Tag: card sort

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Lesson Sketch: Reading Algebra (Card Sort + Critical Thinking)

Topic: Reading Algebra (CCRS: A.SSE.1a)

Why:

Half of the battle with algebra (well, some significant fraction of the battle anyways, because half is always anxiety and focus and  grit and all the metacognitive things) is just reading algebra. The variables, the changes in notation and conventions, it looks so unfamiliar to new learners. And for those inclined to doubt their math abilities, a string of letters and a lack of familiar symbols is often a trigger to shut down.

So, a lesson to get used it to before we try to do anything with it.

What:

  1. A warm up: Sal Kahn answers a darn good question “Why all the Letters in Algebra”
  2. Some translation (aka direct instruction on the conventions)
  3. And, then the core of the lesson. A card sort. We matched cards with a x b to cards with ab, and b x b to b2, and we kept going a x b x b, and b 2, etc. etc.

(I love card sorts. I love how they prompt collaborative work, and aren’t worksheets, make things a tiny bit more tangible. I particularly love them for teaching equivalence. I wrote here about how playing Concentration is a go to activity for me)

Pro Tip: My new favorite way to make card sorts is using GoogleSlides. Subscribe to receive my tips.

  1. But, as much as I love card sorts, I’ve been thinking about how I could raise the bar, and ask students to do some deeper thinking (to mix directional metaphors)

So after we matched the cards, I distributed some critical thinking questions:  Which were hard? Which were easy? Why do certain cards go together? What do the symbols mean? Write your own examples (because, goals )

Results: It was the first math class after vacation, and all of us were having a slow time getting back to work/school, so something like three quarters of my class conveniently, um, overlooked, the question that asked them to write with words the first time through.

But, in the end, I had one of the best student comments I’ve seen in a while:

Student writing "Tho my mind was pudding we eased into learning. Was very nice"

Pudding brain. I totally get this metaphor.

Also, I take that as a victory.

(This if from my metacognitive exit tickets, read more here)

And, those extra questions? I added them in and prettied it up, and put it all on Teachers pay Teaches for the next person teaching their students to read algebra.

Fall 2020 Update: I love this activty, but found it often wasn’t enough practice on it’s own…. so I made 8 different worksheets. #onaroll #differentiation.

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Goals: Student Written Problems

I’m a goals kind of person. I like them, find them helpful, function best when I’m clear on them. (Classic upholder, for any other Gretchen Rubin fans) So, the document that organizes all of my teaching is topped by a bullet pointed list of goals.

(Best goal ever: “Actually use sick time” That was actually helpful)

This fall, one says “incorporate student-written math tasks/problems/questions”

It’s an attempt to share agency, to give a confidence boost (you, yes, you, can write a math problem…), to switch up the formats (no worksheets!), to have open ended tasks.

 

So, this month I’ve tried two formats, with three topics, in two different classes.  (Because, upholder with goals)

 

Version 1: Passing Problems

The order of operations:

Introduce a model, a template, a pattern, a way to isolate a particular skill. (For us, expressions like 5+3×2 and (5+3)x2 that are different only in their parentheses)

               Students write similar problems on index cards.

Check and double check the cards, write answers on the back.

Collect, shuffle, redistribute cards

Do the problem, without writing the card. (Repeat, and repeat, and repeat this instruction. The impulse to write on the cards instead of the scrap paper is strong)

Check the answer

               Pass the card to the right, receive a new card.

Repeat.

 

Version 2:  Card Sort

The order of operations:

Introduce new material

Small groups complete pre-existing card sort

(This so far, is a classic mathacognitive lesson. I have a bin full of card-sort-like activities )

Students write their own pairs of cards to be sorted.

Once checked, the new cards are scrambled and displayed with our doc cam

The class repeats the process of reuniting the pairs with their own newly-written cards. (For my class, students are just writing on notebook paper which goes with which, you could have a whole class activity of physically moving and matching the pairs, or make copies for everyone to cut out and arrange)

 

Particularly with the passing problems, there was a fair amount of incredulous staring, with verbal and non-verbal versions of ‘you want me to write the problem?!?’

But, incredulity/confusion aside, everyone eventually wrote their own problems and solved some of their classmates’, so I’m declaring it a victory and looking for the next spot to have them write the problems.

 

Bonus: It inspired me to upgrade from my previous, handwritten, kind-of-rushed, oops-there’s-an-error cards to a new actually-typed-and-formatted set of my exponent card sort.

Further Bonus: I was on a roll, so I typed up my cards, then kept going until I had a whole pack of different exponent cards and instructions and templates and a lesson plan for student-written cards. They’re available on TeachersPayTeachers if you’re interested)

 

card sort cover