Tag Archives: Math

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.

ConvexPolygon  Pieces  Templates

Click here for “Tangrams: A World of Geometry, Part One”.

Click here for “Tangrams: A World of Geometry, Part Two”.

Three Great Multiplication Posts

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

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

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

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

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

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

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

Do Comics Have a Place in Your Classroom?

One feature of the AIMS Essential Math Units, a series that is targeted for middle school, is the inclusion of comics as a way to show students engaged with some of the activities in a unit. Our hope for the comics was that they would help to make explicit the content knowledge that is the… Continue Reading

Making Word Problems More Engaging, Part Two

Making Word Problems More Engaging, Part Two

Dinnertime is a place stories are told at my house. One of my favorite storytellers is my husband Matt. When he tells a story, you feel like you are there. Stories are memorable, they can take us to another world, and for mathematics, stories bring context to the abstract. Our world is full of exciting… Continue Reading

Making Word Problems More Engaging, Part One

Making Word Problems More Engaging, Part One

As I watched my daughter Bethany do her homework last night I had an Aha Moment. She complains almost every day that she has addition and subtraction homework. Apparently, she does not have her mother’s love of math. (I’m working on that.) Her paper had simple numeric addition and subtraction, and she decided that she… Continue Reading

Teaching Addition and Subtraction, Part Three

Teaching Addition and Subtraction, Part Three

This blog post will be the final in a three-part series on teaching addition and subtraction. Part One talks about the Change Plus/Change Minus, and Part Two talks about Composing/Decomposing. Our last situation is Comparison. After reading Mathematics Learning in Early Childhood, I realized how foundational comparing relations (talking about two sets being more than,… Continue Reading