## How long is a foot?

The first topic of today’s lesson was again measurement, and it began with a story.  The story was taken out of a large storybook that I had when I was little, and that has since been either misplaced or given away.  I bet some of you know it!  It takes place in a kingdom where everyone sleeps on the floor because there are no beds.  One day the king decides to give his queen a bed for her birthday.  But how does he tell his carpenter how big the bed has to be?  He decides to measure the queen with his feet while she is lying down.  He then tells his carpenter that the bed needs to be 5 feet long.  After working for a few days, the carpenter delivers a bed that is 5 feet long, but alas, it is too short for the queen!  In the actual story there is some back and forth with the king getting upset and having different people trying to make the bed (with a happy ending, of course) but our story ended here, at which point I asked the girls what they thought went wrong.

The girls almost immediately started chattering away “how can it be too short?” and “maybe the measurements were done incorrectly,” etc.  Some role play was needed.  We had Katie lie down and I measured her with my feet: 5 exactly!  Then Varya started measuring.  When she made 5 steps I told her to stop; she had covered about half of Katie.  At this point, Varya carefully suggested that perhaps the carpenters feet were not as big as the kings.  I told her that it was a very good explanation and asked Katie what she thought.  Katie was feeling somewhat disagreeable so she still insisted that the carpenter just made a mistake: always a possibility I guess.

To illustrate the point a bit more, I took out paper clips of two different sizes and had Varya measure one side of a table with the larger ones and Katie measure an identical side with the smaller ones.  Not surprisingly (at least to me!), Varya needed fewer paper clips than Katie (10 versus 18).  This time when I asked why this was the case Katie replied right away, saying that it was because hers were smaller.  I asked them how many of the smaller paper clips they thought they’d need to measure Varya’s side of the table.  “I think 18,” said Varya, not very confidently.  But Katie wanted to do the actual measurement, so I suggested they do it together, each laying out the paper clips from different sides.  Since they weren’t being super careful and leaving spaces, they were about to get only 17 on that side.  But I fixed things up quickly before they counted so that there were 18 after all.  I considered not doing that and making a point of having to be careful, but they were getting tired of the topic by this point and I was barely keeping their attention already.  It was time to move on to another topic…

Addendum: The story is called ‘How Long is a Foot?’ and here’s a link to it on amazon.