Visual: SMP-7 Look for and Make Use of Structure #LL2LU

How do our learners determine an equivalent expression to 4(x+3)-2(x+3)?  How would they determine the zeros of y=x²-4? How might we provide opportunities for them to successfully look for and make use of structure?

We want every learner in our care to be able to say

I can make look for and make use of structure.  (CCSS.MATH.PRACTICE.MP7)

But…What if I think I can’t? What if I have no idea what “structure” means in the context of what we are learning?

One of the CCSS domains in the Algebra category is Seeing Structure in Expressions. Content-wise, we want learners to

  • “use the structure of an expression to identify ways to rewrite it. For example, see x^4 – y^4 as (x²)² – (y²)², thus recognizing it as a difference of squares that can be factored as (x² – y²)(x² + y²)”
  • “factor a quadratic expression to reveal the zeros of the function it defines”
  • “complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines”
  • “use the properties of exponents to transform expressions for exponential functions”.

How might we offer a pathway for success? What if we provide cues to guide learners and inspire noticing?

Level 4
I can integrate geometric and algebraic representations to confirm structure and patterning.

Level 3
I can look for and make use of structure.

Level 2
I can rewrite an expression into an equivalent form, draw an auxiliary line, or identify a pattern to make what isn’t pictured visible.

Level 1
I can compose and decompose numbers, expressions, and figures to make sense of the parts and of the whole.

Screen Shot 2014-08-24 at 4.02.39 PM

Screen Shot 2014-08-23 at 6.55.40 PM

.pdf of these visuals

Illustrative Mathematics has several tasks to allow students to look for and make use of structure. We look forward to trying these, along with a leveled learning progression, with our students.

A-SSE Seeing Structure in Expressions Tasks

[Cross posted on Easing the Hurry Syndrome]

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.