Symbol sense is an essential part of mathematical literacy. It is the understanding that undergirds effective symbol manipulation, and perhaps more basically the ability to interpret and create algebraic expressions. Symbol sense, like number sense and operation sense, is not learned so much through listening to a teacher. Rather, it grows as one gets practice… Continue reading Reading Algebra

# Tag: Manipulatives

## Big Dodecagon

A classic activity is to cover a 1-inch-side dodecagon with pattern blocks. This provides a great context to discuss symmetry (see Geometry Labs 5.6.) Here is one way to do it:See many others, found by Simon Gregg's students.In the past few days, I've had fun making a double-size, quadruple-area dodecagon: You too, and… Continue reading Big Dodecagon

## Eclectic

In between June 27 and August 4, 2016, I presented seven to ten workshops (depending on how you count) ranging from a couple of hours to four days. I share most of the handouts, resources, and slides on my Summer Workshops site. (See below my signature for more details on what's there.)The site will remain… Continue reading Eclectic

## Fractions

I have a new Fractions mini-home page, with links to three pages on my site. In this post, I'll use it as an excuse to discuss some general ideas about teaching.Visual RepresentationsIn my Fraction Arithmetic page, I present a visual strategy for figuring out how to add, subtract, and multiply fractions. (There is also a… Continue reading Fractions

## Hoping to see you soon!

Here is a list of my upcoming appearances, ranging from 20 minutes to a full week. Perhaps you can attend one of them!NCTM National Meeting in San FranciscoA Hands-on Approach to Operations and Equivalent Expressions Thursday 14 April, 8:00-9:15am. 3022 Moscone WestThis is a hands-on Lab Gear workshop aimed at grades 6 to 8. The… Continue reading Hoping to see you soon!

## Visual Algebra

I will be teaching two instances of my Visual Algebra workshop this summer: grades 7-11, June 27-30, in Oakland; and grades 6-9, July 25-27, in Saint Louis. (More info). This is probably the topic I have presented the most often in the last 25 years.To many students, not to mention teachers, parents, and administrators, algebra… Continue reading Visual Algebra

## Animated Demonstrations

New on my Web site:→ Animated slides on the Lab Gear model for signed number arithmetic.Note that for each operation, the model is based on what students already know. For addition, you put down the first number, then the second number, and finally count. For subtraction, you put down the first number, take away the… Continue reading Animated Demonstrations

## New Lab Gear Books

As I announced in the November issue of my newsletter, the new Lab Gear books are out, and can be ordered from Didax: Algebra Lab Gear: Basic Algebra, and Algebra Lab Gear: Algebra 1.The Lab Gear is a comprehensive manipulative environment I created for the teaching and learning of algebra. I devote a fair amount… Continue reading New Lab Gear Books

## Northern California December Events

I suspect that some readers of this blog do not subscribe to my newsletter, so I will use this post and the next to let you know about some news in my math education life. If you did get the November issue of the newsletter, you might read on anyway, as I will be going… Continue reading Northern California December Events

## Geoboard Triangles

One way to discover or apply the formula for the area of a triangle is to explore area on the geoboard. The initial activities should be along the lines suggested in my Geometry Labs Lab 8.4. (Free download.)After that, one can zero in on triangles, by asking a question like: "Find triangles of area 15."… Continue reading Geoboard Triangles