MVP 4.1: Introducing Equations

I have been excited and terrified by lesson 4.1 since I first worked through it in PD. I’m excited because it does a phenomenal job of teaching Common Core standard A.REI.1: “Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.”

Basically, students will figure out the solution (x=15), then work backwards to construct an equation Screen Shot 2018-02-25 at 12.01.34 PM based on which operations make sense in the context of the story.

I love this approach because it focuses students’ attention on the fact that every step in a solution process is an equivalent equation. This is such a deeper and more nuanced understanding than how students usually view solving equations, namely as a procedure of steps that yields a magical answer at the end.

That is why I am excited by this lesson. I’m terrified because in order to build the equations from context, this lesson has a LOT of language demands, and unlike other lessons where some of the language might be superfluous to the mathematics, almost every piece of language in this problem is essential to building the mathematical understanding.

Oh yeah, and I got an email from one of the counselors last week that on Monday I’ll have two brand new students in my ELL class who don’t speak a word of English. Welcome to my life! (I’m just hoping they’re in different sections so my classes stay below 36.)

To see what I mean about the language demands of this lesson, check out the story context:

Screen Shot 2018-02-25 at 12.13.08 PM.png

So, how to break this down? I’m going to use the 3 reads strategy. I’ve never used this strategy before, so I can’t speak very authoritatively on it, but here’s the basic idea:

Read 1: I read the story out loud to students. They listen, then write down everything they can remember. I’m going to post a visual with some of the key vocabulary:

Screen Shot 2018-02-25 at 12.16.54 PM.png

Students will then answer the following prompt:

Read #1: What is this story about?

Write down everything you remember from the story.

Read 2: I’m going to give students the story context on a half-sheet to share with their partners. We’ll do a choral read of the story, then students will answer this prompt:

Read #2: What are the quantities in the story?

What numbers are in the story?

What do those numbers represent?

Read 3: One more choral read (maybe a partner read if they hated the choral read) with the following prompt:

Read #3: What mathematical questions can we ask about the story?

Write down math questions that you can ask about the story.

After each read, I’m going to do a think-pair-share: individual time to write, partner time to discuss, whole-class share-out.

Realistically, this is most likely going to take the full period. Students will keep the notes and questions they’ve created to use as a reference on day 2.

 

Day 2: Working Backwards

After reviewing our notes from the 3 reads strategy, I’m going to display the following paired down diagram of the story:

Screen Shot 2018-02-25 at 12.24.29 PM.png

I’m then going to have students try to work backwards to determine the number of trays in each carton at the beginning:

Screen Shot 2018-02-25 at 12.25.44 PM

Students will do this in groups, and I plan to select a student/group who showed each operation carefully to present their work. We’ll discuss why each operation was necessary, and write down the actions that led to using that operation.

The MVP teacher notes suggest introducing equations to represent each stage of this undoing process:

Screen Shot 2018-02-25 at 12.29.36 PM.png

We’ll do this in guided notes for students to keep for reference. The notes will have the paired down story diagram at the top.

We’ll then pretend that we don’t know that the answer is 15, and we’ll try to solve the equation Screen Shot 2018-02-25 at 12.01.34 PM by undoing the operations and connecting each step back to the original story context.

Days 3–5: Building Equations from Post-It Notes

The rest of the week will be spent on the Post-It Notes story context in this lesson. On the first day, which according to this current plan is a Wednesday and has a shortened period, we’ll just decode each Post-It Note and make sure we understand the operation involved. I’ll leave the class hanging with the question of whether or not the order matters:

Screen Shot 2018-02-25 at 12.34.41 PM.png

Then, on Thursday we’ll do question 2:

Screen Shot 2018-02-25 at 12.36.19 PM

And maybe start question 3? I’m hoping that by the end of Friday most students will have a solid understanding of question 3 and be ready for a class discussion about it. That’s the goal anyway…

Screen Shot 2018-02-25 at 12.36.26 PM.png

These are the lesson materials I have so far:

2.26 MVP 4.1 Day 1

2.27 MVP 4.1 Day 2

2.27 MVP 4.1 Sequence of Events Diagram

2.28 MVP 4.1 Day 3 Post-it Notes

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