Students strengthen their understanding of slope as a rate of change with the use of similar triangles. They also recognize connections between rate of change, slope and constant of proportionality as it is represented in different ways. Students represent linear relationships with tables, lines and graphs which represent positive and negative slopes, and also vertical and horizontal lines.
PACING = 3 weeks
∎ Students will compare the quotients of a pair of side lengths in similar triangles to introduce the concept of slope. (8.EE.6) (MP.2)
I can find the slope of a line in a coordinate plane using knowledge of similar triangles. (8.EE.6)
∎ Students will reason abstractly and quantitatively when interpreting slopes, unit rates, or equations of proportional relationships in the form of y=mx+b. (8.EE.5, 8.EE.6) (MP.2)
I can recognize that the coefficient of x in a linear equation is the slope of the line on a graph. (8.EE.6)
I can recognize that a rate is the slope of a line. (8.EE.5)
I can explain that an equation in the form of y=mx will represent the graph of a proportional relationship with a slope of m and y-intercept of 0. (8.EE.6)
I can understand that the intercept changes as a line is translated. (8.EE.6)
I can explain why a positive or negative slope in a particular context makes sense. (8.EE.5)
∎ Students will precisely graph proportional relationships and linear equations. (8.EE.5) (MP.6)
I can draw a graph of a proportional relationship when given a table or an equation. (8.EE.5)
∎ Major Content ⊡ Supporting Content 🌕 Additional Content
New Vocab: rate of change, slope, rise, run, linear equation, slope-intercept form, y-intercept
Review Vocab: congruent (≅), constant of proportionality, interpret, proportional relationships, right triangle, scale factor, similar (~), unit rate, slope
Academic Vocab: constant, define, derive, undefined
*The computational strategies that you practice during number talks does NOT have to align with the core math content. Number talks are meant to practice fluency strategies, not teach new content.
I can recognize that a rate is the slope of a line. (8.EE.5)
I can explain why a positive or negative slope in a particular context makes sense. (8.EE.5)
I can draw a graph of a proportional relationship when given a table or an equation. (8.EE.5)
I can find the slope of a line in a coordinate plane using knowledge of similar triangles. (8.EE.6)
Ready Teacher Toolbox Lesson 8: Graph Proportional Relationships and Define Slope -Sessions 1-4
Assessment Tasks UPDATED 8th gr assessments 8.EE.6 8.EE.5 Proficiency Rubrics 8.EE.6 & EE.5 IAR sample questions 8.EE.5 8.EE.6
Prior knowledge/Just in Time support & Enrichment RTTB Lesson 8: Slope Rules
Nearpod Math lessons Open Middle tasks
Interactive manipulatives
I can recognize that the coefficient of x in a linear equation is the slope of the line on a graph. (8.EE.6)
I can explain that an equation in the form of y=mx will represent the graph of a proportional relationship with a slope of m and y-intercept of 0. (8.EE.6)
I can understand that the intercept changes as a line is translated. (8.EE.6)
Ready Teacher Toolbox Lesson 9: Derive and Graph Linear Equations of the Form y-mx+b -Sessions 1-5
Assessment Tasks UPDATED 8th gr assessments 8.EE.6 IAR sample questions 8.EE.6 Proficiency Rubrics 8.EE.6
Prior knowledge/Just in Time support & Enrichment RTTB Lesson 9: Line Slide
Nearpod Math lessons Open Middle tasks
Interactive manipulatives
“Closure in a lesson does not mean to pack up and move on. Rather, it is a cognitive activity that helps students focus on what was learned and whether it made sense and had meaning.” How the Brain Learns Mathematics (2007) P. 104
There are many ways to wrap up and reflect the day's activities but this step is often overlooked or rushed. Purposely plan and allow time for students to have closure each day (even if it means setting a timer or daily alarm so you don't run out of time).
Ideas for closure activities