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Math Advanced 6 © 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: Integers and Integer Operations (17 days) August 25 – September 17

TEKS: 6.2B, 6.2C, 6.3C, 6.3D, 6.14C, 6.11A

CRM 2: Numerical Reasoning (12 days) September 18 – October 3

TEKS: 6.2A, 6.2B, 6.2C, 6.2D, 6.4F, 6.4G,

6.5C, 6.11A, 7.2A

2nd Six Weeks October 6 – November 7

24 Days

CRM 3: Fraction and Decimal Operations (24 days) October 6 –November 7

TEKS: 6.2E, 6.3A, 6.3B, 6.3E, 6.14G, 6.14H,

7.3A, 7.3B

3rd Six Weeks November 10 – December 18

25 Days

MoY I November 10 – November 25

Weeks 1 - 11

CRM 4: Ratios, Rates, and Percents (25 days) November 10 – December 18

TEKS: 6.4B, 6.4C, 6.4D, 6.4E, 6.4F, 6.4G,

6.4H, 6.5B, 6.14A, 6.14B, 6.14D, 6.14E,

6.14F, 7.4D, 7.13A, 7.13F

4th Six Weeks January 5 – February 20

33 Days

MoY II February 17 – February 27

Weeks 1 - 23

CRM 5: Expressions and Equations (11 days) January 5 – January 20

TEKS: 6.7A, 6.7B, 6.7C, 6.7D, 6.9A, 6.9B,

6.9C, 6.10A, 6.10B, 7.10A, 7.10B, 7.10C,

7.11A, 7.11B

CRM 6: Inequalities (5 days) January 21 – January 27

TEKS: 6.9A, 6.9B, 6.9C, 6.10A, 6.10B,

7.10A, 7.10B, 7.10C, 7.11A, 7.11B

CRM 7: Multiple Representations (10 days) January 28 – February 10

TEKS: 6.4A, 6.5A, 6.6A, 6.6B, 6.6C, 7.7A

CRM 8: Two-Dimensional Figures and Measurement (22 days) (7 days in 4th six weeks, 15 days in 5th six weeks) February 11 – March 13

TEKS: 6.4H, 6.8A, 6.8B, 6.8C, 6.8D, 6.10A,

7.11C

5th Six Weeks February 23 – April 17

34 Days

CRM 9: Data, Statistics and STAAR Review (19 days) March 23 – April 17

TEKS: 6.12A, 6.12B, 6.12C, 6.12D, 6.13A,

6.13B, 7.6G, 7.12A

STAAR Review: 6th Grade TEKS

6th Six Weeks April 20 – June 4

32 Days

STAAR Review (1 day) STAAR Testing (2 days) April 20 – April 22

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 10: Probability (12 days) April 23 – May 8

TEKS: 7.6A, 7.6B 7.6C, 7.6D, 7.6E, 7.6I,

7.6H

CRM 11: Measurement (17 days) May 11 – June 4

TEKS: 7.8C, 7.9B, 7.9C

6th Grade Advanced 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. CRM1: Integers and Integer Operations In this unit on integers and integer operations, students will model integer operations, compare and order integers and simplify expressions involving integers. As you are teaching this unit, you should focus on student’s understanding of integer operations through hands on experiences. As you teach this unit, students should use manipulatives to develop their understanding of integer operations in order to work towards being fluent with integer operations. The process TEKS should be partnered with concepts throughout this unit lending itself to the application of integer operations through real world experiences. This unit was strategically placed first because the concept uses hands on activities to build the student’s understanding and should be spiraled throughout the school year in order for students to be fluent in integer operations.

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

of 3 Updated: June 3, 2014

© Austin Independent School District, 2014 Math Advanced 6 Curriculum Road Map (CRM) 1st Six Weeks CRM 1: Integers and Integer Operations Pacing

• 17 days • August 25 – September 17

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…

• abstract integer operations are made clear when explained using physical and pictorial models.

Essential Questions • How do mathematical

models/representations shape our understanding of mathematics?

• How do mathematical operations relate to each other?

• How do I know which mathematical operation (+, -, x, ÷, exponents, etc.) to use?

Vocabulary absolute value, coordinate plane, quadrant, x-axis, y-axis, integer, negative, number line, operation, opposite, positive, zero pair vocabulary cards Student pre-requisite knowledge This is the first time students will be introduced to negative integers and integer operations with negatives. 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

6.2 Number and operations. The student applies mathematical process standards to represent and use rational numbers in a variety of forms. The student is expected to: 6.2B identify a number, its opposite, and its absolute value RC1

6.2C locate, compare and order integers and rational numbers using a number line

• The notation for absolute value consists of two vertical bars on either side of the number.

• Opposites have the same absolute value.

• Distance is positive.

• Associate the numerical representation of an integer to the real world situation.

• Locate a number and its opposite on a number line.

• Compare and order integers using a number line.

• Connect the procedure with the meaning of absolute value in a context.

• Use developed standardized algorithms to solve integer

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_6_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_6_SupportDocument_6.2B.pdf

http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/MiddleSchool/New_TEKS_Support_Documents/M_6_SupportDocument_6.2C.pdf


problems fluently. 6.3 Number and operations. The student applies mathematical process standards to represent addition, subtraction, multiplication, and division while solving problems and justifying solutions. The student is expected to: 6.3C represent integer operations with concrete models and connect the actions with the models to standardized algorithms 6.3D add, subtract, multiply, and divide integers fluently

• Models of integers support understanding of the algorithms used to add, subtract, multiply, and divide integers.

• Multiplication and Division of integers is a direct extension of multiplication and division for whole numbers.

• Draw and use pictorial representations and concrete models to represent operations with integers.

• Select and use models to solve integer problems.

• Develop standardized algorithms through models and justification.

• Select and use different problem situations to connect operations to the context.

6.11 Measurement and data. The student applies mathematical process standards to use numerical or graphical representations to analyze problems. The student is expected to: 6.11A graph points in all four quadrants using ordered pairs of rational numbers

• In an ordered pair, the x-coordinate is written first and the y-coordinate is written second.

• The vertical axis is the y-axis and the horizontal axis is the x-axis.

• Graph points in all four quadrants using ordered pairs of rational numbers (positive and negative integers only).

6.14 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: 6.14C balance a check register that includes deposits, withdrawals, and transfers

• A withdrawal is represented by a negative number.

• A deposit is represented as a positive number.

• Balance a checkbook register that includes deposits, withdrawals, and transfers.

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.)

Integer Operations This performance tasks allows students to demonstrate their knowledge of using models to solve problems involving integers and connect their actions to standardized algorithms through justification.

