engagement

The Best Estimates

by Jon Orr

So Dan sent out this tweet.

Wasn’t sure if he was asking Andrew to make a blog post or anyone, but I decided to share my thoughts!

If you’re not familiar with Estimation180…..become familiar quick!! The challenges/estimates have been great conversation starters, warm ups, and intros to math concepts in my classes for the last couple years!!!

So, to answer Dan’s question…..My favourite Estimates have been the ones that make the students do a double take! They make us say No Way!!! or How is that right?

Here is my favourite…

Day 52

It’s awesome because of the controversy! Very few kids guess that there are actually 12 ounces/355ml in that glass! Most think it must be more than the can! In my class we have had great discussion on reasons. Most say the camera angle in the picture is deceiving. They get angry because they think I tricked them. From this point on they are skeptical about all given information!! Awesome! Love it!

I love this whole line up of estimates. Great discussion come out of why the tall vase has the same volume as the Dessert Dish on day 54….

….and the glass on day 57

I think the kids get a kick out of watching the video answers too!

I’m a huge fan of these types of estimates too …. ”

How many small vases will it take to fill the large vase?

by these types I mean “How many of these fit in there?” These have worked wonders for some of our problem solving skills. After we reveal the the answer we take, for example the total ounces in the large container and try to work backwards and see if we can figure out how many small containers fit. (by dividing). By using these estimates as warm ups it has been an easy transition to solve problems like…

Screen Shot 2014-11-14 at 6.46.49 PMIn the past my grade 9 applied students have struggled with this type of problem. After using the “how many fit” estimates my students’ ability on this type have dramatically improved!

These are a few of my favourite things…

Again ….check this site out now…..Estimation180. Thanks Andrew Stadel!

 

Stacking Cups!

by Jon Orr

So we did Dan’s Meyer’s stacking cups lesson in class today!!!  I first saw this activity from Andrew Stadel in his 3-Act math collection. Not sure who first came up with it though. But thanks to both of you!

I started class by stacking the cups up in front of them…..allowed them wonder what was going on. They had questions like

“What are you doing?

“Are we having Hot Chocolate?”

“Are we going to use them to drink something?”

“What are your doing?????”

“How many cups do you have?”

and “How tall are you in cups?”

and bingo there we go!

I told them that is our task for today…To discover how tall I am in cups! I then had them estimate how many cups it would be! They were uncomfortable to start. They wanted to guess perfectly so they wanted to know how tall I was. They tried to put cups next to me as I walked around. They wanted me to lie down! I said just make an estimate to start off! I wanted them to guess so we had something to compare their final answers to. I wanted them to continually checking their work against their initial guess.

After a few minutes of estimating one group asked: “Are we stacking them like this…..

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or like this…..

IMG_0965.JPGAwesome!!!! I said “Does it matter?” and they all yelled yes!!! So we then agreed that we had TWO problems to solve. So we put up two sets of estimates!!! We decided to stack them like the second picture first!

Estimates

Estimates

I then asked:

“Did you need anything from me?”

they asked for: Rulers, my height, and Desmos!

I gave them all of those things…….everyone wrote frantically when I said I was 183 cm tall!!!

They worked! I saw groups stacking cups, recording values in Desmos, and measuring!

Almost all groups realized that the stack height was only changing by the lip amount and I saw a lot of this…

IMG_2730.JPGwhich had me excited!!! It gave me a chance to say: “Tell me about this, why do you think this is correct?” It was so interesting to hear their responses…..they were convinced they were right so I said let’s plot this in desmos and see if the equation matches the table

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Oh!!

They knew they were wrong…..but what was awesome is that they knew how to fix it!!!! Desmos is awesome for this. It’s like a visual self correction machine! We discussed that the start of the line didn’t seem to match up with our points. Then the ahaa! happened.

“We didn’t use the zero row for our start value.” They fixed it and were visually rewarded with a correct answer.

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After our equations were in desmos, the kids dragged their finger along the line until they reached a height of 183 cm and read off the number of cups! For the kids who seemed ahead of the game this was my chance to introduce solving equations by using opposite operations!

Finally we stacked the cups to verify.

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Round 2: Stack the cups end to end.

Most groups divided my height with the height of 1 cup…..21 cups….give or take….So great! It gave us context when we discussed opposite operations when solving equations.

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I found it was great that we had two problems in one! We are discussing how to distinguish between partial variation problems and direct variation problems. And here is one scenario where we got to look at each!!! Such a valuable activity!

Oh……did you want to know my height in cups (overlapped)??? —–> 128!

[UPDATE: April 2015]

As an extension use the videos from Andrew Stadel to teach solving linear systems graphically! Access his task here

Below are the list of Ontario Curriculum Expectations covered in this activity—-> Look at them all!!!!

