Similar Triangle intro #MFM2P

This week we explored similar triangles for the first time in MMF2P:summary-2016-09-21

Part 1:

Students, in groups of 3, are provided with a set of triangles all cut out (my first class to ever do this activity cut them out & I save them in envelopes for re-use each year). This set of triangles was created by some teacher candidates in one of my courses a few years back.IMG_1244.JPG
Using a Pear Deck slideshow, I prompted each group to organize their triangles into groups using a common attribute; their choice. We discussed the groups they made; right triangles, acute, obtuse, scalene, isosceles, equilateral, and same shape but different size. One group had even stacked the similar triangles on top of each other, nested russian-doll style, which I showed off to the class. The discussion allowed a great review of vocabulary around triangles.

Part 2:

I asked all the groups to make groups of triangles that were the same shape, but different sizes now (which some had already done).img_20160919_103824
I introduced the terminology “similar triangles” and we drilled down as a group to a proper definition. Since we don’t take notes I asked students to find the definition in their course notes pack & highlight the keyword.

Part 3:

I showed a set of similar triangles with a missing side length to solve for. In 3-act-math style, I asked them a) What do you notice? b) What do you wonder? and c) Estimate the value of x:NWE 2016.09.19.jpg
They worked in their groups at their boards. Here is one group’s solution (I have to get back in the habit of photographing every group’s work) w/ my annotations written in red:IMG_20160919_112807.jpg
I then did a bit of direct teaching to show them how to write a proportion to solve algebraically:
img_20160919_112816
Looking back at this, though, I’m not a fan of having them flip the proportion as I’m sure many don’t understand why that’s allowed (h/t to Nix the tricks). I wish I had showed them to set up the proportion in such a way that we start with the unknown value, x, in the top left position. Next time.

Part 4:

Individual practice solving similar triangle problems on Khan Academy. I gave them a second class period for this & what they didn’t get done was then for homework.

Lesson materials available here.

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)

26 Squares – Sum of Squares #MFM2P

I’ve started my #MFM2P course again this year with a set of activities using the 26 Squares thought up by Al Overwijk & Bruce McLaurin (there’s a write-up about how Al uses them here). The 26 squares are a set of squares cut out of grid paper; a 1×1, 2×2, 3×3, … all the way to a 26×26 square. Each group gets one full set.
Capture

We started with the perimeter investigation that I blogged about last year.
Summary 2016.09.09 (1) (1).png

Our second activity was the area investigation that I blogged about already last year.
Summary 2016.09.13 (1).png

Our third activity involved creating right-angled triangles with our 26 squares, starting with a 3-4-5 triangle:
pythagorean-theorem

Students were asked “What do you notice?” about this and other right-angled triangles made from our squares. Several commented that the area of the two smaller squares add together to make the area of the largest square (well, it took some prompting to get them to express themselves w/ the proper mathematical terminology!). And they remembered from past Math classes that this is the Pythagorean Theorem with the equation a2 + b2 = c2.

I gave students the measurements of 3 sides of a triangle and asked them to verify if it is right-angled or not. I forgot to take photos, but they all had the idea of using the P.T. equation to check that the two side are equal.

Finally I gave them this problem:
A right triangle has two smaller sides measuring 28cm and 45cm.
Determine the length of the longest side:IMG_20160915_113624 (1).jpg

The homework was to practice Pythagorean Theorem on Khan Academy.

Materials:
26 squares
Perimeter investigation w/ Pear Deck
Area investigation w/ Pear Deck
Sum of Squares investigation w/ Pear Deck

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)

#ObserveMe

This week I started seeing photos on Twitter of teachers participating in the #ObserveMe movement; an open invitation to colleagues to visit our classrooms anytime we’re teaching in order to observe & provide us with feedback. The idea is the brainchild of Robert Kaplinsky.

I’ve decided to jump in on this! I’ve always thought that part of our assigned duties in a school should be assisting another teacher in their classroom once per week. It would allow teachers to observe each other more & foster more collaboration & feedback. #ObserveMe is the next best thing.

Here’s my sign:

observemesign-2

ObserveMePhoto (2).jpeg

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)

Podcast w/ @DerekRhodenizer

Last week Derek Rhodenizer invited me to chat on his podcast, Eduthoughts. We talked about innovation VS invention, problem-based learning & its similarity to a flipped classroom, and Twitter as a professional learning network. And maybe a bit about Pokémon Go too😉

Have a listen:

http://derekrhodenizer.ca/rhodenizers-eduthoughts-episode-11-laura-wheeler/

IMG_1798

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)

Problems We Solved in #MFM2P

My plan was to blog about every problem-based learning activity I did this year. I did not succeed; I think I blogged about two from the my MFM2P course? So as a runner up to a full blog post reflection on each, you’re getting one post with a summary image of each activity or problem & a link to my materials for it.
I’ll group them by strand here, but they are not listed in the order that we did the activities. If you’d like to see the progression of activities I used, you can see that here.

