally — that’s the goal. Just like kids who can put numbers together in their heads, kids who can rotate, flip, and think of how shapes fit together in their heads have a powerful tool to analyze not only simple shape puzzles, but dividing up an area that’s a more complex room shape … to look at a piece of artwork … or look at a building … For these kids, all the world around becomes a playground to use mathematical ideas.
— Doug Clements
Problem Solving Development: Composing Shapes
Of course, pattern blocks are good for much more than just filling in worksheet pictures. But I love this peek into how a child’s understanding grows, in bits and spurts — without any numbers at all — until the world itself becomes a playground for mathematical ideas.
Want more?
You know what? Children like mathematics. Children see the world mathematically … When we do a puzzle, when we count things, when we see who’s got more, or who’s taller … Play and mathematics are not on opposite sides of the stage.
— Doug Clements
Why Early Childhood is the Right Time to Start Learning Math
Denise Gaskins' Let's Play Math 