8th Grade Mathematics Curriculum · 8th Grade Mathematics Curriculum. Course Summary: In Grade 8,...

8th Grade Mathematics Curriculum Course Summary: In Grade 8, instructional time will focus on three critical areas: (1) formulating and reasoning about expressions and equations, including modeling and association in bivariate data with a linear equation, and solving linear equations and systems of linear equations; (2) grasping the concept of a function and using functions to describe quantitative relationships; (3) analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem. Scope and Sequence:

Time Frame Unit

34 Days Number Sense, Expressions, and Equations

68 Days Functions and Linear Relationships

27 Days Transformations and Transversals

35 Days Exponential Functions, Pythagorean Theorem, and Volume

Board Approved: July 23, 2015 2 | Page Revised: April, 2016 MLS Alignment: April, 2017

Curriculum Revision Tracking

Changes made in April, 2016:

● Unit 1: o Pacing was adjusted from 32 to 34 days o Sequence of Topics 6, 14, and 15 was changed.


Unit 1: Number Sense, Expressions and Equations

Subject: Mathematics Grade: 8th Grade Name of Unit: Number Sense, Expressions, and Equations Length of Unit: 34 days Overview of Unit: Students will understand that there are numbers which are not rational and approximate them by rational numbers. Students will also analyze and solve linear equations. Priority Standards for unit:

• MA.8.NS.A.1: Explore the real number system. a. Know the differences between rational and irrational numbers. b. Understand that all rational numbers have a decimal expansion that terminates or

repeats. c. Convert decimals which repeat into fractions and fractions into repeating

decimals. d. Generate equivalent representations of rational numbers.

Supporting Standards for unit:

● MA.8.NS.A.2: Estimate the value and compare the size of irrational numbers and approximate their locations on a number line. For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

● MA.8.EEI.C.1: Solve linear equations and inequalities in one variable. a. Create and identify linear equations with one solution, infinitely many solutions

or no solutions. b. Solve linear equations and inequalities with rational number coefficients,

including equations and inequalities whose solutions require expanding expressions using the distributive property and combining like terms.

● ISTE-EMPOWERED LEARNER 1: Students leverage technology to take an active role in choosing, achieving and demonstrating competency in their learning goals, informed by the learning sciences.

● ISTE-KNOWLEDGE COLLECTOR.3: Students critically curate a variety of resources using digital tools to construct knowledge, produce creative artifacts and make meaningful learning experiences for themselves and others.

● ISTE-INNOVATIVE DESIGNER.4: Students use a variety of technologies within a design process to identify and solve problems by creating new, useful or imaginative solutions.

● ISTE-COMPUTATIONAL THINKER.5: Students develop and employ strategies for understanding and solving problems in ways that leverage the power of technological methods to develop and test solutions.


Standard Unwrapped Concepts (Students

need to know)

Unwrapped Skills (Students need to

be able to do)

Bloom’s Taxonomy

Levels Webb's DOK

MA.8.NS.A.1 differences between rational and

irrational numbers. Know Remember 1

MA.8.NS.A.1

all rational numbers have a decimal expansion that terminates

or repeats. Understand Understand 2

MA.8.NS.A.1

decimals which repeat into fractions and fractions into

repeating decimals Convert Apply 2

MA.8.NS.A.1 equivalent representations of

rational numbers Generate Create 2 Essential Questions:

1. In earlier courses you studied rational numbers. What other types of numbers are there? 2. In earlier courses you studied rational numbers. Why do you need them? 3. Why do you write equations?

Enduring Understanding/Big Ideas:

1. There are rational and irrational numbers in the real number system. 2. Know the differences between them can help you understand if a fraction can be made

from the number, or whether or not a decimal and be derived from a fraction or square roots.

3. Complex questions can be solved using the structure of an equation and the process of inverse operations to isolate variables.

Unit Vocabulary:

Academic Cross-Curricular Words Content/Domain Specific

Ratios

Percents

Topic 1 Irrational Numbers

Perfect Square Real Number

Repeating Decimal Square Root

Terminating Decimal

Resources for Vocabulary Development: Use quality tools (See Adult Learning Framework handbook)


digits Topic 1: Rational & Irrational Numbers

Standard Topic & Section Suggested # of Days

Notes

MA.8.NS.A.1 1.1: Expressing Rational Numbers and Decimal Expansion

1

MA.8.NS.A.1 1.2: Exploring Rational Numbers 1

MA.8.NS.A.1 1.3: Approximating Rational Numbers

1

MA.8.NS.A.2 1.4: Comparing and Ordering Rational and Irrational Numbers

1

MA.8.NS.A.1 MA.8.NS.A.2

1.5: Problem Solving 1

Review Day 1.5 Review, Look Over and Test within a three day period (suggested) Test 1.5


digits Topic 2: Linear Equations in One Variable


Notes

Add/Subtract/Multiply/Divide Integers

2 Supplement Algebra 2.5 and 2.6

as needed

Intervention Clusters 10, 11 and 12.1 “Fractions”

Approx. 4 as needed

Use Intervention Lessons, Journal Entries and Intervention

HW assignments as needed

Supplement Distributive Property

1 Supplement May need to create own practice

Supplement Simplifying Expressions (Combining Like Terms)

1 Supplement May need to create own practice

Intervention Cluster 25 “Expressions and Equations”

Approx. 4 as needed

Use Intervention Lessons, Journal Entries and Intervention

HW assignments as needed

MA.7.EEI.B.1 2.1: Solving Two-Step Equations 1 Algebra 3.1 - 3.4

MA.7.EEI.B.1 2.2: Solving Equations with Variables on Both Sides

1 Algebra 3.1 - 3.4

MA.7.EEI.B.2 2.3: Solving Equations Using the Distributive Property

1 Algebra 3.1 - 3.4

REVIEW Solving Equations 1

Quiz Solving Equations 1

MA.7.EEI.B.2 2.4: Solutions - One, None, or Infinitely Many

1

MA.7.EEI.B.2 2.5: Problem Solving 1

Review Topic 2 1.5

Test Topic 2 1.5


Unit 2: Functions and Linear Relationships

Subject: Mathematics Grade: 8th Grade Name of Unit: Functions and Linear Relationships Length of Unit: 68 Days Overview of Unit: Students will understand the concepts related to identifying, creating, manipulating and solving functions and systems of equations. Students will also understand the concepts of using and creating systems of categorical data. Priority Standards for unit:

● 8.EEI.B.1: Graph proportional relationships. a. Interpret the unit rate as the slope of the graph. b. Compare two different proportional relationships.

For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

● 8.EEI.B.2: Apply concepts of slope and y-intercept to graphs, equations and proportional relationships.

a. Explain why the slope (m) is the same between any two distinct points on a non-vertical line in the Cartesian coordinate plane.

b. 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.

● 8.EEI.C.1: Solve linear equations and inequalities in one variable. a. Create and identify linear equations with one solution, infinitely many

solutions or no solutions. b. Solve linear equations and inequalities with rational number coefficients,

including equations and inequalities whose solutions require expanding expressions using the distributive property and combining like terms.

● 8.EEI.C.2: Analyze and solve systems of linear equations. a. Graph systems of linear equations and recognize the intersection as the

solution to the system. b. Explain why solution(s) to a system of two linear equations in two variables

correspond to point(s) of intersection of the graphs. c. Explain why systems of linear equations can have one solution, no solution or

infinitely many solutions. d. Solve systems of two linear equations.

● 8.F.A.3: Investigate the differences between linear and nonlinear functions. a. Interpret the equation y = mx + b as defining a linear function, whose

parameters are the slope (m) and the y-intercept (b). b. Recognize that the graph of a linear function has a constant rate of change c. Give examples of nonlinear functions.


