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

25 Aug

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 x4–y4 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. SMP7_Number SMP7_Algebra   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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6 responses to “Visual: SMP-7 Look for and Make Use of Structure #LL2LU

  1. 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 ……..

     
  2. 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.

     

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