Yearly Itineraries Yearly Itinerary Summary Documents ...curriculum.austinisd.org/schoolnetDocs/mathematics/general...In this unit on numerical reasoning, students will convert numbers

• Yearly Itineraries • Yearly Itinerary Summary Documents • Curriculum Road Maps

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Math Grade 8 © Austin ISD Yearly Itinerary 2014-2015

Grading Period Assessment

Pacing Guide Texas Essential Knowledge and Skills Readiness Standard; Supporting Standard

The mathematical process standards TEKS should be taught in conjunction with the content TEKS; therefore, they are embedded throughout the year.

1st Six Weeks August 25 – October 3

29 Days

CRM 1: Numerical Reasoning (9 days) August 25 –September 5

TEKS: 8.2A, 8.2C, 8.2D

CRM 2: Solving Equations and Inequalities (15 days) September 8 – September 26

TEKS: 8.8A, 8.8B, 8.8C

CRM 3: Foundations for Functions (17 days) (5 days in 1st Six Weeks, 12 days in 2nd six weeks) September 29 – October 22

TEKS: 8.5A, 8.5B, 8.5E, 8.5F, 8.5G, 8.5H, 8.5I, 8.9A

2nd Six Weeks October 6 – November 7

24 Days

CRM 4: Multiple Representations ( 12 days) October 23 – November 7

TEKS: 8.4A, 8.4B, 8.4C, 8.5A, 8.5B, 8.5F, 8.5G, 8.5H, 8.5I,

3rd Six Weeks November 10 – December 18

25 Days

MoY I November 10 – November 25

CRM 5 Pythagorean Theorem ( 11 days) November 10 – November 25

TEKS: 8.2B, 8.6C, 8.7C, 8.7D

CRM 6: Measurement (31 days) (14 days in 3rd six weeks, 17 days in 4th six weeks) December 1 – January 28

TEKS: 8.6A, 8.6B, 8.7A, 8.7B

4th Six Weeks January 5 – February 20

33 Days

MoY II February 2 – February 13

CRM 7: Transformations & Similarity (12 days) January 29 – February 13

TEKS: 8.3A, 8.3B, 8.3C, 8.8D, 8.10A, 8.10B, 8.10C, 8.10D

CRM 8: Data (9 days) (4 days in 4th six weeks, 5 days in 5th six weeks) February 17 – February 27

TEKS: 8.5C, 8.5D, 8.11A, 8.11B, 8.11C

5th Six Weeks February 23 – April 17

34 Days

CRM 9: Personal Financial Literacy and Engaging STAAR Review (20 days) March 2 – April 6

TEKS: 8.12A, 8.12B, 8.12C, 8.12D, 8.12E, 8.12F, 8.12G

*Review 8th grade TEKS during STAAR review STAAR Testing ( 2 days) April 7 – April 8

CRM 10: Solving Equations & Inequalities (7 days) April 9 – April 17

TEKS: 8.8A, 8.8B, 8.8C

6th Six Weeks April 20 – June 4

32 Days

CRM 11: Rational Number Operations through the Process Standards (24 days) April 20 – May 21

TEKS: 8.1A, 8.1B, 8.1C, 8.1D, 8.1E, 8.1F, 8.1G

http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/Processstandards.pdf

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Grading Period Assessment

Pacing Guide Texas Essential Knowledge and Skills Readiness Standard; Supporting Standard

CRM 12: Integrating the Graphing Calculator (8 days) May 26 – June 5

TEKS: A.8B, A.1D

8th Grade Math

The following summaries are intended to give an overview and rationale behind curriculum decisions. The Curriculum Road Maps (CRMs) will provide clarification of specific TEKS and what students should know and be able to do at the conclusion of each unit. To access the instructional resources, exemplar lessons and additional teacher tools, you must reference the CRMs. CRM 1: Numerical Reasoning In this unit on numerical reasoning, students will convert numbers from scientific notation to standard form and standard form to scientific notation. Students will also order sets of rational numbers. As you are teaching scientific notation, you should focus on the idea that each way of stating a number has value and purpose in different contexts. As you teach this unit, students should relate the numbers to real world scenarios and understand the exponent does not tell the number of zeros, which is a common misconception. The process TEKS should be partnered with concepts throughout this unit lending itself to the application of numerical reasoning through real world experiences. This unit was strategically placed first because the concepts learned in this unit can be spiraled throughout the school year.

Math Yearly Itinerary 2014‐2015

Process TEKS should be embedded through each content TEKS, therefore they are taught all year long. When

appropriate MoY questions will be dual‐coded with a content and a process TEKS.

1A 1B 1C 1D 1E 1F 1G

apply

mathematics

to problems

arising in

everyday

life, society,

and the

workplace;

use a problem‐solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem‐solving process and the reasonableness of the solution

select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems

communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate

create and use representations to organize, record, and communicate mathematical ideas

analyze mathematical relationships to connect and communicate mathematical ideas

display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication

Page 1 of 2 Updated: June 2, 2014

© Austin Independent School District, 2014 Math Grade 8 Curriculum Road Map (CRM) 1st Six Weeks CRM 1 Numerical Reasoning Pacing

• 9 days • August 25 – September 5

DESIRED RESULTS Transfer: Students will independently use their learning to display, analyze, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication in order to connect mathematical ideas arising in problems in everyday life, society and careers.

Making Meaning

Enduring Understandings The students will understand that…

• quantities can be represented in different forms and can be used to describe and compare the value of real world quantities. The form of the number used to solve a problem should be based on ease of use.

Essential Questions • How do I determine the best numerical

representation for a given situation? • How is equivalence used in our lives?

Vocabulary rational numbers, fractions, decimals, percents, place value, standard notation, scientific notation, exponent, power, base vocabulary cards Student pre-requisite knowledge In grade 7, students compared and ordered integers and positive rational numbers. They converted between fractions decimals, whole numbers, and percents. This is the first time students will be introduced to scientific notation. Resources: Carnegie Learning adopted textbook; HOM: Hands on Math; Exemplar Lessons; Instructional Resource Portfolios and Zip files; TEA Side by Side; Best Practices for the Middle School Math Classroom; Manipulatives; Differentiation Pre-AP and AP: Advanced Placement Vertical Teams Guide and Pre-AP Resource Bank Gifted and Talented: Exemplar Lessons, GT Scope and Sequence, GT Performance Reports ELPS: Mandated by Texas Administrative Code (19 TAC §74.4), click on the link for English Language Proficiency Standards (ELPS) to support English Language Learners. TEKS Knowledge & Skills Acquisition STAAR: RC = Reporting Category; DC = Dual Coded Skills; Readiness Standard; Supporting Standard Concepts are addressed in another unit.

Students Will Know Students Will Be Able To

8.2 Numbers and operations. The student applies mathematical process standards to represent and use real numbers in a variety of forms. The student is expected to: 8.2A extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of real numbers

8.2C convert between standard decimal notation and scientific notation

8.2D order a set of real numbers arising from mathematical and real-world

• Subsets of real numbers include counting numbers, whole numbers, integers, rational numbers, and irrational numbers.

• Rational numbers comprise the set of all numbers that can be represented as a fraction – or a ratio of an integer to an integer.

• A Venn diagram can represent relationships between sets of numbers.

• Describe relationships between sets of numbers.

• Create sets and subsets of real numbers.

• Distinguish between rational and irrational numbers.

• Convert numbers from scientific notation to standard notation and vice versa.

• Identify when scientific notation should be used.

• Compare and order a set of real

http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/MiddleSchool/ms_vocabulary/ms_vocabulary_final.pdf

http://resources.carnegielearning.com/

http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/MiddleSchool/TEA_sidebyside/m_8_TEKS_sidebyside.pdf

http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/MiddleSchool/best_practices_in_the_ms_math_classroom/ms_ms_document.pdf

http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/MiddleSchool/manipulatives/ms_manipulatives.pdf

http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/MiddleSchool/differentiation/differentiation_strategies.pdf

http://curriculum.austinisd.org/adv_ac/preAP/curriculum.html

http://curriculum.austinisd.org/adv_ac/GT/curriculum.html

http://ritter.tea.state.tx.us/rules/tac/chapter074/ch074a.html#74.4


http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/MiddleSchool/New_TEKS_Support_Documents/M_8_SupportDocument_8.2A.pdf

http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/MiddleSchool/New_TEKS_Support_Documents/M_8_SupportDocument_8.2C.pdf

http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/MiddleSchool/New_TEKS_Support_Documents/M_8_SupportDocument_8.2D.pdf


contexts

• Scientific notation provides a standardized form for writing very large or very small numbers

• Numbers with a positive exponent are greater than one.

