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  • Kyle Ferreira van Leer

    June 17, 2020 at 12:21 pm

    Topic: Comparing Slopes of Proportional Relationships in Different Forms (8th Grade)

    1. Unconsciously Incompetent
      • Can point out that lines look different
      • May be able to use words like ‘steep’ or ‘shallow’
      • Struggles to see slope (steepness) when not in graph (visual) form
    2. Consciously Incompetent
      • Can identify which line is ‘steeper’ when both in visual form [can begin to compare]
      • May be able to identify slope from equation
      • Struggles to make comparisons from table (without visual)
      • Struggles to identify how much steeper something is
    3. Consciously Competent
      • Uses triangles to identify slope visually, with “easy” sides
      • Can use ∆y and ∆x from table (subtraction) to identify the slope as “rise over run”
      • Is able to find slopes independently to say which one is “steeper” and uses subtraction to indicate by how much
    4. Unconsciously Incompetent
      • Can look at two relationships and compare, often using the unit rate (1, r) to make the comparison immediately
    5. Consciously Masterful
      • Understands that the slope appears as the unit rate in proportional relationships, and can demonstrate where it appears in graph, table, and equation form
      • Is able to make the comparison to unit rates in proportional relationships to the slope in a linear relationship, especially in graph forms
      • Make comparisons with division of proportional relationship slopes, and knows that they can look solely at ∆y, so long as ∆x is constant.