What is your process for creating/designing a new lesson on a curricular topic (e.g. completing the square, anti-derivatives, etc.). What do you do? What do you think about? You can think of a specific lesson if you want, if it makes this easier! (I know we don’t often have the opportunity to think about the things we have come to do naturally!)

Can you talk about a lesson that you designed and taught recently that you were super excited about? Did it go well? Did it flop? How do you know?

We like to collaborate in our department -- though it admittedly isn’t easy because of our busy schedules. Have you had the opportunity to collaborate in a meaningful way in your career? Can you talk about how that went? If not, what would be the ideal collaboration for you?

As a department, in the Upper School, we’re moving away from traditional textbooks and more into student discovery and investigation to uncover ideas/concepts. This means that there is more of an onus on teachers to develop curricula -- which can be a lot of work, but it is exciting work. Have you ever had the opportunity to develop parts of a curriculum (or an entire curriculum)? Tell me about that? If not, what are your thoughts about teachers designing their own curricula?

What are ways you’ve experimented in your classroom -- whether they worked out or not?

Many in our department have kids work in groups. Do you use groups in your teaching? If so, how do you use them? If not, how do kids interact with each other in your classroom?

What is something you’ve been consciously working (with regards to your teaching) in your own classes?

What are some things you think students would say about you? Why?

I’m personally trying to become more intentional about a lot of different things that go on in my classroom. Can you think about ways you’re intentional in your practice? Things you’re hyperconscious of either when planning or executing a lesson?

This is just out of curiosity -- there is no right answer! In the math department, different teachers feel differently about real world mathematics and applications (though we all recognize that students really appreciate seeing mathematics become “real” to them). What are your thoughts about pure mathematical work versus real world mathematical work?

]]>I had something a bit more general in mind that is not restricted to adding the same value to numerator and denominator. I'll tweet it out!

]]>It is essentially adding the same value to numerator and denominator of a fraction. a+n/b+n

One concern I have is that some users may not recognize the limitations of this strategy (ex: works differently for improper fractions). Of course, that doesn't mean that it can't be used; we just need to understand when it does and does not apply.

Interestingly, I recently used this same idea as a Sometimes/Always/Never prompt with students: "Adding the same number to the numerator and denominator of the fraction increases the value."

]]>For the 7/13 vs. 5/11 example, imagine if you have completed 11 questions on a test and got 5 of them right, so you are at 5/11. Then you did two more questions and got them both right, so now you are at 7/13.

Well, your overall grade should have INCREASED because you just got the last two questions right, so 7/13 should be larger than 5/11.

]]>Thanks for the comment. I haven't seen my students returning to the flowchart as a reference. However, it does seem as though the creation of the flowchart has helped them process the different strategies and needs of different numbers.

Thank you also for the suggestion of Popplet. I will have to check that out. I have had them work on whiteboards because I didn't like any of the online options. So, maybe this one will change my mind.

Tyler

]]>I may try this approach for our unit on long division with and without decimals.

You may want to explore a free on-line or IPad resource called Popplet. It's a concept map builder that could be used to develop a flowchart like yours, where the boxes are easy to move around and re-arrange. ]]>

I usually introduce them to this wikipedia page (https://en.wikipedia.org/wiki/Divisibility_rule#Divisibility_rules_for_numbers_1.E2.80.9330) which really piques the interest of a few kids. There is always one kid who memorizes rules for 17 or 29. I love that. Later on, they can learn how to show that they work.

]]>Love the sense making in the divisibility rules worksheet. Do you have them then formalize the rules in class perhaps?

]]>Curiously, there's been one school I've been to that committed to one publisher's 4 year sequence... and it's the top ranked high school (as measured by ACT's college readiness benchmark) in the state. [Obvious chicken or the egg question here, and I'm not saying this to insinuate any causation... but it does seem to be an interesting coincidence if nothing else.]

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