Fastest Sticky Sticker

It's rare that I post about something I haven't tried in the classroom. Here's an idea that came to me today, inspired by:

• My File Cabinet task
• Anyone who has asked, "How long did it take to put all those stickies on?" 
• Al's Card Tossing activity
• Jon's Trashketball Spiralled Lesson

I haven't done this activity, yet. If you try it out, please report back or offer suggestions. Thanks!

Competition:

Who is the fastest Sticky Sticker?

Translated: Who is the quickest at covering a 2-dimensional shape with sticky notes?

Materials:

• Whiteboards
• Stickies
• Blue painter’s tape
• Scissors
• Timers

Break students into groups.

Have them time each other sticking 10(?) stickies somewhere (whiteboard, desk, etc.).

• Determine who is the fastest Sticky Sticker of the group.
• Use their cell phone stopwatches as timers
• Use some type of table to predict how long it will take each person to stick different amounts of stickies and write an equation.

• Have each student determine their rate.

Reveal the playing fields

• First, without the dimensions, of course.
• Muster up some trash-talking
• I bet you I could beat anyone in here with one-hand behind my back.
• I might even give you a head start.
• I could beat you blind-folded.
• Have them write down guesses as to how many stickies will cover each shape.
• Have students guess the dimensions.
• Have measuring tapes out for students to measure their shape.

Have all groups figure out how many stickies are necessary for each shape. All dimensions given in inches.

• Square (24x24)
• Rectangle (21x27)
• Triangle (27x24)
• Parallelogram (24x18)
• Trapezoid (b1= 27, b2=21, h=18)
• Circle (d=18)

*The following is where I start thinking out loud and not entirely sure what makes sense since I haven't tested this out with students. Feel free to try it out and please report back.

Have each group randomly pick a shape.

• I'm going to predict that some students or groups will complain/gripe about receiving anything other than the square or rectangle. That's where the scissors come in.
• Give each group the amount of stickies they calculated for their shape
• Include a couple(?) extra stickies for a mistake?
• Give scissors to every group, but the square and rectangle groups.
• Groups who don’t get the square or rectangle must cut their stickies to fit inside
• The Circle group(s) should maybe get a little bit of a cushion (modification).
• The square and rectangle groups need to be challenged while they wait.
• They can help other groups prepare or figure out a reasonable head start.
• Should certain shapes get a head start?
• Should the head start be:
• time?
• stickies?
• Can we modify any of our equations from above?

Ready, Set, GO!

I’d love to see each student participate in the competition. At first, it might appear as though each group picks the fastest Sticky Sticker, but I’d love to make this competition a relay race.

• Have each group divide their total number of stickies by the amount of group members
• Each group member should stick about the same number of stickies.
• Groups determine the order (strategy)
• Could we graph what that might look like?

*At this point, go back to the blog posts by Al and Jon for more tips.

Determine how the head starts will be determined.

Blow the whistle and get kids sticking those stickies.

Congratulate the winners. Take selfies. Play your national anthem...

Round 2

Who can take the sticky notes off the fastest?

Useful Math:

• Area of various 2-D shapes
• Ratio of stickies stuck to time (or time to stickies)
• Rate
• Unit rate
• Writing an equation to model the rate
• Using the rate to predict how long it will take
• Possibly graphing the data (or “constant of proportionality)
• Translate (graphically) the equation above to account for the head start
• Piecewise functions for different members of the group.
• Decompose square units in a defined area

Let me know if you're going to try this one out. I will probably test it out in a few weeks during my summer course and report back here.

Sticky sticker,

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The Ultimate Task for Vertical Planning: Stacking Cups

This past week, I submitted a speaker proposal for NCTM 2016 in San Fransisco. The proposal is for a Grade 6-8 Burst (30 minutes) with the exact same title as this blog post: The Ultimate Task for Vertical Planning: Stacking Cups. I figure if I don't get accepted, at least I can share my thoughts here and you all can help spread the word about my idea if you think it has potential. If it does get accepted, I look forward to giving an update a year from now at NCTM. Here's my session description:

Who says you can't use the same task each year? Come see why Stacking Cups might be the single best secondary math task to get teachers at your school, district, or state to see the importance and necessity of vertical planning. Use tasks that utilize connections from the previous year and extend the mathematics each year. Work smarter, not harder. 

