Pinellas County Schools 2021-2022

GRADE 8 PRE-ALGEBRA

1205070

Instructional Resource: McGraw-Hill: Florida Math, Course 3, Volume 1 & 2, ©2015

Course Pacing Unit of Instruction # of Days Dates of Instruction

Unit 1: Real Number System Intervention Days

5 2

8/16 – 8/20 8/23 – 8/24

Unit 2: Exponent Rules Intervention Days

6 2

8/25 – 9/1 9/2 – 9/3

Unit 3: Scientific Notation Intervention Days

8 2

9/7 – 9/16 9/17 – 9/20

Unit 4: Creating Equivalent Expressions Intervention Days Progress Monitoring (Units 1 – 4)

8 2 1

9/21 – 9/30 10/1 – 10/4

10/5 Unit 5: Solving Equations & Inequalities Intervention Days

10 2

10/6 – 10/20 10/21 – 10/22

Unit 6: Functions Intervention Days

7 2

10/25 - /11/2 11/3 – 11/4

Unit 7: Proportional Relationships & Slope Intervention Days Thanksgiving Break 11/20 – 11/28

15 3

11/5 – 12/2 12/3 – 12/7

Semester Review 3 12/8 – 12/10 Midterm Exam (Units 1-7) 1 12/13 – 12/17 Unit 8: Systems of Equations Intervention Days

14 2

1/5 – 1/25 1/26 – 1/27

Unit 9: Triangles and Angles Intervention Days

12 2

1/28 – 2/14 2/15 – 2/16

Unit 10: Pythagorean Theorem Intervention Days

5 2

2/17 – 2/24 2/25 – 2/28

Unit 11: Transformations, Congruence & Similarity Intervention Days Spring Break is 3/12 – 3/21

9 2

3/1 – 3/11 3/22 – 3/23

Unit 12: Volume (Only for the 2021/2022 SY) Intervention Days

7 2

3/24 – 4/1 4/4 – 4/5

Unit 13: Statistics Intervention Days

8 2

4/6 – 4/18 4/19 – 4/20

Unit 14: Probability Intervention Days

5 2

4/21 – 4/27 4/28 – 4/29

Grade 8 Math FSA 2 5/2 -5/26

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

2 3 4 5 6 3 4 5 6 79 10 11 12 13 MA.8.NSO.1.1 MA.8.AR.2.3 MA.8.AR.4.1 MA.8.AR.4.3 10 11 12 13 14

16 17 18 19 20 MA.8.NSO.1.2 MA.8.AR.4.2 17 18 19 20 2123 24 25 26 27 24 25 26 27 2830 31 31

MA.8.AR.1.1 MA.8.NSO.1.3 MA.8.GR.1.4 MA.8.GR.1.61 2 3 MA.8.GR.1.5 1 2 3 4

6 7 8 9 10 7 8 9 10 1113 14 15 16 17 MA.8.NSO.1.4 MA.8.NSO.1.6 14 15 16 17 1820 21 22 23 24 MA.8.NSO.1.5 MA.8.GR.1.1 MA.8.GR.1.3 21 22 23 24 25

27 28 29 30 MA.8.GR.1.2 28

1 MA.8.AR.1.2 MA.8.NSO.1.7 1 2 3 44 5 6 7 8 MA.8.AR.1.3 MA.8.GR.2.1 MA.8.GR.2.3 7 8 9 10 11

11 12 13 14 15 MA.8.GR.2.2 MA.8.GR.2.4 14 15 16 17 1818 19 20 21 22 21 22 23 24 2525 26 27 28 29 28 29 30 31

MA.8.AR.2.1 MA.8.AR.2.2 MAFS.8.G.3.91 2 3 4 5 18 9 10 11 12 4 5 6 7 8

15 16 17 18 19 MA.8.F.1.1 MA.8.F.1.3 MA.8.DP.1.1 MA.8.DP.1.3 11 12 13 14 1522 23 24 25 26 MA.8.F.1.2 MA.8.DP.1.2 MAFS.8.SP.1.4 18 19 20 21 2229 30 25 26 27 28 29

1 2 3 MA.8.AR.3.1 MA.8.AR.3.4 MA.8.DP.2.1 MA.8.DP.2.3 2 3 4 5 66 7 8 9 10 MA.8.AR.3.2 MA.8.AR.3.5 MA.8.DP.2.2 9 10 11 12 13

13 14 15 16 17 MA.8.AR.3.3 16 17 18 19 2020 21 22 23 24 23 24 25 26 2727 28 29 30 31 30 31

Non-Teacher DayNon-Student Day

February 2022

January 2022

December 2021

November 2021

October 2021

September 2021

August 2021 Building Community in the Math Classroom Re-Building Community in the Math Classroom

May 2022

April 2022

March 2022Intervention Days 9/17 - 9/20

Unit 4: Creating Equivalent Expressions

Window: Dec. 13-Dec. 17Midterm Exam (Units 1-7)

Unit 1: Real Number System

Intervention Days 8/23 - 8/24Unit 2: Exponent Rules

Intervention Days 9/2 - 9/3Unit 3: Scientific Notation

Unit 8: Systems of Equations

Intervention Days 1/26 - 1/27Unit 9: Triangles & Angles

Intervention Days 2/15 - 2/16Unit 10: Pythagorean Theorem

Intervention Days 2/25 - 2/28Unit 11: Transformations, Congruence & Similarity

Intervention Days 3/22 - 3/23Unit 12: Volume (Only for the 2021/2022 SY)

Intervention Days 4/4 - 4/5Unit 13: Statistics

Intervention Days 4/19 - 4/20

Semester Review

Intervention Days 10/1 - 10/4Progress Monitoring (Units 1-4) 10/5

Unit 14: Probability

Grade 8 Math FSAIntervention Days 4/28 - 4/29

State Window: May 2 - May 26

Unit 7: Proportional Relationships & Slope

Intervention Days 12/3 - 12/7

Unit 5: Solving Equations & Inequalities

Intervention Days 10/21 - 20/22Unit 6: Functions

Intervention Days 11/3 - 11/4

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Unit 1: Real Number System Standards Aligned Instruction 5 days August 16 – August 20 Intervention Days 2 days August 23 – August 24

The 2021-2022 school year we are transitioning from the Florida Mathematics Standards (MAFS) to the B.E.S.T. standards (MA).

In the unit guides we have identified which B.E.S.T. standard matches with which MAFS standard(s). Standards Content Limits

MA.8.NSO.1.1 Extend previous understanding of rational numbers to define irrational numbers within the real number system. Locate an approximate value of a numerical expression involving irrational numbers on a number line. • Clarification 1: Instruction includes the use of number line and

rational number approximations and recognizing pi (𝜋𝜋) as an irrational number.

• Clarification 2: Within this benchmark, the expectation is to approximate numerical expressions involving one arithmetic operation and estimating square roots or pi (𝜋𝜋).

• Irrational numbers are limited to pi (𝜋𝜋) and square roots.

• Approximate values of square roots must be based on the value of the square roots of neighboring perfect squares.