  • pose problems, identify variables, and formulate hypotheses associated with relationships between two variables
  • carry out an investigation or experiment involving relationships between two variables, including the collection and organization of data, using appropriate methods, equipment, and/or technology (e.g., surveying; using measuring tools, scientific probes, the Internet) and techniques
  • describe trends and relationships observed in data, make inferences from data, com- pare the inferences with hypotheses about the data, and explain any differences between the inferences and the hypotheses
  • compare the properties of direct variation and partial variation in applications, and identify the initial value
  • express a linear relation as an equation in two variables, using the rate of change and the initial value
  • describe the meaning of the rate of change and the initial value for a linear relation arising from a realistic situation
  • determine values of a linear relation by using a table of values, by using the equa- tion of the relation, and by interpolating or extrapolating from the graph of the relation.

 

Wouldn’t it be awesome…

by Jon Orr

Desmos,

I can’t stop thinking about the great stuff from Penny Circle, Waterline, Central Park, Desman, and Function Carnival. Specifically the collaboration; the crowd sourcing of data and responses!

In Penny Circle, I love the fact that the student gets to do a few instances of selecting a circle and filling it with pennies. Then the data is grouped with the rest of the class….and voila!! we have a scatterplot!

I would love for this option of crowd sourcing content as a regular option. Wouldn’t it be awesome for when we complete the Vroom Vroom activity or the Barbie Bungee activity that we could ask students to record a few pieces of data in their table….like this,

Screen Shot 2014-11-09 at 6.23.40 PM

but up on the projector the class sees this?

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Wouldn’t it also be awesome if I asked the class to draw me a line with slope -2 ….the student would see theirs….

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but we would all see this?

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I’ve been using PearDeck for some lessons lately and we’ve been able to crowd source some stuff like..

Put the moveable point on A solution to the inequality f(x) > 40

Day 23 - Pear Deck!!

Day 23 – Pear Deck!!

We’ve also been able to crowd source by the old fashion way…….everyone write their points up on the board then we can all graph. This is still great don’t get me wrong……i’m just wishing!

Wouldn’t it also be awesome when we go to make Math Art with our Function Art project…..we all work together to make a picture like…

Screen Shot 2014-05-13 at 9.53.09 PM

 

I know that Texas Instruments has TI Navigator which tries to link students up ……but in my opinion it’s not as nice or easy as Desmos is to use!!!! Maybe this is already possible in Desmos and I just don’t know it. Or maybe there is something else out there……but I doubt it.

I would love it if my class could all work together…..keep our technology social! These are just some wishes! Love Desmos no matter what!

Describing Relationships – Active Learning

by Jon Orr

We have started discussing graphing relationships in my grade 9 class.

Our lesson goal was to

I can…

describe a situation that would explain the events illustrated by a given graph of a relationship between two variables

I have loved Graphingstories.com and wanted to incorporate them…and some of Dan Meyer’s graphing stories …into my lessons! This is the perfect place…..here’s how we did it.

Day 1: We start with an estimation…..

I play the video (Poor quality) about 6 different glasses filling up with coloured water.

I pause it after a few seconds and ask: “Which glass will fill up the fastest? Draw the shape of your winning glass on your whiteboard” We take some guesses from the class…..then watch some more video. About 3/4 of the way through I pause again. “Anyone want to switch glasses?” Some of them will switch and some stick to their original guesses. After watching the final result…..I get some boos and “You tricked us”. We discuss why they filled up at the same time….which leads us into saying Volume of all  = Same and comparing the volume of the glass vs. time……which leads us to discuss the rate at which the glasses are filling = Also Same!

From there we jump right into Desmos.com and the WaterLine Activity.

This is one of the most engaging tasks on this topic I’ve seen. The predictions of height of water vs. time and the ability to self correct is amazing! As the kids work through the activities I always take time to discuss their answers to:

 

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We have a great discussion on how this new graph looks and I get them to draw one one on their whiteboards. (wish Desmos could add that prediction/check into the activity!).

WaterLine and its discussion takes the remaining of the period to complete.

Day 2: Graphing Stories & Distance Time!

We begin by watching and drawing different graphing stories from Dan Meyer (Elevation, Distance vs. Time). Check them out and download them! (He doesn’t even charge $4.99 for them!).

We then use Vernier’s LabQuest2 and the motion detector (borrowed from Science). Students walk in from of the detector and the rest of the class watches in real time how their distance changes vs. time. We get the kids to walk slow….then fast, walk away/towards….so they see how the graphs relate to real motion!

 

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Lastly….. The kids are to create their own video graphing story and have peers draw the graphs to match.IMG_2664-0.JPG

  1. They pick a card that has some sort of motion described: “student walks fast away….then backs up slowly”
  2. They create a video that shows that motion. They use their phones or our iPads to capture that motion.
  3. They trade that video with another group and then they have to draw the graph to match!
  4. They keep trading and graphing different relationships!

The first time I ran through this series of activities I freaked out after because we just used two days and the kids didn’t solve/answer any problems from the textbook/worksheet! They don’t have anything written in their notes!!!!

 

IMG_2667.JPGEvery year I realize that there is great thinking and reasoning going on here! We have great discussions on what the graphs should look like. We need less notes and more active learning!! The kids are completing problems because they created them! They lived them! I feel they have understood the main concept at a deeper level!

[UPDATE: April 2015 ] – Read the modifications for Day 2 — the inclusion of a gallery walk. 

anyways……thats all for now!