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


http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/MiddleSchool/New_TEKS_Support_Documents/M_6_SupportDocument_6.3D.pdf

http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/MiddleSchool/New_TEKS_Support_Documents/M_6_SupportDocument_6.11A.pdf


http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/MiddleSchool/Performance_Tasks_1415/M_6_PT1_CRM1_1415.pdf


• 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 Adding Integers (chip model) TEKS: 6.3C Adding Integers (number line model) TEKS: 6.3C Multiplying Integers TEKS: 6.3C Dividing Integers TEKS: 6.3C Subtracting Integers (chip model) TEKS: 6.3C Integer Operations TEKS: 6.3D

http://curriculum.austinisd.org/schoolnetDocs/mathematics/6th/M_ADV6TH_IR_CRM1_1415.pdf


http://curriculum.austinisd.org/schoolnetDocs/mathematics/6th/M_ADV6TH_IR_CRM1_1415.zip



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: Probability In this unit on probability, students will explore theoretical and experimental probability. As you are

teaching this unit, you should focus on probability having two distinct types; theoretical and

experimental. As you teach this unit, students should be participating in experiments or simulations to

explore experimental probability. Students should leave sixth grade with a strong understanding of the

two distinct types of probability. The process TEKS should be partnered with concepts throughout this

unit lending itself to the application of probability through real world experiences. This unit was placed

after STAAR because probability is only taught in 7th grade and students will be covering the majority of

8th grade material in 7th grade advanced.




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 Advanced 6 Curriculum Road Map (CRM) 1st Six Weeks CRM 2: Numerical Reasoning Pacing

• 12 days • September 18 – October 3


Making Meaning


• quantities can be represented in different forms and can be used to describe and compare the value of real-world quantities.

Essential Questions • When is it beneficial to use one

representation of a rational number rather than an equivalent form of the same number?

• How is equivalence used in our lives? • How are benchmark fractions used to

estimate values of fractions, decimals? • How do mathematical

models/representations shape our understanding of mathematics?

Vocabulary absolute value, coordinate plane, equivalent, decimal, fraction, opposite, percent , quadrant, rational number, x-axis, y-axis vocabulary cards Student pre-requisite knowledge This is the first time students will generate equivalent fractions, decimals, and percents. Students should have

knowledge of the terms fraction, decimal, and percent. Resources: Carnegie Learning adopted textbook; HOM: Hands on Math; Exemplar Lessons; Instructional Resource Portfolios and Zip files; Grade 6 TEA Side by Side; Grade 7 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.


6.2 Number and Operations. The student applies mathematical process standards to represent and use rational numbers in a variety of forms. The student is expected to: 6.2A classify whole number, integers, and rational numbers, using a visual representation such as a Venn diagram to describe relationships between sets of numbers 6.2B identify a number its opposite, and

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

• Any rational number, positive or negative, whole or not whole, can be written as a fraction and

• Represent relationships between sets of numbers using a Venn diagram.

• Associate the numerical representation of an integer to the real world situation.

• Locate a number and its
















its absolute value 6.2C locate, compare, and order integers and rational numbers using a number line 6.2D order a set of rational numbers arising from mathematical and real-world contexts

as a decimal.

opposite on a number line. • Locate positive and negative

rational numbers on a number line.

• Compare and order positive and negative rational numbers using a number line

6.4 Proportionality. The student applies mathematical process standards to develop an understanding of proportional relationships in problem situations. The student is expected to: 6.4F represent benchmark fractions and percents such as 1%, 10%, 25%, 33 1/3%, and multiples of these values using 10 by 10 grids, strip diagrams, number lines, and numbers 6.4G generate equivalent forms of fractions, decimals, and percents using real-world problems, including problems that involve money

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

• When it is most appropriate or efficient to use a given form of a rational number.

• Use models to represent benchmark fractions and percents.

• Generate equivalent fractions • Use a variety of strategies to

generate a decimal equivalent to a given fraction, and vice versa.

• Use a variety of strategies to generate a decimal equivalent to a given percent, and vice versa

• Use a variety of strategies to generate a fraction equivalent to a given percent, and vice versa.

6.5 Proportionality. The student applies mathematical process standards to solve problems involving proportional relationships. The student is expected to: 6.5C use equivalent fractions, decimals, and percents to show equal parts of the same whole

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

• Two fractions are equal if they represent the same portion of a whole.

• Express rational numbers in meaningful contexts as fractions, decimals and percents.

6.11 Measurement and data. The student applies mathematical process standards to use coordinate geometry to identify locations on a plane. The student is expected to: 6.11A graph points in all four quadrants using ordered pairs of rational numbers

• In an ordered pair, the x-coordinate is written first and the y-coordinate is written second

• The vertical axis is the y-axis and the horizontal axis is the x-axis.

• Graph points in all four quadrants using ordered pairs of rational numbers.

7.2 Number and operations. The student applies mathematical process standards to represent and use rational numbers in a variety of forms. The student is expected to: 7.2A extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of rational 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.

• Represent relationships between sets of numbers using a Venn diagram.

• Describe relationships between sets of rational numbers.

http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/MiddleSchool/New_TEKS_Support_Documents/M_6_SupportDocument_6.2C_Part2.pdf


http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/MiddleSchool/New_TEKS_Support_Documents/M_6_SupportDocument_6.4F.pdf

http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/MiddleSchool/New_TEKS_Support_Documents/M_6_SupportDocument_6.4G.pdf


http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/MiddleSchool/New_TEKS_Support_Documents/M_6_SupportDocument_6.11A_Part2.pdf





Fractions, Decimals and Percents

This performance task allows students to demonstrate their knowledge of generating equivalent fractions, decimals and percents and representing these values on a number line.



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 Lesson Equivalency TEKS: 6.4G Coordinate Plane TEKS: 6.11A






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: Fraction and Decimal Operations In this unit on fraction and decimal operations, students will explore multiplication and division of fractions and decimals. As you teach this unit, students should know that computation with fractions is built on a strong foundation of whole number operations and fraction sense. The 7th grade TEKS in this unit require students to be fluent in rational number operations. The process TEKS should be partnered with concepts throughout this unit lending itself to application of fraction and decimal operations through real world experiences. This unit was placed third because the concepts build on the numerical reasoning unit and should be spiraled throughout 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 Advanced 6 Curriculum Road Map (CRM) 2nd Six Weeks CRM 3 Fraction and Decimal Operations Pacing

• 24 days • October 6 – November 7


Making Meaning


• multiplication and division are inverse operations. • multiplication with fractions/decimals involves repeated

addition or taking part of a part/whole. • division with fractions/decimals involves breaking a

quantity into equal parts.

Essential Questions • How do mathematical models/representations

shape our understanding of mathematics? • How do I know which mathematical operation

(+, –, x, ÷) to use?

Vocabulary dividend, divisor, quotient, factor, product, reciprocal, rational number, salary vocabulary cards Student pre-requisite knowledge This is the first time students will be introduced to multiplying and dividing fractions and decimals. Resources: Carnegie Learning adopted textbook; HOM: Hands on Math; Exemplar Lessons; Instructional Resource Portfolios and Zip files; 6th TEA Side by Side; 7th 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.


6.2 Numbers and operations. The student applies mathematical process standards to represent and use rational numbers in a variety of forms. The student is expected to: 6.2E extend representations for division to include fraction notation such as a/b represents the same number as a ÷ b where b ≠ 0

• Dividing the numerator of a fraction by its denominator will yield a decimal equivalent.