Calculator: NONE Context: MATHEMATICAL

MA.8.NSO.1.2 Plot, order and compare rational and irrational numbers, represented in various forms. • Clarification 1: Within this benchmark, it is not the expectation

to work with the number 𝑒𝑒. • Clarification 2: Within this benchmark, the expectation is to plot,

order and compare square roots and cube roots. • Clarification 3: Within this benchmark, the expectation is to use

symbols

• Items must include at least one irrational number or radical.

• Irrational numbers are limited to pi (𝜋𝜋), square roots, and cube roots.

• Items requiring students to compare fractions with irrational numbers or decimals are limited to fractions that result in a terminating decimal.

• Items may use the words “is less than,” “is greater than,” or “is equal to.”

• Approximate values of square roots must be based on the value of the square roots of neighboring perfect squares.

Calculator: NEUTRAL Context: MATHEMATICAL

MA.8.AR.2.3 Given an equation in the form of 𝑥𝑥²=𝑝𝑝 and 𝑥𝑥³=𝑞𝑞, where 𝑝𝑝 is a whole number and 𝑞𝑞 is an integer, determine the real solutions. • Clarification 1: Instruction focuses on understanding that when

solving 𝑥𝑥²=𝑝𝑝, there is both a positive and negative solution. • Clarification 2: Within this benchmark, the expectation is to

calculate square roots of perfect squares up to 225 and cube roots of perfect cubes from -125 to 125.

• Items will not require the student to simplify square roots of non-perfect squares, simplify cube roots of non-perfect cubes, or approximate roots.

• Items are limited to one procedural step to isolate the variable.

• Items may require the student to give both the positive and negative solutions for the form 𝑥𝑥2 = 𝑝𝑝.

Calculator: NONE Context: MATHEMATICAL

Essential Vocabulary Vocabulary Definition/Description

Base

In a power, the number that is the common factor. In 43, 4 Is the base. The number multiplied by itself, that is 4x4x4

Cube Root A number which produces a specified quantity when multiplied by itself three times.

Equation An equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value

Exponent

In an expression of the form xn, the exponent is n. It indicates the number of times x is used as a factor. In 43 it is read as 4 to the third power or four cubed.

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Expression Numbers, symbols and operators (such as + and ×) grouped together that show

the value of something. There is no equal sign.

Integer A number with no fractional part (no decimals). The whole numbers and their opposites

Irrational number A real number that can NOT be written as the ratio of two integers, non-repeating, non-terminating decimals.

Numerical Expressions

A numerical expression is a mathematical sentence involving only numbers and one or more operation symbols. Examples of operation symbols are the ones for addition, subtraction, multiplication, and division. They can also be the radical symbol (the square root symbol) or the absolute value symbol.

Rational number

A number that can be written as the ratio of two integers where the denominator is not zero.

Square Root A number which produces a specified quantity when multiplied by itself. Repeating decimal A decimal in which after a certain point, one or more digits repeat themselves to

infinity. Terminating decimal When we say a number terminates, the number does NOT repeat and ends in

zero. Variable

A symbol that stands for an unknown number.

MA.8.NSO.1.1 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Extend previous understanding of rational numbers to define irrational numbers within the real number system. Locate an approximate value of a numerical expression involving irrational numbers on a number line.

MAFS.8.NS.1.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually and convert a decimal expansion which repeats eventually into a rational number. MAFS.8.NS.1.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., 𝜋𝜋2). For example, by truncating the decimal expansion of √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue to get better approximations.

Instructional Learning Objectives Instructional Resources Objective 1: Know that numbers that are not rational are called irrational Objective 2: Classify a number as rational or irrational Objective 3: Understand the concept of square roots and perfect squares

McGraw-Hill Course 3 Chapter 1 Lessons 1, 9 & 10 IXL Identify rational and irrational numbers NV6 Estimate positive and negative square roots 96T Estimate cube roots RLC For NS.1.1

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Objective 4: Approximate square roots using perfect squares Objective 5: Plot irrational numbers on a number line To complete MAFS.8.NS.1.1 • Write repeating decimals as fractions • Locate repeating decimals on a number line The above learning targets will need to be addressed for SY 2021-2022 to fill in the gaps between the MAFS standard and the BEST Benchmarks.

Convert between repeating decimals and fractions AH5 KHAN Academy Introduction to rational and irrational numbers Recognizing irrational numbers Approximating irrational numbers Approximating square roots Illustrative Math Understand and Apply the Definition of Rational Numbers Convert Repeating Decimals into Fractions Repeating or terminating Open Up Resources This is a free resource for teachers. An account is free to make and then you have access to lesson and resources. Unit 8 Lesson 1-Area of squares and their side lengths Lesson 2-Side lengths and area Lesson 4-Square roots on the number line Lesson 5-Reasoning about square roots Lesson 14-Decimal Representations of Rational Numbers Lesson 15-Infinite Decimal expansions EngageNY Grade 8, Module 7, Topic B, Lesson 8 Decimal expansion Grade 8, Module 7, Topic B, Lesson 11 Decimal expansion of roots Grade 8, Module 7, Topic B, Lesson 12 Decimal expansions of fractions

Sample Problems: Within the expression 1 + √30.

1. What kind of number is the √30? a. Rational b.) Irrational

2. What is the approximate value of √30.?

a. Between 3 and 4 b.) Between 4 and 5 c.) Between 5 and 6 3. What could be an approximate range for the expression 1 + √30?

a. Between 4 and 5 b.) Between 5 and 6 c.) Between 6 and 7

4. For each number, indicate whether it is rational or irrational.

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

5. Plot the following on the number line below

MA.8.NSO.1.2 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Plot, order and compare rational and irrational numbers, represented in various forms.

MAFS.8.NS.1.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually and convert a decimal expansion which repeats eventually into a rational number. MAFS.8.NS.1.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., 𝜋𝜋2). For example, by truncating the decimal expansion of √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue to get better approximations.

Instructional Learning Objectives Instructional Resources Objective 1: Compare and order rational and irrational numbers.

Objective 2: Understand the concept of cubes and cubed roots.

Objective 3: Plot, order and compare square and cube roots.

McGraw-Hill Course 3 Chapter 1 Lessons 8-10 IXL Integers on number lines EZE Compare and order integers T2M Graph integers on horizontal and vertical number lines LFR Compare rational numbers MUK Put rational numbers in order QP5 Khan Academy Introduction to cube roots

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Illustrative Math This is a free resource for teachers. An account is free to make and then you have access to lesson and resources other teachers have shared Irrational numbers on a number line Open Up Resources This is a free resource for teachers. An account is free to make and then you have access to lesson and resources. Unit 8 Lesson 12- Edge lengths and volume Lesson 13- Cube roots EngageNY Grade 8, Module 7, Topic B, Lesson 13 Compare and order rational approximations

Sample Problems:

1. A number line is shown. Place the following numbers in the proper location on the number line.

√3 √8 √23

2. What is the approximate value of √3, to the nearest whole number?

MA.8.AR.2.3 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Given an equation in the form of 𝑥𝑥²=𝑝𝑝 and 𝑥𝑥³=𝑞𝑞, where 𝑝𝑝 is a whole number and 𝑞𝑞 is an integer, determine the real solutions.

MAFS.8.EE.1.2 Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

Instructional Learning Objectives Instructional Resources Objective 1: Students will be able to solve algebraic equations using squared roots to determine their real solution. Objective 2: Students will be able to solve algebraic equations using cubed roots to determine their real solution. Objective 3: Students will be able to recognize that when solving an equation using squared roots or cubed roots that the solution could be both positive and negative.

