We’ve been working on solving percent problems for a while now. The concept of identifying percent of a number was introduced using a double Numberline similar to what is shown below.

I’ll admit, when I was in grade school I recall solving percents by cross multiplying. But as with most procedures, I didn’t understand how that strategy connected to the concept of percentage. I just knew the steps to follow to get the correct answer. Fast forward to me implementing a percentage lesson with my students, I was determined to make sure students understood the meaning of percent and applied it to finding the percent of a number. My initial thought was the double number line would be perfect for this.

Using a lesson from Lessons & Activities for Building Powerful Numeracy, students were introduced to modeling part of a whole using the bar model.

(Side note: This post was accidentally updated to an older version. I will try to catch the essence of the published post.)

Students struggled making the sense of the bar model, so we looked at it as a double number line.

This version helped some students but there were some who still had trouble visualizing it. For those students, strip models were introduced.

Percentage Strip Models

Students were given a strip of paper. One side represented 100%. It was split into 10 equal parts making each part 10%. Students were able to see the 10% + 10% that the 20% hash mark represented. The same strip was flipped over and another quantity represented. Students could use the percentage side to find say 30% and flip the strip to determine the equivalent amount to 30% of the whole.

After this, the concept clicked for those who were once confused. And beautiful things like these started to happen:

Young lady torn paper from her notebook to make strip

Random strips left behind after class

There was even a student who torn their scratch paper during our common assessment to make a strip model.

Of course this wasn’t the only strategy discussed. Others came from the unit work, Getting Percentible from nzmaths. I wanted to take a amount to emphasize the beauty in seeing.

*Sorry this version is not as well written as the original. Realizing I had accidentally updated an older draft (using the app on two different devices) really took the wind out of my sail. *

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This is wicked good stuff Jenise! I love the way you’re conceptually building students’ understanding here. Percentages are easy to teach using a procedural approach which leaves students nothing when they walk out of the class. Thanks for making learning sustainable and us all a little smarter!

The young lady who made a model from torn paper…..priceless!