• Convert a fraction to a decimal by dividing the numerator by the denominator.












http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/MiddleSchool/New_TEKS_Support_Documents/M_6_SupportDocument_6.2E.pdf


6.3 Number and operations. The student applies mathematical process standards to represent addition, subtraction, multiplication, and division while solving problems and justifying solutions. The student is expected to: 6.3A recognize that dividing by a rational number and multiplying by its reciprocal result in equivalent values 6.3B determine with and without computation, whether a quantity is increased or decreased when multiplied by a fraction, including values greater than or less than one 6.3E multiply and divide positive rational numbers fluently

• Multiplying by a fraction greater than one increases the quantity.

• Multiplying by a fraction less than one decreases the quantity.

• Multiplication and division involving fractions and decimals can be represented with models.

• Justification of a solution requires explanation of the operation chosen and reasonableness of the answer through the lens of the problem situation.

• Justify why dividing by a rational number and multiplying by its reciprocal result in equivalent values.

• Determine if a quantity is increased or decreased when multiplied by a fraction.

• Justify why a quantity increases when multiplied by fraction greater than one and why a quantity decreases when multiplied by a fraction less than one.

• Use models to multiply and divide rational numbers.

• Use developed algorithms to multiply and divide rational numbers fluently.

• Choose when to use multiplication and division in context.

• Justify the reasonableness of a solution.

6.14 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: 6.14G explain various methods to pay for college, including through savings, grants, scholarships, student loans, and work study 6.14H compare the annual salary of several occupations requiring various levels of post-secondary education or vocational training and calculate the effects of the different annual salaries on lifetime income

• There are a variety of methods available to pay for college.

• Salaries vary depending on the occupation.

• Explain the various methods that are available to pay for college.

• Choose several occupations and compare different annual salaries and explain the effect those different salaries have on lifetime income.

7.3 Number and operations. The student applies mathematical process standards to add, subtract, multiply, and divide while solving problems and justifying solutions. The student is expected to: 7.3A add, subtract, multiply, and divide rational numbers fluently 7.3B apply and extend previous understandings of operations to solve problems using addition, subtraction, multiplication and division of rational numbers

• Multiplication and division involving fractions and decimals can be represented with models.

• With addition, no two quantities can be added unless they are measured or reported in the same units.

• Addition is combining of two or more quantities or the combination of parts of a whole with the whole or one of the parts unknown.

• Use developed algorithms to add, subtract, multiply, and divide rational numbers fluently.

• Choose when to use addition, subtraction, multiplication, and division in context.

• Justify the reasonableness of a solution.





http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/MiddleSchool/New_TEKS_Support_Documents/M_6_SupportDocument_6.14H.pdf




• Subtraction involves separating part of a quantity from the original group.

• A quantity can only be subtracted from another quantity if first a common unit between the two sets is found.

• Division involves breaking a quantity into equal parts.

• Justification of a solution requires explanation of the operation chosen and reasonableness of the answer through the lens of the problem situation.



Multiplying Fractions This performance task allows student to demonstrate their knowledge of multiplying fractions through a real-life scenario. Fitness Math This performance task allows students to demonstrate their knowledge of working with fractions and decimals in a real-world situation.



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



Exemplar Lessons and Instructional Resources PDF Exemplar Lessons and Instructional Resources ZIP Files Exemplar Lessons Multiplying Fractions TEKS 6.3E Dividing Fractions TEKS 6.3E Rational Number Operations TEKS: 7.3B






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: Ratios, Rates and Percents In this unit on ratios, rates, and percents, students will develop their proportional reasoning through activities involving comparing and determining the equivalence of ratios and solving proportions in a variety of problem‐based contexts and situations without recourse to rules or formulas. As you teach this unit, students should have exposure to a variety of strategies for solving proportions or comparing ratios. Most of the strategies are informal strategies rather than prescribed algorithms. The 7th grade TEKS in this unit focus on percent applications, including percent increase, percent decrease, sales tax, sale price and discount. As you teach percents students should begin finding percents using a model, such as percent bars. The process TEKS should be partnered with concepts throughout this unit lending itself to proportional reasoning through real world experiences. This unit was placed fourth because the students need a strong proportional reasoning background for the upcoming CRMs.




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 Advanced 6 Curriculum Road Map (CRM) 3rd Six Weeks CRM 4 Ratios, Rates, and Percents Pacing

• 25 days • November 10 – December 18


Making Meaning


• proportional relationships express how quantities change in relationship to each other.

Essential Questions • When and why do I use proportional

comparisons? • How will my knowledge of credit cards and

debit cards prepare me for the future? Vocabulary proportional relationship, percent, ratio, rate, unit rate, qualitative, quantitative, checking account, check, statement, account balance, deposit, withdrawal, debit, overdraft, debit card, credit card vocabulary cards Student pre-requisite knowledge In 5th grade students use models to relate decimals and fractions. Resources: Carnegie Learning adopted textbook; HOM: Hands on Math; Exemplar Lessons; Instructional Resource Portfolios and Zip files; 6th TEA Side by Side; 7th 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.


6.4 Proportionality. The student applies mathematical process standards to develop an understanding of proportional relationships in problem situations. The student is expected to: 6.4B apply qualitative and quantitative reasoning to solve prediction and comparison real-world problems involving ratios and rates 6.4C give examples of ratios as multiplicative comparisons of two quantities describing the same attribute 6.4D give examples of rates as the comparison by division of two quantities having different attributes, including rates as quotients 6.4E represent ratios and percents with concrete models, fractions, and decimals

• Proportional reasoning involves both qualitative and quantitative process

• Quantitative reasoning focuses on the relationships between and within equivalent ratios.

• Qualitative reasoning focuses on data that can be observed, but not measured.

• The order of numbers in the ratio must match the order of the labels given.

• Although ratios look like fractions, ratios do not necessarily represent a part-to-whole relationship like a fraction

• Make predictions based on qualitative and quantitative changes.

• Use ratios to describe proportional relationships.

• Use rates to describe proportional relationships

• Identify proportional relationships/ ratios in word problems and write in different forms.

• Discuss in cooperative groups how ratio tables can be used to solve problems involving equivalent ratios, rates and proportions.

















6.4F represent benchmark fractions and percents such as 1%, 10%, 25%, 33 1/3%, and multiples of these values using 10 by 10 grids, strip diagrams, number lines, and numbers 6.4G generate equivalent forms of fractions, decimals, and percents using real-world problems, including problems that involve money 6.4H convert units within a measurement system, including the use of proportions and unit rates

does. The ratio may represent a part-to-part relationship.

• A proportion can be made with any two ratios in a ratio table.

• A proportion is two equivalent ratios joined by an equals sign.

• The numerical relationship between the two numerators, two denominators, or a numerator and a denominator is multiplicative, not additive.

• A ratio is a multiplicative comparison of two quantities or measures.

• A rate is a relationship between two units of measure.

• A rate is a special form of ratio.

• Find the missing part of a proportion using equivalent fractions or a ratio table.

• Set up a ratio table to make a prediction.

