Curriculum / Math / 8th Grade / Unit 5: Linear Relationships / Lesson 6
Math
Unit 5
8th Grade
Lesson 6 of 15
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Lesson Notes
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Define slope and determine slope from graphs.
The core standards covered in this lesson
8.EE.B.6 — Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the 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.
The foundational standards covered in this lesson
8.G.A.4 — Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
8.G.A.5 — Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.
7.NS.A.2.B — Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Three staircases are shown below.
a. Which staircase is the steepest? Without doing any calculations, order the staircases from least steep to most steep.
b. Slope is a measure of steepness. The greater the slope, the greater the steepness. Use the measurements provided in the diagram to justify the order of steepness you determined in part A.
c. Another staircase climbs 8 feet over a distance of 10 feet. Where does this staircase fall in the order of steepness?
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Staircase and Steepness by Fawn Nguyen is made available on Finding Ways under the CC BY 4.0 license. Accessed Feb. 24, 2018, 4:53 p.m..
Find the slope of the line in each graph below.
a.
b.
c.
A line is drawn through the points A, C, E, and G as shown in the graph below.
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15-20 minutes
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5-10 minutes
Find the slope of each line graphed below.
For the line in part B, use a different pair of coordinate points to find the slope to show that the slope is the same through any two points on the line.
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
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Determine slope from coordinate points. Find slope of horizontal and vertical lines.
Topic A: Comparing Proportional Relationships
Review representations of proportional relationships.
Standards
8.EE.B.5
Graph proportional relationships and interpret slope as the unit rate.
Compare proportional relationships represented as graphs.
Compare proportional relationships represented in different ways.
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Topic B: Slope and Graphing Linear Equations
Graph a linear equation using a table of values.
8.F.B.4
8.EE.B.6
8.EE.B.68.F.B.4
Graph linear equations using slope-intercept form $${y = mx + b}$$.
8.EE.B.68.F.A.3
Write equations into slope-intercept form in order to graph. Graph vertical and horizontal lines.
Topic C: Writing Linear Equations
Write linear equations from graphs in the coordinate plane.
Write linear equations using slope and a given point on the line.
Write linear equations using two given points on the line.
Write linear equations for parallel and perpendicular lines.
Compare linear functions represented in different ways.
8.F.A.28.F.B.4
Model real-world situations with linear relationships.
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