# Hanging on to Clothesline Math

By: Mary Kienstra on: January 18, 2017  in: Engagement, percent, proportional thinknig

Most concepts are just more easily understood when they are made more concrete.  Clothesline math is the concrete representation of percents that helps students understand.  As my students shared their thinking during one of our clothesline math lessons, I wondered why it took me so long to try this.  Now my students are hanging on to clothesline math.

I was inspired to try clothesline math by two different posts from bloggers that I follow.

Once I saw these ideas, I started thinking about this kind of proportional thinking and how I could use it to help my students.  A double number line or double tab as one text book names it supports that thinking, making it easier to explain and understand.

So when it was time to teach percents, the clothesline was the answer.  I created my clothesline on a portable bulletin board.  It is not too big, but is easy to move around.  Actually, it’s just right for my class.

The first lesson that I used was right from our text.  The question was:  What is 25% of 80?  Most of my students could do that one without the clothesline, but I wanted them to see how the clothesline works.

That led to a series of questions (right from the book) using the clothesline as the concrete model.  My students understood the clothesline easily and were using all kinds of flexible thinking to discover the answers.

I heard conversations that included:

• I know 1% so I can take that times 25 to get 25%
• I know 10% so I can find 5% and then 2 x 10% + 5% will give me 25%
• If I know 50% then I can find 25%

We advanced from there to problems like this:  If 35 is 20%, what is 100%?  These typically are the most difficult problems for 5th graders, but using the clothesline, they could see it right away.

The best news of all is that my students continue to apply this strategy to new problems.

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