• Analyze word problems to accurately identify ratios and proportions.

• Model ratio situations using proportions.

6.5 Proportionality. The student applies mathematical process standards to solve problems involving proportional relationships. The student is expected to: 6.5B solve real-world problems to find the whole given a part and the percent, to find the part given the whole and the percent, and to find the percent given the part and the whole including the use of concrete and pictorial models

• Percent is a special fraction where 100 is the denominator.

• Using percents allows us to easily compare amounts.

• How to use multiple strategies such as percent bars, ratio tables, strip diagrams, or proportions to solve problems.

• How to estimate using friendly numbers and/or rounding.

• Use ratio tables, percent bars, strip diagrams and other strategies to solve problems involving percents.

• Find the percent of a given whole.

• Find the percentage if given the part and the whole.

• Determine the total number if given the percentage and percent of total.

• Estimate percentages. • Solve application problems

involving percent, such as tax, tip, discount and commission.

6.14 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: 6.14A compare the features and costs of a checking account and a debit card offered by different local financial institutions 6.14B distinguish between debit cards and credit cards 6.14D explain why it is important to establish a positive credit history 6.14E describe the information in a credit report and how long it is retained 6.14F describe the value of credit

• A checking account allows customers to safely store money in the bank and write checks against the money that they deposit.

• A statement is a monthly summary of the account balance on the checking account, including all transactions that occur during a given time period. It allows the customer to check his records against the bank’s records.

• A customer may have to pay money to have a checking

• Analyze and explain the features and costs of a checking account for a local financial institute.

• Analyze and explain the features of a debit card.

• Compare a checking account and debit card.

• Explain the characteristics of a credit card.

• Explain the characteristics of a debit card.

• Explain the differences between a credit card and a debit card.

• Describe the information on a credit report.











reports to borrowers and to lenders account. • Banks charge a fee for

overdrafts. • Sometimes customers are

required to keep a minimum amount of money in their account at all times.

• Debit cards are issued by the bank when a customer opens a checking account. When a customer buys an item using a debit card, the money is taken directly from the checking account.

• The amount of money the customer can spend is limited to the balance in the checking account.

• Credit cards are issued by a company when a customer applies to a financial, credit card company.

• When a customer buys an item using a credit card, he can make the purchase whether he currently has the money for it or not.

• The amount of money the customer can spend is based upon the limit the credit card company provides.

• A credit report is a detailed listing of an individual’s credit history along with a credit score.

• A credit score is a number used by lenders to rate how likely a person will repay his or her debts.

• The credit score determines if the person qualifies for a loan, the amount of money he can borrow, and the interest rate for the loan.

• A good credit score is obtained by paying bills on time and avoiding having too much debt.

• Explain the importance of maintaining good credit.

• Determine the significance of a credit report to borrowers and lenders.


7.4 Proportionality. The student applies mathematical process standards to represent and solve problems involving proportional relationships. The student is expected to: 7.4D solve problems involving ratios, rates, and percents, including multi-step problems involving percent increase and percent decrease, and financial literacy problems

• Proportional relationships are used to define equations and determine the constant rate of proportionality.

• Use percent bars and ratio tables to calculate percent increase and decrease.

• Solve real-world personal financial literacy problems.

7.13 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: 7.13A calculate the sales tax for a given purchase and calculate income tax for earned wages 7.13F analyze and compare monetary incentives, including sales, rebates, and coupons

• Sales tax is added to the original price of an item.

• Monetary incentives include sales, rebates and coupons.

• Income tax is subtracted from wages.

• Use percent bars and ratio tables to calculate sales tax for a given purchase.

• Calculate the final price of an item after sales tax.

• Calculate income tax for earned wages.

• Determine which monetary incentive (sales, rebates, coupons) is the most economical in real-world problem situations.



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











Exemplar Lessons and Instructional Resources PDF Exemplar Lessons and Instructional Resources ZIP Files Exemplar Lesson Percents TEKS: 6.5B Percents TEKS: 7.13A, 7.13F




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: Expressions and Equations In this unit on expressions and equations, students explore solving equations through concrete and pictorial models as well as create, apply, and solve equations in problem situations. As you teach this unit, you should focus on the use of manipulatives to develop the understanding of balancing an equation and isolating the variable. The 7th grade TEKS in this unit extend to solving two‐step equations. The process TEKS should be partnered with concepts throughout this unit lending itself to the application of solving equations through real world experiences. This unit was placed fifth because the concepts of equations and expressions learned in this unit will be used in the Two‐Dimensional Figures and Measurement unit and should be spiraled throughout 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 Advanced 6 Curriculum Road Map (CRM) 4th Six Weeks CRM 5 Expressions and Equations Pacing

• 11 days • January 5 – January 20


Making Meaning


• equations 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 • Why is an “order of operations” necessary? • 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 Isolate, variable, balance, equivalent, operation, equation, zero pair, expression vocabulary cards Student pre-requisite knowledge This will be the first time grade 6 students are exposed to solving equations through modeling. This is the first time students are introduced to order of operations with exponents. Resources: Carnegie Learning adopted textbook; HOM: Hands on Math; Exemplar Lessons; Instructional Resource Portfolios and Zip files; Grade 6 TEA Side by Side; Grade 7 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.


6.7 Expressions, equations, and relationships. The student applies mathematical process standards to develop concepts of expressions and equations. The student is expected to: 6.7A generate equivalent numerical expressions using order of operations, including whole number exponents and prime factorization 6.7B distinguish between expressions and equations verbally, numerically, and algebraically 6.7C determine if two expressions are equivalent using concrete models, pictorial models, and algebraic expressions

• Following order of operations provides a consistent process to simplify numerical expressions.

• Order of operations is not simply a process to be memorized, but should promote understanding the relationships between the operations.

• A number next to parentheses means to multiply.

• Fraction bars mean to divide. • 0 and 1 are neither prime nor

composite.

• Develop a strategy to remember the correct sequence for the order of operations. (The common adage “Please Excuse My Dear Aunt Sally” can lead to misconceptions, such as multiplication before division, and that parentheses are the only grouping symbols).

• Use the rules of order of operations to evaluate/simplify expressions.

• Create a numerical

















6.7D generate equivalent expressions using the properties of operations: inverse, identity, commutative, associative, and distributive properties

• Expanded form and exponential form are equivalent.

• Equations are sentences that state that two things are equal.

• An expression is a phrase that represents a single number.

• If an equation contains a variable, it may be proved true or false by replacing the variable with a number.

• If an expression contains a variable, the expression may represent different numbers depending on the value assigned to the variable with a number.

• An equation includes an equal sign.

• Expressions can be entirely numeric or a mixture of numbers and one variable.

• Inverse, identify, commutative, associate and distributive properties are properties of operations.

representation of a real-world situation.

• Create a numerical expression that provides a given answer when simplified.

• Use a variety of strategies to accurately find prime factorization of numbers.

• Determine if a verbal, numerical or algebraic representation is an expression or an equation.

• Use order of operations/properties of operations to determine if two expressions are equivalent.