EngageNY Engage NY Grade 8 Module 7 Lesson 3 Engage NY Grade 8 Module 7 Lesson 5 IXL Solve equations using square roots Solve equations using cube roots McGraw Hill McGraw Hill Course 3, Volume 1: Chapter 1 - Lesson 8 Open Up Resources This is a free resource for teachers. An account is free to make and then you have access to lesson and resources.

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Unit 8 Lesson 12- Edge lengths and volume Lesson 13- Cube roots Better Lessons Simplify radical expressions Square root solutions Cube root solutions

Sample Problems: 1.) 3x² + 12 = 87 x = 5 or -5 2.) 2(x² +12) = 42 x = 3 or -3 3.) A cube has a volume of 125 cm³. What is the length of one side? One side = 5 cm.

4.) Given an equation in the form of h3 = 125 where 125 is a whole number, determine the real solutions

a. 25 and –25 b. 62.5 and –62.5 c. 5 and –5 d. -5 e. 62.5

5.) Given an equation in the form of h2 = 121 where 121 is a whole number, determine the real solutions

a. 4 and –4 b. 60.5 and –60.5 c. 11 and –11 d. 11 e. 60.5

6.) Given an equation in the form of h3 = -125 where 125 is a whole number, determine the real solutions

a. 25 and –25 b. 62.5 and –62.5 c. 5 and –5 d. -5 e. 62.5

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Unit 2: Exponent Rules Standards Aligned Instruction 6 days August 25 – September 1 Intervention Days 2 days September 2 – September 3

The 2021-2022 school year we are transitioning from the Florida Mathematics Standards (MAFS) to the B.E.S.T. standards (MA).

In the unit guides we have identified which B.E.S.T. standard matches with which MAFS standard(s). Standards Content Limits

MA.8.AR.1.1 Apply the Laws of Exponents to generate equivalent algebraic expressions, limited to integer exponents and monomial bases. • Clarification 1: Refer to the K-12 Formulas (Appendix E) for the

Laws of Exponents.

• Items are limited to the use of monomials and one-term algebraic expressions involving multiplication and/or division.

• Items are limited to the use of no more than two variables.

• Items including one variable are limited to no more than three laws.

• Items including two different variables are limited to the application of no more than two Laws of Exponents.

Calculator: NEUTRAL Context: MATHEMATICAL

MA.8.NSO.1.3 Extend previous understanding of Law of Exponents to include integer exponents. Apply the Laws of Exponents to evaluate numerical expressions and generate equivalent numerical expressions, limited to integer exponents and rational number bases, with procedural fluency. • Clarification 1: Refer to the K-12 Formulas (Appendix E) for the

Laws of Exponents.

• Items must incorporate a negative exponent in either the given expression or the student-generated expression.

• Items requiring the student to evaluate numerical expressions must incorporate at least one Law of Exponents or a negative exponent.

• Items will require the student to evaluate a numerical expression with negative exponents, generate an equivalent expression, or generate and evaluate an expression.

Calculator: NEUTRAL Context: MATHEMATICAL

Essential Vocabulary Vocabulary Definition/Description

Laws of Exponents (See Appendix E) Product of Powers Quotient of powers Power of a Power Power of a Product Power of a Quotient Negative Exponent Identity Exponent Zero Exponent

MA.8.AR.1.1 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Apply the Laws of Exponents to generate equivalent algebraic expressions, limited to integer exponents and monomial bases.

MAFS.8.EE.1.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. MAFS.912.N-RN.1.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Instructional Learning Objectives Instructional Resources Objective 1: Students will know and understand the Laws of Exponents. Objective 2: Students will be able to apply the Laws of Exponents to algebraic expressions. Objective 3: Students will be able to use the Laws of Exponents in order to create equivalent algebraic expressions.

McGraw-Hill Course 3, Chapter 1 Lesson 3, 4 and 5 IXL Multiplication and division with exponents Power rule Division with exponents Multiplication with exponents Divide monomials Multiply monomials Multiply and divide monomials Powers of monomials

Khan Academy Exponent properties with products Exponent properties with parentheses Exponent properties with quotients Negative Exponents MARS/Shell Applying Properties of Exponents Apply the properties of exponents by a matching activity. Illustrative Mathematics Raising to the zero and negative powers Use the quotient rule of exponents to help explain how to define the expression. Open Up Resources This is a free resource for teachers. An account is free to make and then you have access to lesson and resources. Unit 7 Lesson 2, Multiplying Powers of Ten Lesson 3, Powers of Powers of Ten Lesson 4, Dividing Powers of Ten Lesson 5, Negative Exponents and the Powers of Ten Lesson 6, Other bases Lesson 7, Practice with Rational Bases Lesson 8, Combining Bases EngageNY Grade 8, Module 1, Topic A, Lesson 4 Base raised to the zero power Grade 8 Mathematics Module 1, Topic A, Lesson 5 Negative exponents Grade 8, Module 1, Topic A, Lesson 6 Integer

Sample Problems: 1) (12𝑟𝑟5)2 = 12𝑟𝑟10

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

2) 3𝑚𝑚 ∙ 3𝑛𝑛 = 3−2 Answers will vary. Sample answer: 𝑚𝑚 = 6 𝑎𝑎𝑎𝑎𝑎𝑎 𝑎𝑎 = −8. 3) (3𝑥𝑥3𝑦𝑦−2)3 = 27𝑥𝑥9𝑦𝑦−6

4.) Select all expressions equivalent to x3?

a. x⁷ ∙ x-4 b. x + x2

c. 𝑥𝑥12

𝑥𝑥4

d. x0 ∙ x3 e. x3 - x0

5.) Write an equivalent expression to (2x2y-3)3

MA.8.NSO.1.3 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Extend previous understanding of Law of Exponents to include integer exponents. Apply the Laws of Exponents to evaluate numerical expressions and generate equivalent numerical expressions, limited to integer exponents and rational number bases, with procedural fluency.

MAFS.8.EE.1.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions.

Instructional Learning Objectives Instructional Resources Objective 1: Students will know the Laws of Exponents. Objective 2: Students will evaluate numerical expressions. Objective 3: Students will create equivalent numerical expressions with exponents.

EngageNY Grade 8, Module 1, Topic A, Lesson 4 Base raised to the zero power Grade 8 Mathematics Module 1, Topic A, Lesson 5 Negative exponents Grade 8, Module 1, Topic A, Lesson 6 Integer exponents McGraw Hill McGraw Hill Course 3 Volume 1: Lesson 5 IXL Positive exponents Exponents with negative bases Negative exponents Understanding negative exponents Evaluate negative exponents Mixed practice Multiplication with exponents Division with exponents Multiplication and division with exponents Evaluate expressions using properties of exponents Identify equivalent expressions involving exponents I Identify equivalent expressions involving exponents II Properties of exponents Power rule Khan Academy Exponent properties with products

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Exponent properties with quotients Negative Exponents Open Up Resources This is a free resource for teachers. An account is free to make and then you have access to lesson and resources. Unit 7 Lesson 2, Multiplying Powers of Ten Lesson 3, Powers of Powers of Ten Lesson 4, Dividing Powers of Ten Lesson 5, Negative Exponents and the Powers of Ten Lesson 6, Other bases Lesson 7, Practice with Rational Bases Lesson 8, Combining Bases

Sample Problems: 1.) 32 (3−5) = 1

33= 1

27

2.) 53(5−5) = 53+(−5) = 5−2 = 152

= 125

3.) 2−1

2−4= 2−1−(−4) = 2−1+4 = 23 = 8

4.) Select all expressions equivalent to 53?

