Tag Archives: Math Puzzles

Have You Done a Good Math Problem Lately?

In work or social settings it is common to hear the question, “Have you read a good book lately?” The question often starts a lively sharing session about books that elicit pleasure, profundity, or insight. A population that regularly engages in these discussions is an indicator of a literate society.

As those appointed by society to help children become literate, educators accept a priori that reading is important. They do their best to provide students with the requisite skills that enable students to read. However, good reading instruction goes beyond basic skills and seeks to inculcate a love of great books and a passion for reading. The hope is that students will choose to read voluntarily, “just for the fun of it.”

It is safe to say that few people have heard the question that is the title of this blog in a work or social setting—unless they work at AIMS. Any statement that includes both the terms “good” and “math problem” is an oxymoron to most literate people who view math as important and utilitarian, but not enjoyable. Unfortunately this is also true of most educators who can readily share a favorite book, but would be hard pressed to come up with a favorite math problem. Those who relish good math problems as much as good books are part of a very small, but important, minority. They realize that math has more than just utilitarian value—it is also a subject that can be enjoyable, and they want to foster this positive attitude in their students so that they might do math voluntarily “just for the fun of it.”

With the new Common Core State Standards for Mathematical Practice informing math teaching, there is an incentive for introducing students to good math problems or tasks. The first of these standards challenges students to make sense of problems and persevere in solving them. This is easier to do with fun problems. AIMS has a number of problem-solving books full of these types of problems (Problem Solving: Just for the Fun of It!, Problem Solving Just for the Fun of It! Book Two, and the Solve It series).

To get teachers started, this week’s blog puzzle is “Total Count-Ability.” This is a great problem that can be solved in at least five valid ways depending on the assumptions you make. Last week’s puzzle was “Cab Conundrums,” which is another good and hopefully enjoyable math problem. Try one or both of these problems out so you can reply in the affirmative when asked “Have you done a good math problem lately?”

The Problem of Anwar’s Camels

I just started reading Fractions in Realistic Mathematics Education by Leen Streefland, and there, on page 5, Streefland gives as an example an old puzzle problem that I remember giving my students more than 40 years ago. “An old Arab, Anwar his name, decreed before he died that his eldest son inherit one-half, his second… 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

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

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

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

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

The Five Triangle Puzzle: Composing and Decomposing

Beginning in first grade and continuing through the grades, the Common Core Math Standards emphasize composing and decomposing shapes. One way to give students experience with composing shapes is through put-together puzzles. Actually, working at put-together puzzles involves lots of composing and decomposing. Sometimes what we compose is a solution; sometimes it’s not. While the… Continue Reading