• Use concrete models, pictorial models, and algebraic expressions to determine if two expressions are equivalent.

• Use the properties of operations (inverse, identity, commutative, associative and distributive) to generate equivalent expressions.

6.9 Expressions, equations, and relationships. The student applies mathematical process standards to use equations and inequalities to represent situations. The student is expected to: 6.9A write one-variable, one-step equations and inequalities to represent constraints or conditions within problems 6.9B represent solutions for one-variable, one-step equations and inequalities on number lines. 6.9C write corresponding real-world problems given one-variable, one-step equations or inequalities

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

• Symbols are used in equations. • Constraints or conditions may be

indicated by words such as minimum or maximum.

• Solutions for equations can be represented on a number line.

• Relate/determine an equation that represents situations in context and vice versa.

• Represent real-world problems that include everyday life, society, the workplace and application of mathematical concepts.

• Represent solutions to one-variable, one-step equations on a number line.






6.10 Expressions, equations, and relationships. The student applies mathematical process standards to use equations and inequalities to solve problems. The student is expected to: 6.10A model and solve one-variable, one-step equations and inequalities that represent problems, including geometric concepts 6.10B determine if the given value(s) make(s) one-variable, one-step equations or inequalities true

• A concrete model and picture relate to an equation.

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

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

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

• A constant is a value that does not change.

• When a variable and a constant are next to each other, there is the hidden operation of multiplication.

• “Key words” do not always equate to operations, but rather actions relate to operations.

• Use concrete models and pictures to solve an equation.

• Relate symbols to a model to solve an equation.

• Solve real-world problems that include everyday life, society, the workplace and applications of mathematical concepts such as measurement.

• Determine if the given value makes a one-variable, one-step equation true.

7.10 Expressions, equations, and relationships. The student applies mathematical process standards to use one-variable equations and inequalities to represent situations. The student is expected to: 7.10A write one-variable, two-step equations and inequalities to represent constraints or conditions within problems

7.10B represent solutions for one-variable, two-step equations and inequalities on number lines.

7.10C write a corresponding real-world problem given a one-variable, two-step equation or inequality

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

• Symbols are used in equations.

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

• Represent real-word problems that include everyday life, society, the workplace and application of mathematical concepts such as measurement.

• Represent solutions to equations on a number line.

7.11 Expressions, equations, and relationships. The student applies mathematical process standards to solve one-variable equations and inequalities. The student is expected to: 7.11A model and solve one-variable, two-step equations and inequalities 7.11B determine if the given value(s) make(s) one-variable, two-step equations and inequalities true

• A concrete model and picture relate to an equation.

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

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

• A constant is a value that does 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.

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

• Relate symbols to a model to solve an equation.

• Solve real-world problems that include everyday life, society, the workplace and applications of mathematical concepts such as measurement.

• Determine if the given value makes an equation true.











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



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



Exemplar Lessons and Instructional Resources PDF Exemplar Lessons and Instructional Resources ZIP Files Exemplar Lesson Modeling Equations TEKS: 6.10A Equations and Problem Situations TEKS 7.10C






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: Inequalities In this unit on inequalities, students will explore the meaning of inequalities and represent them in situations. As you are teaching this unit, students should build on their previous knowledge of writing and solving equations. The process TEKS should be partnered with concepts throughout this unit lending itself to the applications of inequalities through real world experiences. The unit was placed after equations and expressions have been taught so that students can use their background knowledge about equations and expressions to understand the meaning of inequalities. .




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 Advanced 6 Curriculum Road Map (CRM) 4th Six Weeks CRM 6 Inequalities Pacing

• 5 days • January 21 – January 27


Making Meaning


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

Essential Questions • How do mathematical models/representations

shape our understanding of mathematics? • How is solving an inequality similar/different

than solving an equation? • How can an inequality be used to represent a

given situation? Vocabulary inequality, greater than, less than, greater than or equal to, less than or equal to vocabulary cards Student pre-requisite knowledge Students have worked with inequality symbols, but this is the first time students will be solving inequalities. Resources: Carnegie Learning adopted textbook; HOM: Hands on Math; Exemplar Lessons; Instructional Resource Portfolios and Zip files; Grade 6 TEA Side by Side; Grade 7 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.


6.9 Expressions, equations, and relationships. The student applies mathematical process standards to use equations and inequalities to represent situations. The student is expected to: 6.9A write one-variable, one step equations and inequalities to represent constraints or conditions within problems 6.9B represent solutions for one-variable, one-step equations and inequalities on number lines 6.9C write corresponding real-world problems given one-variable, one-step equations or inequalities

• Symbols are used in inequalities. • Constraints or conditions within

the problems may be indicated by words such as “minimum” or “maximum”.

• Represent solutions for one-variable, one-step inequalities on a number line.

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

















6.10 Expressions, equations, and relationships. The student applies mathematical process standards to use equations and inequalities to solve problems. The student is expected to: 6.10A model and solve one-variable, one-step equations and inequalities that represent problems, including geometric concepts.

6.10B determine if the given value(s) make(s) one-variable, one-step equations or inequalities true.

• Symbols are used in inequalities. • When you multiply or divide

both sides of an inequality by a negative number the inequality sign is reversed.

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

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

• Solve real-world problems that include everyday life, society, the workplace, and applications of mathematical concepts.

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

7.10 Expressions, equations, and relationships. The student applies mathematical process standards to use one-variable equations and inequalities to represent situations. The student is expected to:

7.10A write one-variable, two-step equations and inequalities to represent constraints or conditions within problems 7.10B represent solutions for one-variable, two-step equations and inequalities on number lines 7.10C write a corresponding real-world problem given a one-variable , two-step equation or inequality

• Symbols are used in inequalities. • Constraints or conditions within

the problems may be indicated by words such as “minimum” or “maximum”.

• Represent solutions for one-variable, two-step inequalities on a number line.

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

7.11 Expressions, equations, and relationships. The student applies mathematical process standards to solve one-variable equations and inequalities. The student is expected to: 7.11A model and solve one-variable, two-step equations and inequalities 7.11B determine if the given value(s) make(s) one-variable, two-step equations and inequalities true

• Symbols are used in inequalities. • When you multiply or divide

both sides of an inequality by a negative number the inequality sign is reversed.

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

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

• Solve real-world problems that include everyday life, society, the workplace, and applications of mathematical concepts.

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











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



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



Exemplar Lessons and Instructional Resources PDF Exemplar Lessons and Instructional Resources ZIP Files Exemplar Lesson Inequalities TEKS: 6.10A Inequalities TEKS: 7.11B







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: Multiple Representations In this unit on multiple representations, students will explore a variety of ways to represent mathematical data. As you are teaching this unit, you should focus on tables, graphs and equations to represent mathematical data. As you teach this unit, students should be creating and justifying problem situations with multiple representations. The process TEKS should be partnered with concepts throughout this unit lending itself to the application of multiple representations through real world experiences. This unit was placed after students have learned about equations and inequalities.




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 Advanced 6 Curriculum Road Map (CRM) 4th Six Weeks CRM 7 Multiple Representations Pacing

• 10 days • January 28 – February 10


Making Meaning


• linear relationships can be represented in different ways.