• Numbers with a negative exponent are less than one.

• Changing the form of a number doesn’t change the value.

numbers.

ASSESSMENT EVIDENCE Student Work Products/Assessment Evidence

Performance Tasks Other Evidence (i.e. unit tests, open ended exams, quiz, essay, student work samples, observations, etc.)

Scientific Notation – Convincing Argument This performance task allows students to demonstrate their knowledge of scientific notation through writing in the math classroom.

Short Cycle Assessment • SCA items are available under the Assessment tab in

Schoolnet for use in teacher created assessments.

Additional Suggestions for Assessments • Homework • Exit slips • Teacher-created assessments • Discussions • Journal responses • Projects • Games

LESSON PLANNING TOOLS In the course of lesson planning, it is the expectation that teachers will include whole child considerations when

planning such as differentiation, special education, English language learning, dual language, gifted and talented, social emotional learning, physical activity, creative learning, and wellness.

Exemplar Lessons and Instructional Resources PDF

Exemplar Lessons and Instructional Resources ZIP Files Exemplar Lessons Scientific Notation TEKS: 8.2C Order a Set of Real Numbers TEKS: 8.2D

http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/MiddleSchool/Performance_Tasks_1415/M_8_PT1_CRM1_1415.pdf

http://curriculum.austinisd.org/schoolnetDocs/mathematics/8th/M_8TH_IR_CRM1_1415.pdf

http://curriculum.austinisd.org/schoolnetDocs/mathematics/8th/M_8TH_IR_CRM1_1415.zip

8th Grade Math

The following summaries are intended to give an overview and rationale behind curriculum decisions. The Curriculum Road Maps (CRMs) will provide clarification of specific TEKS and what students should know and be able to do at the conclusion of each unit. To access the instructional resources, exemplar lessons and additional teacher tools, you must reference the CRMs. CRM 2: Solving Equations and Inequalities In this unit, students will represent verbal quantitative situations algebraically. They will evaluate these expressions given replacement values for the variables. Students will also simplify algebraic expressions and equations. As you teach this unit, focus on students understanding of solving one and two step equations both algebraically and modeling. This will allow the students to be able to make the connection when they begin to solve multi‐step linear equations and inequalities with one variable. Equations should include rational number coefficients and constants. The process TEKS should be partnered with concepts throughout this unit lending itself to the application of solving equations and inequalities through real world experiences. This unit was placed here so that teachers can ensure students have a strong understanding of solving equations before introducing functions.




1A 1B 1C 1D 1E 1F 1G

apply

mathematics

to problems

arising in

everyday

life, society,

and the

workplace;








© Austin Independent School District, 2014 Math Grade 8 Curriculum Road Map (CRM) 1st Six Weeks CRM 2 Solving Equations and Inequalities Pacing

• 15 days • September 8 – September 26


Making Meaning


• equations and inequalities are an algebraic way of representing a real world mathematical situation.

• solving equations using models is a visual way to “unpack” a variable while keeping the equation balanced. It is related to simplifying expressions using order of operations.

Essential Questions • How do mathematical models/representations

shape our understanding of mathematics? • How is equivalence used in our lives? • How are algebraic expressions used to analyze

or solve problems?

Vocabulary equation, solution of an equation, inequalities, inequality symbols, inverse operation, balance, equal vocabulary cards Student pre-requisite knowledge Students solved equations in 7th grade using concrete and pictorial models. Resources: Carnegie Learning adopted textbook; HOM: Hands on Math; Exemplar Lessons; Instructional Resource Portfolios and Zip files; TEA Side by Side; Best Practices for the Middle School Math Classroom; Manipulatives; Differentiation Pre-AP and AP: Advanced Placement Vertical Teams Guide and Pre-AP Resource Bank Gifted and Talented: Exemplar Lessons, GT Scope and Sequence, GT Performance Reports ELPS: Mandated by Texas Administrative Code (19 TAC §74.4), click on the link for English Language Proficiency Standards (ELPS) to support English Language Learners. TEKS Knowledge & Skills Acquisition STAAR: RC = Reporting Category; DC = Dual Coded Skills; Readiness Standard; Supporting Standard Concepts are addressed in another unit.


8.8 Expressions, equations, and relationships. The student applies mathematical process standards to use one variable equations or inequalities in problem situations. The student is expected to: 8.8A write one-variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants

8.8B write a corresponding real-world problem when given a one-variable equation or inequality with variables on both sides of the equal sign using rational number coefficients and constants

• Constraints or conditions within the problems may be indicated by words such as “minimum” or “maximum”.

• Symbols are used in equations. • An “equal sign” does not mean

“equals”, but instead “equals” means “balanced” or “same value/quantities.”

• Real-world problem situations can be described by number sentences.

• A constant is a value that does

• Determine if the value in the solution is part of the solution set or not.

• Relate/determine an equation or inequality that represents a situation in context and vice versa.

• Use academic vocabulary to describe the steps involved in solving an equation and inequality.

• Use a concrete model and picture to solve an equation.












http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/MiddleSchool/New_TEKS_Support_Documents/M_8_SupportDocument_8.8B.pdf


8.8C model and solve one-variable equations with variables on both sides of the equal sign that represent mathematical and real-world problems using rational number coefficients and constants

not change. • A variable represents an

unknown amount. • When a variable and a constant

are next to each other, there is the hidden operation of multiplication.

• How to simplify and recognize equivalent expressions.

• Relate symbols to a model to solve an equation.

• Solve one-step and multi-step equations with grouping symbols.

• Solve one-variable inequalities.



Solving Equations with Fractions This performance task allows students to demonstrate their knowledge of solving equations through a real-world problem.







Exemplar Lessons and Instructional Resources ZIP Files Exemplar Lessons: Solving Equations TEKS: 8.8C Solving Inequalities TEKS: 8.8A, 8.8B





8th Grade Math

The following summaries are intended to give an overview and rationale behind curriculum decisions. The Curriculum Road Maps (CRMs) will provide clarification of specific TEKS and what students should know and be able to do at the conclusion of each unit. To access the instructional resources, exemplar lessons and additional teacher tools, you must reference the CRMs. CRM 3: Foundations for Functions In this unit, students will begin their study of functions. They will learn about independent and dependent variables and how variables are assigned based on a given situation. As you teach this unit, focus on proportional and non‐proportional situations. You should use the process TEKS to integrate real world data to formulate equations and functions. Seeing connections to real world applications helps students to see how and why learning mathematics is useful. Students are not expected to interpret or use functional notation in 8th grade. This unit was placed third as it will help build a strong foundation for the 8th grade math.




1A 1B 1C 1D 1E 1F 1G

apply

mathematics

to problems

arising in

everyday

life, society,

and the

workplace;








© Austin Independent School District, 2014 Math Grade 8 Curriculum Road Map (CRM) 1st/2nd Six Weeks CRM 3 Foundations for Functions Pacing

• 17 days • September 29 – October 22


Making Meaning

Enduring Understandings The student will understand that…

• mathematicians formulate equations or functional relationships to communicate generalizations (general patterns, rules and connections to prior concepts that are at the core of the problem) so that specific problems can be solved more efficiently.

Essential Questions

• How can you determine if a relationship is a function?

• How can different representations be used to write a rule or expression for a function?

• What does a significant point on a graph represent in the context of the problem?