A) 57 x 5-4 B) 5 + 52

C) 512

54

D) 50 x 53 E) 53 - 50

5.) Evaluate the following numerical expression to its simplest form: 2−2 ∙ 34 ∙ �57

56� + (65 ∙ 6−3 ∙ 6−2)

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Unit 3: Scientific Notation Standards Aligned Instruction 8 days September 7 – September 16

Intervention Days 2 days September 17 – September 20

The 2021-2022 school year we are transitioning from the Florida Mathematics Standards (MAFS) to the B.E.S.T. standards (MA).

In the unit guides we have identified which B.E.S.T. standard matches with which MAFS standard(s). Standards Content Limits

MA.8.NSO.1.4 Express numbers in scientific notation to represent and approximate very large or very small quantities. Determine how many times larger or smaller one number is compared to a second number.

• Clarification 1: Instruction focuses on building the Law of Exponents from specific examples. Refer to the K-12 Formulas (Appendix E) for the Laws of Exponents.

• Items may require the student to rewrite numbers in scientific notation or in standard form.

Calculator: NONE Context: BOTH

MA.8.NSO.1.5 Add, subtract, multiply and divide numbers expressed in scientific notation with procedural fluency.

• Clarification 1: Refer to the K-12 Formulas (Appendix E) for the Laws of Exponents.

• Clarification 2: Within this benchmark, for addition and subtraction with numbers expressed in scientific notation, exponents are limited to within 2 of each other.

• Items may require the student to rewrite numbers in scientific notation or in standard form.

• Numbers are limited to the thousandths place or less when expressed in scientific notation.

Calculator: NONE Context: MATHEMATICAL

MA.8.NSO.1.6 Solve real-world problems involving operations with numbers expressed in scientific notation.

• Clarification 1: Refer to the K-12 Formulas (Appendix E) for the Laws of Exponents.

• Clarification 2: Instruction includes recognizing the importance of significant digits when physical measurements are involved.

• Clarification 3: Within this benchmark, for addition and subtraction with numbers expressed in scientific notation, exponents are limited to within 2 of each other.

• Items may require the student to rewrite numbers in scientific notation or in standard form.

• Numbers are limited to the thousandths place or less when expressed in scientific notation.

Calculator: NONE Context: REAL-WORLD

Essential Vocabulary Vocabulary Definition/Description

Base The number that gets multiplied when using an exponent. Examples: 82, 8 is the base, and the result is 8 × 8 = 64

Standard Notation The normal way of writing numbers. For example, 102 𝑤𝑜𝑢𝑙𝑑 𝑏𝑒 100 𝑖𝑛 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑓𝑜𝑟𝑚

Order of Magnitude The order of magnitude of a finite decimal is the exponent in the power of 10 when that decimal is expressed in scientific notation. For example, the order of magnitude of 192.7 is 2, because when 192.7 is expressed in scientific notation as 1.927 × 102, 2 is the exponent of 102. Sometimes we also include the number 10 in the definition of order of magnitude and say that the order of magnitude of 192.7 is 102.

Scientific Notation (The scientific notation for a finite decimal is the representation of that decimal as the product of a decimal s and a power of 10, where 𝑠 satisfies the property that it is at least 1, but smaller than 10, or in symbolic notation, 1 ≤ 𝑠 < 10. For example, the scientific notation for 192.7 is 1.927 ×102.)

exponential notation Written in the form 𝐵𝑥.

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

exponents In 42, 2 is the exponent, the number that dictates how many times the base multiplies by itself. 42 = 4(4)

monomial base When the base is a number, a variable or a product of a number and a variable where all are exponents or whole numbers.

power A product of repeated factors using an exponent and a base. The power of 73 is read as, seven to the third power, or seven cubed and the power of 72 is read as, seven to the second power, or seven squared.

MA.8.NSO.1.4 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards

Express numbers in scientific notation to represent and approximate very large or very small quantities. Determine how many times larger or smaller one number is compared to a second number.

MAFS.8.EE.1.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States

as 3 × and the population of the world as 7 × , and determine that the world population is more than 20 times larger.

Instructional Learning Objectives Instructional Resources

Objective 1: Students will express numbers in scientific notation. Objective 2: Students will evaluate numerical expressions. Objective 3: Students will express numbers in standard notation.

McGraw Hill McGraw Hill Course 3 Volume 1: Lesson 6 McGraw Hill Course 3 Volume 1: Lesson 7 McGraw Hill Course 3 Volume 1: Lesson 7 Inquiry Lab CPALMS Tutorial: Scientific Notation Comparing Numbers IXL Convert between standard and scientific notation (8-G.1) Compare numbers written in scientific notation (8-G.2) Scientific Notation (5-A.10)

EngageNY Engage NY: Grade 8 Mathematics Module 1, Topic B, Lessons 9-11 Illustrative Mathematics This is a free resource for which teachers can sign up. Click here for the Grade 8 resources: Grade 8 For this standard, use the following lessons from Grade 8, Unit 7 in the IM Curriculum. Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Virtual Nerd What’s Scientific Notation How Do You Convert from Decimal Notation to Scientific Notation? Nearpod Lessons and Activities (editable) Scientific Notation Scientific Notation (comparing large numbers) Scientific Notation (comparing small numbers)

Sample Problems: 1) Roderick is comparing two numbers shown in scientific notation on his calculator. The first number was

displayed as 2.3147E27 and the second number was displayed as 3.5982E-5. Which number is bigger and by how much? Write your answer in scientific notation.

2) The half-life of uranium–238 is 4.5 × 109 years. The half-life of uranium-234 is 2.5 × 105 years. How many times greater is the half-life of uranium-238 than that of uranium-234?

3) Express in Standard Form: 1.2𝑥1010 4) Express in Scientific Notation: 93,700,000 5) Estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and

determine that the world population is more than 20 times larger.

MA.8.NSO.1.5 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards

Add, subtract, multiply and divide numbers expressed in scientific notation with procedural fluency.

MAFS.8.EE.1.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

Instructional Learning Objectives Instructional Resources

Objective 1: Students will know the Laws of Exponents. Objective 2: Students will evaluate numerical expressions.

McGraw Hill McGraw Hill Course 3 Volume 1: Lesson 7 McGraw Hill Course 3 Volume 1: Lesson 7 Inquiry Lab CPALMS Pennies in Heaven

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Objective 3: Students will add, subtract, multiply, and divide using numbers in scientific notation.

