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.
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:
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. *