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Random Winner Game – MEL3E Day 6

by Jon Orr

I’ve decided to spread some skills (expectations) around as warm ups. Today our warm up involved pay schedules.screen-shot-2016-09-13-at-11-52-17-am

They highlighted every two weeks on their sheet to indicate pay days…..and seeing which months had 3 payments allowed us to have a short discussion on making budgets around our pay cheques.

We picked up where we left off from yesterday’s practice sheet with percent. We talked again about different ways to get paid, including an example of getting paid by commission. I brought in the random winner game to give a little more excitement to just practicing. I usually use the Smartboard and sticky notes but this always ends up with a huge waste of expensive stickies. This time I re-used the 100 grid from the Explain Everything file from yesterday.


 I assigned each person a colour (I only have 13 students—-otherwise assign each pair a colour). Each time they get their question checked by me and it’s correct they earn a tile. If it’s incorrect give them some feedback and ask to try again. WHEN correct they go to the iPad and randomly choose one of the squares to cover. At the end of class we randomly chose one of the squares….and whoever is covering that square is the winner!

Now since we’re dealing with teenagers…..this excited some of my students and for others……not so much. Although one student didn’t want to place any tiles on the grid she still had all her answers checked by me for feedback.

Tomorrow will be our first mastery day. We’ll spend the day working on skills from the week plus a quiz.

Grab the Explain Everything File 

Percent Pile Up – MEL3E Day 5

by Jon Orr

Today I wanted to see what my class’s prior knowledge was around percent. Since they are 16-17 year olds they have been exposed to percent quite a lot. But since their math skills are operating anywhere between a grade 5 level through to a grade 9 level I wanted us all on the same page.

I started off with an Explain Everything file I put together. The slides start at a basic level but then creates a need to determine equivalent values that match a certain percentage.

Slide 1:

Getting the explain everything file onto each students iPad, or getting them connected to the wifi, or showing them how to type in a URL can take some time…..so slide 1 is an easy intro that students who are waiting can work on.

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Slide 2,3,4

I wanted to make sure that when we know the whole is 100 that just counting the tiles covered gives us the percentage. These were too easy for my students but it gave us some time to review writing a fraction as a decimal and as a percent. I asked students to tell me the percentage they covered and then we converted to a decimal and fraction. They had the option to record what they were thinking.

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Slide 5,6,7

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Right away almost all students covered 10 squares. I then asked them to convert their new fraction (10/50) into a decimal to see if we get 0.1 ….and then some shock on their faces appeared. Some students then knew their mistake and made some corrections. But we spent some time here going over the visual interpretation …..10% means that 10/100 are covered. This board had been cut in half so only 5 must be 10%.

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Slide 8-12

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This is where we generated a need for an algebraic (proportion) method. The students could estimate how tall he could be….but they had a hard time determining with accuracy how tall he would be. So this is where I stepped in and showed them how to calculate. The remaining slides with Fido and then with piles of gold and then finally with no visuals at all were to practice this method.

After all slides were finished they started on some more practice questions on paper. We’ll finish those tomorrow as most students just started it.

Grab a copy of the Explain Everything project file

Sneaking in Factoring

by Jon Orr

I started a series of new warm ups for my MPM2D class today. My goal is to sneak in factoring as warmups throughout the semester. By the time we need to learn it (like when we need to factor to solve equations) we will have mastered it already. I also previously snuck in multiplying binomials when we tackled quadratic patterns as Mary Bourassa did in her 2D class.

So today I gave them this slide and said I want you to solve a puzzle!

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They broke out their iPads and used the Algebra Tile app to put together the rectangle. The kids worked away and you could see them trying to put tiles in a way to make the rectangle

….and they soon found out that they had to fit a certain way!! 
On take up we made sure everyone had either my rectangle or a rotated version.

Then we did this one…..

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After we were done I asked the class: “If the combination of squares and rectangles makes up the area, what are the dimensions of the rectangle?” They had a little bit of a hard time here, but finally could see the x + 4 and the x + 2 as the length and the width. I then wrote …

 And then I heard some “aaah”s. We had previously seen both versions of the quadratic expressions and discussed why the factored form helped us out quite a bit if we wanted to find the x-intercepts.

We stopped there….It only took us 15 minutes. Tomorrow we will do a few more…..always writing the factored form after. I will also try to get students to notice efficient strategies to make the rectangles.

  • Why did you put 4 x terms along the width and 2 x terms along the length?
  • How does that relate to the number of singles?

Where I hope to go with these warm ups is to factor all types of trinomials:

  • Perfect Squares

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    This time…..make a square

… and get this…

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  • Trinomials of the Type ax^2 +bx + c


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  • Completing the square too!!!!
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This time…make a square




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We’ll be definitely working our way out of the app and onto paper with area diagrams…

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Factoring

 

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Completing the square

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Completing the square

I think working with these puzzles for the next few weeks first will give us a strong base when it’s time to factor to help solve equations and then complete the square. I think I’ll track all the warm ups we do like this and I’ll post them all!

Desmos Challenges in iTunesU, Multi-Touch Book, and Web Version

by Jon Orr

For many years now my classes have been completing a course wide project on Picture Modelling. Before Desmos (B.D.) I use to send home copies of Geometer’s Sketchpad for students to generate a picture using only functions.Screen Shot 2015-08-28 at 12.41.47 PM
After Desmos showed up it was now super easy for students to generate art and access graphing software from any device.

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The project has been so successful at engaging students to learn about various functions and their transformations I extended it to all grades! For the last few years the project spans grades 9 through 12. Each year learning new functions and creating art.

Screen Shot 2015-06-10 at 1.49.50 PMThis summer while at the Apple Distinguished Educator Institute in Miami I started a project that would create a digital resource that would link the Modelling Functions with Art Project with function challenges created by Michael Fenton, Dylan Kane, and myself.

If you are in an one-to-one iPad room or have access to iPads the resources are in an iTunesU course and multi-touch book for iPad  otherwise they are linked on this site for any device (see below).

Each chapter starts with linking patterns, tables, graphs and equations in pre-made Desmos graphs or in pre-made Desmos activities made using Activity Builder.Screen Shot 2015-08-17 at 7.49.53 PM
Following that, activities ask students to match functions to specific criteria like Michael Fenton’s Match My Line or in my Match My Trig Function. Again the teacher can choose to use the activities in the Multi-touch book or from the pre-made Desmos activity.

Every so often in the challenges students are asked to show their thinking by uploading a picture of their work on a Padlet page. Students can crowd source different ways to solve the same problem. 

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Finally, at the end of each chapter students are to create a working piece of art and share it on a Padlet gallery page! Students can see each others work and comment.

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Each chapter covers different functions but many chapters can be done in the same course:

Ontario curriculum suggested chapters:

  • Chapter 1 – Linear Functions  – grade 9 & 10
  • Chapter 2 – Quadratic Functions – Grades 10 & 11 & 12
  • Chapter 3 – Various Functions (function notation, cubic, square root, reciprocal, non-functions).  – Grades 11 & 12
  • Chapter 4 – Trigonometric Functions  – Grades 11 & 12
  • Chapter 5 – Exponential & Logarithmic Functions – Grades 11 & 12 (Coming soon!).

The project page has more details on how to access the course, book, and web resources.

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