Unit 5 functions and linear relationships homework 5 the slope formula

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Assessment

The following assessments accompany Unit 5.

Pre-Unit

Have students complete the Pre-Unit Assessment and Pre-Unit Student Self-Assessment before starting the unit. Use the Pre-Unit Assessment Analysis Guide to identify gaps in foundational understanding and map out a plan for learning acceleration throughout the unit.

Mid-Unit

Have students complete the Mid-Unit Assessment after lesson 9.

Post-Unit

Use the resources below to assess student mastery of the unit content and action plan for future units.

Unit Prep

Intellectual Prep

Unit Launch

Prepare to teach this unit by immersing yourself in the standards, big ideas, and connections to prior and future content. Unit Launches include a series of short videos, targeted readings, and opportunities for action planning.

Internalization of Standards via the Post-Unit Assessment

• Take the Post-Unit Assessment. Annotate for: 
  • Standards that each question aligns to
  • Strategies and representations used in daily lessons
  • Relationship to Essential Understandings of unit 
  • Lesson(s) that Assessment points to

Internalization of Trajectory of Unit

• Read and annotate the Unit Summary.
• Notice the progression of concepts through the unit using the Lesson Map.
• Do all Target Tasks. Annotate the Target Tasks for: 
  • Essential Understandings
  • Connection to Post-Unit Assessment questions
• Identify key opportunities to engage students in academic discourse. Read through our Teacher Tool on Academic Discourse and refer back to it throughout the unit.

Unit-Specific Intellectual Prep

• Read the Progressions for the Common Core State Standards in Mathematics, 6-8, Expressions and Equations for the relevant standards for this unit.
• Read the Progressions for the Common Core State Standards in Mathematics, Grade 8, High School, Functions for the relevant standards for this unit.

Essential Understandings

• A proportional relationship can be represented by the equation $${ y=mx}$$ and by a straight line in the coordinate plane passing through the origin. A non-proportional linear relationship can be represented by the equation $${y=mx+b}$$  and by a straight line in the coordinate plane that crosses the $$y$$-axis at point $${(0, b)}$$.
• The slope of a non-vertical line is the measure of vertical change over the measure of horizontal change between any two points on the line. In a proportional relationship, the slope of the graph is the same as the unit rate.
• Linear relationships can be represented and compared by writing equations, drawing graphs, and identifying the slope and $$y$$-intercept. Linear functions can be used to model and make sense of real-world situations. 

Vocabulary

initial value

linear equation

proportional relationship

rate of change

slope

table of values

unit rate

undefined slope

y-intercept

zero slope

Materials

• Graph Paper (2-3 sheets per student)
• Ruler (1 per student)
• Patty paper (transparency paper) (1 sheet per student)
• Optional: Matching game (1 per pair of students)

Lesson Map

Topic A: Comparing Proportional Relationships

Topic B: Slope and Graphing Linear Equations

Topic C: Writing Linear Equations

Common Core Standards

Core Standards

The content standards covered in this unit

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Expressions and Equations

• 8.EE.B.5 — Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

• 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.

Functions

• 8.F.A.2 — Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

• 8.F.A.3 — Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

• 8.F.B.4 — Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Foundational Standards

Expressions and Equations

• 6.EE.C.9

• 7.EE.B.4

• 8.EE.C.7

Geometry

• 8.G.A.1

• 8.G.A.2

• 8.G.A.4

• 8.G.A.5

Ratios and Proportional Relationships

• 7.RP.A.2

The Number System

• 7.NS.A.1

• 7.NS.A.2.B

Future Standards

Creating Equations

• A.CED.A.2

Expressions and Equations

• 8.EE.C.8

Reasoning with Equations and Inequalities

• A.REI.D.10

Standards for Mathematical Practice

• CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.

• CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.

• CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.

• CCSS.MATH.PRACTICE.MP4 — Model with mathematics.

• CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.

• CCSS.MATH.PRACTICE.MP6 — Attend to precision.

• CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.

• CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.