Manipulatives in Math

Before the semester had started, I had stumbled upon Joe Sisco's (@joe_sisco) interactive word walls Google Drawings for Google Drive (Link to complete folder here: http://bit.ly/INTERACTIVE_WORD_WALLS)

TEASER... the first of many INTERACTIVE MATH WORD WALLS using Google Drawings http://t.co/I0FbiMSazv

— Joe Sisco (@joe_sisco) April 3, 2015

I started by using first the Linear Relations drawing and the drawing for Quadratic Functions. As I progressed in the Quadratics units, I kept going back to the "! - Using Algebra Tiles" Google Drawings with both of my MPM2D classes. I used it to launch into many ideas or concepts, or I made my own drawings to quickly illustrate ideas.

It all started when we started to need to expand terms and factor trinomials. I remembered the awesomeness of using algebra tiles with my MFM1P class from long ago. I also remembered how students either rolled their eyes and groaned and then refused to use the tiles because I couldn't really assess them/get them to hand anything in. IN STEPS GOOGLE CLASSROOM!

To start, we practiced modeling trinomial expressions. All I wanted students to do was to review how to visualize the terms in a polynomial expression. Here is what students received:

Using Google Classroom, each student got the above Drawing file. I gave them the verbal instructions to model the expression, using the tiles on the side. The goals of this first sheet were for students to model the expression with algebra tiles, learn how to get and hand-in work within google classroom.

Here are some examples of student work:

 I switched it up in the second activity and gave them the drawing and got them to give me the expression (in standard form):

In the third slide I had students collect like terms and use the "zero pair" principal:

I wish I could say that I am a math genius and that I put the zero pairs concept in there on purpose, but when we got to completing the square much later on, WOW, was I happy that I had introduced this at this point, much earlier.

I finished off with expanding (there was a ton of guidance given in class to pull this off). 

Student work:

Really this was the goal of the lesson, but by doing the algebra tile work on the previous three examples, it really helped later on. Using google classroom was a huge help. Students really focused and knew that they were handing their work in. It added to the "validity" of the activity and my buy-in was huge. I cycled around the classroom and was able to provide feedback on the spot for students who seemed off track. I would finish each manipulative worksheet off by showing off a couple examples and discussing the work. It was a great learning opportunity for all (me included).

BUT it didn't stop there!

I then used the template to make "perfect square" examples and questions for Peardeck. Great to visualize perfect squares and their roots.

First:

Then:

And Finally:

There were a lot of numerical examples too (don't worry).

When we got to completing the square, there were examples of how to complete the square visually, using algebra tiles. So I set-up 4 practice questions using Google Drawings and Google Drive. Note in the question about "Zero-pairs". When I brought this up, it was not a crazy idea or concept due to the work we had done before.

I gave them this (for our first example):

And they made me:

I even went so far as to showing them (not making them do) an example for when "a" is not equal to one. I really enjoyed making it too.

So I was thinking about fractions and some work I had done with helping students in grade 9 with EQAO prep and general math concepts help from some years ago. I had used the Pattern Blocks for visualizing fractions and I started wondering if there was such a thing made on Google Drawings. I couldn't find anything, so I made these:

Link to google drawing file: http://bit.ly/PatternBlocksDrawing

I hope to use them in the future with other teachers within my board, but I'd love to hear how you use them in your class and/or any feedback (I tried really hard to align them properly so they actually work).

Progress - two first ideas

Back in the classroom after ict consulting has been great. I have been fortunate to have access throughout the first 1/2 of the semester to a 1/2 class set of Chromebooks and a departmental 1/2 class set of iPads. I am teaching two MPM2D (grade 10 math) classes and one SCH3U (grade 11 chemistry) class. There have been some common uses of the technology and some purposely different.

In the spring last year I met with Dave Kay in the SMCDSB at a school in Barrie. Dave had started a mind mapping unit review with his class for on-going creation and review. I really liked the idea because in SCH3U in the past, students would not do the readings as review. I got the students set up on mindomo because of its gafe affiliation. Now students have adopted it and have made some fantastic maps. I have been able to see how students are conceptualize their understanding of content in chemistry.
Examples of student work:

Sample provided to students (in math):

I was fortunate enough to have a year subscription to peardeck provided for me. To get ready I participated in a couple (awesome) live tours given by peardeck. I have been using peardeck as a formative assessment tool in both math (mosty) and in chemistry. Combined with an interactive white board, I have been able to collect assessment data instantly, discuss misconceptions and review old concepts. In math, this has been AMAZING. Tomorrow I am hoping to use a second device (phone/tablet) as students participate so I can walk around them for more guide on the side vs sage on the stage feedback.

Examples:

Both technologies/softwares allow me the opportunity for some metacognitive thinking aswell. With the mindmaps, students reflect back and review concepts, self identifying key parts of the lesson. With peardeck I ask reflective questions. The formative feedback with peardeck has been amazing. Being able to quickly identify student misconceptions right away has been great. Students enjoy the activities and will also verbally ask follow-up questions within the lesson.

Learn Math Flowchart

I had seen a "How to Learn Math" flow chart a while back from Sarah Hagan in her post about Growth Mindsets,

I like the bulletin board, but I wanted to make it more flow charty. In reading her blog, it seems that she was inspired by the post on Everybody is a Genius on Standards Based Grading I also know that I can't make a bulletin board as nice as Sarah Hagan's, so instead I hopped onto my computer opened up Lucidchart and make a hand-out for the first week. I may even blow it up to poster size to post on the wall (more my style).

Here is an image of my work:

Here is the .pdf copy.

Please feel free to provide feedback!

End one thing...start another

End of the year. I have learnt a lot over the past semester in my role as an Integrated Learning Technology Consultant. I have been exposed to so many awesome ideas, tools and resources that I now want to explore over this coming year.

This is my first serious foray in blogging. Another member of the ILT Consulting team (@gkyfranzen) has been encouraging me to blog my 2015-2016 teaching year. I have enjoyed reading a following other educational bloggers. I am not sure what I will bring to blogging but I do know that for reflection and goal setting I feel that it will help me.

Next school year I will be teaching two grade 10 academic math classes and a grade 11 university chemistry class. I hope to:

• use Mindomo in a variety of ways. Dave Kay from the SMCDSB shared with me some great ways to use mindmapping as a metacognitive tool for students. I hope to bring this and other uses of mindmaps into my SCH3U class.
• use desmos and geogebra in my MPM2D classes to help students understanding and comprehension and to help them explore mathematical concepts. I have started to play with geogebra to make an activity.
• explore and play with 3-act math and other problem based questions in math. Maybe I will even make my own activity or two?
• use the GAFE tools effectively in my classes and not just as a flashy gimmick.
• continue to tweet
• start blogging.