Data Landmarks and Spreadsheets

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My fourth grade class reviewed data landmarks this week.  On Monday the class explored examples of the maximum, minimum, median, mean and mode.  I had to review the terms multiple times throughout all of Monday.  Kids kept on asking about the difference between median and mean.  During this process I was finding that students needed additional practice with the terms.  They seemed to need another way to remember the difference between the data landmarks.  After contemplating a few different review lessons I decided to check out my school’s laptops.  I vaguely remember reading about a teacher that used spreadsheets to reinforce math terms.  I decided to go that route for Tuesday.

So Tuesday arrived and students received their laptops.  I modeled the different components of Excel.  This took more time than I thought it would.  I reviewed the idea of a cell and the components of a spreadsheet.  During this time I had a lot of hands fly up in the air with questions.  The questions revolved around how to change the column/row size, what a cell is, where’s the formula bar and many others.  To get the ball rolling I had the students take some personal data and use it for this project.  The class formatted the spreadsheet and we were about ready to start putting in formulas and then … class ended.

We started back up on Wednesday and began the lesson by explaining how to use formulas in Excel.  I modeled the first formula of how to find the maximum of the data set =maximum(b2:b14).  Students followed the example with their own data.  We then moved on to minimum, which they easily constructed.  Median and mean were a bit more challenging but the students explored and found the formulas using the first example. The magic started when students were asked to manipulate the data in the non-formula cells.  Students started to observe how the data landmarks change when the data changes.  This sparked a classroom conversation on the difference between the mean and median and which indicator might represent the data better.

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Afterwards, students were able to print out their creation and take it home.  The class will be discussing this in more detail next week.

 

Using Excel to Explore Rates and Proportions


My fifth graders are currently studying rates and proportions. Earlier in the week they explored rates by looking at unit prices and solving problems with some type of cross-multiplication strategy.  Although they’ve made progress I still feel as some many still need to cement their understanding of a ratio and proportion. So it was time to switch up the instruction model.

I decided to go with using a spreadsheet. In this case, the spreadsheet would be in the form of an Excel document. Each student grabbed a laptop and opened up Excel. The students used Excel earlier in the year so they were familiar with some of the basic functions.

After entering a few text cells, students were asked to put a random number above zero in cells B4 and C4. Then the class discussed what GCD stood for. Most of the students said “greatest common denominator.” That response made sense because that’s heavily emphasized in fourth grade as students add and subtract fractions. In this case, GCD means greatest common divisor. The class then discussed what that meant when comparing two numbers and the helpfulness in finding the GCD when exploring equivalent fractions. The discussion then transitioned from equivalent fractions to finding ratios.

Students entered in the formula =GCD(b4,c4) to find the GCD of the two different numbers. Students observed how the GCD changed as they updated their numbers.

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The next part was a bit tricky. I asked the students to write a formula to express the ratio in simplest form. The class used the GCD and trial and error to come up with the ratio formula. Once students wrote the formula and placed it in E4.  Students then explored how the ratio changed when their numbers were updated.

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The class then reviewed why the formula actually worked.  The class discussed that basically the formula took each number and divided it by the GCD of both numbers. What was great was that students were starting to connect the reasoning behind the creation of a ratio. Instead of just cross-multiplying, students are starting to show a deeper understanding of how ratios are constructed and the process used to simplify. The students were able to save and print out their spreadsheets for later review.

Resources:

Excel Template

Example for Class Use