Buying Calculators Problem #MFM1P/#MPM1D #PrBL

As an introduction to linear direct variation, I put together a quick problem-based learning task that was proportional for my combined academic & applied class:summary-2017-02-15-m9-1

Scenario:

Buying calculators.jpg

What do you notice?

Capture.JPGI had to use the Pear Deck dashboard to hide some responses that involved calculating the price per calculator as this was part of solving the later problem. I suppose I could have left them up, but I wanted to leave the calculating part until later when students were in their groups.

What do you wonder?Capture.JPG

How much would it cost to buy a class set of 25 calculators?
Best estimate: ________$
capture

Solve:

You can find the Pear Deck slideshow in this folder. Also in the folder is a follow up slideshow exploring the concept of Direct Variation.

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

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Yard Space #MPM1D/#MFM1P #PrBL

I took the typical “find the largest area given a specific perimeter” problem and created a hands-on, problem-based learning task for my combined grade 9 Math class (academic & applied combined):summary-2017-02-13-m9

Scenario:
capture
Ms. Wheeler wants to build a fenced in yard for Sally to run around in.
She buys 16 1-metre long sections of fence.

What do you wonder?

Physical & Visual Representations:

The yard must be fully enclosed. Use toothpicks to create show different ways of placing the 16 pieces of fencing (I forgot to take photos of this part but they made stuff like this):IMG_20170220_112029-01.jpeg

Draw your shape & label its dimensions:

Capture.JPG

How should the pieces be set up to create the largest enclosed area possible?

What shape offers the largest area?

square.JPG

We discussed that while a square was the largest rectangle possible, there were other shapes possible with greater areas.

How should the pieces be set up to create the largest enclosed area possible if Ms. Wheeler uses a wall of the house as one side of the enclosure?

We have some more exploration to do here. I left this pretty open and they explored various shapes. But I’m not sure they’ve drawn any solid conclusions just yet for the case where we have 1 side of the shape already accounted for.

Get the Pear Deck slideshow here.

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

Height VS Foot length #MFM1P/#MPM1D #3ActMath

As an introduction to Linear Relations with my combined 1D/1P grade 9 Math class we investigated height VS foot length and the guinness record holder for the tallest woman:Summary 2017.02.08 (1).jpg

I asked students to measure their height and foot length and record it on a Google Spreadsheet we had up on the projector:

Capture.JPG

What do you notice?Capture.JPG

What do you wonder?Capture.JPG

I posed this question:

Zeng Jinlian was born in 1964 in Yujiang village in the Bright Moon Commune, Hunan Province, China. She holds the record as the tallest woman. She measured 2.48 m (8 ft 1.75 in) when she died on 13 February 1982. How long were her feet?

Estimate: _____ cmCapture.JPG

Students were sent in their VRG groups to their VNPS boards to solve. Here are their boards:

Since it is still early in the semester I scaffolded the activity a bit by instructing them to create a scatter plot of the data on their board to help them solve the problem. I did not however instruct them to use a line of best fit, although many groups used that strategy to help them come up with an answer. Some groups had graphs with a Height axis that went high enough to lookup Zeng’s height and find the corresponding foot length from the line of best fit. Other groups made an educated guess based on the trend the points were showing.

Each student was asked to determine her foot length based on their graph:Capture.JPG

Her real foot length was 35.5cm!

The following day students were assigned some individual practice with scatterplots on Khan Academy.

Activity materials (include a slide deck for Pear Deck) available here.

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

Equation Headbands

Last year, I read a post about Quadratic Headbanz by Mary Bourassa and thought it sounded like a great game!

I’ve been teaching mostly all MFM2P classes (applied grade 10 Mathematics) for the last two semesters. In the 2P course we only get into quadratic equations superficially. So I’ve been making mostly linear headbands for my groups. I’ve used the game in both my grade 9 and grade 10 applied classes so far. Here’s how it works:

I bought wide ribbon from the Dollar Store & cut lengths long enough to tie around their heads in a bow at the back; about 1 meter long I think? Then I wrote out a variety of linear equations on strips of paper that I taped to the ribbons:IMG_7869

Playing the game:

  • Each student is given an equation headband.
  • They are instructed to put the headband they were given on someone else who is not seated at their group ensuring that the person can’t see the equation you are putting on them.
  • Students walk around the room asking yes/no questions of their classmates. Questions such as “Is my slope positive?”. Classmates may answer yes, no or I don’t know. They are not allowed to ask the same classmate two questions in a row.
  • When they think they know their equation, they come to me and tell me their answer. If wrong, I send them back out to their classmates to keep trying. If they are correct, I remove their headband for them and send them back out to answer the questions of those students still working to determine their equations.

In the past few weeks I added a new step to this game: graphing. Not only did you need to determine your equation, but you had to create a correct graph on a handheld whiteboard with the Cartesian plane.
IMG_7824
My students found it tough but they did it! A good number of my kids knew their equation but were struggling to graph it. It was awesome to watch the stronger students that finished first go back and help teach their peers how to use the slope and y-intercept to make their graph (I had to remind them often not to graph it for them, help them by explaining & asking questions … “don’t touch their marker!”).IMG_7823

I use this game as a bellwork (although it takes longer than the usual bellwork task) on days when we might be doing more individual practice and thus fairly sedentary for the rest of class. This is a great way to have everybody up and moving around the room, talking to different classmates before settling in to the main seat work on a given day.

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