# Math

### 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

### One Object Three Shapes: The Solution

In an earlier post, One Object Three Shapes, we posed the problem of finding an object that would appear to be a triangle when viewed in one way, a square when viewed in another way, and a circle when viewed in yet a third way. The challenge was to create an object that would fit… Continue Reading

### What’s the Difference?

I was helping my daughter, who is in kindergarten, with her homework. She claimed the homework was too hard. She was working on subtraction in her class and the instructions for her homework were: FIND THE DIFFERENCE. I thought to myself, does she even understand subtraction as a comparison situation? Was that the thinking her… Continue Reading

### Five Squares, One Square

A while back I posted a five triangle puzzle that involved putting together five 30-60-90 triangles to form a single triangle. Of all of the dozens of puzzles that I own and have made over the years, that is one of my favorites because of the opportunities it provides for students to think about important… Continue Reading

### Decomposing Numbers with Kindergarteners Part Two

In my last post, I talked about the connection between decomposing numbers and place value. Understanding how numbers can be decomposed into parts lays the foundation for breaking apart numbers into specific groups. These specific groups could be anything, but for our numeration system they will be ten. You may want to check out the… Continue Reading

### The Five Triangle Puzzle: Solutions

The Five Triangle Puzzle was the subject of a post back on February 11. I’m hopeful that some of you will have downloaded the pieces and solved the puzzle. The challenge was to put all five pieces together to form a triangle and then to determine if there were other triangles that could be formed… Continue Reading

### Decomposing Numbers with Kindergarteners Part One

Field Testing Experience During my recent field-testing in Kindergarten, students worked with different pictures of teddy bear counters and with five frames. I would give the students a picture and they would build the picture in their five frame, then fill in their sentence frames and read them. They did a great job! They were… Continue Reading

### One Object Three Shapes: Circle Square Triangle

Front and back, top and bottom, and left and right are ideas that we use to describe objects in our three-dimensional world. Young children learn these positional words in Kindergarten. In fact, learning the meaning of these words is one of the Common Core Kindergarten geometry standards. In reality these are big ideas that are… Continue Reading

### Month, Day, Year: A Number Sequence

Daily journaling is one of the constants in my life. Over many years, I don’t believe there has been a single day when I did not make at least half a dozen entries in my journal. Each entry is dated, so on any given day I will write the date at least half a dozen… Continue Reading

### Using Sentence Frames to Talk about Math

As I talked about in my earlier posts, I am really interested in learning about the Japanese methods of teaching math concepts. As I was exploring a 1st grade Japanese textbook that Phil Daro recommended, I noticed something I wanted to field test. The textbook had the students placing counters on top of the pictures… Continue Reading