In previous posts about “Duke is Missing,” I blogged about launching and exploring. The next step, traditionally, is summarizing. I’ve been thinking a lot recently about one kind of summarizing, “how do I know I’m right?” A big classroom goal for me is for students to be in charge of answering that question, instead of looking to me to be the arbiter. I want my students to know that math makes sense and they are smart enough and have the authority to figure out if their answer makes sense.

This submitter shows us the work they did, but I’m curious, how do they know their answer is right?

head=6in
tail=head + 1/2 body=6in+ 1/2 body
body=head+tail=9in +1/4 body

tail=12in
body=18in

Some good questions to help confirm you’re right are:

  • Is my answer reasonable?
    • (In this case, yeah, 3 feet long is reasonable for a setter.)
  • Does my answer match the constraints of the problem?
    • (No, if Duke’s body is 18″ then his tail should be 6″ + 9″ = 15″, since the mean brother says his tail is the length of his head plus half of his body.)
  • Is my work accurate?
    • (I think it’s inaccurate to say “head+tail=9in +1/4 body” since head + tail = head + head + 1/2body and 9in + 1/4body = head + half the tail which is not the same.)
  • Can I confirm my answer with another method?
    • (Maybe guess and check would be a good next method for this student to try?)

Telling the story of how you know you’re right can help you catch your own mistakes, as well as help you solidify your own understanding and help other people who might read your work. It’s a great habit and one we hope to get good at with the PoWs during the year.

How do you help your students take charge of knowing their right? What checking work strategies or routines are you using or wondering about?

Some “Duke is Missing” links in case you are interested: