8th Grade - Unit 1 - Moving Straight Ahead (23 days) (7 th grade book) Things to Emphasize:

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8th Grade - Unit 1 - Moving Straight Ahead (23 days) (7

th

grade book)

Things to Emphasize:

 Unit rate

 Proportional vs. Non-proportional

 Functions represented in 4 different ways (words, tables, symbols, and graphs)

 Solving equations

Standards:

8.EE.5(b) - Interpret the slope of a graph as the unit rate.

8.EE.6(a) - Determine slope between any two distinct point on a graph. 8.EE.6(b) - Interpret the equation y= mx+b from a graph.

8.EE.7(a) - Solve linear equations without using distributive properties.

8.EE.7(b) - Solve linear equations by expanding expressions using distributive properties. 8.EE.8(a) - Solve systems of linear equations by a graph using real world problems. 8.F.1 - Determine the output (input) by knowing the function and input (output). 8.F.2 - Compare functions represented in an different way(equation, graph, table,

and/or context).

8.F.3 – Interpret the equation y=mx+b as defining a linear function, whose graph gives a

straight line; give examples of functions that are not linear.

8.F.4(a) - Determine the rate of change and initial value from a table, graph, and

equation.

8.F.4(b) - Interpret the rate of change and initial value into the context of the situation.

Materials/Technology:

 Frayer Model (WTSG)

 Meter sticks

 Stopwatch

 Grid paper

Additional Resources:

 DPI Lessons for Learning – Perplexing Puzzle

 DPI Lessons for Learning – Bow Wow Barkley

 DPI Lessons for Learning – Sandy’s Candy Corporation

Quick Glance:

Inv 1 (all): Walking Rates

Inv 2 (all): Exploring Linear Relationships

Inv 3 (all but 3.1): Solving Equations

Inv 4 (all but 4.4): Exploring Slope

Vocabulary:

 Coefficient  Equality  Linear function  Linear relationship  Proportional

relationship  Slope  Solution  Unit Rate  Variables

(independent/dependent)  Y-intercept

Evidence of Learning:

 Unit Readiness Assessment

 2 Check Ups

 1 Partner Quiz

 1 Unit Test

 2 Unit Projects

 1 School Net Assessment - Named: 8th_{Grade – Moving} Straight Ahead

Important Notes:

 Do NOT go past what it does in the book, do not need too much detail here, these concepts will come back around in other units to reinforce and build on concepts

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8th Grade - Unit 2 – Thinking With Mathematical Models (23 days)

 Trend lines

 Scatterplots

 Positive vs. negative slope

 Linear vs. non-linear data set

 Relative frequency

Standards:

8.EE.5(a) – Compare different proportional relationships in different ways (graphs, equations…) 8.EE.5(b) - Interpret the slope of a graph as the unit rate.

8.EE.6(a) - Determine slope between any two distinct point on a graph. 8.EE.6(b) - Interpret the equation y=mx+b from a graph.

8.EE.8(a) - Solve systems of linear equations by a graph using real world problems.

8.F.2 - Compare functions represented in an different way(equation, graph, table, and/or context). 8.F.3 - Determine which functions are linear and non-linear and give examples.

8.F.4(a) - Determine the rate of change and initial value from a table, graph, and equation. 8.F.4(b) - Interpret the rate of change and initial value into the context of the situation. 8.F.5 - Analyze a graph and describe where it is increasing, decreasing, constant, linear, and nonlinear.

8.SP.1 – Construct to interpret a scatterplot by describe patterns such as clusters, outliers, pos. / neg. assoc., linear, and non-linear.

8.SP.2 - Create a line of best fit (linear model) on a scatterplot and assess its closeness. 8.SP.3 – Create and use a linear equation from a scatterplot to solve problems. 8.SP.4(a) - Construct data on two way relative frequency tables.