Vocabulary function, mapping, input, output, proportional, non-proportional, linear, direct variation vocabulary cards Student pre-requisite knowledge Students have worked with proportional relationships and unit rates in 7th grade. Resources: Carnegie Learning adopted textbook; HOM: Hands on Math; Exemplar Lessons; Instructional Resource Portfolios and Zip files; TEA Side by Side; Best Practices for the Middle School Math Classroom; Manipulatives; Differentiation Pre-AP and AP: Advanced Placement Vertical Teams Guide and Pre-AP Resource Bank Gifted and Talented: Exemplar Lessons, GT Scope and Sequence, GT Performance Reports ELPS: Mandated by Texas Administrative Code (19 TAC §74.4), click on the link for English Language Proficiency Standards (ELPS) to support English Language Learners. TEKS Knowledge & Skills Acquisition STAAR: RC = Reporting Category; DC = Dual Coded Skills; Readiness Standard; Supporting Standard Concepts are addressed in another unit.


8.5 Proportionality. The student applies mathematical process standards to use proportional and non-proportional relationships to develop foundational concepts of functions. The student is expected to: 8.5A represent linear proportional situations with tables, graphs, and equations in the form of y = kx

8.5B represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠ 0

8.5E solve problems involving direct

• All proportional situations are equations in the form y = kx.

• Graphs of proportional situations are straight lines that pass through the origin.

• Quantities that have a proportional relationship have a constant ratio or rate of change.

• In non-proportional situations one value is constant.

• When two variable quantities have a constant ratio, their relationship is called direct

• Set up and solve proportion problems by determining the constant multiplier or unit rate.

• Write an equation (including rational number coefficients and constants) given a graph or table.

• Interpret data in graphs, tables, and problem situations to solve problems and make predictions.

• Identify examples of proportional and non-proportional situations by













http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/MiddleSchool/New_TEKS_Support_Documents/M_8_SupportDocument_8.5E.pdf


variation

8.5F distinguish between proportional and non-proportional situations using tables, graphs, and equations in the form of y= kx or y = mx + b, where b ≠ 0

8.5G identify functions using sets of ordered pairs, table, mappings, and graphs

8.5H identify examples of proportional and non-proportional functions that arise from mathematical and real-world problem situations

8.5I write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations

variation • A proportional relationship is a

direct variation. • Proportional and non-

proportional relationships can be represented using tables, graphs, and equations.

• A non-proportional linear relationship is a straight line that does not pass through the origin.

• A function is a relation for which each value from the set of first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pairs.

• Functions can be identified using sets of ordered pairs, tables, mappings and graphs.

comparing tables, graphs, and equations for proportional and non-proportional functions.

• Distinguish between relations and functions.

• Make informed decisions and predictions by analyzing organized data.

• Explain the definition of a function.

8.9 Expressions, equations, and relationships. The student applies mathematical process standards to use multiple representations to develop foundational concepts of simultaneous linear equations. The student is expected to: 8.9A identify and verify the values of x and y that simultaneously satisfy two linear equations in the form y = mx + b from the intersections of the graphed equations

• Two linear functions may be considered simultaneously.

• Perform calculations to verify that x- and y- values for the point of intersection satisfy both graphed equations.

• Explain the meaning of the intersection point’s values in terms of the given situation.

http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/MiddleSchool/New_TEKS_Support_Documents/M_8_SupportDocument_8.5F.pdf

http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/MiddleSchool/New_TEKS_Support_Documents/M_8_SupportDocument_8.5G.pdf

http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/MiddleSchool/New_TEKS_Support_Documents/M_8_SupportDocument_8.5H.pdf

http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/MiddleSchool/New_TEKS_Support_Documents/M_8_SupportDocument_8.5I.pdf





Proportional and Non-Proportional This performance task allows students to demonstrate their knowledge of proportional and non-proportional linear situations through a real-world problem situation.







Exemplar Lessons and Instructional Resources ZIP Files Exemplar Lessons Identify Functions TEKS: 8.5G Linear Equations TEKS: 8.9A




8th Grade Math

The following summaries are intended to give an overview and rationale behind curriculum decisions. The Curriculum Road Maps (CRMs) will provide clarification of specific TEKS and what students should know and be able to do at the conclusion of each unit. To access the instructional resources, exemplar lessons and additional teacher tools, you must reference the CRMs. CRM 4: Multiple Representations In this unit, students will study the multiple representations of functions by investigating and analyzing linear function families and their characteristics graphically, tabular and algebraically. They will discover the connections between the rate of change, slope, and intercepts in different representations of the same function. As you teach this unit, focus on how multiple representations of data are different with relations, functions and linear functions. The process TEKS should be partnered with concepts throughout this unit lending itself to the application of the multiple representations through real world experiences. This unit on multiple representations was placed after foundations for functions because of how closely they are aligned.




1A 1B 1C 1D 1E 1F 1G

apply

mathematics

to problems

arising in

everyday

life, society,

and the

workplace;








© Austin Independent School District, 2014 Math Grade 8 Curriculum Road Map (CRM) 2nd Six Weeks CRM 4 Multiple Representations Pacing

• 12 days • October 23 – November 7


Making Meaning

Enduring Understandings The student will understand that…

• mathematicians formulate equations or functional relationships to communicate generalizations (general patterns, rules and connections to prior concepts that are at the core of the problem) so that specific problems can be solved more efficiently.

• data can be represented in multiple ways.

Essential Questions

• How are the table, graph, equation, and verbal description of a linear relationship connected?

• Is one representation sometimes better to describe a given problem or authentic situation than another?

• Why would we want to represent ideas in different ways?

Vocabulary proportional, non-proportional, slope, dependent variable, independent variable, y-intercept, vocabulary cards Student pre-requisite knowledge This is the first time students have been introduced to slope. Students worked with functions in CRM 3. Resources: Carnegie Learning adopted textbook; HOM: Hands on Math; Exemplar Lessons; Instructional Resource Portfolios and Zip files; TEA Side by Side; Best Practices for the Middle School Math Classroom; Manipulatives; Differentiation Pre-AP and AP: Advanced Placement Vertical Teams Guide and Pre-AP Resource Bank Gifted and Talented: Exemplar Lessons, GT Scope and Sequence, GT Performance Reports ELPS: Mandated by Texas Administrative Code (19 TAC §74.4), click on the link for English Language Proficiency Standards (ELPS) to support English Language Learners. TEKS Knowledge & Skills Acquisition STAAR: RC = Reporting Category; DC = Dual Coded Skills; Readiness Standard; Supporting Standard Concepts are addressed in another unit.


8.4 Proportionality. The student applies mathematical process standards to explain proportional and non-proportional relationships involving slope. The student is expected to: 8.4A use similar right triangles to develop an understanding that slope, m, given as the rate comparing the change in y-values to the change in x-values, (y2 – y1)/(x2 – x1), is the same for any two points (x1, y1) and (x2, y2) on the same line. 8.4B graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship

• The slope of a line represents a constant rate of change between the dependent and independent variable.

• Identify the slope and y-intercept given any multiple representations such as tables, graphs, equations and verbal descriptions.

• Slopes are classified as positive, negative, zero, and undefined.

• Rate of change is the slope and

• Develop the slope formula through investigation.

• Determine slopes from graphs, tables, and algebraic representations

• Calculate the slope of a line when given an equation in standard form or slope-intercept form.

• Calculate the slope of a line given the coordinates of any two points on the line. (Coordinates












8.4C use data from a table or graph to determine the rate of change or slope and y-intercept in mathematical and real-world problems

the starting point is the y-intercept.

• Changing the values of “m” and “b” will change the graph of the line.

• Parallel lines have equal slopes and different y-intercepts.

• The product of the slopes of perpendicular lines is –1 unless one of the lines has an undefined slope.

• Understand and define proportional relationships.

may contain variables.) • Find the value of the x or y

coordinate so that the points lie on the line with the given the slope.

• Identify the slope as positive, negative, zero, or undefined from multiple representations.

• Interpret; make decisions, predictions or critical judgments using slope and y-intercept from multiple representations.

• Describe the effects on the graph of a linear function if the slope or y-intercept is changed.

8.5 Proportionality. The student applies mathematical process standards to use proportional and non-proportional relationships to develop foundational concepts of functions. The student is expected to: 8.5A represent linear proportional situations with tables, graphs, and equations in the form of y = kx

8.5B represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠ 0

8.5F distinguish between proportional and non-proportional situations using tables, graphs, and equations in the form of y= kx or y = mx + b, where b ≠ 0

8.5G identify functions using sets of ordered pairs, table, mappings, and graphs

8.5H identify examples of proportional and non-proportional functions that arise from mathematical and real-world problem situations

8.5I write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations

• All proportional situations are equations in the form y = kx.

• Graphs of proportional situations are straight lines that pass through the origin.

• A non-proportional linear relationship is a straight line that does not pass through the origin.

• Quantities that have a proportional relationship have a constant ratio or rate of change.

• In non-proportional situations one value is constant.

• Proportional and non-proportional relationships can be represented using tables, graphs, and equations.

• A function is a relation for which each value from the set of first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pairs.

• Functions can be identified using sets of ordered pairs, tables, mappings and graphs.

• The same set of data can be represented in tables, graphs, equations or verbal descriptions.

• Create and read different representations of data using tables, graphs, equations or verbal descriptions and make connections between the different representations

• Write an equation given a graph or table.


• Explain the definition of a function using tables, graphs and equations.

• Write an equation (including rational number coefficients and constants) given a graph or table.


• Identify examples of proportional and non-proportional situations by comparing tables, graphs, and equations for proportional and non-proportional functions.

• Distinguish between relations and functions.

• Create one representation (table, graph, verbal, equation) when given another representation (table, graph, verbal, equation).





http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/MiddleSchool/New_TEKS_Support_Documents/M_8_SupportDocument_8.5H.pdf

http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/MiddleSchool/New_TEKS_Support_Documents/M_8_SupportDocument_8.5I.pdf




Multiple Representations This performance task allows students to demonstrate their knowledge of multiple representations through a real-world problem situation.







Exemplar Lessons and Instructional Resources ZIP Files Exemplar Lesson Similar Right Triangles and Slope TEKS: 8.4A Multiple Representations TEKS: 8.5I Unit Rate as Slope TEKS: 8.4B




8th Grade Math

The following summaries are intended to give an overview and rationale behind curriculum decisions. The Curriculum Road Maps (CRMs) will provide clarification of specific TEKS and what students should know and be able to do at the conclusion of each unit. To access the instructional resources, exemplar lessons and additional teacher tools, you must reference the CRMs. CRM 5: Pythagorean Theorem In this unit on the Pythagorean theorem, students will investigate and apply the Pythagorean theorem. As you are teaching this unit, you should focus on the Pythagorean relationship; if a square is constructed on each side of a right triangle, the areas of the two smaller squares will together equal the area of the square on the longest side, the hypotenuse. As you teach this unit, students should investigate the Pythagorean relationship using manipulatives and explain the Pythagorean theorem verbally using mathematical terms. The process TEKS should be partnered with concepts throughout this unit lending itself to the application of the Pythagorean theorem through real world experiences. This unit was placed here because students will use content learned in previous units to help them be successful at using the Pythagorean theorem to solve problems.




1A 1B 1C 1D 1E 1F 1G

apply

mathematics

to problems

arising in

everyday

life, society,

and the

workplace;








© Austin Independent School District, 2014 Math Grade 8 Curriculum Road Map (CRM) 3rd Six Weeks CRM 5 Pythagorean Theorem Pacing

• 11 days • November 10 – November 25


Making Meaning


• the Pythagorean Theorem is an algebraic representation of the geometric relationship between the lengths of the legs and the hypotenuse of a right triangle.

Essential Questions • What are the real life applications of the

Pythagorean Theorem? • Why does the Pythagorean Theorem work? • When is it appropriate to use estimation

and/or approximation? • How important are estimations in real life

situations? Vocabulary Pythagorean Theorem, hypotenuse, leg, right triangle, area, rational/irrational numbers, square root, perfect square Student pre-requisite knowledge This is the first time students have been introduced to Pythagorean theorem. Students learned about squares and square roots. Resources: Carnegie Learning adopted textbook; HOM: Hands on Math; Exemplar Lessons; Instructional Resource Portfolios and Zip files; TEA Side by Side; Best Practices for the Middle School Math Classroom; Manipulatives; Differentiation Pre-AP and AP: Advanced Placement Vertical Teams Guide and Pre-AP Resource Bank Gifted and Talented: Exemplar Lessons, GT Scope and Sequence, GT Performance Reports ELPS: Mandated by Texas Administrative Code (19 TAC §74.4), click on the link for English Language Proficiency Standards (ELPS) to support English Language Learners. TEKS Knowledge & Skills Acquisition STAAR: RC = Reporting Category; DC = Dual Coded Skills; Readiness Standard; Supporting Standard Concepts are addressed in another unit.


8.2 Number and operations. The student applies mathematical process standards to represent and use real numbers in a variety of forms. The student is expected to: 8.2B approximate the value of an irrational number, including π and square roots of numbers less than 225, and locate that rational number approximation on a number line.

• Each irrational number can be represented by an estimated value.

• Give the approximate value of an irrational number.

• Give examples of irrational numbers.

• Identify perfect squares and their square roots.

• Locate rational number approximations on a number line.












8.6 Expressions, equations, and relationships. The student applies mathematical process standards to develop mathematical relationships and make connections to geometric formulas. The student is expected to: 8.6C use models and diagrams to explain the Pythagorean theorem

• Pythagorean Theorem is only used for right triangles.

• Models can be used to show characteristics of the Pythagorean Theorem.

• A model can be created to represent the Pythagorean Theorem.

• Pythagorean Theorem can be used to determine if a right angle exists in a triangle.

• Identify models and characteristics that represent the Pythagorean Theorem.

• Solve to find missing measurements of a right triangle using the Pythagorean Theorem.

8.7 Expressions, equations, and relationships. The student applies mathematical process standards to use geometry to solve problems. The student is expected to: 8.7C use the Pythagorean theorem and its converse to solve problems. 8.7D determine the distance between two points on a coordinate plane using the Pythagorean Theorem

• The Pythagorean Theorem can be used to find a missing distance.

• The Pythagorean Theorem can be used to determine if a right angle exists in everyday situations.

• The converse states that whenever the sum of the squares of two sides equal to the square of the third side of the triangle, the triangles is a right triangle.

• Solve for missing distances/lengths in a right triangle.

• Prove the situation has a right triangle.

• Find the distance between two points on a coordinate plane using the Pythagorean Theorem (do not use the distance formula).



Pythagorean Theorem This performance task allows students to demonstrate their knowledge of the Pythagorean theorem through a real-life problem.












Exemplar Lessons and Instructional Resources ZIP Files Exemplar Lesson Introduction to the Pythagorean Theorem TEKS: 8.6C, 8.7C, 8.7D Pythagorean Theorem Applications TEKS: 8.6C, 8.7C, 8.7D



8th Grade Math

The following summaries are intended to give an overview and rationale behind curriculum decisions. The Curriculum Road Maps (CRMs) will provide clarification of specific TEKS and what students should know and be able to do at the conclusion of each unit. To access the instructional resources, exemplar lessons and additional teacher tools, you must reference the CRMs. CRM 6: Measurement In this unit on measurement, students will explore the volume of a cylinder and the relationship between the volume of a cylinder and a cone having both congruent bases and heights and connect this relationship to the formula. Students will use their previous knowledge of surface area to make connections to the formulas for lateral and total surface area. As you are teaching this unit, it is important that you focus on why the formulas work and not just giving the students the formula to plug in numbers. Students should connect the relationships they have explored to the formulas. The process TEKS should be partnered with concepts throughout this unit lending itself to the application of surface area and volume through real world experiences. This unit was placed here so that teachers can spiral this concept throughout the remainder of the school year.




1A 1B 1C 1D 1E 1F 1G

apply

mathematics

to problems

arising in

everyday

life, society,

and the

workplace;








© Austin Independent School District, 2014 Math Grade 8 Curriculum Road Map (CRM) 3rd/4th Six Weeks CRM 6 Measurement Pacing

• 31 days • December 1 – January 28


Making Meaning


• measurement involves a comparison of an attribute of an item or situation with a unit that has the same attribute. Lengths are compared to units of length, areas to units of area, time to units of time, and so on.

• area and volume formulas provide a method of measuring these attributes by using only measures of lengths.

Essential Questions

• How is the area of the base (B) and height (h) related to the dimensions of a 3-dimensional figure?

• What are some relationships between three-dimensional figures?

• How does the relationship between the dimensions of the figure relate to the formula for volume?

• How are lateral and total surface area related?

Vocabulary lateral surface area, total surface area, nets, volume, cylinder, cone, sphere, rectangular prism, triangular prism vocabulary cards Student pre-requisite knowledge This is the first time students are being introduced to surface area. The revised TEKS introduce surface area in 7th grade, but this year many of the 8th graders will not come with knowledge of surface area. Students found volume of rectangular and triangular prisms in 7th grade. Resources: Carnegie Learning adopted textbook; HOM: Hands on Math; Exemplar Lessons; Instructional Resource Portfolios and Zip files; TEA Side by Side; Best Practices for the Middle School Math Classroom; Manipulatives; Differentiation Pre-AP and AP: Advanced Placement Vertical Teams Guide and Pre-AP Resource Bank Gifted and Talented: Exemplar Lessons, GT Scope and Sequence, GT Performance Reports ELPS: Mandated by Texas Administrative Code (19 TAC §74.4), click on the link for English Language Proficiency Standards (ELPS) to support English Language Learners. TEKS Knowledge & Skills Acquisition STAAR: RC = Reporting Category; DC = Dual Coded Skills; Readiness Standard; Supporting Standard Concepts are addressed in another unit.


8.6 Expressions, equations, and relationships. The student applies mathematical process standards to develop mathematical relationships and make connections to geometric formulas. The student is expected to: 8.6A describe the volume formula V = BH of a cylinder in terms of its base area and its height. 8.6B model the relationship between the volume of a cylinder and a cone having both congruent bases and heights and connect that relationship to the

• Volume is the measure of the number of cubic units (cubes) it takes to fill a three-dimensional figure, even if the figure is curved as in a cylinder.

• The area of the base determines how many cubes can be placed on the base, forming a single

• Describe the volume formula for a cylinder in terms of its base area and its height.

• Explain the relationship between the volume of a cylinder and a cone having both congruent bases and heights

• Determine the formula for












formulas

unit – a layer of cubes. • The height of the figure then

determines how many of these layers will fit in the figure.

• The volume of a cylinder is three times the volume of a cone with the same height and radius.

volume of cone through the investigation of the relationship between volume of a cone and volume of a cylinder with the same bases and heights.

8.7 Expressions, equations, and relationships. The student applies mathematical process standards to use geometry to solve problems. The student is expected to: 8.7A solve problems involving the volume of cylinders, cones, and spheres. 8.7B use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determining solutions for problems involving rectangular prisms, triangular prisms, and cylinders.

• Standard units of volume are expressed in terms of length units, such as cubic inches or cubic centimeters.

• Surface area can be found by determining the area of the shape’s net.

• Develop formulas in conceptual ways.

• Determine the volume of cylinders, cones, and spheres using formulas.

• Determine the volume of a sphere, cylinder, or cone in terms of pi.

• Find the missing dimension of a figure when the volume is given.

• Connect a 3-dimensional figure or concrete model to its net.

• Find the lateral and total surface area of rectangular prisms, triangular prisms, and cylinders using nets.

• Identify and connect formulas for surface area to the appropriate 3-dimensional figure.

• Find the lateral surface area of rectangular prisms, triangular prisms and cylinders in real world problem situations.

• Find the total surface area of rectangular prisms, triangular prisms and cylinders in real world problem situations.

• Find the missing dimension of a figure when the total or lateral surface area is given.

ASSESSMENT EVIDENCE


Student Work Products/Assessment Evidence Performance Tasks Other Evidence (i.e. unit tests, open ended exams, quiz,

essay, student work samples, observations, etc.)

Sports Bag This performance task allows students to demonstrate their knowledge of measurement through a real-world problem situation.







Exemplar Lessons and Instructional Resources ZIP Files Exemplar Lessons Volume TEKS: 8.6A, 8.7A Surface Area TEKS: 8.7B




8th Grade Math

The following summaries are intended to give an overview and rationale behind curriculum decisions. The Curriculum Road Maps (CRMs) will provide clarification of specific TEKS and what students should know and be able to do at the conclusion of each unit. To access the instructional resources, exemplar lessons and additional teacher tools, you must reference the CRMs. CRM 7: Transformations & Similarity In this unit on transformations and similarity, students will explore attributes of similarity and apply this knowledge to solve similarity problems. Students will rotate, reflect, translate and dilate two‐dimensional shapes on a coordinate plane. As you are teaching this unit, you should differentiate between the transformations that preserve congruence and those that do not. Students should be able to explain the effect of translations and reflections over the x‐axis or y‐axis. The process TEKS should be partnered with concepts throughout this unit lending itself to the application of transformations and similarity through real world experiences. This unit was placed here because students have background knowledge from 7th grade on similarity, translations, reflections and dilations and therefore can build on that knowledge to deepen their understanding of transformations.




1A 1B 1C 1D 1E 1F 1G

apply

mathematics

to problems

arising in

everyday

life, society,

and the

workplace;








© Austin Independent School District, 2014 Math Grade 8 Curriculum Road Map (CRM) 4th Six Weeks CRM 7 Transformations and Similarity Pacing

• 12 days • January 29 – February 13


Making Meaning


• if two figures are similar, corresponding angles are congruent and corresponding sides are in proportion.

• shapes can be moved in a plane or in space. These changes are to be described in terms of translations, reflections, and rotations.

• similar geometric objects have proportional dimensions and provide visual representations of proportionality.

Essential Questions

• What is similarity and how does it connect to proportional reasoning?

• How are the lengths of the sides of two figures used to determine if the figures are similar?

• How are proportional relationships in similar two-dimensional figures used to find missing measurements?

• How are angle relationships used to find missing measurements?

Vocabulary corresponding sides, corresponding angles, vertical angles, alternate interior angles, alternate exterior angles, same-side interior angles, same-side exterior angles, corresponding angles, adjacent angles, supplementary angles, parallel lines, transversal line, angle-angle criterion, scale factor, dilation, reflection, rotation, translation, transformation vocabulary cards Student pre-requisite knowledge Students have worked with translations, reflections and rotations in 7th grade. Resources: Carnegie Learning adopted textbook; HOM: Hands on Math; Exemplar Lessons; Instructional Resource Portfolios and Zip files; TEA Side by Side; Best Practices for the Middle School Math Classroom; Manipulatives; Differentiation Pre-AP and AP: Advanced Placement Vertical Teams Guide and Pre-AP Resource Bank Gifted and Talented: Exemplar Lessons, GT Scope and Sequence, GT Performance Reports ELPS: Mandated by Texas Administrative Code (19 TAC §74.4), click on the link for English Language Proficiency Standards (ELPS) to support English Language Learners. TEKS Knowledge & Skills Acquisition STAAR: RC = Reporting Category; DC = Dual Coded Skills; Readiness Standard; Supporting Standard Concepts are addressed in another unit.


8.3 Proportionality. The student applies mathematical process standards to use proportional relationships to describe dilations. The student is expected to: 8.3A generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation. 8.3B compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane

• Corresponding angles are congruent in similar figures.

• Corresponding sides are proportional in similar figures.

• A dilation is a nonrigid transformation that produces similar two-dimensional figures.

• Use scale factor to create dilation of a figure including enlargements and reductions.

• Generate dilations on a coordinate plane.

• Use strategic learning techniques such as drawing to acquire terms: scale factors, dilations, reflections, and translations on a














8.3C use an algebraic representation to explain the effect of a given positive rational scale factor applied to two-dimensional figures on a coordinate plane with the origin as the center of dilation

coordinate grid. • Compare side length ratios

(between the original shape and its dilation)

• Compare angle measures.

8.8 Expressions, equations, and relationships. The student applies mathematical process standards to use one-variable equations or inequalities in problem situations. The student is expected to: 8.8D 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.

• The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.

