Reply To: Lesson 4-1: The Stages of Mastery Action

[Kyle Ferreira van Leer]

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.