Supporting Standards for unit: ● 8.EE.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.

● 8.EE.7 Solve linear equations in one variable. a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

● 8.DSP.A.1: Construct and interpret scatter plots of bivariate measurement data to investigate patterns of association between two quantities.

● 8.DSP.A.2: Generate and use a trend line for bivariate data, and informally assess the fit of the line.

● 8.DSP.A.3: Interpret the parameters of a linear model of bivariate measurement data to solve problems.

● 8.DSP.A.4: Understand the patterns of association in bivariate categorical data displayed in a two-way table.

a. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects.

b. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.

● 8.F.A.1: Explore the concept of functions. (The use of function notation is not required.) a. Understand that a function assigns to each input exactly one output. b. Determine if a relation is a function. c. Graph a function.

● 8.F.A.2: Compare characteristics of two functions each represented in a different way. ● 8.F.B.1: Use functions to model linear relationships between quantities.

a. Explain the parameters of a linear function based on the context of a problem. b. Determine the parameters of a linear function. c. Determine the x-intercept of a linear function.

● 8.F.B.2: Describe the functional relationship between two quantities from a graph or a verbal description.



Standard Unwrapped Concepts

(Students need to know)


be able to do)

Bloom’s Taxonomy

Levels Webb's DOK

8.EEI.B.1 Proportional relationships Graph Apply 2

8.EEI.B.1 Unit rate as the slope of the

graph Interpret Understand 2

8.EEI.B.1 Two different proportional

relationships Compare Analyze 2

8.EEI.B.2

Concepts of slope and y-intercept to graphs, equations and proportional relationships

Apply Apply 2

8.EEI.B.2

why the slope (m) is the same between any distinct points on a non-vertical line in the Cartesian

coordinate plane. Explain Understand 3

8.EEI.B.2

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. Derive Create 2

8.EEI.C.1 Systems linear equations in and

inequalities in one variable Solve Apply 2

8.EEI.C.1

linear equations with one solution, infinitely many solutions or no solution Create Create 3

8.EEI.C.1

linear equations with one solution, infinitely many solutions or no solution Identify Remember 1

8.EEI.C.1

linear equations and inequalities with rational number

coefficients, including equations and inequalities whose solutions require expanding expressions using the distributive property

and combining like terms Solve Apply 2 8.EEI.C.2 Systems of Linear Equations Analyze Analyze 2 8.EEI.C.2 Systems of Linear Equations Solve Apply 2

8.EEI.C.2

systems of linear equations and recognize the intersection as the

solution to the system. Graph Apply 2


8.EEI.C.2

why solution(s) to a system of two linear equations in two

variables correspond to point(s) of intersection of the graphs Explain Understand 3

8.EEI.C.2

why systems of linear equations can have one solution, no solution or infinitely many

solutions. Explain Understand 3 8.EEI.C.2 systems of two linear equations Solve Apply 2

8.F.A.3 the differences between linear

and nonlinear functions. Investigate Understand 1

8.F.A.3

the equation y = mx + b as defining a linear function, whose parameters are the slope (m) and

the y-intercept (b). Interpret Analyze 2

8.F.A.3 that the graph of a linear function

has a constant rate of change Recognize Understand 1 8.F.A.3 examples of nonlinear functions. Give Understand 2

8.DSP.A.1

scatter plots of bivariate measurement data to investigate patterns of association between

two quantities. Construct Apply 2

8.DSP.A.1

scatter plots of bivariate measurement data to investigate patterns of association between

two quantities. Interpret Analyze 3

8.DSP.A.2

trend line for bivariate data, and informally assess the fit of the

line. Generate Create 2

8.DSP.A.2

trend line for bivariate data, and informally assess the fit of the

line. Use Understand 2

8.DSP.A.3

parameters of a linear model of bivariate measurement data to

solve problems. Interpret Understand 2

8.DSP.A.4

patterns of association in bivariate categorical data

displayed in a two-way table. Understand Understand 2

8.DSP.A.4

two-way table summarizing data on two categorical variables

collected from the same subjects. Construct Create 2 8.DSP.A.4 two-way table summarizing data Interpret Analyze 2


on two categorical variables collected from the same subjects.

8.DSP.A.4

relative frequencies calculated for rows or columns to describe possible association between the

two variables. Use Understand 2 8.F.A.1 the concept of functions Explore Evaluate 3

8.F.A.1 a function assigns to each input

exactly one output Understand Understand 1

8.F.A.1 if a relation is a function Determine

Understand 2 8.F.A.1 a function Graph Apply 2

8.F.A.2

characteristics of two functions each represented in a different

way. Compare Analyze 3

8.F.B.1 functions to model linear

relationships between quantities. Use Understand 3

8.F.B.1

the parameters of a linear function based on the context of

a problem Explain Understand 3

8.F.B.1 the parameters of a linear

function Determine Understand 2

8.F.B.1 the x-intercept of a linear

function Determine Understand 3

8.F.B.2

the functional relationship between two quantities from a graph or a verbal description. Describe Evaluate 3

Essential Questions:

1. What is a function? How are functions used? Enduring Understanding/Big Ideas:

1. A function is a relationship between x and y, such that for every x input there is one and only one y output. Functions are used to describe and predict relationships between bivariate sets of data.

Unit Vocabulary:


Scatter Plot Initial Values

Topic 7 Function


Trend Line Outlier Cluster

Bivariate Data

Independent Variable Dependent Variable

Experiment Group

Control Group

Relationship

Linear Function Non-Linear Function

Interval Rate of Change

Relation Vertical Line Test

Topic 5

Linear Equation Slope

Slope of a line y-intercept

Proportional Relationship Rate of Change

Topic 8 Linear Function Rule

Initial Value Unit Rate

Topic 14 Cluster

Gap Outlier

Scatter Plot Trend Line

Positive or Negative Association Linear or Nonlinear Association

Topic 6

Solution of a System of Linear Equations System of Linear Equations

Topic 15

Bivariate Categorical Data Bivariate Data

Categorical Data Measurement Data

Two-way Frequency Table Two-way Relative Frequency Table



digits Topic 7: Defining & Comparing Functions


Notes

8.F.A.1 7.1: Recognizing a Function 1

8.F.A.1 7.2: Representing a Function 1

8.F.A.2 7.3: Linear Functions 1

8.F.A.2 7.4: Nonlinear Functions 1

8.F.A.3 7.5: Increasing and Decreasing Intervals

1

8.F.A.1 7.6: Sketching a Function Graph 1

8.F.A.1 8.F.A.2 8.F.A.3


Review 1.5

Test 1.5


digits Topic 5: Proportional Relationships, Lines, & Linear Equations

digits Topic 8: Linear Functions


Notes

MA.8.EEI.B.1

5.1: Graphing Proportional Relationships

1 Algebra 4.1-4.3 as needed

8.F.A.2 8.1: Defining a Linear Function Rule

1 Algebra 4.5 as needed

MA.8.EEI.B.2 5.2: Linear Equations y = mx 1 Algebra 4.5-4.6 as needed

8.F.A.2 8.2: Rate of Change 1 Algebra 4.4 as needed

MA.8.EEI.B.1

5.3: Slope of a Line 1 Algebra 4.4 as needed

MA.8.EEI.B.1 5.4: Unit Rates and Slope 1 Algebra 4.4 as needed

8.F.A.2 8.F.A.3

8.3: Initial Value 1 Algebra 4.5 as needed

MA.8.EEI.B.2 5.5: Y-intercept of a Line 1 Algebra 4.5 as needed

MA.8.EEI.B.2 5.6: Linear Equations: y = mx + b

1 Algebra 5.1-5.2 as needed

MA.8.EEI.C.1 8.4: Comparing Two Linear Functions

1

MA.8.EEI.C.1 5.7: Problem Solving 1

8.F.A.2 8.F.A.3


Topic 8 Review 2

Test Topic 8 2


digits Topic 6: Systems of Two Linear Equations


Notes

8.EEI.C.2 6.1: What is a System of Linear Equations in Two Variables

2

8.EEI.C.2 6.2: Estimating Solutions of Linear Systems by Inspection