Linear Relations

26 Squares: This one I did manage to blog about.Summary (11).jpg

Banquet Hall2016.04.22 2P summary.png

Phone Charging2016.05.19 2p.JPG

Phone Plans2016.04.27 2p.png

Gummy Bears: I did blog about this one here.Summary 2016.02.29 2P.jpg

Measurement & Trigonometry

Lamppost: w/ shadows 2016.04.15 2P Summary.jpg

School Height: w/ mirrors 2016.05.25 (1).JPG

Tree Height: w/ clinometer 2016.05.11 2p summary.jpg

Wheelchair ramp2016.06.08 2p (1).JPG

Filing cabinet post-itsSummary Filing Cabinet 3-Act.jpg

Pyramid Post-its2016.05.13 2p (1).JPG

Quadratic Relations

26 Squares: I did blog about this one2d 2016.02.08 (1).JPG

Visual Pattern2016.04.12 2p summary (1).JPG

Not every lesson we did was problem-based. Sometimes I need to do some direct teaching right from the get go, like with expanding & factoring. Other times we explore & investigate by drawing & cutting out shapes, like with similar triangles & trigonometry. But in any case, maybe someone new to the MFM2P course (or not so new to it) will find these activities useful!

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)

#Sketchnote: 5 Practices for Orchestrating Mathematics Discussions

I’ve been hearing about this book lately, 5 Practices for Orchestrating Productive Mathematics Discussions By Mary Kay Stein, Margaret Schwan Smith. I still haven’t gotten around to ordering & reading the entire book, but I did read a shorter article that one of the authors wrote on the same topic. And as I’ve been doing more & more lately, I created a sketchnote summary of the article to help me organize my thoughts & to share with others:

5 Practices Orchestrating Mathematical Discussions.PNG

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)

OAME sketchnotes

At the start of May I attended the OAME conference in Barrie. This was my 2nd year attending. I was disappointed to have my session cut due to low enrollment 5 weeks before registration closed, but c’est la vie! Next year in Kingston I have an idea of how to better “sell” my session in the description. Fingers crossed to not get the final session block on the Saturday either – that drags your numbers down for sure.

The food was the definite low point of the trip. Georgian College offered a poor continental breakfast in the residence and OAME provided all vegetarians with gluten free bread that wasn’t suited for human consumption. Let’s hope the Kingston organizers manage something a notch above.

I thought I would share some sketchnotes I made in order to summarize my new learnings. Let’s start with the Ignite sessions which I think are my highlight of the conference each year. Ignite speakers get 20 slides that auto-advance every 15 seconds to total 5 brief minutes to try & get a strong message across.

OAME Ignite 2016 Part 1

OAME Ignite 2016 Part 2.PNG

I was pretty active on the Twitter feed for the conference as well:

Lastly, I usually try to make an effort to seek out OAME sessions by teachers that I can’t see or work with at home but my colleague Lynn Pacarynuk‘s session on test design & assessment made me think more & harder about my own practices. So much so that I summarized some of her ideas in 2 different sketchnotes:

OAME Test Design Process Lynn Pacarynuk.PNG

OAME Shifts in Assessment & Test Design Lynn Pacarynuk.PNG

Until next year, OAME!

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)

Pear Deck; interactive slideshows+ #edtech

This year I have been working with Pear Deck as part of their certified coach program (similar to the Google Certified Educator). Pear Deck has invited a group of teachers that are heavy users of their product to be trained as coaches. Once trained, the coaches present at various conferences and PD days on behalf of Pear Deck to spread the Pear love. Last weekend while I was at the Montréal GAFEsummit event and took some time to create a sketchnote that summarizes what Pear Deck is, the great features it offers, and the benefits to your classroom. Enjoy!

Pear Deck Sketchnote.png

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)

Jo Boaler’s Visual Maths – a #Sketchnote

Jo Boaler has written (with a co-author) a new paper on Visual Maths. Jo Boaler is kind of a rockstar in the Math teaching world lately. She’s started a new  website called youcubed.org with lots of activities & resources backed up by research.

I read the paper this weekend & sketchnoted a summary for myself that I then shared on Twitter. Thought I would share it here too:Jo Boaler Visual Math (1)

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)