• A transversal is a line that intersects two or more lines.

• When two parallel lines are cut by a transversal, alternate interior angles are congruent.

• When two parallel lines are cut by a transversal, alternate exterior angles are congruent.

• When two parallel lines are cut by a transversal, same-side interior angles are supplementary.

• When two parallel lines are cut by a transversal, same-side exterior angles are supplementary.

• When two parallel lines are cut by a transversal, corresponding angles are congruent.

• Vertical angles are two non-adjacent angles formed by intersecting lines or line segments

• If two angles of one triangle are congruent to the corresponding angles of another triangle, then the triangles are similar.

• Identify congruent, adjacent, vertical, alternate interior, alternate exterior, corresponding, same side interior, same side exterior, and supplementary angles.

• Determine the measure of alternate interior angles, alternate exterior angles, same-side interior angles, same-side exterior angles, and corresponding angles.

• Use informal arguments to establish facts about the angle relationships.

8.10 Two-dimensional shapes. The student applies mathematical process standards to develop transformational geometry concepts. The student is expected to: 8.10A generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of two-dimensional shapes on a coordinate plane 8.10B differentiate between transformations that preserve congruence and those that do not

• A dilation with a scale factor of 1 preserves congruence, a scale factor between 0 and 1 creates a reduction, and a scale factor that is greater than 1 creates an enlargement.

• Differentiate between the transformations using multiple representations, including

• Justify the transformation using algebraic representations, such as (x,y)→(2x,2y) for a dilation, (x,y)→(-x,y) for a reflection, (x,y)→(x+2,y+1) for a translation.

• Justify that dilations with a scale factor of 1, reflections and translations preserve






8.10C explain the effect of translations, reflections over the x-or y-axis, and rotations limited to 90⁰, 180⁰, 270⁰, and 360⁰ as applied to two-dimensional shapes on a coordinate plane using an algebraic representation 8.10D model the effect on linear and area measurements of dilated two-dimensional shapes

algebraic representations, such as (x,y)→(2x,2y) for a dilation, (x,y)→(-x,y) for a reflection, (x,y)→(x+2,y+1) for a translation.

• (x, y) →(y, –x) represents a 90⁰ clockwise rotation.

• (x, y) →(–x, –y) represents a 180⁰ clockwise rotation.

• (x, y) →(–y, x) represents a 270⁰ clockwise rotation.

• A 180⁰ rotation may have the same result as the composition of a translation and a reflection.

• Reflections preserve congruence. • Translations preserve

congruence. • The perimeter of a dilated

polygon changes by a scale factor that is equal to the scale factor.

• The area of a dilated polygon changes by a factor that is equal to the scale factor squared.

congruence. • Rotate two-dimensional shapes

90⁰, 180⁰ and 270⁰. • Describe and model the effect

on perimeter and area of a dilated polygon.

• Describe and model the effects on linear and area measurements of dilated two-dimensional shapes numerically or algebraically.

•



Transformation This performance task allows students to demonstrate their knowledge of transformations through a real-world problem situation.











Exemplar Lessons and Instructional Resources ZIP Files Exemplar Lesson Scale Factor TEKS:8.3C



8th Grade Math

The following summaries are intended to give an overview and rationale behind curriculum decisions. The Curriculum Road Maps (CRMs) will provide clarification of specific TEKS and what students should know and be able to do at the conclusion of each unit. To access the instructional resources, exemplar lessons and additional teacher tools, you must reference the CRMs. CRM 8: Data In this unit on data, students will contrast bivariate sets of data that suggest a linear relationship, with bivariate sets of data that do not suggest a linear relationship. Students will construct and analyze scatter plots. As you teach this unit, you should focus on students being able to interpret the data, as well as create displays of data. The process TEKS should be partnered with concepts throughout this unit to make connections between displays of data and real world experiences. This unit was placed after linear equations because students will be working with data that suggests linear relationships.




1A 1B 1C 1D 1E 1F 1G

apply

mathematics

to problems

arising in

everyday

life, society,

and the

workplace;








© Austin Independent School District, 2014 Math Grade 8 Curriculum Road Map (CRM) 4th/5th Six Weeks CRM 8 Data Pacing

• 9 days • February 17 – February 27


Making Meaning


• valid data collection and its organization creates context so that what seems random may be quite predictable.

• data are gathered and organized in order to answer questions about the populations from which the data come. With data from only a sample of the population, inferences are made about the population.

Essential Questions • Why is data collected and analyzed? • How can predictions be made based on data?

Vocabulary scatterplot, bivariate sets of data, positive trend, negative trend, linear, non-linear, mean absolute deviation, line of best fit vocabulary cards Student pre-requisite knowledge This is the first time students are being introduced to scatterplots. Resources: Carnegie Learning adopted textbook; HOM: Hands on Math; Exemplar Lessons; Instructional Resource Portfolios and Zip files; TEA Side by Side; Best Practices for the Middle School Math Classroom; Manipulatives; Differentiation Pre-AP and AP: Advanced Placement Vertical Teams Guide and Pre-AP Resource Bank Gifted and Talented: Exemplar Lessons, GT Scope and Sequence, GT Performance Reports ELPS: Mandated by Texas Administrative Code (19 TAC §74.4), click on the link for English Language Proficiency Standards (ELPS) to support English Language Learners. TEKS Knowledge & Skills Acquisition STAAR: RC = Reporting Category; DC = Dual Coded Skills; Readiness Standard; Supporting Standard Concepts are addressed in another unit.


8.5 Proportionality. The student applies mathematical process standard to use proportional and non-proportional relationships to develop foundational concepts of functions. The student is expected to: 8.5C contrast bivariate sets of data that suggest a linear relationship with bivariate sets of data that do not suggest a linear relationship from a graphical representation.

8.5D use a trend line that approximates the linear relationship between bivariate sets of data to make predictions

• Data can be organized and analyzed to determine trends and make predictions.

• A scatterplot is one form of representing a given data set.

• Describe trends observed in scatterplots, such as negative trend, positive trend, or no trend.

• Use trend lines to make predictions.














8.11 Measurement and data. The student applies mathematical process standards to use statistical procedures to describe data. The student is expected to: 8.11A construct a scatterplot and describe the observed data to address questions of association such as linear, non-linear, and no association between bivariate data 8.11B determine the mean absolute deviation and use this quantity as a measure of the average distance data are from the mean using a data set of no more than 10 data points 8.11C simulate generating random samples of the same size from a population with known characteristics to develop the notion of a random sample being representative of the population from which it was selected

• Positive trend, negative trend, and no trend can be used to describe the association.

• How to construct a scatterplot. • Scatterplots can be used for

linear and non-linear situations. • How to look at the spread and

shape of data through the lens of variation from the mean.

• Samples should be representative of a population.

• The larger the sample size, typically the more representative the sample is of the population.

• Construct a scatterplot and describe the observed data.

• Determine if a set of bivariate data has a positive trend, negative trend or no trend.

• Calculate the mean absolute deviation.

• Compare data points to the mean absolute deviation in order to describe data.

• Determine that a random sample has characteristics that are representative of the whole population.



Data This performance task allows students to demonstrate their knowledge of data through a real-world problem situation.







Exemplar Lessons and Instructional Resources ZIP Files Exemplar Lesson Scatterplots TEKS: 8.11A








8th Grade Math

The following summaries are intended to give an overview and rationale behind curriculum decisions. The Curriculum Road Maps (CRMs) will provide clarification of specific TEKS and what students should know and be able to do at the conclusion of each unit. To access the instructional resources, exemplar lessons and additional teacher tools, you must reference the CRMs. CRM 9: Personal Financial Literacy and Engaging STAAR Review In this unit on personal financial literacy, students will develop an economic way of thinking and problem solving that will be useful in one’s life as a knowledgeable consumer and investor. As you are teaching this unit, you should focus on real world situations that are or will be relevant to students. Students should calculate and compare simple interest and compound interest. Students should also estimate the cost of a two‐year and four‐year college education and develop a periodic savings plan for accumulating the money needed to contribute to the total cost of attendance for at least the first year of college. The process TEKS should be partnered with concepts throughout this unit lending itself to the application of personal financial literacy through real world experiences. This unit was placed so that students are able to use their knowledge from previous CRMs to solve real world personal financial literacy problems. Time has been built in to this CRM for STAAR Review. Teachers should plan their STAAR review based on their students’ needs.




