The 4th grade has just started their fraction unit, so I was curious how that may impact their work with the Cuisenaire rods. I started just like I did in Kindergarten and 3rd grade, with a notice and wonder:
There were two of the ideas that really struck me as things I want to have the students explore further later: First was, “2 of the staircases (the staggered rods in order of size) could make a square.” They had them arranged on their desks like the picture below…but I want them to answer:
- Is that a square?
- If not, could we make it a square?
Then I started to wonder, do we call it a square? Should we say square face? Then what about area…would we say, “What is the area of the rectangle?”? That feels wrong because they keep calling the white rod a cube (which it is). But then asking about volume is not 4th grade. BUT, the tiles we use for area in 3rd grade are also 3-dimensional. <–would love thoughts on any of that in the comments!
One student noticed that the orange rod was the height of the staircase and I thought of area again since it was said right after the comment above. This idea would be really helpful for the students above when they are determining if their figure is a square.
I loved that one group noticed that any of the rods could be a whole and another group wondered if orange was the whole. Great lead into what I was thinking I wanted them to explore!
I asked them to find values for the rods based on their relationships. Of course the very first group I call on had 2 as the whole, which blew a lot of students minds, so I want to revisit that a bit later and ask them to explain how that works.
All of the other groups had orange as either 1 or 10, so I asked them to find the other values if the orange was 5 and 100. They played with that for a bit and then I began to hear a lot of aha’s, so I set them off to find more and they could have gone on forever.
I left them with the prompt, “Tell me about the patterns and relationships you notice.” and for those who looked like they were struggling to answer that question, I added, “If you are struggling with that, tell me how you could find the rest of the values if I gave you one of them and which one would you want?”
I loved how this student chose the orange, white and yellow as the easiest end, beginning, and half. I also like the red x 2 is purple, but we need to talk through that notation a bit.
This was the most common response, seeing the numbers get smaller as the rod got shorter.
This student’s noticing could be an interesting number choice question to pose: Why do you think groups chose numbers for orange that were doubles or halves of the other numbers we already had?
This student disagreed with the student who gave the responses in the first column because he is determined the white is 1/10 because the orange is 1. Would be great to pair them up and have them come to an agreement.
This student is seeing the white value adding to each value above it to get the next. I also love how she writes notes about how neat her handwriting is:)
I would love to have them play around with this first pattern in this entry! What other relationships could they find after they explored this one?
So much fun! Cannot wait to get into other grade levels to see if I can begin to find a progression of ideas with these rods!