How do our learners determine an equivalent expression to 4(x+3)-2(x+3)? How would they determine the zeros of y=x^{2}-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 (x^{2})^{2}–(y^{2})^{2}, thus recognizing it as a difference of squares that can be factored as (x^{2}–y^{2})(x^{2}+y^{2})”
- “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. ** ** 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. 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 A-SSE Seeing Structure in Expressions Tasks

Animal Populations

Delivery Trucks

Seeing Dots

Equivalent Expressions

Leveled learning progression posters [Cross posted on Experiments in Learning by Doing]

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howardat58

August 25, 2014 at 8:46 am

I followed the link to “Equivalent expressions” only to find a most unimaginative example, only a 1% improvement on “the old ways”.

This is what I see as “look for and make use of structure” :

1. find an equivalent fraction to 27/33 …… Oh look, 27 is divisible by 3, its digits add up to 9

2. what can you say about the equation sqr(x) – 6.25 = 2(x + 2.5) ?

…….(can’t do superscripts here)…….

…..Oh look, 6.25 is 2.5 squared, then we have a difference of two squares ……..

Ronald Fischman

August 27, 2014 at 4:52 pm

Anyone had to suffer with Saxon Math? Gross. If CCSS only made people throw away every Saxon textbook ever printed, that would be a major win for the students.