Giant Burgers Multiplying in Scientific Notation (Tutorial) Khan Academy Subtracting in Scientific Notation Multiplying in Scientific Notation Dividing and multiplying in scientific Notation Practice Adding in Scientific Notation IXL Add and subtract numbers written in scientific notation (8-G.3) Multiply numbers written in scientific notation (8-G.4) Divide numbers written in scientific notation (8-G.5) EngageNY Module 1, Topic B, Lesson 9 Module 1, Topic B, Lesson 10 Virtual Nerd How Do You Multiply Two Numbers Using Scientific Notation? Nearpod Lessons and Activities (editable) Scientific Notation: Multiplication Scientific Notation: Division Scientific Notation: Gamified Quiz Scientific Notation: Matching Pairs Illustrative Mathematics This is a free resource for which teachers can sign up. Click here for the Grade 8 resources: Grade 8 For this standard, use the following lessons from Grade 8, Unit 7 in the IM Curriculum. Lesson 14 Lesson 15

Sample Problems:

1) Determine the value of the following expression: 5.61 × 103 + 1.0098 × 105

2) Determine the value of the following expression: 2.7 × 105 ÷ 3 × 103

3) Simplify and write in scientific notation: (1.08 × 10−3)(9.3 × 10−3)

4) Simplify and write in scientific notation: 4×104

3.63×10−4

5) Simplify and write in scientific notation: 2.3𝑥105 − 3.1 × 104

MA.8.NSO.1.6 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Solve real-world problems involving operations with numbers expressed in scientific notation.

MAFS.8.EE.1.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. MAFS.8.EE.1.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.

Instructional Learning Objectives Instructional Resources

Objective 1: Students will be able to apply the Laws of Exponents to algebraic expressions. Objective 2: Students will be able to use scientific notation to describe situations. Objective 3: Students will be able to use scientific and standard notation in a real-world context.

McGraw Hill McGraw Hill Course 3 Volume 1: Lesson 6 McGraw Hill Course 3 Volume 1: Lesson 7 McGraw Hill Course 3 Volume 1: Lesson 7 Inquiry Lab IXL Compare Numbers Written in Scientific Notation (A-W.2) Khan Academy Scientific Notation Word Problems EngageNY Module 1, Topic B, Lesson 11 Module 1, Topic B, Lesson 12 Module 1, Topic B, Lesson 13 Nearpod Lessons and Activities (editable) Using Scientific Notation to Estimate Products Better Lesson This is a free resource for teachers. An account is free to make and then you have access to lesson and resources other teachers have shared. How Many Times Larger? Flexible problem solving with scientific notation Sun Facts (Part 1 of 2) Sun Facts (Part 2 of 2)

Sample Problems:

1) In 2013 the Los Angeles Dodgers opening day payroll was about $2.16 × 108 and the Houston Astros opening day payroll was about $2.4 × 107. How much higher was the Dodgers’ payroll?

2) A TV show had 3.5 × 106 viewers for their first episode and 8.5 × 106 viewers for their second episode. How

many viewers did they have overall?

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

3) In 2012, New York City (NYC) and Los Angeles (LA) has the highest populations of any cities in

the United States. NYC’s population was about 8.1 × 106 and LA’s population was about 3.8 × 106.

What is the population of these two cities combined?

4) Geographers keep track of how many people live in different areas of the world. They are especially interested in how the populations of certain area change. The table below shows the population of different regions in 1985 and in 2005.

How many more people inhabited Earth in 2005 than in 1985?

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Unit 4: Creating Equivalent Expressions Standards Aligned Instruction 8 days September 21 – September 30 Intervention Days 2 days October 1 – October 4 Progress Monitoring (Units 1 – 4) 1 day October 5

The 2021-2022 school year we are transitioning from the Florida Mathematics Standards (MAFS) to the B.E.S.T. standards (MA).

In the unit guides we have identified which B.E.S.T. standard matches with which MAFS standard(s). Standards Content Limits

MA.8.AR.1.2 Apply properties of operations to multiply two linear expressions with rational coefficients. • Clarification 1: Problems are limited to products where at least

one of the factors is a monomial. • Clarification 2: Refer to Properties of Operations, Equality and

Inequality (Appendix D).

• N/A Calculator: NEUTRAL Context: MATHEMATICAL

MA.8.AR.1.3 Rewrite the sum of two algebraic expressions having a common monomial factor as a common factor multiplied by the sum of two algebraic expressions.

• Algebraic expressions must be given. • Items are limited to the use of no more than two

different variables. Calculator: NEUTRAL Context: MATHEMATICAL

MA.8.NSO.1.7 Solve multi-step mathematical and real-world problems involving the order of operations with rational numbers including exponents and radicals. Example: (−1

2)2 + �(23 + 8 is equivalent to 1

4+ √16 which is

equivalent to 14

+ 4 which is equivalent to 174

. • Clarification 1: Multi-step expressions are limited to 6 or fewer

steps • Clarification 2: Within this benchmark, the expectation is to

simplify radicals by factoring square roots of perfect squares up to 225 and cube roots of perfect cubes from -125 to 125.

• Decimals are limited to the thousandths place or less.

• Expressions must be given and must incorporate a negative exponent and/or a radical.

• The value of the radicand must be a perfect square or perfect cube.

• Integer exponents are limited to values between -3 and 3, inclusive.

• Expressions that include the use of both fractions and decimals must use fractions that only result in a terminating decimal.

Calculator: NONE Context: BOTH

Essential Vocabulary Vocabulary Definition/Description

Algebraic expression A combination of variables, numbers, and, at least, one operation Brackets Symbols, such as parentheses, that are most often used to create groups or

clarify the order that operations are to be done in an algebraic expression or equation.

Coefficient The numerical factor of a term that contains a variable. Cubed root One of the three equal factors of a number. If a^3 = b, then a is the cube root of

b. The cube root of 64 is 4 since 4^3 = 64. Exponent In a power, the number of times the base is used as a factor. Expression Numbers, symbols and operators grouped together that show the value of

something. Factor Numbers, or expressions, we can multiply together to get another number, or

expression. Linear expression An expression that contains numbers, variables, or a mixture of the two and, of

which, none are raised to a power greater than one. Monomial A number, a variable, or a product of a number and one or more variables Operations A mathematical process where the most common are add, subtract, multiply,

and divide.

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Order of operations The rules that say which calculation comes first in an expression. They are: • do everything inside parentheses/brackets first • then do exponents, like x^2. X^3, etc • then do multiplication and division from left to right • then do the addition and subtraction from left to right

Polynomial An expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables

Product The result of two, or more, quantities being multiplied. Radical A square root, a cube root, etc and is symbolized by this: √𝑥𝑥, where x is a

number/expression Radicand The value inside the radical symbol – for example, √𝑥𝑥 means “x” is the radicand Rational Number Numbers that can be written as the ratio of two integers in which the

denominator is not zero. All integers, fraction, mixed numbers, and percents are rational numbers.

Square root One of the two equal factors of a number. If a^2 = b, then a is the square root of b. A square root of 144 is 12 since 12^2=144.

MA.8.AR.1.2 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Apply properties of operations to multiply two linear expressions with rational coefficients.

MAFS.7.EE.1.1 Apply properties of operations as strategies to add subtract, factor, and expand linear expressions with rational coefficients. MAFS.8.EE.1.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions.

