Many Many Volumes

In our senior math classes (advanced functions & calculus) we come across a problem like this….Screen Shot 2014-11-26 at 7.00.47 AM

I really like these problems, they have great potential but not really in this form. Let’s jazz it up and spend an entire class with this

Start with this video:

Ask What questions do you have about this?

What size is that rectangle?
Why are the corners cut?
Is volume always the same?


My question:

What size of that square do we cut out so the box has the biggest volume?

Play the video again and have them yell out when they think the box has the largest volume.

Have them guess
What is too small?
What is too large?

Have them take their guess for the size of the corner and find the volume of the box

Draw a picture of the “card board” label the dimensions.

Draw the squares to cut out. Optional (Cut them out) make the boxes.


What’s the new length?
What’s the new width?
What’s the height?

What’s the volume?

Is this the max?
How can we check?
Have them do another? And another.

Have them come up to your computer and enter their height and volume in the Desmos page for each box.

Screen Shot 2014-11-26 at 7.09.50 AM


Now, let’s generalize!
This time let your guess be x and find an expression for the volume.

What’s the new width? Take 8 and subtract twice your guess. (8-2x) Now the length? What is the height now??

Put that expression into Desmos and let them see the function, let them point to the maximum.

Screen Shot 2014-11-26 at 7.13.32 AM

For calculus: have them find the maximum using derivatives!

Show them this video to check their guesses.

From here we can solve problems like our original textbook question. The kids are invested now and they are ready to use the equation to find the value of x where the volume is say 24 cubic units.

Further reading: Jonathan Newman’s volume of a box Activity 

Credits: Algebra in motion for the Geometers Sketchpad file. Dan Meyer – this lesson mimics his Circle Square lesson.

UPDATE [Nov. 27, 2014]

Luke Walsh created a Desmos Sketch that seems super useful!

My first Lesson with Pear Deck


Today we gave PearDeck a try. It was awesome….. so far here are the best features:

  1. When I asked students to: “Place a moveable dot on the point where the function gives a value of 40”. On their own screen they see just their dot, but on the projector screen they see everyone’s. — on this particular example the class was split on the two points where the volume is 40. This was awesome because we could all see that there are two solutions. I then asked “Now place a dot where the function gives a value greater than 40” Again they could see in live time everyone’s responses……but it was great for explaining that there are infinite solutions to that question (Our lesson goals were to solve inequalities using graphs)!!!
  2. It worked on all devices!!! It worked on their phones, iPads, tablets and computers…..this was great. I didn’t need to book a lab or for everyone to have an iPad with a specific app! It’s web/cloud based so they just need to access a webpage.
  3. Works with Google Drive….load files right from the Drive….it also saves to the drive. When kids join the class they are asked to sign into their google drive account. So on the dashboard I can see their name!

Some Feedback

Noticed that I had to switch between projector view and dashboard view so that we could see the entire class’s responses to the drawing questions. It would have been nice to see their drawings overlapped just like when you place a dot!
[update: there is a check box that allows the overlay of drawings!!]
More to come. Totally worth the subscription fee though!!

Guess Who!!!

One of my kids’ favourite game is Guess Who…..remember this one?



You remember it! I wanted my students to practice recognizing characteristics of polynomials without having to just complete questions out of the text book… I thought this game could work great! When you play this game you ask characteristic questions about the person you have picked and try to narrow the choices down…..all before the other person has guessed yours!

Perfect for characteristics of functions!!! Could also be great for my grade 9s who will later learn characteristics of linear relations.

I put this “board” together for the possible choices.

Screen Shot 2014-09-08 at 8.52.31 AM


And kids will use dry-erase markers and “paper protector” sheets so they can re-use the Game boards.


Here are some pictures of my students playing the game

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Game of Risk

Recently read a blog post of a review game …. Risk from Angie (@aeakland) . I love review games instead of just textbook questions… i adapted this game to be played in my MHF4U Advanced Functions class.

Here are the rules….

  • In teams, each team starts with 100 points. Write your points and names on the board.
  • Complete any of the Risk Questions in any order. (They are just the Review questions from the textbook).
  • For each question: After coming up with a solution, wager any or all of your points.
    • If you are correct – – add the points to your total!!! Yay!
    • If you are incorrect — subtract that many points from your total. Boo!
  • The top three teams with the most points were eligible to enter the draw at the end for the prize!!!

photo 4-2

Great things about the game…

Kids were cheering — when getting the problems right!……that doesn’t happen when just working on review problems from the book.

Kids were self /peer assessing their work — by betting they were deciding how confident they were on their work! They took their time, and thought about their answers making sense!

Kids were doing math!

The winning team won their choice of a geek sticker!