Thoughts on Big Ideas and Supports

Posted on March 21, 2019


So I’m working w/ lessons for Illustrative Mathematics.    I’m going to try to brainstorm for myself…. what are some of the number sense obstacles that are *not* “quick-fixable” but which could, if I put them in a mess of times…. be eroded.

I’m inspired by the students who have been coming in this Spring Break week… one struggles a lot but *so much less* this week, which I can’t help but think is because … it’s spring break so there’s actually enough sleep/ less stress happening.   This student has started to understand that looking at decimal division, you can figure out if your decimal’s in the right place thinking about what the numbers mean.   THis student had started out dividing by 1000 or 10 with long division and utter confusion.   Now… 13.2 divided by 1.1  — isn’t 130, isn’t 1.3… it should be close to 13.2… *and* there was a sense of satisfaction and sense-making 🙂 🙂 🙂

So yes, that’s one BIG honking idea — “it’s not what it looks like — it’s what it means.”   (The thinking of meaning also helped the student with the long division and knowing how to move decimals.  Learning that “movign the decimal point changes what it means” was a revelation, happening about the fourth time I put the numbers in sentences.)

Another is … FRACTIONS and Percents and the connection between “taking 15% off” and seeing, feeling, and knowing that … therefore you are keeping 85%.  Oh, and let’s just connect the common fractions and percents that way.   Let’s make sure — as the other student has learned and it totally paid off in that last “knowledge check — that if the question says 43 is what percent of 35… it’s gonna be over 100 %.

(I’m not sure I want to actually broadcast that Other Thing — if it makes no sense if you multiplied, divide! and vice versa…)

Finally… not sure how overt I want this to be — it’s how we do things in our “Transitions” course — teaching the understanding of the relationship of wholes and parts.   Knowing that “how much did this change” and “How much more do you need” and “how much *did* you add”   … are subtraction scenarios, even if words like “total” and “add” are in there.

Oops not quite finally.   This might be the way around using “part whole” language, and understanding this would mean not having to go through the “if you multiplied and it didn’t make sense, then divide!”  arbitrariness… it’s the ability to see the “big picture” and to work forward *or* backwards with information.

Students come back next week… 6 more weeks… so it’ll be more evenings and weekends but fortunately *this* was the “meeting every night!” week  🙂   THe “fourth week of the month” is easier…