Lamp post height #MFM2P #3ActMath

Last week we used similar triangles to find the height of lamp post out front of the school:2016.10.17 summary (1).png

Act 1

Scenario:
img_1752

What do you notice about the lamppost? (FACTS) What do you wonder about the lamppost? (QUESTIONS)
The pole is taller then the person What is the height difference between to man and the lamppost
It’s a lot taller then the person how much taller is the lamppost compared to the person?
its a tall lamppost How tall is the lamppost?
The iamppost tall than the boy What height the lamppost and what the height of the boy
there’s a person beside the lamp post how much of that person does it takes to get the height of the lamp post
The lamppost is tall What is the height of the lamppost?
What’s the height of the lampost What’s the height of the lamppost
– The post is taller than the person
– The structure of the lamp post is sturdy
– How much taller is the lamppost than the person?

– How tall is the lamppost?

– How many persons will it take to reach the height of the lamppost?

The lamppost is taller than the person What is the hieght of the lamppost/person
A person is next to the lamp What’s the height of the person and lamppost?
the lamppost is tall
The lamppost is black
How tall is the lamppost
(who is that person)

2016-10-17-estimation-1

Act 2

Students were shown this diagram and asked which of these lengths/heights they could physically measure:2016.10.17 diagram.JPG

Then we headed outside to measure whatever we could with metre sticks & record on a handout of the above diagram in our small groups.

We returned to class & students solved at their boards (red/orange annotations on boards are mine during the whole class discussion afterwards):

We discussed the different boards & their strategies. We grouped the boards by strategy; proportion solving vs scale factor.

Act 3

The next day I poked a hole through a foam stress ball & fed some string through it – leaving the roll of string trailing behind. We went outside & took turns trying to throw the ball over the top of the lamppost. It took a good 20+ minutes, but we got it (“we” is a strong word since my throws did not work & my student Ahmed got it over!) and the students then measured the length of string that hung down to the ground; 10.16 m was the actual height (which was fairly close to their solutions on the boards).

The rest of the day 2 class was dedicated to individual practice. Some students never completed the first practice from earlier in the semester on similar triangles, so they were assigned the basic exercise set on Khan Academy. Those that had completed that skill were assigned a more advanced exercise set involving similar triangles nested inside of one another.

Lesson materials available here.

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

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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)

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)

River Width task #MFM2P #3ActMath

I’ve been neglecting my posts sharing my activities from MFM2P lately. As school wraps up for the holiday break I am hoping to catch up!

Summary (8).jpg

A few weeks back I created this River Width task for us to look at similar triangles again.

Act 1

Using a map of the Rideau River near Ottawa I asked my class to estimate the width of the river at this point:IMG_1452.PNGTheir estimates:Capture

Act 2

I gave them some measurements (based on the similar triangle curriculum expectation that I was trying to hit on that day):IMG_1453.PNG

I sent them to their boards to solve. Most groups calculated the scale factor & then used that to find the missing length:IMG_0369.JPGOthers set up a proportion to solve:IMG_0370.JPG

Act 3

Answer reveal: Capture (1).JPGThe answer was ~108 m and many of them were pretty close in their estimate!

Lately I’ve taken to creating a “consolidation” handout for the following day where we can work on describing our steps, tools & strategies from various solutions. Here’s the handout for that.

And as always here’s the entire folder of materials for this activity.

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

Similar Triangles Mirror Activity

Today in my MFM2P class we solved the problem How tall is the flagpole out front of the school? We made estimates of the height (act 1) before going outside to collect data in order to solve (act 2):Similar Triangles Mirror Activity - Flagpole

Most groups got an answer around 10m which seems pretty reasonable. This is one activity where we can’t do act 3 (unless I send a kid to climb up the flagpole w/ a measuring tape to drop down; probably not the best plan!).

Activity available here.

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