Essential Questions • 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 relationship, independent quantity, dependent quantity, additive relationship, multiplicative relationship vocabulary cards Student pre-requisite knowledge Students described characteristics of data presented in tables and graphs in 5th grade. Resources: Carnegie Learning adopted textbook; HOM: Hands on Math; Exemplar Lessons; Instructional Resource Portfolios and Zip files; 6th TEA Side by Side; 7th 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.


6.4 Proportionality. The student applies mathematical process standards to develop an understanding of proportional relationships in problem situations. The student is expected to: 6.4A compare two rules verbally, numerically, graphically and symbolically in the form y = ax or y = x + a in order to differentiate between additive and multiplicative relationships

• In an input-output table, if the difference between x and y is constant it is an additive relationship.

• In an input-output table, if the quotient between x and y is constant it is a multiplicative relationship.

• Use an input-output table to compare two rules to differentiate between additive and multiplicative relationships.














6.5 Proportionality. The student applies mathematical process standards to solve problems involving proportional relationships. The student is expected to: 6.5A represent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs and proportions

• Ratio and rates can be represented using scale factors, tables, graphs and proportions.

• Represent ratios and rates using scale factors.

• Represent ratios and rates using tables and graphs.

6.6 Expressions, equations and relationships. The student applies mathematical process standards to use multiple representations to describe algebraic relationships. The student is expected to: 6.6A identify independent and dependent quantitates from tables and graphs 6.6B write an equation that represents the relationship between independent and dependent quantities from a table. 6.6C represent a given situation using verbal descriptions, tables, graphs, and equations in the form y = kx or y = x + b

• Liner relationships can be represented with a table of paired values (input-output table).

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

• Describe the relationship between dependent and independent variables.

• Write an equation that represents a linear relationship.

• Analyze patterns and represent the continuation of those patterns through diagrams, tables, verbal descriptions, algebraic descriptions and graphs.

• Create and represent situations using tables, graphs, equations, or verbal descriptions and make connection between the different representations.

7.7A Expressions, equations, and relationships. The student applies mathematical process standards to represent linear relationships using multiple representations. The student is expected to: 7.7A represent linear relationships using verbal descriptions, tables, graphs, and equations that simplify to the form y = mx + b

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

• Linear relationships can be proportional or non-proportional.

• Create and represent linear relationships using tables, graphs, equations (rational number coefficients and constants), or verbal descriptions and make connections between the different representations.

• Determine if a given relationship is proportional or non-proportional using evidence from the graph, table, equation, and verbal description.



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



Additional Suggestions for Assessments









• Homework • Exit slips • Teacher-created assessments • Discussions • Journal responses • Projects • Games



Exemplar Lessons and Instructional Resources PDF Exemplar Lessons and Instructional Resources ZIP Files Exemplar Lesson Multiple Representations TEKS: 6.6C Independent and Dependent Quantities TEKS: 6.6A






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: Two‐Dimensional Figures and Measurement In this unit on two‐dimensional figures and measurement, students will explore attributes of triangles and relationships between their side lengths and measures of angles and investigate area formulas. As you teach this unit, students should use manipulatives to develop their understanding of these relationships and formulas. The 7th grade TEKS in this unit require students to solve equations using geometric concepts, including the sum of the angles in a triangle, and angle relationships. The process TEKS should be partnered with concepts throughout this unit lending itself to the application of geometry and measurement through real world experiences. This unit was placed after equations, expressions, inequalities and multiple representations have been taught because students will use their knowledge of these topics when setting up expressions and equations to explore the relationships in this unit. The concepts learned in this unit should be spiraled 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 Advanced 6 Curriculum Road Map (CRM) 4th/5th Six Weeks CRM 8 Two-Dimensional Figures and Measurement Pacing

• 22 days • February 11 – March 13


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 formulas provide a method of measuring these attributes by using only measures of lengths.

Essential Questions • What does it mean to find the area? • How is the area of the base (B) and height (h)

related to the dimensions of a 3-dimensional figure?

Vocabulary rectangle, parallelogram, trapezoid, triangle, right rectangular prism, complementary, supplementary, equation, variable, area, volume vocabulary cards Student pre-requisite knowledge Students found area of rectangles and volume of right rectangular prisms in 5th grade. Solving area and volume problems using equations is new to 6th grade. Resources: Carnegie Learning adopted textbook; HOM: Hands on Math; Exemplar Lessons; Instructional Resource Portfolios and Zip files; Grade 6 TEA Side by Side; Grade 7 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.


6.4 Proportionality. The student applies mathematical process standards to develop an understanding of proportional relationships in problem situations. The student is expected to: 6.4H convert units within a measurement system, including the use of proportions and unit rates.

• Multiplication, division, and ratio tables are used to convert between different units of measurement within systems.

• Use a ratio table to perform conversions in metric or customary measures.

• Use measurement conversions as necessary when finding area and volume.















6.8 Expressions, equations, and relationships. The student applies mathematical process standards to use geometry to represent relationships and solve problems. The student is expected to: 6.8A extend previous knowledge of triangles and their properties to include the sum of angles of a triangle, the relationship between the lengths of sides and measures of angles in a triangle, and determining when three lengths form a triangle

6.8B model area formulas for parallelograms, trapezoids, and triangles by decomposing and rearranging parts of these shapes

6.8C write equations that represent problems related to the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prims where dimensions are positive rational numbers

6.8D determine solutions for problems involving the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers.

• Equilateral triangles have congruent side lengths.

• Isosceles triangles have two congruent side lengths.

• Scalene triangles have no congruent side lengths.

• Acute triangles have all acute angles.

• Right triangles have one right angle.

• Obtuse triangles have one obtuse angle.

• An equilateral triangle is always an isosceles triangle.

• An isosceles triangle is not always an equilateral triangle.

• The sum of the measures of the interior angles of a triangle is 180⁰.

• In a triangle, the longest side is across from the largest angle.

• In a triangle, the shortest side is across from the smallest angle.

• The lengths of any two sides of a triangle must be greater than the third side.

• Area formulas for parallelograms, trapezoids, and triangles can be modeled by decomposing and rearranging parts of these shapes.

• “Area equals base times height” can be used to find the area for all parallelograms.

• “Area of the base times the height” can be used for volume of right rectangular prisms.

• Determine when three lengths form a triangle.

• Classify a triangle according to its sides and angles.

• Use properties of a triangle to solve problems.

• Develop formulas for parallelograms, trapezoids, and triangles.

• Model area formulas for parallelograms, trapezoids, and triangles by decomposing and rearranging parts of these shapes.

• Write equations that represent problems related to area of parallelograms, trapezoids and triangles.

• Write equations that relate to volume of right rectangular prisms.

• Use equations to solve for missing measurements related to area of rectangles, parallelograms, trapezoids and triangles.

• Use equations to solve for missing measurements related to volume of right rectangular prims.

• Determine which measure to find – area or volume-when presented with an application problem.