Instructional Learning Objectives Instructional Resources Objective 1: Multiply two linear expressions. IXL

BB.6 Multiply monomials TR9 CPalms Lessons and Activities Equivalent Expressions (7.EE.1.1) Total Recall (Lesson – 7.EE.1.1) Open-Up Resources Distinguishing between Two Types of Situations BetterLesson Most lessons will need to be modified to meet the rigor of the benchmark as there are no resources, yet, that support the new benchmarks. Area and the Distributive Property Area and Combining Like Terms Equivalent Expressions: Distributive Property

Sample Problems: 1) The product of (1.1 + 𝑥𝑥) and (−2.3𝑥𝑥) 𝑐𝑐an be expressed as − 2.53𝑥𝑥 − 2.3𝑥𝑥2 𝑜𝑜𝑜𝑜 −2.3𝑥𝑥2 − 2.53𝑥𝑥.

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

2) How else can the product (1.1 + 𝑥𝑥) 𝑎𝑎𝑎𝑎𝑎𝑎 (−2.3𝑥𝑥) can be expressed? ANSWER: −2.53𝑥𝑥 − 2.3𝑥𝑥2 𝑂𝑂𝑂𝑂 − 2.3𝑥𝑥2 − 2.53𝑥𝑥

3) What is the area of the following rectangle: Answer: 6𝑥𝑥𝑥𝑥 − 14𝑥𝑥

MA.8.AR.1.3 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Rewrite the sum of two algebraic expressions having a common monomial factor as a common factor multiplied by the sum of two algebraic expressions.

MAFS.8.EE.3.7 Solve linear equations in one variable. a. Give examples of linear equations in one

variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Instructional Learning Objectives Instructional Resources Objective 1: Rewrite algebraic expressions Objective 2: Create equivalent expressions

IXL V.17 Factors of linear expressions EGA BetterLesson Most lessons will need to be modified to meet the rigor of the benchmark as there are no resources, yet, that support the new benchmarks. Applying the Distributive Property to Algebraic Expressions Factor Algebraic Expressions Using the Distributive Property Factoring Using a Common Factor Khan Academy The Distributive Property & Equivalent Expressions

Sample Problems: 1) The expression 99𝑥𝑥 − 11𝑥𝑥3 can be written as 11𝑥𝑥(9 − 𝑥𝑥2) or as 11𝑥𝑥(−9 + 𝑥𝑥2).

2) What is a greatest common factor of the two terms in the following expression: −64𝑥𝑥𝑥𝑥 − 16𝑥𝑥? Answer: (-16y) 3) The area of a rectangle is 6𝑥𝑥2 + 3𝑥𝑥. What are the dimensions (length and width) of the rectangle? Answer: (3x)(2x +1)

3𝑥𝑥 − 7

2𝑥𝑥

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

MA.8.NSO.1.7 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Solve multi-step mathematical and real-world problems involving the order of operations with rational numbers including exponents and radicals.

MAFS.8.EE.1.2 Use square root and cube root symbols to represent solutions to equations of the form 𝑥𝑥2 =𝑝𝑝 and 𝑥𝑥3 = 𝑝𝑝, where p is a positive rational number. Evaluate square roots of perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

Instructional Learning Objectives Instructional Resources Objective 1: Recognize and apply the order of operations. Objective 2: Solve one and two step numerical expressions and equations. Objective 3: Identify exponents and radicals Objective 4: Understand that the answer to a problem involving exponents can have more than one answer. (ex. 𝑥𝑥2 = 25 𝑥𝑥 = 5 𝑜𝑜𝑜𝑜 𝑥𝑥 = −5) Objective 5: Solve multi step equations with rational numbers including exponents and radicals.

IXL C.8 Evaluate numerical expressions involving integers Y6W E.9 Evaluate numerical expressions involving rational numbers 5E3 F.12 Evaluate expressions using properties of exponents UTY F.15 Square roots of perfect squares 9RS F.17 Positive and negative square roots 8TF F.19 Relationship between squares and square roots 8W2 F.21 Cube roots of positive perfect cubes RYG M.1 Multi-step word problems EHX CPalms Generalizing Patterns: The Difference of Two Squares (8.EE.1.2) Discovering Kepler's Law for the Periods of Planets (8.EE.1.2) Maximizing Area: Gold Rush (7.EE.2.3) MARS/Shell Generalizing Patterns: The Difference of Two Squares BetterLesson Most lessons will need to be modified to meet the rigor of the benchmark as there are no resources, yet, that support the new benchmarks. Evaluating Expressions Pre-Algebra: Evaluating Expressions

Khan Academy Solving Equations with One Unknown

Sample Problems: 1) Simplify the following expression: (−1

2)2 + √23 + 8 (answer 17

4)

2) A side of a square measures (42 + √64 − 15) feet. What is the perimeter? Answer: p = 92 feet

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Unit 5: Solving Equations & Inequalities Standards Aligned Instruction 10 days October 6 – October 20 Intervention Days 2 days October 21 – October 22

The 2021-2022 school year we are transitioning from the Florida Mathematics Standards (MAFS) to the B.E.S.T. standards (MA).

In the unit guides we have identified which B.E.S.T. standard matches with which MAFS standard(s). Standards Content Limits

MA.8.AR.2.1 Solve multi-step linear equations in one variable, with rational number coefficients. Include equations with variables on both sides. • Clarification 1: Problem types include examples of one-variable

linear equations that generate one solution, infinitely many solutions or no solution.

• Items must give the equation and include more than two procedural steps to solve.

• Items may require the student to state whether there is one solution, no solution, or infinite solutions.

Calculator: NEUTRAL Context: MATHEMATICAL

MA.8.AR.2.2 Solve two-step linear inequalities in one variable and represent solutions algebraically and graphically • Clarification 1: Instruction includes inequalities in the forms

𝑝𝑝𝑝𝑝 ± 𝑞𝑞 > 𝑟𝑟 and 𝑝𝑝(𝑝𝑝 ± 𝑞𝑞) > 𝑟𝑟, where 𝑝𝑝, 𝑞𝑞 and 𝑟𝑟 are specific rational numbers and where any inequality symbol can be represented.

• Clarification 2: Problems include inequalities where the variable may be on either side of the inequality.

• Inequalities must be given, will be presented in the forms 𝑝𝑝𝑝𝑝 ± 𝑞𝑞 > 𝑟𝑟 or 𝑝𝑝(𝑝𝑝 ± 𝑞𝑞) > 𝑟𝑟, and will use the relational symbols >,≥, <, or ≤.

Calculator: NEUTRAL Context: MATHEMATICAL

Essential Vocabulary Vocabulary Definition/Description

Coefficient A number used to multiply a variable; in 3x + 7; “3” is the coefficient Constant A fixed value in an equation, in 3x + 7; “7” is the constant Distributive Property Property that states that multiplying a sum by a number is the same as

multiplying each addend by the number then adding the products. If a, b and c are real numbers, then 𝑎𝑎 (𝑏𝑏 + 𝑐𝑐) = (𝑎𝑎 ∙ 𝑏𝑏) + (𝑎𝑎 ∙ 𝑐𝑐)

Equation A statement using an equal sign (=) showing that two expressions have the same value.

