They’re related- an attempt at a 3-Act Task



  • « converting » from one non-standard unit to another non-standard unit;
  • proportional reasoning


Watch the video:

What do you notice?  What do you wonder?

  • How many orange rods does it take to span the length of the table?
  • How long is the table?
  • Write an estimate you know is too high. Write an estimate you know is too low.



What information do you need?

Number of purple rods

Orange vs purple


The number of orange rods


4 réflexions sur “They’re related- an attempt at a 3-Act Task

  1. Pierre,
    You are braver than I – no ideas yet so congrats! Some quick comments:
    Realizing you don’t have colour choices for the rods, it is difficult to see the difference with orange and red (last small one).
    Also might be good to zoom/pan out to show the whole table at the end.
    I wonder if students might (and that’s OK) think more about area (i.e.covering the table surface) versus just the length.


    1. Hi Norma,
      Thanks for the comments! Yes, I agree, the colours are difficult to see. I’m hoping that when I use a better quality camera that the difference will show up better in the video. As for the pan out to the show the whole table at the end, it’s noted. As for the length vs. surface area, I was (am) hoping that the rods suggest more about length than area… Once I reshoot it, we can test it out more to see what students wonder the « most » about. Thanks again for the feedback and if you think of anything else, please let me know!


  2. Hi pierre — I really like the orange vs purple in the Act II. It was a clever way to help me think about the length. In the reveal, is it possible to also have a photo with both the purple and the orange next to each other? If we wanted to find the exact measurement, can you also provide how long the purple rods are? What ideas do you have about how students might solve the problem?


    1. Hi Elham,

      Thanks- I really like relational rods to get kids thinking about (eventually) converting measurement units (i.e.- How do we go from kilometers to meters? Do we divide or multiply? Why?) As for the picture of both purple and orange, yes for sure. Graham suggested something similar. I’ll make sure to include it in the next iteration. The length of the orange rod is 10cm and the purple is 4cm- all Cuisenaire rods have the same measurements (white is 1 cm, red is 2 cm, etc.) but I’m guessing (now) that not all kids will necessarily know this… so yes, good point. As for possible student solutions, they could use the information that 2 orange rods equal 5 purple rods and count it out using the picture – « I’ll touch 5 purple rods at a time on the picture and note 2 orange »; they could form groups of 5 purple rods on the picture (if they have a paper copy in hand) then write 2 over top of the groups; they could take the total number of full purple rods and divide by 5 to get the number of orange rods; they could possibly use a table of values to see a pattern or extend it to the « end ». Could you see students using any other strategies?

      Thanks for the comments and questions- it all helps to push my thinking when trying to create one of these things… not as easy as Graham, Andrew, Dan, etc. make it look!



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