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Order of Operations via Computer-Based Math

25 Nov

Toward the end of our unit on rational numbers and rational number operations, my team worked to address standard 7.NS.3 “Solve real-world and mathematical problems involving the four operations with rational numbers.”  As I searched for problems that could be modeled via computer programs, I realized some of them also addressed standard 7.EE.2 “Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.””

I have been teaching my students JavaScript via Khan Academy as a way of teaching math.  Here is a list of some lessons I did on these two standards!

1.  Area and Perimeter.

First, a video on how to create and assign variables, and display text.
https://docs.google.com/a/psdschools.org/file/d/0B2H_6bIuJrltMjExNjNERmF0TDQ/edit

The students’ task: draw a rectangle and use formulas to calculate area and perimeter.
https://docs.google.com/a/psdschools.org/file/d/0B2H_6bIuJrltcVFROGw0RW9OVEk/edit

2.  The averaging problem.
As we got more into learning about order of operations, I thought about this idea as a way of modeling an “order of operations” problem on the computer.  I gave the students this program, put them into groups, and told them it did not look quite right.  I asked them to please troubleshoot it for me.
https://www.khanacademy.org/cs/problem-with-averaging/2374277154

order_of_ops_program

The broken “averaging” program. Click the link above to see the program, and you can look at the spin-offs to see some student solutions (many incorrect ones or “discussion starters” as I call them)

 

This activity was AWESOME.  Students noticed the bar for “119” was the same as the bar for “312” right away, and that was one of the errors.  Many of the students noticed that the average was not calculated right.  It’s an order of operations problem because my formula for the mean has no parentheses in it.  Students actually found multiple approaches to fix it, and this problem generated some great discussion.

3.  The Cricket Problem.

I posed this problem on the board: “Jennifer owns reptiles.  The lizards each eat 2 crickets per day.  The snakes each eat 6 crickets per day. The bearded dragons each eat 10 crickets per day. Jennifer wants to write a computer program to calculate the number of crickets needed for 1 week.  She has this so far.

var L;  // lizards
var S; // Snakes
var BD;  // Bearded Dragons
var C;  // crickets
Write a computer command that will calculate the weekly number of crickets and display that to the screen.”

Many students were extremely baffled by writing an expression that had variables in it instead of using numbers I gave them.  We did “catch-and-release” as a class several times before groups made sufficient progress.  Eventually a few different solutions came out of this.  Two are in this program.

https://www.khanacademy.org/cs/reptiles/4712437831958528

Tony and Maggie’s two solutions modeled the distributive property, something I hadn’t even planned to come out of this.  We did not fully process the distributive property at this time, but focused on the expression and the use of parentheses and the order of operations.  It was a great discussion.  The lesson was great for many kids, but was out of reach of some at this time. I think often about how much I’m asking kids to reach out of their comfort zone.  This one might have been too far, but if I don’t ask them to reach at all, they will not grow.  I struggle with the “just right” balance.  More formative assessment would help me, perhaps.  And I could have built some background knowledge a little better.

4.  The Money Program.

The final mini-project in this unit was for the students to create a program that would use variables to represent pennies, nickels, dimes, quarters, and dollars – and to calculate how much money you had with those amounts of coins.  I got some good results from kids, but I also had many students that got stuck and stayed stuck.  Part of the problem, I know, was the amount of time I dedicated to this (it was a little over 1 class period, but that did not feel like enough time) and that it was the same program for everyone and thus had no creative component.  I did decide that we had to end the unit because the Ratio / Proportion unit was next, and that is more of a power standard than order of operations at this time.  Here is a skeleton of the Money Program.  The project had a lot of potential, and I might have taken it farther if it could have been more creative for the kids.  Maybe I should have had them invent their own money system!

https://www.khanacademy.org/cs/money-program-starter/2399879722

Coming next: lessons and project for Ratio and Proportion unit!

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Posted by on November 25, 2013 in Uncategorized

 

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