Inequality A statement that two values are not equal. The symbols are <, >, ≤, ≥ 𝑎𝑎𝑎𝑎𝑎𝑎 ≠ Inverse Operation Are opposite operations that undo each other. Addition and subtraction are

inverse operations, multiplication and division are inverse operations. Linear Equation An equation whose graph is a straight line. Reciprocal Two numbers whose product is 1. Each number is the multiplicative inverse of

the other. The reciprocal of 23 is 3

2, their product is 1.

Variable A symbol that stands for an unknown number.

MA.8.AR.2.1 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Solve multi-step linear equations in one variable, with rational number coefficients. Include equations with variables on both sides.

MAFS.8.EE.3.7 Solve linear equations in one variable. a. Give examples of linear equations in one

variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

forms, until an equivalent equation of the form 𝑝𝑝 = 𝑎𝑎,𝑎𝑎 = 𝑎𝑎, or 𝑎𝑎 = 𝑏𝑏 results (where a and b are different numbers).

b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Instructional Learning Objectives Instructional Resources Objective 1: Solve linear equations. Objective 2: Determine if an equation has one solution, no solution or infinite many solutions.

McGraw-Hill Course 3, Chapter 2 Inquiry Lab: Equations with Variables on Each Side; Lesson 4 and 5 IXL Solve two-step equations (8-W.8) JXD Solve multi-step equations (8-W.9) 55K Solve equations involving like terms (8-W.10) Q2B Solve equations with variables on both sides (8-W.11) ZYL Solve equations: mixed review (8-W.12) HZZ Solve equations: complete the solution (8-W.13) PGH Solve equations: word problems (8-W.14) HCP Find the number of solutions (8-W.15) XDE Create equations with no solutions or infinitely many solutions (8-W.16) 7TY

KHAN Academy Number of Solutions to Equations Equations with variables on both sides Distributive property and rational coefficients Illustrative Mathematics Predict How Many Solutions a Linear Equation Has Check Solutions to Linear Equations MARS/Shell Solving Linear Equations in One Variable Tasks require students to use rational coefficients, collect like terms, expand using distributive property, and categorize equations as one, none, or infinitely many solutions. (Whole class instruction, small group and assessment tasks are available.)

Sample Problems: How many solutions does the equation have?

14

(𝑝𝑝 − 3) = 3𝑝𝑝 −114𝑝𝑝 − 3

How many solutions does the equation 3𝑝𝑝 + 5 − 𝑝𝑝 = 2(𝑝𝑝 + 1) − 4

a) No Solution b) One solution x = -7

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

c) One solution, x = 0.75 d) Infinite solutions

How many solutions does the equation 2

3𝑝𝑝 − 4 = 12 − 2𝑝𝑝 have? Explain.

MA.8.AR.2.2 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Solve two-step linear inequalities in one variable and represent solutions algebraically and graphically

MAFS.7.EE.2.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

b. Solve word problems leading to inequalities of the form 𝑝𝑝𝑝𝑝 + 𝑞𝑞 > 𝑟𝑟 or 𝑝𝑝𝑝𝑝 + 𝑞𝑞 < 𝑟𝑟, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.

Instructional Learning Objectives Instructional Resources Objective 1: Solve two-step inequalities with rational numbers Objective 2: Graph inequalities

McGraw Hill This topic is currently found in Course 2, the 7th grade McGraw Hil book IXL Solve two-step inequalities (8-X.6) N9D Graph solutions to two-step inequalities (8-X.7) WHT

KHAN Academy Multi-Step Inequalities Illustrative Math This is a free resource for teachers. An account is free to make and then you have access to lesson and resources other teachers have shared Sports equipment sets Write and solve an inequality from a word problem Fishing Adventures 2 Write and solve inequalities, and represent the solutions graphically.

Open Up Resources This is a free resource for teachers. An account is free to make and then you have access to lesson and resources. Grade 7 Unit 6 Lesson 13: Reintroducing Inequalities Lesson 14: Finding solutions to inequalities in context Lesson 15: Efficiently solving inequalities

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

EngageNY Module 3, Topic B, Lesson 13 Students understand that an inequality is a statement that one expression is less than (or equal to) or greater than (or equal to) another expression, such as 2x + 3 < 5 or 3x + 50 ≥ 100. Students interpret a solution to an inequality as a number that makes the inequality true when substituted for the variable. Module 3, Topic B, Lesson 14 Students solve word problems leading to inequalities that compare px + q and r, where p, q, and r are specific rational numbers. Students interpret the solutions in the context of the problem. Module 3, Topic B, Lesson 15 Students graph solutions to inequalities taking care to interpret the solutions in the context of the problem.

Sample Problems: For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

Solve the inequality and graph its solution on the number line. 84 ≥ −7(𝑣𝑣 − 9)

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Unit 6: Functions Standards Aligned Instruction 7 days October 25 – November 2 Intervention Days 2 days November 3 – November 4

The 2021-2022 school year we are transitioning from the Florida Mathematics Standards (MAFS) to the B.E.S.T. standards (MA).

In the unit guides we have identified which B.E.S.T. standard matches with which MAFS standard(s). Standards Content Limits

MA.8.F.1.1 Given a set of ordered pairs, a table, a graph or mapping diagram, determine whether the relationship is a function. Identify the domain and range of the relation. • Clarification 1: Instruction includes referring to the input as the

independent variable and the output as the dependent variable. • Clarification 2: Within this benchmark, it is the expectation to

represent domain and range as a list of numbers or as an inequality.

• Items will present domain and range as a list of values in braces or as an inequality.

• Items may refer to input as the independent variable or domain, and to output as the dependent variable or range.

Calculator: NEUTRAL Context: MATHEMATICAL

Also assesses MA.8.AR.3.1 MA.8.F.1.2 Given a function defined by a graph or an equation, determine whether the function is a linear function. Given an input-output table, determine whether it could represent a linear function. • Clarification 1: Instruction includes recognizing that a table may

not determine a function.

• Items will present a relationship as a table, a graph, an equation, or a written description.

• For MA.8.AR.3.1, items represented as a written description must state that the relationship is linear and will require the student to identify whether it is proportional.

Calculator: NEUTRAL Context: BOTH

MA.8.F.1.3 Analyze a real-world written description or graphical representation of a functional relationship between two quantities and identify where the function is increasing, decreasing or constant. • Clarification 1: Problem types are limited to continuous

functions. • Clarification 2: Analysis includes writing a description of a

graphical representation or sketching a graph from a written description.

• Items may require the student to identify increasing, decreasing, or constant intervals from a graph.

• Intervals will not be expressed in inequality or interval notation.

Calculator: NEUTRAL Context: REAL-WORLD

Essential Vocabulary Vocabulary Definition/Description

Constant A value that does not change. Continuous function A function is said to be continuous at point (x, y) if it is defined at that point and

passes through that point without a break.

Decreasing To lower in value or size Dependent variable The variable in a relation whose value depends on the value of the independent

variable.

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Domain The set of the first numbers or abscissas of the ordered pairs in a relation. Function A relation in which exactly one element of the range is paired with each element

of the domain. Increasing To rise in value or size Independent variable The variable in a function whose value is subject to choice. Input A value/variable placed into a function where it can then be evaluated to

determine the output. Input-output table Similar to a mapping diagram, rather it is a table that lists the inputs and their

corresponding output values to determine if a set of values is a function. Linear function A function in which the graph of the solutions forms a line defined by y = mx + b

where m and b are real numbers. Mapping diagram A diagram that illustrates how each element of the domain is paired with an

element in the range.

