Students compare proportional relationships, define and identify slope from various representations, graph linear equations in the coordinate plane, and write equations for linear relationships.
In Unit 5, eighth-grade students zoom into linear functions, extending several ideas they learned in the previous unit on Functions. They begin the unit by investigating and comparing proportional relationships, bridging concepts from seventh grade, such as constant of proportionality and unit rate, to new ideas in eighth grade, such as slope. Students formally define slope and learn how to identify slope in various representations including graphs, tables, equations, and coordinate points. Investigating slope is an opportunity for students to engage in MP.8, as they use the repeated reasoning of vertical change over horizontal change to strengthen their understanding of what slope is and what it looks like in different functions. Lastly, students will spend time writing equations for linear relationships, and they’ll use equations as tools to model real-world situations and interpret features in context (MP.4).
Just as in Unit 4, students will draw on previous understandings from sixth and seventh grades related to rates and proportional relationships, and the equations and graphs that represent these relationships.
The concepts and skills students learn in this unit are foundational to the next unit on systems of linear equations. In Unit 6, students will investigate what happens when two linear equations are considered simultaneously. In high school, students will continue to build on their understanding of linear relationships and extend this understanding to graphing solutions to linear inequalities as half-planes in the coordinate plane.
Pacing: 19 instructional days (15 lessons, 3 flex days, 1 assessment day)
This assessment accompanies Unit 5 and should be given on the suggested assessment day or after completing the unit.
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initial value
y-intercept
unit rate
linear equation
rate of change
slope
zero slope
undefined slope
proportional relationship
table of values
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8.EE.B.5
Review representations of proportional relationships.
8.EE.B.5
Graph proportional relationships and interpret slope as the unit rate.
8.EE.B.5
Compare proportional relationships represented as graphs.
8.EE.B.5
Compare proportional relationships represented in different ways.
8.F.B.4
Graph a linear equation using a table of values.
8.EE.B.6
Define slope and determine slope from graphs.
8.EE.B.6
8.F.B.4
Determine slope from coordinate points. Find slope of horizontal and vertical lines.
8.EE.B.6
8.F.A.3
Graph linear equations using slope-intercept form $${y = mx + b}$$.
8.EE.B.6
Write equations into slope-intercept form in order to graph. Graph vertical and horizontal lines.
8.EE.B.6
8.F.B.4
Write linear equations from graphs in the coordinate plane.
8.EE.B.6
8.F.B.4
Write linear equations using slope and a given point on the line.
8.EE.B.6
8.F.B.4
Write linear equations using two given points on the line.
8.EE.B.6
Write linear equations for parallel and perpendicular lines.
8.F.A.2
8.F.B.4
Compare linear functions represented in different ways.
8.F.B.4
Model real-world situations with linear relationships.
Key: Major Cluster Supporting Cluster Additional Cluster
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