After completing the two Making Algebra Meaningful activities we spent time using algebra tiles to help collect like terms and simplify algebraic expressions. Our math department has sets of these tiles, but over the last couple of years I have used the Algebra Tiles app from BrainingCamp. It’s a pretty decent app that allows 3 modes.

1. Blank whitespace – for collecting like terms, simplifying expressions.

2. Split – Two spaces – for use with solving equations.

3. Factors – a set up for multiplying expressions, distributive property, and possibly factoring, and completing the square.

A super nice feature is the visualization of the zero principle. If you drag a +1 onto a -1 it disappears….visually showing nothing.

We were using the blank space to drag tiles onto, sort and read off the corresponding expressions. We did a little of mix and match…..I give you an expression, you create the tiles that match, and viceversa. I wanted them to get comfortable with an x-tile representing an unknown value….just like the length of Dora.We moved from writing expressions into simplifying them.

After we got the basics down I gave out our practice sheet.

Click the picture to access the file

Instead of students flipping to the back of the book to check answers, we made use of our QR code scanner Qrafter. A quick scan of the QR code reveals a picture of the answer. I know it’s pretty gimmicky but I felt the kids seemed to identify with seeing my written answers in short bursts than dealing with seeing ALL answers at once in the back.

Next up in our spiral…..Water balloons exploding using proportional reasoning, volume of spheres and linear relations.

SlackMath —- another resource that uses QR codes to check answers.

A video from last year (a little too long now that I look at it) of using Algebra Tiles app to solve equations.

First – Learn about the square root function & see how a function is translated vertically.

We had a class discussion on which points they picked and how those points changed in the function f(x) + 3.

They are then led down a Desmos Trail to complete a few mini-challenges trying their knowledge of using function notation and vertical translations matching the “home” function to the translated one. Each challenge then links to the next!

We did the same for challenge 2, the basic rational function, and horizontal translations. The handout served as our class note.

After our discussions the Desmos Trail continues, starting at challenge 3 until challenge 9. Each testing our knowledge of equations and translations. You may also see I threw in a few reflections in there too!

Here are a few students working away on the challenges.

Next on Making Algebra Meaningful – Dora to the Rescue!

Our goal is to tackle this beast from our expectations:

add and subtract polynomials involving the same variable up to degree three [e.g., (2x + 1) + (x^2 – 3x + 4)],using a variety of tools

and

multiply a polynomial by a monomial involving the same variable to give results up to degree three [e.g., (2x)(3x), 2x(x + 3)], using a variety of tools

My first thought when creating my lessons is how can I get students curious! Sometimes curiosity will come out from Act 1 of a 3 Act math task. Or sometimes it’s from a puzzelly type open activity that makes students struggle.

Here is MY new struggle:

How can I make students curious when teaching collecting like terms, and eventually the distributive property?

Last year’s opener to teach collecting like terms:

Give them a perimeter problem where the sides have an unknown value.

Ask for an expression for the perimeter in terms of x.

Now here is x….find the perimeter.

And that’s it! Every time I do this kids are confused and ask “Why didn’t we just have the value of x to begin with?”

I want a task that makes us curious and need to use like terms to simplify an expression.

Here was how our conversation in math class (MFM1P) went…..How many pieces make up this Star wars Lego ship? We started with that picture and had a great conversation around Lego.

Then I showed this one.

Does the pool/hot tub have more pieces/less pieces/ or the same? This turned into “boy” Lego vs. “girl” Lego. My personal opinion is its all great…. My 3 daughters are just as excited to play with Yoda as they are with Disney princesses. Girls in the class agreed that they didn’t need their own line of lego!!!

I moved our conversation a little forward with asking Which costs more? And which should cost more?

To get students to be interested in it I wanted them to be “dying” to figure it out.

I thought about putting them in a place where they had to struggle— I wanted to open up the middle!
Michael Fenton has a series of Match my Parabola challenges and I thought of those. I modified his challenges a bit to include those examples from my tweet.