• Find the area of rectangles, parallelograms, trapezoids and triangles where dimensions are positive rational numbers.

• Find the volume of right rectangular prisms where dimensions are positive rational numbers.






6.10 Expressions, equations, and relationships. The student applies mathematical process standards to use equations and inequalities to solve problems. 6.10A model and solve one-variable, one-step equations and inequalities that represent problems, including geometric concepts


• How to set up and solve equations to find missing measures of angles in a triangle given the other measures.

• Set up equations to find missing measures of angles in a triangle given the other measures.

• Set up equations to find the supplement or complement of an angle.

7.11 Expressions, equations, and relationships. The student applies mathematical process standards to solve one-variable equations and inequalities. The student is expected to: 7.11C write and solve equations using geometry concepts, including the sum of the angles in a triangle, and angle relationships.


• How to set up and solve equations to find missing measures of angles in a triangle given the other measures.

• Complementary angles are two angles whose measures have a sum of 90 degrees.

• Supplementary angles are two angles whose measures have a sum of 180 degrees.

• Set up equations to find missing measures of angles in a triangle given the other measures.

• Set up equations to find the supplement or complement of an angle.



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










Exemplar Lessons and Instructional Resources PDF Exemplar Lessons and Instructional Resources ZIP Files Exemplar Lesson Equations with Geometric Concepts TEKS: 6.10A Volume of Right Rectangular Prisms TEKS: 6.8D Sum of Angles in a Triangle TEKS: 7.11C






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: Data, Statistics and STAAR Review In this unit on statistics, students will explore and interpret a variety of displays of data. As you teach this unit, you should focus on students being able to interpret the data, as well as create a variety of 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. The 7th grade TEKS taught in this unit require student to use dot plots and box and whisker plots to compare data. This unit was placed right before STAAR review because it allows students to create and explore while using background knowledge of material learned previously. Time has been built into this CRM for STAAR review.




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 Advanced 6 Curriculum Road Map (CRM) 5th Six Weeks CRM 9 Data, Statistics and STAAR Review Pacing

• 19 days • March 23 – April 17


Making Meaning


• Different types of graphs and other data representations provide different information about the data and, hence, the population from which the data was taken. The choice of graphical representation can affect how well the data are understood.

• Both graphs and statistics can provide a sense of the shape of the data, including how spread out or how clustered they are. Having a sense of the shape of data is having a big picture of the data rather than a collection of numbers.

Essential Questions • Why is data collected and analyzed? • How do people use data to influence others? • How can predictions be made based on data? • How can the shape of data be described?

Vocabulary mean, median, mode, range, interquartile range, stem-and-leaf plot, box plot, dot plot, histogram, measure of center, measure of spread, outlier, variability vocabulary cards Student pre-requisite knowledge In grade 5 students made line graphs with whole number coordinates. They are introduced to median, mode, and range in 5th grade. Students are introduced to mean in 6th grade. Dot plots, stem-and-leaf plots and box plots are introduced in 6th grade. Resources: Carnegie Learning adopted textbook; HOM: Hands on Math; Exemplar Lessons; Instructional Resource Portfolios and Zip files; 6th TEA Side by Side; 7th 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.


6.12 Measurement and data. The student applies mathematical process standards to use numerical or graphical representations to analyze problems. The student is expected to: 6.12A represent numeric data graphically, including dot plots, stem-and-leaf plots, histograms, and box plots

6.12B use the graphical representation

• Data can be represented in multiple ways.

• Choose an appropriate representation for data given a set of data.

• The shape of data can be

• Create a dot plot, stem-and-leaf plot, histograms and box plots given a set of data.

• Describe the center (median and mean), and spread (range) based on graphical representations of















of numeric data to describe the center, spread, and shape of the data distribution

6.12C summarize numeric data with numerical summaries, including the mean and median (measures of center) and the range and interquartile range (IQR) (measures of spread), and use these summaries to describe the center, spread, and shape of the data distribution

6.12D summarize categorical data with numerical and graphical summaries, including the mode, the percent of values in each category (relative frequency table), and the percent bar graph, and use these summaries to describe the data distribution

symmetrical (bell curve) or skewed (right or left).

• If the shape is symmetrical the mean and median are equal.

• If the shape is skewed right the mean is greater than the median.

• If the shape is skewed left the mean is less than the median.

• The median is not affected by very small or very large data values.

• The median, mean, and mode describe the center of data.

• The range describes the spread of data.

• The mean and median of a set of data are used to describe the shape of the data distribution.

• The range and interquartile range are used to describe the spread of the data distribution.

• An outlier has an effect on the mean.

• An outlier does not have an effect on the median.

numeric data. • Describe the shape of data as

symmetrical, skewed right or skewed left.

• Determine interquartile ranges from a set of data represented by a box plot.

• Find the mean by “leveling” a set of data.

• Find the mean by adding the data points and dividing by the number of data points.

• Find the median, mode and range of a set of data.

• Use the mean and median to describe the shape of the data distribution.

• Use the range and interquartile range to describe the spread of the data distribution.

• Use mode to describe the data distribution.

• Use a percent bar graph to describe the data distribution.

6.13 Measurement and data. The student applies mathematical process standards to use numerical or graphical representations to solve problems. The student is expected to: 6.13A interpret numeric data summarized in dot plots, stem-and-leaf plots, histograms, and box plots 6.13B distinguish between situations that yield data with and without variability

• Data can be represented in multiple ways.

• Problem situations can yield data with and without variability.

• Analyze and interpret the data represented in a dot plot, stem-and-leaf plot, histogram and box plot (box-and-whisker plot) given a set of data.

• Distinguish between situations that yield data with and without variability.

7.6 Proportionality. The student applies mathematical process standards to use probability and statistics to describe or solve problems involving proportional relationships. The student is expected to: 7.6G solve problems using data represented in bar graphs, dot plots, circle graphs, including part-to-whole and part-to-part comparisons and equivalents.

• Circle graphs, dot plots, and circle graphs can be used to compare part to part and part to whole relationships.

• Analyze and interpret the data represented in bar graphs, dot plots, and circle graphs.

• Use data from bar graphs, dot plots, and circle graphs to solve real-world problem situations.







7.12 Measurement and data. The student applies mathematical process standards to use statistical representations to analyze data. The student is expected to: 7.12A compare two groups of numeric data using comparative dot plots or box plots by comparing their shapes, centers, and spreads

• Box plots are a method for visually displaying the center (median), the range and spread of data.

• Dot plots are counts of things along a numeric scale.

• If the shape is symmetrical the mean and median are equal.

• If the shape is skewed right the mean is greater than the median.

• If the shape is skewed left the mean is less than the median.

• The median, mean, and mode describe the center of data

• The range describes the spread of data.

• The mean and median of a set of data are used to describe the shape of the data distribution.

• The range and interquartile range are used to describe the spread of the data distribution.

• Describe the center (median and mean), and spread (range) based on graphical representations of numeric data.

• Describe the shape of data as symmetrical, skewed right or skewed left.

• Compare two groups of numerical data by comparing their shapes, centers, and spreads.