Let's first back up a bit. I attended Alex Overwijk's session at NCTM Boston a few weeks back. I had already read his awesome blog post "Open Strategy Cup Stacking" and knew there are multiple teaching moments with Stacking Cups. I remember teaching Math 8 a few years ago and getting a lot of use out of Stacking Cups as you can see a couple times here and here. I was preparing for a training with math teachers from grades 6-12 and THAT's when it hit me: I could have a room full of math teachers from grades six through twelve and they all could:

• be working on this task
• see the different skills and tools necessary for solving
• know the expectation of each grade level

I've heard comments from teachers numerous times like, 

"Well, if they do File Cabinet in 6th grade, I can't do it in 7th grade with my students."

"If they've done Stacking Cups in Math 8, then I can't do it in Algebra."

"If the 5th grade teachers use Estimation 180 with students, then I can't." 

YES! YOU CAN! It's called vertical planning.

YES, YOU CAN! Instead, let's ask different questions like, "How can we use the same task to extend the mathematics each year?" and  "How can we make connections to prior learning from the previous grade level?"

Let's work smarter, not harder.

I will spend the rest of this blog post highlighting each grade level and suggested uses for Stacking Cups. It won't be complete or the final version as this is through the lens of one person. I'm confident, with your help and critique, we can make it even better.

Math 6
Question: How many cups do we need to stack (alternating) to reach someone's height?
We talk about rate. We organize our information on a number line, in a table, using a tape diagram, etc. We explore the rates using various models.

Math 7
Question 1: How many cups do we need to stack (alternating) to reach someone's height?
We continue the conversation started in Math 6 revolving around rates, using constant of proportionality. All of this can be represented in a table, as an equation, and in a coordinate plane.

Question 2: How many cups do we need to stack (consecutively) to reach someone's height?
We now shift our thinking a bit where there is still a constant increase with each cup, but there is an initial amount (the cup handle). Students explore how to write an equation to represent this situation and solve it.

Question 3: What would be possible dimensions of a box that would contain the cups to stack to someone's height? Which dimensions would be the most cost effective?
Imagine students understanding surface area and volume and how they're related to each other, especially if we model with mathematics, by identifying variables such as:

• cardboard cost
• delivery truck capacity 
• store storage sizes
• consumer trends with buying cups
• more

Math 8
Question 1: How many cups do we need to stack (consecutively) to reach someone's height?
Similar to question 2 in Math 7. However, we extend the mathematical understanding as we explore constant rate of change (slope), input and output, linear, and how our situation can be represented in the form y = mx + b.

Question 2: When will two stacks of different sized cups be equal in height and have the same number of cups in each stack?
We introduce students to linear systems using this task. Students can organize the information about each cup in a table. We can extend prior knowledge to represent the situation using graphs, equations, and functions.

*By the end of Math 8, it might be helpful to mention (at least informally) to students the significance of discrete functions.

Algebra
We tighten up the math (both questions) previously learned in Math 8. How can we extend the mathematics. Add more challenging situations like the stacks start on different objects like desks, boxes, etc.
Question 3: How many cups would we need to stack in a triangular formation to someone's height?
This questions really extends the mathematics for students, but we can still use the tools they've learned from previous grades. Maybe students start by organizing the data in a table. Maybe they graph the data and notice it isn't linear. Maybe we can use desmos with sliders or a line of regression to explore quadratics.

Beyond Algebra and Geometry:
I'll admit this is where I'm a little rusty and would need you high school pros to jump in and contribute. I think with the triangle stacking, it can be taken from quadratic to a divergent series. I've also seen high school teachers come up with the following representations:

Al Overwijk also stacked cups in a triangular pyramid which is awesome.

Let's keep this vertical planning going. If you would like a couple charges, here you go:

Go to your site and/or district and push for Stacking Cups to be a signature task at all sites and secondary grade levels. Help support your colleagues with vertical planning. Report back.

Look for other tasks out there like Robert Kaplinsky's Hot Dogs or Dan Meyer's Penny Circle or Mathalicious' Wheel of Fortune or Graham Fletcher's Water Boy that can be used with vertical planning. Report back.

Vertical,
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