8.SP.4(b) - Interpret and describe data on two way relative frequency tables. Materials/Technology:

 Paper bridges, paper cups, pennies, flat toothpicks

 DPI - Lessons for Learning – The Case of the Vase

 DPI - Lessons for Learning – Sandy’s Candy Corporation

 DPI - Lessons for Learning – Bow Wow Barkley Quick Glance:

Inv 1 (all): Exploring Data Patterns

Inv 2 (all): Linear Models and Equations

Supplement: Analyzing Graphs

Inv 4 (all but 4.4): Variability and Associations in Numerical Data

Inv 5 (all): Variability and

Vocabulary:

 Categorical variable  Function  Line of best fit  Linear  Mathematical

model  Outliers  Scatterplot  Slope  Two-way

frequency  Unit rate

 2 Check Ups

 1 Partner Quiz

 1 Unit Test

 1 Self-Assessment

 1 School Net Assessment - Named: 8th_{Grade –}

Thinking With Mathematical Models

 Analyzing graphs can be done in a variety of ways, writing stores from graphs, draw a graph from a story, etc. (can refer back to 6th_Grade

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Associations in Categorical Data  Y-intercept

8th Grade - Unit 3 – Looking for Pythagoras (25 days)

 Irrational vs. Rational Numbers

 Pythagorean Theorem

 Square Root

 Perfect Squares vs. Non-perfect Squares

Standards:

8.NS.1(a) Determine which numbers are rational or irrational.

8.NS.1(b) Represent rational numbers in different ways (decimals and fractions). 8.NS.2 - Estimate irrational numbers value and locate them on a number line.

8.EE.1 – Know and apply properties of integer exponents to generate equivalent numerical

expressions.

8.EE.2(a) - Evaluate square root and identify which is a perfect square or irrational number. 8.EE.2(b) - Evaluate cube root symbols to determine which is a perfect cube or irrational

number.

8.G.6 - Explain a proof of the Pythagorean Theorem.

8.G.7 - Apply the Pythagorean Theorem to determine unknown side lengths in real world

situations.

8.G.8 - Apply the Pythagorean Theorem to find a distance on a coordinate system.

 Additional Resources: What's Your Angle Pythagoras by Julie Ellis

 DPI - Lessons for Learning – Real Number Race

 DPI - Lessons for Learning – The Laundry Problems

 The Pythagorean Relationship by AIMS

 Discovering the Pythagorean Theorem

 Proof of the Pythagorean Theorem Quick Glance:

Inv 1 (1.3): Coordinate Grids

Inv 2 (2.2, 2.4): Squaring Off

Supplement: Discovering the Pythagorean Theorem

Inv 4 (all): Understating the Pythagorean Theorem: understanding Real Numbers

Supplement: More Practice with Pythagorean Theorem

Vocabulary:

 Diagonal  Hypotenuse  Irrational number  Legs

 Perfect cubes  Perfect squares  Pythagorean

Theorem  Radical

 Rational number  Real numbers  Repeating decimal  Root

 1 Check Ups

 1 Partner Quiz

 1 Unit Test

 1 Unit Project

 1 School Net Assessment - Named: 8th_{Grade – Looking} for Pythagoras

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 Terminating decimal

8th Grade - Unit 4 – Growing, Growing, Growing (15 days)

 Properties of Exponents

 Scientific Notation

 Non-linear Example

Standards:

8.EE.1 – Know and apply the properties of integer exponents to generate equivalent

numerical expressions.

8.EE.3 – Use numbers expressed in the form of a single digit times an integer power of 10 to

estimate very large or very small quantities, and to express how many times as much one is than the other.

8.EE.4 – Perform operations with numbers expressed in scientific notation.

8.F.1 – Understand that a function is rule that assigns to each input exactly one output. 8.F.3 – Inteprety the equation y=mx+b as defining a linear functions, whose graphs is a

straight line; give examples of functions that are not linear.