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









Exemplar Lessons and Instructional Resources PDF Exemplar Lessons and Instructional Resources ZIP Files STAAR Review Modules Exemplar Lesson Box Plots TEKS: 6.12A Data Representations TEKS: 7.6G





http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/MiddleSchool/M_6_STAAR_Review_Modules.zip


© Austin Independent School District, 2014 Math Advanced 6 Curriculum Road Map (CRM) 6th Six Weeks CRM 10 Probability Pacing

• 12 days • April 23 – May 8


Making Meaning


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

Essential Questions • How can I use probability to make wise

decisions in my life? • Why is data collected and analyzed? • How can predictions be made based on data? • What is the relationship between an event and

its complement? • How can data be organized to show all the

possible outcomes?

Vocabulary sample space, simple experiment, compound experiment, probability, independent event, dependent event, qualitative, quantitative, theoretical probability, experimental probability vocabulary cards Student pre-requisite knowledge sample space, simple experiment, compound experiment, probability, independent event, dependent event, net worth, assets, liabilities, qualitative, quantitative, theoretical probability, experimental probability, dot plots, box plots, circle graphs, mean, median, mode, range, interquartile range vocabulary cards 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.


7.6 Proportionality. The student applies mathematical process standards to use probability and statistics to describe or solve problems involving proportional relationships. The student is expected to: 7.6A represent sample spaces for simple and compound events using lists and tree diagrams.

7.6B select and use different simulations to represent simple and compound

• A sample space contains all the possible outcomes for an event.

• Sample space of independent events is used to find the theoretical probability of those events.

• Simulation is a technique used for answering real-world

• Make a sample space including tree diagrams and tables when given a simple or compound experiment.

• Recognize a sample space for a given event.

• Use different simulations (spinners, coins, two-color















events with and without technology

7.6C make predictions and determine solutions using experimental data for simple and compound events

7.6D make predictions and determine solutions using theoretical probability for simple and compound events

7.6E find the probabilities of a simple event and its complement and describe the relationship between the two

7.6H The student is expected to solve problems using qualitative and quantitative predictions and comparisons from simple experiments

7.6I determine experimental and theoretical probabilities related to simple and compound events using data and sample spaces

questions or making decisions in complex situations where an element of chance is involved.

• The probability of an event is between 0 and 1 that can be expressed as a fraction, decimal, or percent.

• Data should be used for experimental probabilities and sample spaces should be used for theoretical probabilities.

• Probability can be expressed as a fraction where the numerator expresses the number of desired outcomes and the denominator expresses the total number of possibilities.

• The complement of an event is the probability that the desired event does NOT occur.

• An example of a qualitative comparison is “more likely”, less likely” or “equally likely”.

• An example of a quantitative comparison is “twice as likely”.

• How to determine both experimental and theoretical probabilities.

counters, calculators) to represent simple and compound events.

• Find the theoretical and experimental probabilities of an event.

• Find the probability of independent events.

• Find the probability of simple and compound events.

• Find the probabilities of a simple event and its complement and describe the relationship between the two.

• Use proportional relationships and ratio tables to make predictions based on probability.

• Solve problems using qualitative comparisons from simple experiments.

• Solve problems using quantitative comparisons from simple experiments.

• Use data to determine experimental and theoretical probabilities of simple and compound events.

• Use sample space to determine experimental and theoretical probabilities of simple and compound events.



Probability This performance task allows students to demonstrate their knowledge of probability through a real-world problem.








http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/MiddleSchool/New_TEKS_Support_Documents/M_7_SupportDocument_7.6I.pdf





Exemplar Lessons and Instructional Resources PDF

Exemplar Lessons and Instructional Resources ZIP Files Exemplar Lesson Probability TEKS: 7.6I




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: Measurement In this unit on measurement, students will explore area and circumference of circles, as well as area of composite figures. As you are teaching this unit, you should focus on relationships that can be observed among measures of different parts of the circle. As you teach this unit, students should develop a clear understanding of pi as the ratio of circumference to diameter in any circle regardless of size. Students should also be able to deconstruct composite figures to determine the area of these figures. The process TEKS should be partnered with concepts throughout this unit lending itself to the application of measurement through real world experiences. This unit was placed here in order to prepare students to enter the 7th grade advanced math course.




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 Advanced 6 Curriculum Road Map (CRM) 6th Six Weeks CRM 11 Measurement Pacing

• 17 days • May 11 – June 4


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 formulas provide a method of measuring these attributes by using only measures of lengths.

Essential Questions • What does it mean to find the area? • What does it mean to find the circumference? • How does the relationship between the

dimensions of a two-dimensional figure relate to the formula for area or perimeter?

Vocabulary circumference, pi, radius, diameter, area, rectangle, square, parallelogram, trapezoid, triangle vocabulary cards Student pre-requisite knowledge This is the first time students are introduced to area and circumference of circles. 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.


7.8 Expressions, equations, and relationships. The student applies mathematical process standards to develop geometric relationships with volume. The student is expected to: 7.8C use models to determine the approximate formulas for the circumference and area of a circle and connect the models to the actual formulas.

• The relationship between the radius, diameter, and circumference of a circle.

• Develop formulas for the circumference and area of a circle through investigation activities.













7.9 Expressions, equations, and relationships. The student applies mathematical process standards to solve geometric problems. The student is expected to: 7.9B determine the circumference and area of circles. 7.9C determine the area of composite figures containing combinations of rectangles, squares, parallelograms, trapezoids, triangles, semicircles and quarter circles

• Circumference is a one-dimensional measure of the distance around the edge of a circle; it measures approximately 3.14 diameters.

• Area is a two-dimensional measure of the space inside a shape and can be measured for polygons as well as circles.

• The formulas for areas of quadrilaterals are based on the formula for area of a rectangle.

• Composite figures can contain combinations of rectangles, squares, parallelograms, trapezoids, triangles, semicircles and quarter circles.

• Find the circumference of a circle when given diameter or radius.

• Find the circumference of a circle in terms of π .

• Find the diameter of a circle when given radius or circumference.

• Find the radius of a circle when given the diameter or circumference.

• Find the area of a circle when given the diameter or radius

• Find the area of a circle in terms of π .

• Find the missing dimension when given the area of a circle.

• Find the area of composite figures containing combinations of rectangles, squares, parallelograms, trapezoids, triangles, semicircles and quarter circles.

• Determine which measure to find – perimeter, circumference, or area—when presented with an application problem.



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










Exemplar Lessons and Instructional Resources PDF

Exemplar Lessons and Instructional Resources ZIP Files Exemplar Lesson Circles TEKS: 7.8C, 7.9B




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: Numerical Reasoning In this unit on numerical reasoning, students will explore fractions, decimals, percents and whole numbers. As you are teaching this unit, you should focus on relationships between sets of numbers and equivalency. As you teach this unit, students should use manipulatives to develop their understanding of equivalency. 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 placed second because having a strong background in numerical reasoning will help students reason through problems throughout the school year.




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

apply

mathematics

to problems

arising in

everyday

life, society,

and the

workplace;







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