# Pumpkin Challenge #3ActMath #MFM2P

It all started with a trip to the grocery store where I noticed a giant pumpkin on display & a prize of \$50 in gift certificates if you could guess the weight of the pumpkin:

I went back a couple of days later to take some measurements of the giant pumpkin, bought 4 smaller pumpkins of varying sizes & we were on our way!

Day 1

Act 1

What do you know / notice?

What do you wonder?

Estimate the weight of the pumpkin in pounds:
I passed around a 1lb bag of barley that all the student We start with a guess that’s too high (but not silly like 5000 lbs), then too low (but not silly like 1 lb). Then they make their best estimate:

Then I have them do a turn & talk with their group (visibly random groups of 3) to discuss what they need to a) measure, b) Google c) calculate in order to solve this problem.

Students made a prediction about which characteristic of the pumpkin the weight would depend on most:

Act 2:

I revealed some measurements I’d taken of the giant pumpkin:

We had 4 pumpkins of various sizes at stations around the room with a scale to measure weight and rulers & measuring tapes. Groups were sent to their vertical non-permanent surfaces to begin collecting & recording data about any measurements they thought they might need for the pumpkins to help predict the giant’s weight:

Groups recorded measurements and started calculations for volume, etc. in order predict the giant pumpkin’s weight:

At this point we hit the end of the class period. Some groups had some volume calculations but none of them had got to (or really thought of) creating a table or a graph of weight depending on another variable to make a prediction.

Day 2

I was away this day & so students had the period to do some independent practice on Volume & Surface area word problems on Khan Academy.

Day 3

I wanted students to graph weight VS diameter, weight VS surface area, & weight VS volume. So I created a Desmos Activity to walk them through that process:

I provided students with the raw data they would need (as they had already worked on these types of SA & Volume calculations the previous period – today’s learning goal was all about the linear & quadratic relations between different variables):

They found the line of best fit and quadratic curve of best fit. We had a class discussion about which one fit the data better … quadratic!

They they used that curve to predict the weight of the giant pumpkin based on diameter:

I walked them through that first set of tasks step by step as a whole class making sure everyone understood. Then I turned the Desmos Activity to student-paced mode & let them continue the same graphing tasks for weight VS surface area & then volume (although many of my students gave up working on it once I was no longer leading the class through the activity slide by slide).

Each student had filled out an entry slip for the pumpkin contest at the end of day 1, and I allowed them to adjust their entry if they wanted based on today’s work. I then dropped off all of their entries after school:

Day 4

Started class by revealing the weight of the giant pumpkin.
DRUM ROLL PLEASE . . . 166 pounds!!!

I then presented them with a the 3 models we created, each showing the giant pumpkin’s actual weight as an orange dot & asked which model was the best predictor for the giant pumpkin:

I finished by having the students drag dots to any Math from our course that we used over the last few days with this activity:

Students had the rest of the period to do some individual practice on “Graphing linear functions word problems” on Khan Academy.

My folder with everything for this activity can be found here. The unassociated files are the Pear Deck interactive slide decks.

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

# Banquet Hall problem #MFM2P #PBL

This is my 2nd or 3rd time doing this activity, but hadn’t yet blogged about it. So here goes … I made lots of changes, even from one period to the next.

Prompt:

Notice-Wonder-Estimate:

Solve:
At your boards (whiteboard / chalkboard) in groups of 2-3 randomly assigned (VNPS & VRG).

Most groups started calculating the cost per person for each teacher. I stressed to them multiple times that all 3 teachers were paying along the same formula or “price plan”. They really struggled with how that could be. In first period there was 1 group whose board had a table on it & they had started using 1st differences to calculate the rate of change. I called all the groups over & led a discussion about the strategy and asked about what sort of deposit (a cost for 0 people) might have to be made by the teachers & sent all the groups back to continue, strongly urging them to explore the table idea. In 3rd period, none of the groups started the table, so I called all the groups over to some spare board & said “here’s something I saw in 1st period” & proceeded to have the same conversation with them.

Here are their boards:

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We got to the point on day 1 where everyone solved for the cost for 150 guests. Time ran out, & bell rung.

Between periods 1 & 3 today I added some extra slides & questions to my slide deck to make it better.

Day 2:

Yesterday I added a slide asking students to graph the 3 points from the original data set in the original prompt. Today we started on that slide in Pear Deck :
I asked them if this was linear or nonlinear. Why? In 1st period this also resulted in a conversation about 1st differences when the x values don’t have a constant increase.
I asked if the line of best fit would pass through the origin?

I then sent groups to their boards with the task of using Desmos to find the equation for the line of best fit . Their boards:

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Once they had done a linear regression to find the equation, I asked them to use their equation to solve for the number of guests I invited if my party cost \$3545 at the banquet hall. I coached a few groups through the proper format in which to show their work when solving an equation.

