Clothesline Math

November 11, 2016 (posted April 28, 2017<---oops)

Last weekend I had the amazing opportunity to attend CMC South. It was invigorating! Not only did meet many illustrious educators, I got to hear them speak about their passions, successes, and failures during their journey.

Many sessions mentioned number talks, one of which by Dan Luevanos (@danluevanos) from San Diego, CA. He gave several awesome secondary examples of number talks using clothesline math.


Essentially, it is an interactive double number line. He challenged us to decide if we had a true conceptual understanding of concepts such as systems of equations using elimination, distributive property, and sale price.

Obviously I do....right?

This picture is an example of solving systems of equations by elimination. No calculations, no writing.

Mind blown!


Anyway, I needed to try this out ASAP. The opportunity presented itself today at a principal's meeting. We were trying to give our principal's an example of number sense in a secondary classroom as well as the power of discourse in mathematics classrooms. 

Example: Sale Price  
For the official lesson, stolen from Dan Luevanos :) visit http://bit.ly/2ffzq2V .

I started with a basic idea: "I buy a shirt". Then I put the units on the clothesline. Top: $, Bottom: %. 
I then showed them 3 cards:
            Sale Price
            Savings 
            Original Price
                                                 
                                       and asked..."Where would you put these"?

This brought out that full price was 100% (for which I had a card and added to the clothesline). 

Here's the fun part: 
"Where would you put Sale Price and Savings?"

-"There's no numbers!"
-"How much is the discount?"

What we want them to decide is that the sale price will be the same distance from one end as the discount is from the other. 

Advancing question: When would they be the same? 


Slowly you add information to the problem so it can be processed conceptually rather than with algorithms. 

After each additional piece of information, we show it on the number line. 



Here, most people can derive the answer "in their head". The magic is having them explain HOW. Many think they calculate with the algorithm. In fact, most people reduce down to the unit value (10% of 40 is 4) then iterate (repeated addition, etc.) up. 



Once we finished the discussion, we pointed out to the principal's how lively their discussion was and how engaged they were without ever handing them a worksheet. We challenged them to imagine a worksheet of percent problems that would engage students to have a conceptual understanding equivalent to this discussion.
It was impressive. 


Our picture isn't great because we were so carried away with the discussion, we forgot to document!

For more clothesline activities you can check out:

Chris Shore  www.clotheslinemath.com
Dan Luevanos https://mathrockstarsblog.wordpress.com
Andrew Stadel www.estimation180.com




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