Intentional Thinking Map for PLC Planning (Questions 1 & 2) Title of Unit: Understand the connections between proportional relationships, lines, and linear equations. Standard(s) being addressed? (Use) similar triangles to (explain) why the slope m is the same between any two distinct points on a non-­‐
vertical line in a coordinate plane; (derive) the equation y=mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Circle the Verbs and underline the key concepts (important nouns and noun phrases). PLC question #1: What do we expect all students to learn? à PLC question #2: How will we know if and when they have learned it? Know Declarative knowledge: Facts, vocabulary, information Vocabulary: Right triangle, leg, hypotenuse, similar triangles, ratio, and y-­‐intercept “m” represents the slope “b” represents the y-­‐intercept The equation y = mx has a y-­‐intercept of zero Understand Do “Essential understandings,” or generalizations, and represent ideas that are transferable to other contexts. Procedural knowledge: Skills, strategies and processes that are transferrable to other contexts. Slope is a constant rate of change on a non-­‐
vertical line that can be represented using similar triangles. y=mx and y=mx+b are two ways to represent a linear equation. Level 1 (Retrieval) Level 2 (Comprehension) Level 3 (Analysis) Derive the equation y=mx for a line through the origin. Derive the equation y=mx+b for a line intercepting the vertical axis at b. Using similar triangles, explain why the slope is the same through any two distinct points on a coordinate plane. Level 4 (Knowledge Utilization) Prerequisite skills: What prior knowledge (skills from previous grade levels) do students need to have mastered to be successful with this standard(s)? coordinate plane, slope, vertical line is undefined, horizontal line has a slope of zero Learning Goal(s)/Objective(s): Write equations of lines in slope intercept form that go through the origin and through the y-­‐axis. Use similar triangles to explain why the slop of the line is the same through any two points on the line. DSBPC-­‐OTL Intentional Thinking Map for PLC Planning (Questions 1 & 2) Standard MACC.8.EE.2.6: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-­‐vertical line in a coordinate plane; derive the equation y=mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Sample Task(s) Aligned to the Cognitive Complexity of the Learning Name___________________________________________&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
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ACTIVITY: Finding explain Slopes
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why the slope is • Use similar triangles, explain why the slope is the intercept form. the same through any Work with a partner.
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