8.EEI.C.2 6.3: Solving Systems of Linear Equations by Graphing


8.EEI.C.2 6.4: Solving Systems of Linear Equations using Substitutions


8.EEI.C.2 6.5: Solving Systems of Linear Equations using Elimination (Addition)


8.EEI.C.2 6.6: Solving Systems of Linear Equations using Elimination (Subtraction)


8.EEI.C.2 Problem Solving 2

Review 2

Test 2


digits Topic 14: Scatter Plots


Notes

8.DSP.A.1 14.1 Interpreting Scatter Plots 1

8.DSP.A.1 14.2 Constructing Scatter Plots 1

8.DSP.A.1 14.3 Investigating Patterns: Clustering and Outliers

1

8.DSP.A.1 14.4 Investigating Patterns: Association

1

8.DSP.A.2 14.5 Linear Models- Fitting a Straight Lines

1

8.DSP.A.2 14.6 Using the Equation of a Linear Model

1

8.DSP.A.2 14.7 Problem Solving 1

Review 1.5

Topic 4 TEST 1.5


digits Topic 15: Analyzing Categorical Data *This unit is considered modular, and may be moved to a different time of the

year to accommodate time and testing constraints.


Notes

MA.8.DSP.A.4 15.1: Bivariate Categorical Data 1

MA.8.DSP.A.4 15.2: Constructing Two-way Frequency Tables

1

MA.8.DSP.A.4 15.3: Constructing Two-way Relative Frequency Tables

1

MA.8.DSP.A.4 15.4: Constructing Two-way Relative Frequency Tables

1

MA.8.DSP.A.4 15.5: Interpreting Two-way Relative Frequency Tables

1

MA.8.DSP.A.4 15.6: Choosing a Measure of Frequency 1

MA.8.DSP.A.3 MA.8.DSP.A.4


Review 1.5

Test 1.5


Unit 3: Transformations and Transversals Subject: Mathematics Grade: 8th Grade Name of Unit: Transformations and Transversals Length of Unit: 27 Days Overview of Unit: Students will understand the concepts of identifying similar figures and translating those figures on the coordinate plane. Priority Standards for unit:

• MA.8.GM.A.1: Verify experimentally the congruence properties of rigid transformations. a. Verify that angle measure, betweeness, collinearity and distance are preserved

under rigid transformations. b. Investigate if orientation is preserved under rigid transformations.

• MA.8.GM.A.2: Understand that two-dimensional figures are congruent if a series of rigid transformations can be performed to map the pre-image to the image.

a. Describe a possible sequence of rigid transformations between two congruent figures.

• MA.8.GM.A.3: Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.

• MA.8.GM.A.4: Understand that two-dimensional figures are similar if a series of transformations (rotations, reflections, translations and dilations) can be performed to map the pre-image to the image.

a. Describe a possible sequence of transformations between two similar figures. • MA.8.GM.A.5: Explore angle relationships and establish informal arguments.

a. Derive the sum of the interior angles of a triangle. b. Explore the relationship between the interior and exterior angles of a triangle. c. Construct and explore the angles created when parallel lines are cut by a

transversal. d. Use the properties of similar figures to solve problems.

Supporting Standards for unit:

● MA.8.GM.A.1 Verify experimentally the congruence properties of rigid transformations. a. Verify that angle measure, betweeness, collinearity and distance are preserved under

rigid transformations. b. Investigate if orientation is preserved under rigid transformations.

● MA.8.GM.A.2 Understand that two-dimensional figures are congruent if a series of rigid transformations can be performed to map the pre-image to the image.

