Using Benchmarks

My third grade students have been exploring how to convert decimals, fractions and percents this week.  Many students are beginning to feel comfortable converting fractions to decimals.  Some problems are starting to arise when converting a decimal to a percent.  I’d estimate that around 50% of the students come in with prior knowledge of “move the decimal two to the right” technique.   This can be challenging because students might not exactly move the decimal the correct amount and have problems when the percent is less than 1%.  So this week I spent a good amount of time looking at different strategies to convert fractions and decimals to percents.

Later in the week students started to find discounts.  They were asked to find the percent discount of items on Amazon.  I used this activity but added additional scaffolding for a third grade group.  Students first tackled a few discount problems in groups before I gave them an individual project.  Students seemed to have a decent grasp of how to take a discount amount and find the percent off.  Students used calculators to find the percent off.  Some of the students were able to check their work to ensure that their discount was correct.  Other students seemed to come up with  a percent by dividing numbers in their calculator.  When pressed, the students were confident that their answer was correct.  They thought that the procedure was correct, therefore the answer was correct.  This is where I found myself looking at student answers that weren’t reasonable.  For example, a student wrote that 15% off of $120 was $8.  This student was adamant that it was $8 and then proceeded to tell me that he divided to find the answer.  I soon found that he actually completed 120/15 to get 8.  I started to notice that other students were having similar issues.  I asked students to turn in their work as it was the end of class.

That night I reviewed the student answers.  Around a third of the students were coming up with solutions that weren’t reasonable. I decided that the class was going to discuss benchmarks and the reasonable of their answers.

So the next day the class had a conversation about the reasonableness of some of their answers.  After some reflection, it was become ever-increasingly evident that students were relying much more on the procedure, rather than checking whether their answer was reasonable.  The class discussed how benchmarks could be used to help determine whether their answer was in the correct ballpark.  We discussed how fraction benchmarks can help us create estimates.  Students connected this to how they multiply and divide numbers with decimals.  They estimate first, use an algorithm to find a solution and then check to see if their solution is similar to the estimate.  The class co-created an anchor chart that looked similar to the image below.

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I asked the students to recheck their assignments.  Students changed up their answers and placed estimates next to them.  I used the 15% off of 120 for the example.   I modeled a few different examples and students practiced similar problems.

 

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All students put an estimate next to their answers while some changed their actual answers.  For the most part students moved beyond the idea of just using the procedure and keystrokes on a calculator to checking their solutions using benchmarks.  Having this small step beforehand seemed to help students identify whether their answer was actually reasonable or not.

Exploring Discounts and Amazon Prices

Exploring Discounts, Percentages and Amazon
Exploring Discounts, Percentages, and Amazon

Today one of my classes explored discounts and percentages.  This particular class reviewed how to convert fractions and decimals yesterday.  Today’s step was to introduce students to the idea of taking a percentage off of a set number.

So I dug through some of my resource from the past and came across a sheet asking students to go on a shopping spree.  Yes, that caught my attention.  A shopping spree not only sounds fun but could be a great way to connect discounts and percentages.  From there I edited the document and decided that the students will be given a specific amount of money to spend and a site to visit to find the items.  Amazon.com wasn’t blocked by my school district so I went with that store.  Students were also required to use coupons (10%, 20%, 25% …) to purchase the items.  The winner of the contest will be the student that has a sum closest to $500.

Click for file
Click for file

Students could buy whatever items they wanted.  I’m sure this could be repurposed and have the students buy items for a specific reason.  After I explained the directions each student was given an iPad or computer and asked to visit Amazon.com and find five items.

Students initially started looking at whatever caught their interests.

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Some students looked at shoes while others were finding flying drones.  Yes … I said drones. Thankfully all the searches came up without being blocked by the firewall.  Students then found the original price and calculated the discount.  Their sale price was documented and students went to the next item.

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I found that students started to have a challenging time with the last couple of items.  They had to carefully consider the coupon before writing down their options.  You could tell that they were trying to account for the discount. Understanding the magnitude of the discount started to take priority in the students’ minds.

Not all the students finished, but they will tomorrow.  I’m looking forward to comparing the total dollar amounts tomorrow and see who’s closest to $500.  Overall, this activity helped students see discounts from a different perspective.  This may be an activity that I’d like to edit and use with my other classes.


The idea in this post was adapted from this product.  Feel free to download and use for your own classroom.