Reflection: Intervention and Extension Moving Toward Mastery: Completing the Square (Day 2) - Section 1: Opener: Area Problem With a Leading Coefficient of 2


With the unit coming to an end, we are in full-on review mode.  I would love for all students to be ready to tackle (and master!) completing the square; the reality is that somewhere between 1/3 and 3/4 of my students are really ready for that in any given class.  As I've noted before, that's a truth to be reckoned with and not ignored, and it's exactly the purpose of a lesson like this.  Every student should be getting what they need.

Before they dig deeper into completing the square, some students still need to demonstrate that they've mastered polynomial multiplication (SLT 6.1) or factoring (SLT 6.2), and others want a little more practice to make sure they're confident about those skills.  So there's one level of differentiation happening there: students choose to focus on one SLT or another.

What I'd really like to focus on here is another kind of differentiation that's so easy to implement, and yields such powerful results.  Textbooks attempt do it for us, and used thoughtfully, it goes such a long way: when we vary the values and the kinds of numbers in a problem, not only does the cognitive demand of a problem change, but so does the set of background knowledge that we've got to access.  

Compare these polynomial multiplication exercises, for example.  By now, all students should be able to do the top one.  I'd like for students to be able to extend that knowledge and be able to complete the second, but note also that a more comprehensive definition of like terms is prerequisite to correctly finishing the problem.  For the last one, binomial multiplication will be the least demanding part of the problem for most students.  By using a few problems like this, students can cement their understanding of the learning target, while also getting some important review of fraction arithmetic.

Finally, there's nothing "fun" about the last problem.  It's wicked drudgery.  But when a student has already been successful with simpler examples, and I provide a small set of problems like this one (between 2 and 4, no more), they're game to give it a try.  I'll also tell students that I just want to check in on what they recall about fractions -- they shouldn't stress about this, but hopefully they're able to figure it out.  That message goes a long way with kids.

  Intervention and Extension: Differentiating by Numbers
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Moving Toward Mastery: Completing the Square (Day 2)

Unit 10: Quadratic Functions
Lesson 18 of 21

Objective: SWBAT graph quadratic functions with irrational roots by rewriting equations in vertex form, and to solve quadratic equations by completing the square.

Big Idea: Students will continue to see that graphing quadratic equations and solving them work in tandem: the better we understand one, the more sense the other will make!

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u6 l18 graphing example
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