# K-2

### Tangram Polygons: Composing and Decomposing

In my last post, *Tangrams: A World of Geometry, Part Two*, I talked about the thirteen convex polygon shapes that can be formed with the seven tangram pieces. In the video, I showed how to make five of them, and then I left a challenge for you to look for the remaining eight convex shapes. By way of encouragement, I provided downloads of two of the eight shapes, but left it to you to put the puzzle pieces together to form these two shapes.

In the following video, I review putting together the five shapes. You’ll see that I’ve made the tangram pieces in two different colors. I think it makes it easier to notice patterns and relationships between the shapes and the way the pieces go together to form the shapes.

Now we’ve reviewed putting the five shapes together, and you’ve seen how the colors help us think about the different ways the pieces can be put together. The next video will start by showing those two shapes for which I provided you with downloads in my previous post. Then we follow that up with finding the remaining six shapes. For some of these shapes, there may be multiple ways they can be put together. I don’t claim to have exhausted all of those ways.

Below are several attachments that you can download. The first shows all of the convex polygon shapes that are possible; the second shows one way to put the pieces together to form each shape. Then, there are three pages that have templates for all 13 of the shapes, and finally there are two pages of multiple copies of the tangram pieces in case you want to run them off on two different colors of cardstock.

It is my hope that many of you will find ways to use the tangrams as way to challenge students to look at composing and decomposing shapes. Each of these quadrilaterals, pentagons, and hexagons are composed of the same pieces and so have the same area.

For students in seventh and eighth grade it might be interesting to look at the perimeters of these thirteen shapes. If we took a side of the square tangram piece as the unit of length measure, what would be the lengths of the sides of each of the pieces? Then we could ask about the perimeters of each of the shapes.

Well, maybe that will be a future post.

### Partitioning Shapes: Is it Geometry or Fractions?

How early should we teach words like half, thirds, and fourths to children? I know that I have often heard that we give young children things they are not developmentally ready for, and I agree. But when it comes to having language identify a concrete experience, I think children can handle it. I was measuring… Continue Reading

### Three Great Multiplication Posts

How to Equip Your Students to Better Understand Multiplication, Part One As I have coached and taught in the classroom, the three most popular ways to describe multiplication is showing ______ groups of ______, using repeated addition and making arrays. Now all of these methods have their place in a student’s understanding of multiplication, but… Continue Reading

### Finding Math in Unexpected Places

I was reading Inchworm and a Half with my 6-year-old daughter, Bethany, last night for the 40th time. She loves reading the section, “Squirmy, wormy, hoppity-hoop! We measure everything, loopity loop.” Even before she could read books she memorized this section and would “read” it. The book is about an inchworm that loves to measure… Continue Reading

### Do We Really Understand What Math Is?

What would you or your students say math is? Some common answers could be numbers, addition, subtraction . . . Below are the posters a group of AIMS trainers created answering that question. Most people don’t understand what math really is. If you have read some of my previous posts, you know my elementary and… Continue Reading

### How to Equip Your Students to Better Understand Multiplication, Part Three

I never liked word problems as a student. It was difficult for me to figure out which procedure to use, but I really didn’t like problems like this: Robert is three times as old as his younger brother Mark. Mark is 7 years old. How old is Robert? As I reflect on my experience, I… Continue Reading

### How to Equip Your Students to Better Understand Multiplication, Part Two

Using arrays has become much more prominent in the classroom. At first glance arrays seem very straightforward and simple for students. But what are the connections that are essential for students to build understanding of the concept of multiplication through arrays? Arrays are a model of multiplication. Just because your students can build an array… Continue Reading

### Friday Institute: A Common Core Resource

I want to share with you two very helpful, quite extensive Common Core Math resources that are available from the Friday Institute for Educational Innovation at North Carolina State University. The first resource is an interactive map of all of the Common Core Content Standards organized into 18 learning trajectories or progressions http://www.turnonccmath.net/index.php?p=map. For example,… Continue Reading

### How to Equip Your Students to Better Understand Multiplication, Part One

As I have coached and taught in the classroom, the three most popular ways to describe multiplication is showing ______ groups of ______, using repeated addition and making arrays. Now all of these methods have their place in a student’s understanding of multiplication, but if these methods are all they know, their understanding is limited.… Continue Reading

### Making Word Problems More Engaging, Part Three

This is my last post in the series; Making Word Problems More Engaging. Creating analogies for students to understand addition and subtraction is important. Whether you use Trevon, Bobby, Jada, and Maya, or come up with your own characters is not important. What is important is giving students a complete conceptual understanding of addition and subtraction.… Continue Reading