Look at the title. Did you guess that this was a description of an acute triangle?
This description was from a student in my third grade class. Let me assure you, this student knows how to recognize an acute triangle and how to draw one. But verbal descriptions are much trickier for them.
I believe that verbal descriptions are just as important for communicating math as they are in literature, history, science, etc. That is why we play games and do activities in my math class that practice precisely this skill.
The description in the title came about from one such game that we played. We had just finished a unit on shapes (mostly focused on polygons) where the students encountered a lot of new terminology about angles, triangles, quadrilaterals, and other polygons.
I gathered all of the terms and wrote each one on its own slip of paper. The papers were then all placed into a “hat” (this can be a box, a bag, an actual hat, or anything that can store the papers and the students can reach into without seeing the words on the slips).
Play proceeds as follows: two students are called to the front, one to be the “explainer” and one the “guesser” (I made up a schedule so that all the students had an equal number of opportunities to play both roles and so that everyone had a chance to explain to everyone else). One minute is put on the clock (we tried 30 seconds at first, but that didn’t seem to be sufficient).
When the moderator says “go”, the explainer takes out a piece of paper from the hat at random and attempts to explain the word to the guesser. The rule is that you can’t use any word or part of word that is written on the paper (so if the term is “right angle” or “triangle” you can’t use the word “angle” in your explanation).
When a word is guessed, the explainer takes out another word and goes on to explain that one. The explainer continues to take out new slips and explain the words until the time runs out.
If the explainer gets stuck on a word (either because they don’t know what it means, they don’t know how to explain it, or the guesser is just not getting it), they can put it aside and take another one. The rule, though, is that you can do that with only one word per turn (later I thought that perhaps allowing to put aside 2 or 3 would have worked better).
The first few rounds that we played, no words were guessed. This was mostly due to descriptions being like the one in the title and the students still getting a feel for the game.
But soon the students started feeling a little more comfortable with what they were doing and putting a bit more thought into their explanations. Here is what some of the early ones to be guessed sounded like:
“They can be of different types. A rectangle can be one, a square can be one, and there are many others of these. Well, you know, with 4 sides.”
Up until the explainer mentioned the 4 sides, the guesser looked very confused, but as soon as the 4 sides were mentioned, the word quadrilateral was said immediately.
Often, concepts were described by what they are not. For example, “acute angle” was described as “it is not obtuse or right.” Or “rectangle” might be described as “it is not a square but a…”
But overall, the descriptions got more precise as the game went on. Some of my favorites were, “It is the shape of a stop sign” (octagon), “It is both a rhombus and a rectangle” (square), “It is a stupid shape with three sides” (obtuse triangle).
What sort of games and activities do you do with your students to practice communicating mathematics?