 Additional Resources: DPI - Lessons for Learning – Nonlinear Functions

Quick Glance: Inv 1 (1.1 and LfL): Exponential Growth

Inv 5 (5.1, 5.2, supplement, 5.4): Patterns With

Exponents

Vocabulary:

 Base

 Exponent

 Exponential form

 Non-linear

 Power

 Scientific notation

 Standard form

 1 Check Ups

 1 Partner Quiz

 1 Unit Test

 1 Unit Project

Growing, Growing, Growing

 The focus on this unit is not for students to learn about exponential functions; students need to know what makes something non-linear, properties of exponents, and scientific notation

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 Dilations

 Transformations (rotation, reflection, translation)

 Angle Measures

 Similarity

 Congruence

Standards:

8.G.1 - Rotate, reflect, and translate geometric shapes and their parts.

8.G.2 - Identify congruent figures and describe a sequence of rotations, reflections, and

translations.

8.G.3 - Describe the effects of dilations, translations, rotations, and reflections.

8.G.4 - Identify similar figures and describe a sequence of dilations, rotations, reflections,

and translations.

8.G.5(a) - Calculate angle measures of two dimensional shapes.

8.G.5(b) - Explain similarity of triangles based on angle measures. Materials/Technology:

 Patty Paper ( an get at deli in grocery store)

 Transformations Using Patty Paper Quick Glance:

Inv 1 (all): Symmetry and Transformations

Inv 2 (2.1, 2.2): Transformations and Congruence

Inv 3 (3.1-3.3): Transforming Coordinates

Inv 4 (all): Dilations and Similar Figures

Vocabulary:

 Angle  Congruence  Coordinate plane/grid  Dilation  Polygon  Reflection  Rotation  Scale factor  Similarity  Symmetry  Transformation  Translation

 2 Check Ups

 1 Partner Quiz

 1 Unit Test

 1 Unit Project

Butterflies, Pinwheels, and Wallpaper

 Can skip Inv 1 if time is tight, just introduce transformations in some way

 Animation and video games can be a great place to be in real life component to reference throughout unit

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 Distributive property

 Factoring

 Solving multi-step equations

 Volume of 3D shapes

Standards:

8.EE.7(b) - Solve linear equations by expanding expressions using distributive properties. 8.F.1 - Determine the output (input) by knowing the function and input (output).

8.F.2 - Compare functions represented in an different way(equation, graph, table, and/or

context).

8.F.3 – Determine which functions are linear and non-linear and give examples.

8.F.4(a) - Determine the rate of change and initial value from a table, graph, and equation. 8.F.4(b) - Interpret the rate of change and initial value into the context of the situation. 8.G.9 - Apply the formulas for volume for a cone, cylinder, and sphere to solve real world

problems.

 Additional Resources: DPI - Lessons for Learning – Gift Box Dilemma

 DPI - Lessons for Learning – Meltdown

 DPI - Lessons for Learning – Perplexing Puzzle

 Pull from 7th_{grade Filling and Wrapping for Volume if needed} Quick Glance:

Inv 1 (all but 1.3): Making Sense of Symbols: Equivalent Expressions

Inv 2 (all): Combining Expressions

Inv 3 (3.1, 3.2, practice): Solving Equations

Inv 4 (4.1, 4.2): Looking Back at Functions

Vocabulary:

 Cone  Cylinder

 Distributive property  Equivalent

expressions  Expanded form  Expression  Factored form  Properties of equality  Sphere

 Volume

 2 Check Ups

 1 Partner Quiz

 1 Unit Test

 1 Unit Project

 1 School Net Assessment - Named: 8th_{Grade – Say It} With Symbols

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 System of Equations

 Equivalency

 What it means to solve a system of equations

Standards:

8.EE.8(a) - Solve systems of linear equations by a graph using real world problems. 8.EE.8(b) - Solve systems of linear equations algebraically using real world problems.

 Additional Resources: DPI - Lessons for Learning – Cookie Calorie Conundrum

Quick Glance:

Inv 1 (all): Linear Equations With Two Variables

Supplement: Solving Linear Systems Symbolically

Vocabulary:

 Combination method  Expense

 Income  Linear

 Point of intersection  Profit

 Solve the system  Standard form  Substitution method  System of equations

 2 Check Ups

 1 Partner Quiz

 1 Unit Test

 1 School Net Assessment - Named: 8th_{Grade – It’s In} The System

 Make sure to review linear function with the rule, table, and graph before diving deep into this unit