1A 1B 1C 1D 1E 1F 1G

apply

mathematics

to problems

arising in

everyday

life, society,

and the

workplace;








© Austin Independent School District, 2014 Math Grade 8 Curriculum Road Map (CRM) 5th Six Weeks CRM 9 Personal Financial Literacy and Engaging STAAR Review Pacing

• 20 days • March 2 – April 6


Making Meaning


• in order to make financially responsible decisions you need to be a knowledgeable consumer and investor.

Essential Questions • How will my knowledge of loans and credit

help prepare me for the future? • What can help you make financially

responsible decisions? • What are some things you can do to help

prepare to pay for college? Vocabulary simple interest, compound interest, cash advance, loan, work study, grant vocabulary cards Student pre-requisite knowledge This is the first time students have been introduced to the personal financial literacy standards. Resources: Carnegie Learning adopted textbook; HOM: Hands on Math; Exemplar Lessons; Instructional Resource Portfolios and Zip files; TEA Side by Side; Best Practices for the Middle School Math Classroom; Manipulatives; Differentiation Pre-AP and AP: Advanced Placement Vertical Teams Guide and Pre-AP Resource Bank Gifted and Talented: Exemplar Lessons, GT Scope and Sequence, GT Performance Reports ELPS: Mandated by Texas Administrative Code (19 TAC §74.4), click on the link for English Language Proficiency Standards (ELPS) to support English Language Learners. TEKS Knowledge & Skills Acquisition STAAR: RC = Reporting Category; DC = Dual Coded Skills; Readiness Standard; Supporting Standard Concepts are addressed in another unit.


8.12 Personal financial literacy. The student applies mathematical process standards to develop an economic way of thinking and problem solving useful in one’s life as a knowledgeable consumer and investor. The student is expected to: 8.12A solve real world problems comparing how interest rate and loan length affect the cost of credit

8.12B calculate the total cost of repaying a loan, including credit cards and easy access loans, under various rates of interest and over different periods using an online calculator

8.12C explain how small amounts of money invested regularly, including money saved for college and

• An investment/loan with compound interest increases much more quickly than the same investment/loan with simple interest.

• The terms of an investment include the amount of money invested, the interest rate, the length of time of the investment, and the method of the interest is calculated, whether it be as simple interest or compound interest.

• Simple interest calculations produce a constant rate of

• Calculate simple and compound interest using real-world problem situations.

• Compare investment earnings from simple and compound interest accounts.

• Explain how small amounts of money invested regularly grow over time.

• Analyze the terms of a loan in order to make financially responsible decisions.

• Choose loans that cost less money based on the terms of the investment.















retirement, grow over time

8.12D calculate and compare simple interest and compound interest earnings

8.12E identify and explain the advantages and disadvantages of different payment methods

8.12F analyze situations to determine if they represent a financially responsible decision and identify the benefits of financial responsibility and the costs of financial irresponsibility

8.12G estimate the cost of a 2-year and 4-year college education including family contribution and devise a periodic savings plan for accumulating the money needed to contribute to the total cost of attendance for at least the 1st year of college

change and a linear graph. • Interest rates vary depending

upon the lender, the length of time of the loan, and the borrower’s credit rating.

• When making the minimum payment on a credit card, a small debt may take years to pay and end up costing many times more than the original debt.

• A cash advance is a service provided by credit card companies that allows their customers to take out money directly from a bank or ATM.

• A cash advance is more costly than regular use of a credit card for a purchase. A percentage of the cash advance is added to the original cash advance amount and a higher interest rate is applied than what is used for credit card purchases.

• College tuition costs vary widely, and there is an option that makes sense and is affordable for every student.

• The Free Application for Federal Student Aid (FAFSA) is an application that makes students potentially eligible for grants, loans, and work study funds.

• Use online calculators to make financially responsible decisions.

• Critically analyze information about college.

• Research several colleges, determining the admission requirements and cost.

• Develop a financial plan for attending college.



Personal Financial Literacy This performance task allows students to demonstrate their knowledge of personal financial literacy through a real-world problem situation.













Exemplar Lessons and Instructional Resources ZIP Files 8th Grade STAAR Review Modules Exemplar Lesson Simple and Compound Interest TEKS: 8.12D



http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/MiddleSchool/M_8_STAAR_Review_Modules.zip


© Austin Independent School District, 2014 Math Grade 8 Curriculum Road Map (CRM) 5th Six Weeks CRM 10 Solving Equations and Inequalities Pacing

• 7 days • April 9 – April 17


Making Meaning


• equations and inequalities are an algebraic way of representing a real world mathematical situation.

• solving equations using models is a visual way to “unpack” a variable while keeping the equation balanced. It is related to simplifying expressions using order of operations.

Essential Questions • How do mathematical models/representations

shape our understanding of mathematics? • How is equivalence used in our lives? • How are algebraic expressions used to analyze

or solve problems?

Vocabulary equation, solution of an equation, inequalities, inequality symbols, inverse operation, balance, equal vocabulary cards Student pre-requisite knowledge Students solved equations and inequalities earlier in the year in CRM 2. Resources: Carnegie Learning adopted textbook; HOM: Hands on Math; Exemplar Lessons; Instructional Resource Portfolios and Zip files; TEA Side by Side; Best Practices for the Middle School Math Classroom; Manipulatives; Differentiation Pre-AP and AP: Advanced Placement Vertical Teams Guide and Pre-AP Resource Bank Gifted and Talented: Exemplar Lessons, GT Scope and Sequence, GT Performance Reports ELPS: Mandated by Texas Administrative Code (19 TAC §74.4), click on the link for English Language Proficiency Standards (ELPS) to support English Language Learners. TEKS Knowledge & Skills Acquisition STAAR: RC = Reporting Category; DC = Dual Coded Skills; Readiness Standard; Supporting Standard Concepts are addressed in another unit.


8.8 Expressions, equations, and relationships. The student applies mathematical process standards to use one variable equations or inequalities in problem situations. The student is expected to: 8.8A write one-variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants

8.8B write a corresponding real-world problem when given a one-variable equation or inequality with variables on both sides of the equal sign using rational number coefficients and constants

• Constraints or conditions within the problems may be indicated by words such as “minimum” or “maximum”.

• Symbols are used in equations. • An “equal sign” does not mean

“equals”, but instead “equals” means “balanced” or “same value/quantities.”

• Real-world problem situations can be described by number sentences.

• A constant is a value that does

• Determine if the value in the solution is part of the solution set or not.

• Relate/determine an equation or inequality that represents a situation in context and vice versa.

• Use academic vocabulary to describe the steps involved in solving an equation and inequality.

• Use a concrete model and picture to solve an equation.














8.8C model and solve one-variable equations with variables on both sides of the equal sign that represent mathematical and real-world problems using rational number coefficients and constants

not change. • A variable represents an

unknown amount. • When a variable and a constant

are next to each other, there is the hidden operation of multiplication.

• How to simplify and recognize equivalent expressions.

• Relate symbols to a model to solve an equation.

• Solve one-step and multi-step equations with grouping symbols.

• Solve one-variable inequalities.



Solving Equations This performance task allows students to demonstrate their knowledge of solving equations through a real-world problem.







Exemplar Lessons and Instructional Resources ZIP Files Exemplar Lessons: Solving Equations TEKS: 8.8C








8th Grade Math

The following summaries are intended to give an overview and rationale behind curriculum decisions. The Curriculum Road Maps (CRMs) will provide clarification of specific TEKS and what students should know and be able to do at the conclusion of each unit. To access the instructional resources, exemplar lessons and additional teacher tools, you must reference the CRMs. CRM 10: Solving Equations and Inequalities In this unit on solving equations and inequalities, students will deepen their understanding of solving equations and inequalities. As you are teaching this unit, you should continue to focus on using algebra tiles to model equations as well as having the students solve the equations algebraically. As you teach this unit, students should be solving equations with variables on both sides with rational number coefficients. Students should also be working with problems involving inequalities. The process TEKS should be partnered with concepts throughout this unit lending itself to the application of solving equations and inequalities through real world experiences. This unit was placed after STAAR because it covers equations at a deeper level preparing students to enter Algebra I.