The rest of the period was dedicated to individual practice on a Khan Academy problem set called “Slope intercept equation from graph“.

Find the whole lesson here (the unassociated file is Pear Deck).

As a final note, this whole problem-based teaching can be hard for the student to grasp sometimes. Today this happened:

How do you handle it when students question your teaching skills or pedagogy? Let me know in the comments below!

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

# Running VS Walking Headstart #MPM1D #MFM2P #3ActMath

A month ago or so I read a post by Mr. Hogg about his Fast Walker activity. I thought it would be a great way to introduce linear systems graphically to my combined grade 9 math class before the end of the semester. I also did this activity with my Grade 10 applied students – next semester I’ll use it as an introduction to systems graphically with them earlier in the course.

What turned out to be super awesome is that a student in my grade 9 class just won gold at OFSAA last week! So I tweaked Mr. Hogg’s activity to use Joe’s winning data in our problem. I also structured the activity to be a 3 act math task. Here’s what we did:

Act 1: Notice – Wonder – Estimate

What do you know / notice?

What do you wonder?

If you want to cross the finish line at the same time as Joe, what distance head start will you need?

Act 2: Measure & Solve

Students were told they had to stay in class when taking measurements; my idea being to force them to time themselves walking over shorter distances (the length of our classroom) and then use that to model their speed for this problem given. Each student had to calculate their own head start:

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Act 3: Check & Reflect

We went out to our 400m track and students measured out their starting position. They staggered themselves according to their calculation (photo below – tried to take video but my phone battery died). Most students were around 100m before the finish line (~300m head start). We counted down & Joe started running & the class started walking. I so wish I’d gotten the video because it was awesome how close they all finished to each other!

I had my grade 9s graph their walk & Joe’s run on the same grid. Here are their graphs overlaid on top of each other:

Most students had the right idea, and I talked to a few with incorrect graphs individually but when I look at this overlay now I can see that I missed helping a few students correct their work 😦

We discussed which line was partial variation & which one was direct. I then introduced the language of “linear system” and “point of intersection”. My 2P class time to create an equation for each line also.

The next time I try this, I’d like to add an individual follow up question such as if you only had a 50m head start, at what distance would you & Joe meet? At what time would that be?

Here are my files for this activity (the unassociated one is the Pear Deck slideshow).

Tech Tip: Did you know you can add the same Google Doc/file to multiple folders without copying it? I didn’t until recently. It was useful for this lesson because I wanted to have it in the folder for each of the 2 classes I did the lesson with! Once you’ve clicked on the file just press Shift+Z :

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

# 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:

Scenario:

What do you notice?

I 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?

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

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)

# 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:

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

What do you notice?

What do you wonder?

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: _____ cm

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:

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)

# Flight Costs #MFM2P

I’ve done this activity once previously. I changed how I did it for this second go. I will change it again for next semester.

Here’s how it went this time …

Students were presented with this data:

The task for day 1: Determine the initial value & rate, on average, for flights with Air Canada.

Some groups went to Desmos straight away. Others needed some reminding that Desmos can be very helpful with data like this.

On day 2, groups were asked to determine the distance they could fly for \$500 using their equations from the previous day. I only took a photo of one group’s board that day:

I think next semester I will change this up. I think I will present the name of a city & ask students to estimate the cost of flying there. Then I’ll give them the set of data for cost & distance for multiple cities, but with the first city blanked out; perhaps allowing them to adjust their estimate if they like. We’ll do notice & wonder, and then proceed to solve for the price. I won’t specify modelling algebraically but will perhaps create a Desmos activity builder they can do to practice that in the case where they don’t use an algebraic model to solve.

Update: Find the Desmos activity builder follow-up here

Activity available here.

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

# Cup Stacking #MFM2P #3ActMath

This activity is another one that stems from one by Al Overwijk, but a bit more directed than his. In Al’s activity, he opens it up to any model of cup stacking which results in relations that are linear, quadratic & beyond. Maybe my class can come back to this later in the course & do it that way. For now, we stuck to a nested cup model that I knew would result in a linear pattern since that was my learning goal for this activity.Also different from Al is we used a stool simply because we don’t have enough solo cups to get to the height of a person when they’re nested inside each other 😦

The Scenario:

Act 1: Notice, Wonder & Estimate

 What do you notice (facts)? What do you wonder (Q’s)? What is the height of the chair The cup is way smaller then the stool How many cups do you need to get the same height Each picture has more cups How many cups does each picture have there more than 1 cup. why do you have only 3 chairs? Each picture has different number of cup How many cups that can be same hight with the chair there’s more cups in each picture how much cups does it Stool and cups How many cups we need to put together so that they have the same height with the stool? What’s the height of the chair The number of cups increase Why are there cups – There are a different number of cups in each picture. – The stool is much taller than the stacked cups. – The only thing that changed is the number of cups – How many cups will it take to stack it as high as the stool? More cups in each picture How many cups do we need to cover the hight of the chair cups what is the volume of each cups? The number of cups is increasing How many cups would it take to be the same height as the stool 3 stools, cups is increasing How many cups it will take to reach the height of the stool In each picture there is a certain amount of cups The chair is always the same How many cups it increases at a time

