Welcome to ... The Price is Right

Good morning, readers! Currently our eighth grade class is working on estimating the value of non-perfect square roots and placing them on a number line.  This is a difficult concept for many of our students as we are introducing them to the idea of irrational numbers. Additionally, many students have the misconception that the square root means "divide by two." 

To help with this, we play a game based on a VERY popular game show - The Price is Right. 

Here is how we play.  Students are given an imperfect square (such as 40) and asked to estimate the square root.  We have a double-number line tool card which was developed by a teacher at my school to help students visualize where they are on the integer number line. Using this card, they identify the two perfect squares that the imperfect square is between. They then decide which perfect square is closer to the imperfect square.  The initial goal is for them to identify if the imperfect square is larger or smaller than the half mark.

For example, if they had the square root of 40, students would identify the square root of 36 and 49, decide that they are closer to the square root of 36, which means the value is larger than 6 but less than 6.5.  We would get estimates that range from 6.1 to 6.4. 

Once we have done a few practice problems, the game begins!

I randomly call four students to the front with their tool cards. I play the music as they 'come on down' and then display the 'fabulous new prize'

It is the BEAUTIFUL square root of 10!

The four contestants then start their work while the 'studio audience' (other students) do as well. After 90 seconds or so, I have the students in the audience start calling out bids, much like the actual game show. Contestants up front can listen to the suggestions or stick with their answer. 

Each contestant shares their answer with me and I write their estimate on the board.  I then reveal the correct answer, usually to three decimal points.  Students then have to decide who is the winner - the person that is closest without going over. 

We do this for a number of rounds and the winner of each round gets to go into the showcase showdown at the end of class.  This determines our daily winner.

It is amazing how good students get at estimating values. At first they start with one decimal point but after some time, practice, and friendly competition, they start going out to two and three decimal points. 

This strategy and game has really increased our students accuracy as well as confidence. They never use a calculator during the entire lesson and are able to estimate the square root of imperfect squares with amazing precision!  The results of the final round are below: 

After the game, we do return back to the learning target - estimating the square root of non-perfect squares. It is important to return to this, because student "H" in the image above didn't win as they had an answer that was 'over', but all four answers met the target of the lesson.  It was a good day!