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?
I can integrate geometric and algebraic representations to confirm structure and patterning.
I can look for and make use of structure.
I can rewrite an expression into an equivalent form, draw an auxiliary line, or identify a pattern to make what isn’t pictured visible.
I can compose and decompose numbers, expressions, and figures to make sense of the parts and of the whole.
- 3.OA Patterns in the Multiplication Table
- 4.OA Multiples of 3, 6, and 7
- 5.OA Comparing Products
- 6.G Same Base and Height, Variation 1
[Cross posted on Easing the Hurry Syndrome]