Tape diagrams, Bar models, tomato, toMAHto

Just this morning I found myself down the rabbit hole that is Twitter when I stumbled across this Twitter post…

BARVEMBER? What the heck is that?!?!? What does that curious word have to do with llamas and alpacas and math? (Or perhaps maths.)

Scrolling down the thread, I quickly learned that White Rose Maths was spending November to celebrate problem-solving with bar models. Immediately I was hooked.

I must confess, however, that upon my first reading of the Llamas and Alpacas problem my first thought was of some sort of Venn diagram. That may have worked, but I decided to try solving this problem using a bar model. For my first attempt I drew two bars of equal length, shaded the units to indicate what was sold, but then immediately found myself cheating! Well…not exactly cheating…I had switched from using the bar model in favor of using a system of equations.

This would have worked, but it wouldn’t have REALLY been using bar models in the spirit of BARVEMBER. After many some productive struggle and lots of false startsI finally found a solution method that fully used bar models, some logic, and simple arithmetic. This is the solution method I was striving for!

Here is my work, tidied up for public consumption…

So, why am I writing this post? Three reasons.

  1. I wanted remind all math teachers that it is our JOB (and hopefully our PASSION) to do math recreationally. Every once in a while we should do math for no other reason than because it is fun and we love it. This is how we become better mathematicians, better problem solvers, and better teachers. (Imagine a music teacher who never played music for fun. Silly, right?)
  2. A reminder of the power of the bar model! (Or tape diagram…or whatever you want to call it.) I’ve met many teachers who hate bar models and fail to see their importance. Even in my “failed” first attempt, the bar model made it easy for me to SEE a system of equations that could have led me to the solution. Bar models allow mathematicians to display their thinking on paper that then creates space for the solution method to pop out! If you want more practice with bar models, try this wonderful site!
  3. I suggest you follow White Rose Maths.  






  1. I came here because I am trying to figure out how bar models are useful for my son who in learning maths. Unfortunately you’ve reinforced my notion that bar models aren’t useful by solving for the wrong problem (I.e. the number of llamas that AREN’T sold at market) ☹️