● MA.8.GM.A.4 Understand that two-dimensional figures are similar if a series of transformations (rotations, reflections, translations and dilations) can be performed to map the pre-image to the image.





Standards

Unwrapped Concepts (Students need to

know)


be able to do) Bloom’s

Taxonomy Levels Webb's DOK

MA.8.GM.A.4

two-dimensional figures are similar if a series of

transformations (rotations, reflections,

translations and dilations) can be

performed to map the pre-image to the image. Understand Understand 2

MA.8.GM.A.4

possible sequence of transformations between

two similar figures. Describe Understand 2

MA.8.GM.A.5

angle relationships and establish informal

arguments. Explore Understand 3

MA.8.GM.A.5 sum of the interior angles of a triangle. Derive Create 2

MA.8.GM.A.5

relationship between the interior and exterior angles of a triangle Explore Understand 3

MA.8.GM.A.5

the angles created when parallel lines are cut by a

transversal Explore Understand 3

MA.8.GM.A.5

properties of similar figures to solve

problems. Use Analyze 2


Essential Questions: 1. What does it mean for two figures to be identical? 2. How do geometric properties and logical reasoning allow you to form arguments and

make conclusions about relationships in geometry? Enduring Understanding/Big Ideas:

1. Two figures are identical if you can map one to the other by a sequence of rigid motions, such as translations, reflections, and rotations.

2. You can use what you know about transversals, parallel lines, and Pythagorean Theorem to identify, compare, or contrast geometric shapes.

Unit Vocabulary:


Flip Turn Slide

Enlarge Shrink

Increase Decrease

Similar

Corresponding Interior Exterior

Topic 9 Congruent Figures

Image Reflection

Rigid Motion Rotation

Transformation Translation

Topic 10 Dilation

Enlargement Reduction

Scale Factor Similar Figures

Topic 11

Alternate Interior Angles Corresponding Angles Deductive reasoning

Exterior angle of a triangle Transversal



digits Topic 9: Congruence


Notes

MA.8.GM.A.1 9.1: Translations 1

MA.8.GM.A.1 9.2: Reflections 1

MA.8.GM.A.1 9.3: Rotations 1

MA.8.GM.A.1 9.1 - 9.3 Review 1

9.1 - 9.3 QUIZ 1

MA.8.GM.A.2 9.4: Congruent Figures 1

MA.8.GM.A.1 MA.8.GM.A.2


Review 2

Topic 9 TEST 1


digits Topic 10: Similarity


Notes

MA.8.GM.A.3 10.1: Dilations 1

MA.8.GM.A.4 10.2: Similar Figures 1

MA.8.GM.A.4 10.3: Relating Similar Triangles and Slope

1

MA.8.GM.A.3 MA.8.GM.A.4



digits Topic 11: Reasoning in Geometry


Notes

MA.8.GM.A.5 11.1: Angles, Lines and Transversals

1

MA.8.GM.A.5 11.2: Reasoning and Parallel Lines

1

MA.8.GM.A.5 11.3: Interior Angles of Triangles

1

MA.8.GM.A.5 11.4: Exterior Angles of Triangles

1

MA.8.GM.A.5 11.5: Angle to Angle Triangle Similarity

1

MA.8.GM.A.5 11.6 Problem Solving 1

Review 2

Test Topic 11 1


Unit 4: Exponential Functions, Pythagorean Theorem and Volume

Subject: Mathematics Grade: 8th Grade Name of Unit: Exponential Functions, Pythagorean Theorem and Volume Length of Unit: 35 Days Overview of Unit: Students will work with radicals and integer exponents and understand the concepts of geometric reasoning as it relates to the Pythagorean Theorem. Students will also solve real-world and mathematical problems involving volume. Priority Standards for unit:

● MA.8.GM.B.1 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

● MA.8.GM.C.1 Solve problems involving volume of cones, pyramids and spheres. ● MA.8.EEI.A.1 Know and apply the properties of integer exponents to generate equivalent

numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27. Supporting Standards for unit:

● MA.8.GM.B.1 Explain a proof of the Pythagorean Theorem and its converse. ● MA.8.GM.B.3 Apply the Pythagorean Theorem to find the distance between two points

in a coordinate system. ● MA.8.GM.C.1 Solve problems involving surface area and volume.

a. Understand the concept of surface area and find surface area of pyramids. b. Understand the concepts of volume and find the volume of pyramids, cones

and spheres. ● MA.8.EEI.A.2 Solve equations of the form x2 = p and x3 = p, where p is a positive

rational number. ● MA.8.EEI.A.2 Evaluate square roots of perfect squares less than or equal to 625 and cube

roots of perfect cubes less than or equal to 1000. ● MA.8.EEI.A.2 Recognize that square roots of non-perfect squares are irrational. ● MA.8.EEI.A.4: Use scientific notation to solve problems.

a. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used.

b. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities.




● ISTE-INNOVATIVE DESIGNER.4: Students use a variety of technologies within a design process to identify and solve problems by creating new, useful or imaginative solutions.


Standards Unwrapped Concepts

(Students need to know)


be able to do) Bloom’s

Taxonomy Levels Webb's DOK

MA.8.EEI.A.1

the properties of integer exponents to generate equivalent numerical

expressions Know Remember 1

MA.8.EEI.A.1

the properties of integer exponents to generate equivalent numerical

expressions Apply Apply 2

A.8.GM.B.1

models to demonstrate a proof of the Pythagorean Theorem

and its converse Use Apply 2

MA.8.GM.B.2

the Pythagorean Theorem to determine unknown side

lengths in right triangles in problems in two- and three-

dimensional contexts. Use Apply 2

A.8.GM.C.1 problems involving surface

area and volume. Solve Apply 2

MA.8.EEI.A.4

scientific notation and choose units of appropriate size for

measurements of very large or very small quantities. Use Apply

2

MA.8.EEI.A.4

scientific notation and choose units of appropriate size for

measurements of very large or very small quantities. Use Apply 2


Essential Questions: 1. How do geometric properties and logical reasoning allow you to form arguments and

make conclusions about relationships in geometry? 2. Measurements frequently involve very large or very small numbers. How can you make

such measurements easy to use and compare? 3. How can you tell whether a linear equation models a proportional relationship? 4. What methods can you use to solve pairs of simultaneous linear equations in two

variables? Enduring Understanding/Big Ideas:

1. You can use what you know about Pythagorean Theorem to identify, compare, or contrast geometric shapes.

2. The process of scientific notation can be used to work with and express extreme values. 3. Understanding the forms of linear equations such as y = mx + b can give you the ability

to determine the type of line presented in equation form. 4. You may use graphing, substitution or elimination to determine if a solution exists and

then to find the solution to set of equations. Unit Vocabulary:


Topic 3 Cube Root

Negative Exponent Property Perfect Cube

Zero Exponent Property

Topic 4 Scientific Notation

Topic 12

Proof Theorem

Hypotenuse Leg of a Right Triangle Pythagorean Theorem

Converse of Pythagorean Theorem

Topic 13 Base Cone

Cylinder Height


Lateral Area Lateral Surface

Radius Right Cone

Right Cylinder Slant Height

Sphere Surface Area

Vertex Volume



digits Topic 3: Integer Exponents


Notes

MA.8.EEI.A.2 3.1: Perfect Squares, Square Roots, and Equations of the form x2 = p

