Tuesday, November 22, 2016

More Faculty Lounge Math

My teaching life pre-MTBoS was certainly different than it is now.  I look at student work differentlyplan lessons and activities differentlyprovide feedback differently, even think of myself as a math learner in a different way than I did before becoming an active part of this amazing community.  But nothing has changed more than the way I look at what I see around me.  My friend Graham Fletcher has taught me that what I'm doing is called mathematizing the world, and now that I've started, I can't seem to stop.  In that spirit, here's another edition of Faculty Lounge Math.

Pretzels
This is more like a 2-Act than a 3-Act...

 What fraction of the container is filled with pretzels?
 Does this help?

Muffins
This one got tweeted out:

 Fractions anyone?

A Faculty Lounge 3-Act

Act 1

Washing Up from Joe Schwartz on Vimeo.

Main Question: How many squirts will the machine dispense until it runs out of soap?

Act 2

 Inside.  According to the company, 0.4 mL of liquid foam soap is dispensed each time it's activated.
 The dispenser holds 1 bag.  Each bag holds 1,200 mL of foam soap.
Act 3

My first attempt at figuring this out didn't go so good.

 I added 3 + 10 + 100.  I don't know... 113 handwashings just seemed too low.

So I tried something different...

 3,000 was more like it!
Where did I go wrong?

Act 4: The Sequel

The dispenser can be set to squirt 0.7 mL of soap per activation.  How many hand washings per bag?

A jar of pretzels, trays of muffins, a cookie, a soap dispenser; in my previous life they would have been things to eat and a way to promote good hygiene.  But thanks to DanAndrewGrahamMarilynRobertTraceyMichaelSimonKristinFawnMax,  Annie, Andy, and the rest of the MTBoS crew, I now see them as opportunities to notice and wonder, estimate, spark a number talk, and create and solve problems.  It's a gift I'm thankful for.  Hope they don't mind if I re-gift.

Monday, November 7, 2016

Two New Routines

Courtesy of Sarah Carter, a pair of high yield geometry routines I experimented with last month with our fifth graders:

Quick Build

I flashed this image on the SmartBoard for a few seconds, then took it down:

Using snap cubes, students had to build the structure from memory:

 It's OK to show it a second and even a third time.

After all had built the structure, I asked them to share how they had visualized it in their minds, and their responses were quite varied.  Some saw a 2 by 3 rectangular prism with a two-step staircase attached, others saw a three-step staircase with a 1 by 3 rectangular prism attached.  Still others saw 3 levels: 4 on the bottom, 3 in the middle, and 2 on the top.
Then I asked about the structure's volume, and they generated lots of equations:

 AM class

 PM class

I liked this activity for several reasons:
• It reinforced the idea of finding the volume of non-overlapping right rectangular prisms, which is a major grade 5 focus.
• It reinforced order of operations and writing equations, another grade 5 standard.
• It inspired a little number talk.
Also, the kids loved it!  They want to do it again, but next time with, as one student put it, "Harder shapes."  So I have this one loaded up:

Quick Draw

This activity comes from Grayson Wheatley.  Again, flash the image for a few seconds, then take it down.  Ask kids to draw the figure from memory.

 I chose this one for our first try.
One student's effort:

quick draw video from Joe Schwartz on Vimeo.

Another:

As with quick build, I asked the kids how they visualized:
• "A square, with a box around it, with 4 trapezoids."
• "A box in a box with 4 lines connecting the corners."
• "A  3-D cube facing me."
• "A room with a ceiling, two walls, and a floor."
• "A pyramid with the top cut off."
Lots of great vocabulary was generated:

 Parallel and intersecting lines, right, acute, and obtuse angles, corners, sides, 2- and 3- dimensional shape names...what's not to like?
Number talks, counting circles, estimation180, subitizing; we've done a good job infusing these routines into our instructional practice.  That's a balance weighted heavily on the number sense side. These two routines, which emphasize spatial reasoning and geometry, are a needed and important counterweight, and I look forward to more experimentation across grades K-5.  And again, thanks to Math = Love for the inspiration!