Math: Express Multiple Ways

What we are working on in my math class is the 8 mathematical principles. Can students communicate their thinking over show your work? Do they actually understand it or do they have memorized a set of steps? If students can not approach a problem from multiple ways they are going to struggle applying it to a non standard situation. When in life do we get math problems exactly like we saw them in the textbook?

Trust me, students (at least in high school) will NOT appreciate your making them do it multiple ways. "I got the answer." ... yea, so did photomath or your calculator so that really isn't the point. Can you show me you are THINKING (not memorizing or reguritating)? Can you apply strategies? Can you feel confident approaching a math problem you have never seen before?

I asked my high school students to do a number talk to express the number 12 in as many ways as possible. I asked them to take a string of numbers that are plus/minus and use associative, commutative, and other strategies to simplify it DIFFERENTLY (zero sum pairs, making 18 into 10 and 8, etc...), I showed them how you can subtract 2 digit numbers and NOT borrow or carry 42 - 37 = 10 - 5 ... if you just use negative numbers this is not a problem.

I made a follow up "worksheet" just to give them some more practice with these techniques. I made it in a Google Sheets spreadsheet so that every student gets a unique copy so they can not copy off their neighbor. Yesterday, I wrote the questions on the board and the students had large butcher paper where their entire group was writing the different ways they were doing the math problems on the same sheet. That was awesome, it allows them to value doing different approaches. To not feel they have to do things the same way. But you also get that they can just copy what another student did. So for the follow up practice I used a spreadsheet to generate random numbers so that each student is doing something different than their neighbor. Because I want their STRATEGY not their answer!

=randbetween(1,9)

Using the formula =randbetween(1,9) will give me a single digit number between one and 9.

=randbetween(1,9)&randbetween(0,9) will concatenate (I love that word, it means smash together) a single digit number for the tens place and a single digit number for the ones place.

In the spreadsheet template above, double click on a cell to see the math formula I used to generate the math problems.

TemplateTab

I use TemplateTab (coded by me!!!). After I made the template with random numbers I used the Add-on menu to setup TemplateTab which lets me paste my roster (or I just put person 1, person 2 since I am going to print this on paper) and it makes a copy for each person on the roster. But since the formulas use RANDBETWEEN the numbers re-randomize each time you make an edit so then all 150 versions are DIFFERENT!