Act 2: Collect data & solve

Each group received 8 cups and were instructed not to share their cups with any other group. They quickly grabbed rulers & began measuring. They made tables of values on their boards to record their measurements. But quickly most groups began to look for patterns after taking 2 measurements & then continued their tables based on their assumptions of how it will continue to grow. But I let them continue with that thinking for now. Here were there boards:

I then asked them to take one of the equations for line of best fit that they’d found in their group and go to their boards to solve for the number of cups needed to match the stool’s height:

Act 3

We stacked the cups as a group next to the school and the actual answer was 73! We discussed possible reasons for differences between our first answers, our answers after using Desmos & the real answer.

A third day was spent practicing two skills that had been assigned via Khan Academy over the previous days of work:
Graph from slope-intercept form
Slope-intercept equation from graph

The entire activity is 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.

Measurement & Trigonometry

School Height: w/ mirrors

Tree Height: w/ clinometer

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)

# 26 Squares – Perimeter #MFM2P

26 squares is an introductory investigation I use in MFM2P. It comes from Al Overwijk & Bruce McLaurin. The idea is that you can use the same set of manipulatives – 26 squares of varying sizes with an overlaid grid – to run investigations/activities to introduce each of the 3 strands in the course; linear relations, quadratic relations, and measurement & trigonometry (similar triangles, Pythagorean Theorem, trig). Today’s first investigation introduced linear relations.

Investigation Question

What is the relationship between the side length & the perimeter of a square?

Students were asked to predict the relationship. A sample of responses:

Table of Values: Groups were sent to their VNPS station to create a table of values of side length & perimeter using their squares to collect data.

Some groups correctly counted the perimeter using the grid. At least one group was squaring side length, so I went over and we talked about counting perimeter using the grid & they changed their table of values. One group (red marker) decided to measure the lengths with a ruler instead of counting w/ the grid.

Graph: Back at their desk students graphed their data by hand on this handout (forgot to take photos of student work here). I then had them all decide whether or not this was a linear relation & why. This led to a class discussion of the graph being a straight line as well as the pattern in the perimeters. At this point, groups were sent back up to their boards to determine the first differences for their table & we discussed their findings (again, I forgot photos here).

Equation: Back at their desks once again students worked their way through this short Desmos activity I created asking them to create a graph & perform a linear regression to find the line of best fit. A summary of the student work from Desmos:Students then completed 4 practice problems on the earlier handout to solve for either perimeter or side length given the other. This all took 2 days and they had time at the end to start the homework which was a Khan Academy exercise set titled “Slope Intuition”.

Update: I added a 3rd day to wrap-up this activity and talk about representations. Students completed this handout:They had to name the 3 different representations & explain how they are all related to each other. After 5 minutes of working on it themselves, I had them get up & walk around the room to read each others’ sheets in a gallery walk type style. Then they returned to their seats & could add, change or erase anything from their own notes. I then led a class discussion about the connections of slope & y-intercept between the 3 different representations.

Reflection: I wish I’d included a “word” representation such as “Perimeter is equal to 4 times the side length”.

Handouts & Pear Deck interactive slideshow here
Desmos activity here
26 squares here

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

# Phone Charging activity #MFM2P #3ActMath

This activity comes from the awesome Michael Fenton. He also has a Desmos version of it which I posted on my website so that any absent students could do that version of the activity at home.

Act 1

I asked “What do you notice?”:Then I asked “What Mathematical questions do you have?”

I then presented them with the question I had chosen ahead of time to address the curriculum expectation “Create graphs and equations of linear relations” & asked for an estimate that was too high, too low & best estimate:

Act 2

I asked what information they would need in order to solve this problem & got answers such as . . .  . . . so I gave them:

They went to their boards & solved. Some groups counted up the entire way using a table of values: Other groups determined a rate of charging that they used to multiply by the % charge left to go:These two groups above had some guidance along the way from me in terms of questioning the values they picked for the change in charge and the change in time; both groups reworked their solution at least once.
One group, with help from a discussion with me, created a proportion:This group had the proportion idea on their own but needed some guidance in how to set it up properly.

Act 3

Answer reveal:Michael does a great job of breaking down why the actual answer is so different from the models my students made here on his original blog post.

The following day we worked through this handout which forced them to create a graph & determine an equation for the relation.

And, as always, here is the folder with all the materials for this activity.

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