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!