Tag: algebra

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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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Turning the Tables – Error Correction (Lesson Sketch)

Theory:

Catching your own errors is hard. It’s helpful (and more fun) to practice catching someone else’s errors. (Especially the teacher’s) (Also, to do it, you have to pay close attention to the correct method)

 

In practice:  

Do the worksheet you would have given your students… badly. (I usually aim for about a 50/50 error rate.) Plan your errors for the kind your students are mostly likely to make. (I’ll be forgetting to treat both sides of an equation equally, and reversing operations this week)

Give students the error-filled page(s) and a red pen. Their assignment: correct your work.

But not just correct it, give the kind of detailed feedback that would help this poor struggling teacher student learn. I ask my students to:

-Mark each question right/wrong

-Circle the specific error

-Write the correct method

-At the end of the worksheet, write a note with the reminders this student might need. (The notes are really sweet, I hope they talk to themselves as encouragingly as they write)

 

((Bonus, they will now appreciate how much work grading/your job is))

 

Easily adapted to:  Just about any topic. In my experience, it works best with multistep calculation tasks where procedure/precision matter.

Resource:  Algebra by Example (Example-based problem sets, many of them correcting an error)