Education Unboxed has posted some playful addition games for young learners. And there’s much more on their website. Be sure to click around and explore!
Six is Having a Party! – Math Facts with Cuisenaire Rods
PUFM 1.3 Addition
Photo by Luis Argerich via flickr. In this Homeschooling Math with Profound Understanding (PUFM) Series, we are studying Elementary Mathematics for Teachers and applying its lessons to home education.
The basic idea of addition is that we are combining similar things. Once again, we meet the counting models from lesson 1.1: sets, measurement, and the numberline. As homeschooling parents, we need to keep our eyes open for a chance to use all of these models — to point them out in the “real world” or to weave them into oral story problems — so our children gain a well-rounded understanding of math.
Addition arises in the set model when we combine two sets, and in the measurement model when we combine objects and measure their total length, weight, etc.
One can also model addition as “steps on the number line”. In this number line model the two summands play different roles: the first specifies our starting point and the second specifies how many steps to take.
— Thomas H. Parker & Scott J. Baldridge
Elementary Mathematics for Teachers
Math Teachers at Play #50 via Mathematics for Teaching
[Photo by By Willi Heidelbach via flickr.]
Fifty is the smallest number that is the sum of two non-zero square numbers in two distinct ways: 50 = 12 + 72 and 50 = 52 + 52. … I’m a teacher I have to ask: “So what’s the next bigger number to 50 that is the sum of two non-zero square numbers in two distinct ways?” …
There is always something to investigate in math. One of the major objectives of school math is to get students into this thinking habit without us telling them to do so but I’m digressing from my topic now.
Let’s get to the great posts submitted for this edition.
How to Count Infinity via Minute Physics
Tell Me a (Math) Story
[Feature photo above by Keoni Cabral via Flickr (CC BY 2.0).]
My favorite playful math lessons rely on adult/child conversation — a proven method for increasing a child’s reasoning skills. What better way could there be to do math than snuggled up on a couch with your little one, or side by side at the sink while your middle-school student helps you wash the dishes, or passing the time on a car ride into town?
As soon as your little ones can count past five, start giving them simple, oral story problems to solve: “If you have a cookie and I give you two more cookies, how many cookies will you have then?”
The fastest way to a young child’s mind is through the taste buds. Children can easily visualize their favorite foods, so we use mainly edible stories at first. Then we expand our range, adding stories about other familiar things: toys, pets, trains.
Quotable: The Art of Teaching
Most remarks made by children consist of correct ideas very badly expressed. A good teacher will be very wary of saying ‘No, that’s wrong.’ Rather, he will try to discover the correct idea behind the inadequate expression. This is one of the most important principles in the whole of the art of teaching.
Thinking (and Teaching) like a Mathematician
Most people think that mathematics means working with numbers and that being “good at math” means being able to do (only slower) what any $10 calculator can do. But then, most people think all sorts of silly things, right? That’s what makes “man on the street” interviews so funny.
Numbers are definitely part of math — but only part, and not even the biggest part. And being “good at math” means much more than being able to work with numbers. It means making connections, thinking creatively, seeing familiar things in new ways, asking “Why?” and “What if?” and “Are you sure?”
It means trying something and being willing to fail, then going back and trying something else. Even if your first try succeeded — or maybe, especially if your first try succeeded. Just knowing one way to do something is not, for a mathematician, the same as understanding that something. But the more different ways you know to figure it out, the closer you are to understanding it.
Mathematics is not just memorizing and following rules. If we want to teach real mathematics, we teachers need to learn to think like mathematicians. We need to see math as a mental game, playing with ideas. James Tanton explains:
Continue reading Thinking (and Teaching) like a Mathematician
A Bit of Arithmetic Fun
Singing Banana (James Grime) recorded this video at the Mathematical Association annual conference dinner, 2011. I’ve shared it before, but that was over a holiday weekend, so many of you may have missed it. It relates, in a way, to our PUFM lesson this week.
Enjoy!
PUFM 1.2 Place Value
Photo by Chrissy Johnson1 via flickr. In this Homeschooling Math with Profound Understanding (PUFM) Series, we are studying Elementary Mathematics for Teachers and applying its lessons to home education.
Our decimal system of recording numbers is ingenious. Once learned, it is a simple, versatile, and efficient way of writing numbers. … But the system is not obvious nor easily learned. The use of place value is subtle, and mastering it is the single most challenging aspect of elementary school mathematics.
Ironically, these challenges are largely invisible to untrained parents and teachers — place value is so ingrained in adults’ minds that it is difficult to appreciate how important it is and how hard it is to learn.
— Thomas H. Parker & Scott J. Baldridge
Elementary Mathematics for Teachers
In other words, we take place value for granted. I know this was true of me when I started teaching my kids. Every year, their textbooks would start with the obligatory chapters on place value, which seemed to me just busywork. I began to appreciate the vital importance of place value when I read Liping Ma’s book and saw how the American teachers were unable to properly explain subtraction or multi-digit multiplication.
Place value is the heart of our number system, the foundation on which all the rest of arithmetic must be built. Because of place value, “The simplest schoolboy is now familiar with facts for which Archimedes would have sacrificed his life.”
PUFM 1.1 Counting
Photo by Iain Watson via flickr. In this Homeschooling Math with Profound Understanding (PUFM) Series, we are studying Elementary Mathematics for Teachers and applying its lessons to home education.
Many things in mathematics need to be understood relationally — that is, in relationship to other concepts. But some things just need to be memorized. How do you know which is which? A homeschooling friend pointed out that one thing children definitely need to memorize is the counting sequence from 1-100 and beyond. While there are some patterns that make counting easier, one does just have to memorize which “nonsense sounds” we have attached to each number.
Another sort-of counting that young students should master is subitizing — recognizing at a glance how many items are in a small group. Children do this instinctively, but we can help them develop the skill by playing subitizing games.
[Aside: In writing this blog post, I ran into some nostalgia. Back when we first did these PUFM lessons, my daughter Kitten was only a toddler. I wrote, “I’ve tried to do lots of counting with my youngest, who hasn’t quite gotten beyond, ‘…eleven, twelve, firteen, firteen, nineteen, seven,…’ The numbers tend to start appearing randomly after she gets past 10.” Ah, memories.]
Denise Gaskins' Let's Play Math 