blog reboot and getting outside

I'm trying a reboot of my blog. My goal is to keep posts short, update what is going on with what I'm doing as a teacher and to make up for the years of blog posts that I spewed disgusting technology and data focused ideas...

This year I've made it a goal to get students out of the classroom on a weekly basis to see the math that we are learning appearing in the world around us. 

We walked the perimeter of the school grounds which I learned (after being here for 14 school years) is actually about a mile. Our shoes got wet but we now have a good memory to connect with perimeter!

We went into the cafeteria to find the area and that looked like counting floor tiles and subtracting areas of the room that had closets or protruding sections of wall. 

We went outside to look for right triangles and determine if objects being measured represented right angles.

I'm finding the students are enjoying getting out to be active and the more often we do this I'm able to see the students' creativity in finding ideas present I wouldn't have thought of. 

Reverse it to see what they know

We are working on solving systems of equations in Algebra class right now. As a class warmup today I asked students to do this:

Write a system of equations that has a solution of (3,-2) that you think most (all) students would think it is easiest solved using the linear combination [elimination] method.

It was really fun to see their thinking and push back on them a little bit with--"Hmm...I'm not sure if I'd solve that one with  linear combinations. You haven't made it appealing enough to me yet." What I love about tasks like this is some students do it exactly in the way I was hoping based on what we've already done in class and others do something more intuitive (and sometimes simpler) than what I had in mind.

We started our unit of solving linear systems with this activity and I have been really happy with the deeper understanding students have had because of the greater focus on the properties of equality. In a couple classes we even looked at doing similar operations using matrices and ideas from my college linear algebra class. (I think I went through that course hardly knowing why I could do what I did to those matrices and hated how much notebook paper it took to do it...)

Here are a couple of examples of what students said in class today when I talked with them and asked them to share their process with the class:

Hayden: 
I started with 3x = 9 because I wanted x=3 and then I made the equation x + y = 1 because that equation was easy to have the correct solution.

3x = 9 (starts in the middle of the problem in a way)

x = 3 

x + y = 1  (back to the beginning)

Then I made 2x - y = 8 because the 2x would give me the 3x I needed and the 8 would make the 9 when I combine the equations.

x + y = 1  

2x - y = 8 (manipulating the y's to cancel and to get his 3x = 9 situation)

The y's would also make zero to make someone want to use the combinations method.


Lucy: 
I just made up some numbers on the left side and put in the coordinates to see what they would evaluate to:

2x + 3y --> 2(3) + 3(-2) = 0 so the equation 2x + 3y = 0 has a solution of (3,-2).

Then I made the next equation to have a -2x because I wanted the x's to cancel when I do combinations and the y-term could be anything. I put in the coordinate again to see what the number on the right side of the equation had to be:

-2x + (anything)y = whatever you get back

-2x + 4y --> -2(3) + 4(-2) = -14 so then the equation -2x + 4y = -14 also has a solution of (3,-2).

I wasn't sure how well the activity would go but the student seemed very engaged from the start and those that I talked to had great strategies in how to go about solving the problem.

It didn't take a whole lot of planning up front and it gave the students the opportunity to be creative and come up with unique products that demonstrate their understanding of the concept in the reverse direction. 

I believe that in doing so students will also have a better understanding of when to use the combinations method instead of the substitution or graphing method when appropriate.

 

 

#codemaths: Student outlining his approach to coding an algebra solution.

We are up and running in class today. This morning I caught a glitch that caused any use of commas to break the code but that is fixed. I had students working in class on this that were already proficient in solving equations with variables on both sides and understanding the causes for no solutions and infinite solutions.

The task for the group working in #codemaths was this:

Code an equation w/variables on both sides. Try to avoid no solutions and ∞ solutions. https://t.co/irksPBOASt

Before you watch the video keep in mind that these students have had little or no experience up to today in writing computer code.

Google calendars and html

Embedded classroom calendars
In Google calendars a colleague of mine (Kyle Sellers) discovered that you can actually use html in calendar event descriptions. This is great for use in an embedded classroom calendar for daily classroom activities for parents and students to check out. They can subscribe to the calendar and have important class details and resources only a click away.

Some key html help for those new to it:

Links
To make a link like mine above you would use this code in the description you type for that sentence:

We looked at the <a href = "www.mrschwen.blogspot.com">classroom website</a> in class and the information that can be accessed there. [You would want to edit the text in blue to say what you want.]

Formatting
To make that same link bold and underlined you could add in <b><u> in front of the text and </b></u> after the text like so:

<a href = "www.mrschwen.blogspot.com"><b><u>classroom website</b></u></a>

The <b> turns on the bold formatting and the </b> turns it off. Otherwise all the following text would become bold.