Filling it up!

by Jon Orr

In our grade 9 applied class we are finishing off linear relations and moving into solving equations. I want an activity that is hands-on, engaging, and shows a purpose to solving linear equations.

Here is some thoughts on an activity I want to try. Let me know what you think. Any feedback would be greatly appreciated.

Here it is: Filling it up!!

Show them this picture….

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Let them wonder, let them ask what that thing in the pitcher is.

ME:

“How many would be too much?”

“How many would be not enough?”

“How many is just right?”

Have them record the guess. “We’ll compare our answer to our guess”

Next,

ME: Let’s find out how many.

Organize them into groups of 3.

ME: What are we going to need?

We’ll need volume of the pitcher, volume of the cup, and volume of the weight.

Have discussion on:

What shape is the cup? …..is it more like a cylinder or a cone? Which is it closest to? What formula for volume will you use? Will you be right?

What shape is the pitcher? What shape is the weight?

Choose 1 member of you group to find the volume of the cup; choose 1 member for volume of the pitcher; choose 1 member to find volume of the weight.

Have the items around the room like stations:

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IMG_2772Each member will find the volume of their object and bring it back to the group.

Allow the students to work

Here are some scaffolding questions I can use (Please feel free to give me some more)

  • What’s changing as you fill up the pitcher?
  • Does it start with zero volume? What volume of the pitcher is already taken up?
  • What volume is left after the weight?

Here is a possible solution….

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My idea is this could be great context for introducing solving equations using opposite operations! Use their technique  and show how the volume grows as the cups increase. Use Desmos and relate it to y = mx + b.

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show them how their strategy is the same as solving 5562 = 1511 + 335x. Boom! Context for solving equations!

My ideas for extensions would be to put objects like….

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in the pitcher. Count how many cups to fill the pitcher now. Use our equation to solve for the volume of the car. [Corresponding Grade 9 Academic learning goal: Find the y-intercept (initial value) of a linear equation given the slope (rate of change) and a point. ]

What do you think?? Think it would work? I would love some feedback!

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!

 

Amazing Race Review Activity

by Jon Orr

We should not attach speed as a factor in our math learning but I love the intensity my students show when we do the Amazing Race Review.

I first saw this activity from a friend of mine Brian McBain. He created a review game where students travelled around the school completing challenges.The first to make it back to the room after completing all challenges was the winner…..just like in the show The Amazing Race.

Today was a review day on trigonometric expressions. I just grabbed some “Knowledgey” questions from the review section of the text. My goal here was to get them to practice the basics. I wanted to provide them some feedback on the application type questions….so i didn’t include them in the race.

I made clues like this…..

A

 

and  like…

Ewhere they are to complete the review question and then use their answer to figure out where to go next.

I also threw in some like….

D

 

 

F

where they had to come back to my room and complete a challenge.

 

Each clue was placed around or in the room indicated. With permission from the teachers of the room the students had to actually go in a classroom and look around for the clue.

When found each clue looked like…

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They had to scan the QR code which revealed the clue.

Making the QR codes is pretty easy…..

1. Take a picture of your clues and put them in a Google Drive folder.

2. For each clue, grab the shareable link and paste it into the QR code generator here: http://www.qrstuff.com/

3. Download that QR code and paste it into a sheet like above. And you’ve got a clue!!!

I staggered the start so each group didn’t just follow each other from room to room. I gave them a recording sheet so they could keep track of their clues and work. I set them off and said “Complete all clues in the correct order and you will be eligible to crack the code for the prize.”

 

Here is the code to crack….

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This years class was pretty intense. The kids were racing each other down the halls and blocking each other from looking at their work. When all groups made it back to the room it was a heated match of “who can crack the code” first!! When finally the group opened the lock …..the class erupted! Some in cheers and some not so much!! You could put anything in that box for the prize and they would be happy!!! Stickers is usually my go to choice!!! Kids have a fun time practicing some skills!!

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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.