I put this on the board and asked,

*"If you were a conspiracy theorist, what connection might there be between the 3, 5, 8 and 15?"*

They got the connection between the numbers almost immediately. We then moved on to a quick intro to factoring powerpoint with personal whiteboards.

After this, we moved onto day 1 of our simplified factoring notes.

We covered trinomials where A=1 and B and C are both + on day 1. The next day, I walked my students through this factoring template that I plan to use throughout our entire factoring unit.

One of my students who took both Algebra 1 and Geometry last year, immediately turned off when I introduced our factoring unit this year. He said he already learned it.

When he wasn't sure how to find the factors of C (24 in this case), and I showed him the calculator divide trick (24/2 --> write down 2 x 12, etc...) that works well for students who don't know their times tables, he exclaimed,

**"Oh, you can use division to find them?"**

I really emphasize making this list with my students because it cuts down on the time going over and over the same numbers. This list is especially helpful for my kids with working memory weaknesses.

Since we started with a trinomial where A=1 and both B and C are +, we didn't really need to add signs to our factors of C. But, I thought it was good practice for later.

On the last day before vacation, I gave every student a scorecard to record their answers to our zooming Prezi. It wasn't quite a Kahoot, which they love so much, but it still worked pretty well to keep them all engaged on an exciting day.

All of the trinomials in the Prezi have an A value of 1 and + B and C values. If their answers were correct, my students checked the boxes in the very top row.

I was able to use my phone as a clicker to advance the Prezi (a few students were impressed - ha!). When we come back from break, we need to finish this Prezi and move on to trinomials with GCFs and - B and/or C values.

**How about when A isn't 1?**

The best way I have found to teach kids with math disabilities factoring when A does not equal 1 (and is not the GCF) is with the AC method. Here is a student reference sheet for the AC method.

I like this method because there is absolutely no guess and check, which frustrates my students who already have a tough time with multiplication tables.

Students find the factors of AC that add to B, then replace B with the factors.

I write more about activities to teach quadratics in the post Fun with Quadratics.

You can find the "AC method" factoring reference sheet for

**free**here.

I pretty much only use this method for factoring. It works so well, and I'll start using the quick check for warm ups since this is a skill they lose if they aren't using it often enough.

ReplyDeleteThe hardest part for my kids is the factors of C. Do you find that to be true? It's hard working around my students' multiplication facts without making them feel self-conscious. I did give out a multiplication chart again this year and no one complained. My aunt has said that skip counting is the best way to teach the multiplication facts to kids who struggle to memorize, but I am not sure how to work this in.

DeleteSteps 6 and 7 aren't equivalent. Step 7 should read: (6x^2+4x)-(15x+10) or (6x^2+4x)+(-15x-10)

ReplyDeleteAbsolutely, and I explain this to my students. Flipping the signs confuses them to where the process is lost, so I explain that the ( ) are just used as a tool to move to the next step. Do you have your students change the signs?

DeleteI have students factor the first two and repeat their factor in the second set to see which number needs to be pulled out.

DeleteExample:

2x^2 + 8x - 7x - 28

2x(x + 4) ___ (x + 4)

I find this helps with the negative/positive signs too!

This is great, Lauren. That second ( ) is always harder because of the funky signs that can happen. Do you notice less mistakes this way?

DeleteI teach my students to underline the terms they are grouping with a wavy underline. That way there is no misleading () and they can keep their signs straight.

ReplyDeleteAlso, I use my own version of the "Berry" method from the Yay math website. Very similar to AC/ grouping but organizes it a little differently with less room for error. You MUST be sure that any GCFs are removed first, though.

I love AC/grouping. I know a lot of teachers like the Punnett Square method but my kids really seem to like how direct AC/grouping is. Thanks for commenting! I'll have to check out that Berry method...

DeleteDo you have a way for 5th grade math students to make the connection/difference between factors and multiples? And a way to figure out factors? I've tried a few different ways, but none of them have seemed to stick. I know this is a basic understanding they will need as they progress.

ReplyDeleteHi Laura, thanks so much for commenting. I'm a big fan of prime factoring using prime numbers, taking my number and dividing it by 2, 3, 5, 7, 11... each as many times as I can until moving to the next larger prime number. For 24 I'd do 24/2 = 12 ; 12/2 = 6 ; 6/2 = 3 to get (2, 2, 2, 3). Combining this with divisibility rules would help kids skip some of the numbers that they know won't divide evenly into the given number.

DeleteThere's a really cool way to find GCF that I learned about in grad school. It's called the Euclidean Algorithm. Here is a video: https://www.youtube.com/watch?v=AJn843kplDw

Finding the LCM is a lot harder for me. It feels so counterintuitive! Here's a Khan video I found that helped explain it to me when I needed to make a math pennant for GCF, LCM and prime factors. http://bit.ly/2iWicws

I also have this free flowchart that can help kids make prime factor trees. Then from there they can find GCF or LCM... http://bit.ly/2hHRJ5D

I hope I helped in even a small way!