1A 1B 1C 1D 1E 1F 1G

apply

mathematics

to problems

arising in

everyday

life, society,

and the

workplace;








© Austin Independent School District, 2014 Math Grade 8 Curriculum Road Map (CRM) 6th Six Weeks CRM 11 Rational Number Operations through the Process Standards Pacing

• 24 days • April 20 – May 21


Making Meaning

Enduring Understandings Students will understand that…

• There can be different strategies to solve a problem, but some are more effective and efficient than others.

• The context of a problem determines the reasonableness of a solution.

Essential Questions • How do I know where to begin when solving a

problem? • How do I decide what strategy will work best in

a given problem situation? • How do I know when a result is reasonable? • How does explaining my process help me to

understand a problem’s solution better? Vocabulary fraction, decimal, percent, integers, rational numbers vocabulary cards Student pre-requisite knowledge Students began working with problem solving in elementary school. Students worked with rational number operations in 7th grade. Resources: Carnegie Learning adopted textbook; HOM: Hands on Math; Exemplar Lessons; Instructional Resource Portfolios and Zip files; TEA Side by Side; Best Practices for the Middle School Math Classroom; Manipulatives; Differentiation Pre-AP and AP: Advanced Placement Vertical Teams Guide and Pre-AP Resource Bank Gifted and Talented: Exemplar Lessons, GT Scope and Sequence, GT Performance Reports ELPS: Mandated by Texas Administrative Code (19 TAC §74.4), click on the link for English Language Proficiency Standards (ELPS) to support English Language Learners. TEKS Knowledge & Skills Acquisition STAAR: RC = Reporting Category; DC = Dual Coded Skills; Readiness Standard; Supporting Standard Concepts are addressed in another unit.


8.1 The student uses mathematical process standards to acquire and demonstrate mathematical understanding. The student is expected to: 8.1A apply mathematics to problems arising in everyday life, society, and the workplace 8.1B use a problem solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem solving process and the reasonableness of the solution 8.1C select tools, including real objects,

• Strategies for problem solving are identifiable methods of approaching a task that are completely independent of the specific topic or subject matter.

• Problem solving strategies could include draw a picture, act it out, use a model, look for a pattern, guess and check, make a table or chart, try a simpler form of the problem, make an organized list, and write an equation.

• How to solve problems involving

• Complete tasks or problems involving fractions, decimals, percents and integers for which there is no prescribed or memorized rules or methods needed.

• Complete tasks or problems involving fractions, decimals, percents and integers with multiple entry and exit points.

• Complete tasks and problems involving fractions, decimals, percents, and integers that have















manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems 8.1D communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate 8.1E create and use representations to organize, record, and communicate mathematical ideas 8.1F create and use representations to organize, record, and communicate mathematical ideas 8.1G display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication

fractions, decimals, percents, and integers using a variety of strategies.

relative context. • Justify solutions to tasks or

problems. Involving fractions, decimals, percents, and integers.



Rational Number Operations This performance task allows students to demonstrate their knowledge of rational number operations through a real-world problem situation.













Exemplar Lessons and Instructional Resources ZIP Files Exemplar Lesson Rational Number Operations through the Process Standards TEKS: 8.1A, 8.1B, 8.1C, 8.1D, 8.1E, 8.1F, 8.1G



8th Grade Math

The following summaries are intended to give an overview and rationale behind curriculum decisions. The Curriculum Road Maps (CRMs) will provide clarification of specific TEKS and what students should know and be able to do at the conclusion of each unit. To access the instructional resources, exemplar lessons and additional teacher tools, you must reference the CRMs. CRM 11: Rational Number Operations through the Process Standards In this unit on rational number operations through the process standards, students will review rational number operations through real world scenarios to ensure students have the basic skills needed for Algebra I. As you are teaching this unit, you should focus on integer operations and fraction and decimal operations. Students should be fluent in these upon leaving 8th grade.




1A 1B 1C 1D 1E 1F 1G

apply

mathematics

to problems

arising in

everyday

life, society,

and the

workplace;








© Austin Independent School District, 2014 Math Grade 8 Curriculum Road Map (CRM) 6th Six Weeks CRM 12 Integrating the Graphing Calculator Pacing

• 8 days • May 26 – June 5


Making Meaning


• systems of linear equations model real-world situations and one way to solve linear equations is by graphing.

• systems of equations can be used as mathematical models for real-world situations.

• multiple representations are used to communicate mathematical ideas.

Essential Questions • What is a system? How can equations form

systems? • How can a system of equations support you in

solving real-world problems? • What does the solution to a system, or the

intersection point, represent in the context of the problem situation?

• What types of situations use systems of equations to solve a problem?

Vocabulary systems of equations, linear equation, function vocabulary cards Student pre-requisite knowledge Students were introduced to systems of equations earlier in the year, but did not have to solve systems of equations. Resources: Carnegie Learning adopted textbook; HOM: Hands on Math; Exemplar Lessons; Instructional Resource Portfolios and Zip files; TEA Side by Side; Best Practices for the Middle School Math Classroom; Manipulatives; Differentiation Pre-AP and AP: Advanced Placement Vertical Teams Guide and Pre-AP Resource Bank Gifted and Talented: Exemplar Lessons, GT Scope and Sequence, GT Performance Reports ELPS: Mandated by Texas Administrative Code (19 TAC §74.4), click on the link for English Language Proficiency Standards (ELPS) to support English Language Learners. TEKS Knowledge & Skills Acquisition STAAR: RC = Reporting Category; DC = Dual Coded Skills; Readiness Standard; Supporting Standard Concepts are addressed in another unit.


A.1 Foundations for functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is expected to: A.1D represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities

• How to connect multiple representations of functions to each other.

• Describe the relationship found in numerical patterns using words, tables, graphs, or a mathematical sentence.

• Determine if a relationship is a functional relationship.

• Use the graphing calculator to create graphs when given a table, equation or inequality.












A.8 Linear Functions. The student formulates systems of linear equations from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to: A.8B solve systems of linear equations using concrete models, graphs, tables, and algebraic methods

• Solutions to a system can be one point, infinitely many solutions or no solution.

• A system of linear equations with exactly one solution is characterized by the graphs of two lines whose intersection is a single point, and the coordinates of this point satisfy both equations.

• A system of linear equations with no solution is characterized by the graphs of two lines that are parallel.

• A system of linear equations having infinite solutions is characterized by two graphs that coincide (the graphs will appear to be the graph of one line), and the coordinates of all the points on the line satisfy both equations.

• Systems of two linear equations can be used to model two real-world conditions that must be satisfied simultaneously.

• Solve systems of linear equations in two variables by graphing.

• Solve systems of linear equations in two variables by using the graphing calculator.



Systems of Equations This performance task allows students to demonstrate their knowledge of systems of equations through a real-world problem situation.









Exemplar Lessons and Instructional Resources ZIP Files Exemplar Lesson Integrating the Graphing Calculator TEKS: A.1D, A.8D



8th Grade Math

The following summaries are intended to give an overview and rationale behind curriculum decisions. The Curriculum Road Maps (CRMs) will provide clarification of specific TEKS and what students should know and be able to do at the conclusion of each unit. To access the instructional resources, exemplar lessons and additional teacher tools, you must reference the CRMs. CRM 12: Integrating the Graphing Calculator In this unit on integrating the graphing calculator, students will work with the graphing calculator to represent equations and inequalities and solve linear equations using tables. As you are teaching this unit students should be confident in their ability to use the calculator to enhance their understanding of the concepts. Students should also practice simplifying order of operations problems using the calculator specifically with more than two grouping symbols and division. This unit was placed last so that students will enter Algebra I with knowledge of the graphing calculator.




1A 1B 1C 1D 1E 1F 1G

apply

mathematics

to problems

arising in

everyday

life, society,

and the

workplace;





