# Author Archives: Richard Thiessen

### The Forty-Yard-Line is Opposite the Forty-Yard-Line?

One of the Common Core Standards for Mathematical Practice includes a focus on students knowing and using correct mathematical language and using clear definitions in discussions with others. There are times when everyday words are used in special ways in school mathematics, and it is important that students come to understand the precise mathematical meaning… Continue Reading

### How to Make Your Own O’Beirne’s Puzzle

Last week I showed you the O’Beirne puzzle and 30 of you very quickly responded to the offer of a free puzzle. I hope you’ve gotten it by now. In future posts I’ll explore with you some ways to use the puzzle to engage students with Common Core Standards for Mathematical Practice as well as… Continue Reading

### Further Explorations with O’Beirne’s Cube

This post is a quick follow-up to the one from last Monday in which I showed you the O’Beirne cube puzzle. After we finished filming for that post, we still had the six puzzles on the table and we got to talking about the sequence in which the puzzle comes apart and goes back together… Continue Reading

### O’Beirne’s Cube

This post is a bit of an experiment. First of all, I want to tell you about and show you a put-together-puzzle called O’Beirne’s cube. This is not just any puzzle. It is one of the most amazing, delightful, and elegant puzzles ever invented. There are people who know about things like this who rank… 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

### 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

### Five Squares, One Square: Solution

In two previous blog posts I talked about a puzzle made up of five two by two squares, where each square was cut in two along a line from a vertex to the midpoint of a side. The challenge, which I gave in the first post, was to put the ten pieces together to form… Continue Reading

### What Does Twice as Big Mean?

I’m often puzzled by the way we use phrases like twice as big. What does that mean? For example, I understand that if my debt 5 years ago was $10,000 and today it’s $20,000, then my debt is twice as big today as it was 5 years ago. I also understand that if one two-by-four… Continue Reading

### Taking Apart and Putting Together Cubes

In earlier posts I’ve mentioned Friedrich Froebel and his geometric gifts. The third of his geometric gifts was a box containing eight cubes. Instead of the students simply opening the lid and dumping the cubes on the table, he would have the students place the box with the lid down on the table, slide the… Continue Reading

### Five Squares, One Square: Some Hints and an Extension

In an earlier blog post I proposed a puzzle made of five 2 by 2 squares, each of which had been cut along a line from a corner to the midpoint of an opposite side so as to form a right triangle and a trapezoid with two right angles. The challenge of the puzzle was… Continue Reading