1

MA.8.EEI.A.1 3.2: Perfect Cubes, Cube Roots, and Equations of the form x3 = p

1

MA.8.EEI.A.1 3.3: Exponents and Multiplication 1

MA.8.EEI.A.1 3.4: Exponents and Division 1

MA.8.EEI.A.1 3.5: Zero and Negative Exponents 1

MA.8.EEI.A.1 3.6: Comparing Expressions with Exponents

1

MA.8.EEI.A.1 3.7: Problem Solving 1

Review Topic 3 1.5

TEST Topic 3 1.5


digits Topic 12: Using the Pythagorean Theorem


Notes

MA.8.GM.B.1 12.1: Reasoning and Proof 1

MA.8.GM.B.1 MA.8.GM.B.2

12.2: Pythagorean Theorem 1

MA.8.GM.B.2 MA.8.EEI.A.1

12.3: Finding Unknown Leg Lengths

1

MA.8.GM.B.1 12.4: Converse of Pythagorean Theorem

1

MA.8.GM.B.3 12.5: Distance in the Coordinate Plane

1

MA.8.GM.B.1 MA.8.GM.B.2


Review 1.5

Topic 12 TEST 1.5


digits Topic 13: Surface Area and Volume


Notes

A.8.GM.C.1 13.2: Volume of Cylinders 1

A.8.GM.C.1 13.4: Volume of Cones 1

A.8.GM.C.1 13.6: Volume of Spheres 1

A.8.GM.C.1 13.7: Problem Solving 1

Review 1.5

Topic 13 QUIZ 1.5


digits Topic 4: Scientific Notation


Notes

MA.8.EEI.A.3 4.1 Exploring Scientific Notation 1

MA.8.EEI.A.3 4.2 Using Scientific Notation to Describe Very Large Quantities

1

MA.8.EEI.A.3 4.3 Using Scientific Notation to Describe Very Small Quantities

1

MA.8.EEI.A.3 4.4 Operating with Numbers Expressed in Scientific Notation

1

MA.8.EEI.A.3 MA.8.EEI.A.4

4.5 Problem Solving 1

Review 1.5

Topic 4 TEST 1.5


Unit of Study Terminology Appendices: All Appendices and supporting material can be found in this course’s shell course in the District’s Learning Management System. Assessment Leveling Guide: A tool to use when writing assessments in order to maintain the appropriate level of rigor that matches the standard. Big Ideas/Enduring Understandings: Foundational understandings teachers want students to be able to discover and state in their own words by the end of the unit of study. These are answers to the essential questions. Engaging Experience: Each topic is broken into a list of engaging experiences for students. These experiences are aligned to priority and supporting standards, thus stating what students should be able to do. An example of an engaging experience is provided in the description, but a teacher has the autonomy to substitute one of their own that aligns to the level of rigor stated in the standards. Engaging Scenario: This is a culminating activity in which students are given a role, situation, challenge, audience, and a product or performance is specified. Each unit contains an example of an engaging scenario, but a teacher has the ability to substitute with the same intent in mind. Essential Questions: Engaging, open-ended questions that teachers can use to engage students in the learning. Priority Standards: What every student should know and be able to do. These were chosen because of their necessity for success in the next course, the state assessment, and life. Supporting Standards: Additional standards that support the learning within the unit. Topic: These are the main teaching points for the unit. Units can have anywhere from one topic to many, depending on the depth of the unit. Unit of Study: Series of learning experiences/related assessments based on designated priority standards and related supporting standards. Unit Vocabulary: Words students will encounter within the unit that are essential to understanding. Academic Cross-Curricular words (also called Tier 2 words) are those that can be found in multiple content areas, not just this one. Content/Domain Specific vocabulary words are those found specifically within the content. Symbols: This symbol depicts an experience that can be used to assess a student’s 21st Century Skills using the rubric provided by the district. This symbol depicts an experience that integrates professional skills, the development of professional communication, and/or the use of professional mentorships in authentic classroom learning activities.

8th Grade Mathematics Curriculum · 8th Grade Mathematics Curriculum. Course Summary: In Grade 8,...

Documents

Transcript of 8th Grade Mathematics Curriculum · 8th Grade Mathematics Curriculum. Course Summary: In Grade 8,...