Output The value/variable/expression of a function that is determined after the input

has been evaluated through the stated function Range The set of second numbers in the ordered pairs of a relation. Qualitative data/graph Data – describes a subject and cannot be expressed as a number

Graph - used to represent situations that do not necessarily have numerical values

MA.8.F.1.1 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Given a set of ordered pairs, a table, a graph or mapping diagram, determine whether the relationship is a function. Identify the domain and range of the relation.

MAFS.8.F.1.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

Instructional Learning Objectives Instructional Resources Objective 1: Understand what is consider an input and what is an output. Objective 2: Understand an independent variable from a dependent variable. Objective 3: Know what a function is and is not. Objective 4: Know what a domain is and how it relates to a function. Objective 5: Know what a range is and how it relates to a function. Objective 6: Given a set of order pairs determine if it is a function.

Illustrative Mathematics This is a free resource for which teachers can sign up. Click here for the Grade 8 resources: Grade 8 For this standard, use the following lessons from Grade 8, Unit 5 in the IM Curriculum. Lesson 1 "Input Output" Lesson 2 "Introduction to Functions" McGraw-Hill Chapter 4 Lesson 2: Relations IQL Lesson 3: Inquiry Lab – Relations and Functions Lesson 3: Functions Lesson 4: Linear Functions Lesson 7: Linear and Non Linear Functions

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Objective 7: Given a table determine if it is a function. Objective 8: Given a graph determine if it is function. Objective 9: Given a mapping diagram determine if it is a function. Objective 10: Given a set of ordered pairs, a table, a graph or mapping diagram, determine whether the relationship is a function. Objective 11: Given a relation identify the domain and range.

IXL Identify Functions ELJ Identify independent and dependent variables FSF Domain and range of functions JZD Better Lesson Introduction to Functions EngageNY Module 5, Topic A, Lesson 1 Module 5, Topic A, Lesson 2

Sample Problems:

1) Select all the representations that ARE functions: a. b. c. d. {(5, 6), (8, 6), (9, 6)} e.

2) Write the domain and range of the function as shown at right:

Domain:___________________ Range: _____________________

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

MA.8.F.1.2 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Given a function defined by a graph or an equation, determine whether the function is a linear function. Given an input-output table, determine whether it could represent a linear function.

MAFS.8.F.1.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. MAFS.8.F.1.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. MAFS.8.F.1.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

Instructional Learning Objectives Instructional Resources Objective 1: Identify if a function is linear given a graph

Objective 2: Identify if a function is linear given an equation

Objective 2: Identify if a function is linear given an input-output table

Objective 3: Determine if a function is linear given a graph

Objective 4: Determine if a function is linear given an equation

Objective 5: Determine if a function is linear given an input-output table

Illustrative Mathematics This is a free resource for which teachers can sign up. Click here for the Grade 8 resources: Grade 8 For this standard, use the following lessons from Grade 8, Unit 5 in the IM Curriculum. Lesson 8 "Linear Functions" Lesson 9 "Linear Models" McGraw-Hill Chapter 3 Slope-Intercept Form Chapter 4 Lesson 4: Linear Functions Lesson 7: Linear and Nonlinear Functions IXL Identify linear and nonlinear functions: graphs and equations XB8 Identify linear and nonlinear functions: tables VGS Khan Academy Recognizing Linear Functions Linear & Nonlinear Functions: Table Linear & Nonlinear Functions: Word Problem EngageNY Module 5, Topic A, Lesson 3 Module 5, Topic A, Lesson 4

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Module 5, Topic A, Lesson 5 Module 5, Topic A, Lesson 6

Sample Problems:

1) Select all the choices that are not linear: a. 𝑦𝑦 = 𝑥𝑥

5

b. 𝑦𝑦 = 5 − 𝑥𝑥2 c. −3𝑥𝑥 + 2𝑦𝑦 = 4 d. 𝑦𝑦 = 3𝑥𝑥2 + 1 e. 𝑦𝑦 = −5𝑥𝑥 − 2 f. 𝑦𝑦 = 𝑥𝑥3

2) Why does the equation −12𝑥𝑥 + 3𝑦𝑦 = 18 represent a linear function?

3) How can you demonstrate that the following table is, or is not, a linear function:

X -3 -1 2 5 Y -3 -1 7 13

MA.8.F.1.3 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Analyze a real-world written description or graphical representation of a functional relationship between two quantities and identify where the function is increasing, decreasing or constant.

MAFS.8.F.1.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. MAFS.8.F.2.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Instructional Learning Objectives Instructional Resources Objective 1: Identify a relationship between two functions

Objective 2: Identify an increasing relation on a graph

Objective 3: Identify a decreasing relation on a graph

Objective 4: Identify a constant relation on a graph

Illustrative Mathematics This is a free resource for which teachers can sign up. Click here for the Grade 8 resources: Grade 8 For this standard, use the following lessons from Grade 8, Unit 5 in the IM Curriculum. Lesson 10 " Interpreting Qualitative Graphs" McGraw-Hill Chapter 4

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Lesson 7: Linear and Non Linear Functions Lesson 8: Quadratic Functions Lesson IQL 8: Inquiry Lab – Graphing Technology: Families of Non-Linear Functions Lesson 9: Qualitative Graphs IXL Interpret points on the graph of a linear function 9E8 Find values using function graphs 7N2 Complete a table for a function graph 7EK Better Lesson Describe Functions Understand Distance-Time graphs Sketching Qualitative Graphs I Sketching Qualitative Graphs II Introducing Function Graphs: Day 1 of 3 Introducing Functions Graphs: Day 2 of 4 Introducing Functions Graphs: Day 3 of 4 Introducing Function Graphs Completed: Day 4 of 4 Mathematics Assessment Project Interpreting Distance-Time Graphs Khan Academy Interpreting a graph example EngageNY Module 6, Topic A, Lesson 2 Module 6, Topic A, Lesson 3 Module 6, Topic A, Lesson 4 Module 6, Topic A, Lesson 5

Sample Problems: 1) Which section of the graph is decreasing:

a. Between A and B b. Between B and C c. Between C and D d. Between D and E

2) The graph to the right shows the altitude of an airplane over time. Which story matches the graph?

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

a. The aircraft rose quickly into the air at takeoff, and then it continued at a constant altitude.

b. The aircraft rose steadily over the entire flight. c. The aircraft rose quickly to its maximum height, and then it

immediately began going back down toward the ground. d. The aircraft rose quickly into the air at takeoff, and then it rose

slowly for the rest of the flight.

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Unit 7: Proportional Relationships and Slope Standards Aligned Instruction 15 days November 2- December 2 Intervention Days 3 days December 3 – December 7

Thanksgiving Break is November 20 – November 28

The 2021-2022 school year we are transitioning from the Florida Mathematics Standards (MAFS) to the B.E.S.T. standards (MA).

In the unit guides we have identified which B.E.S.T. standard matches with which MAFS standard(s). Standards Content Limits

Assessed with MA.8.F.1.2 MA.8.AR.3.1 Determine if a linear relationship is also a proportional relationship. • Clarification 1: Instruction focuses on the understanding that

proportional relationships are linear relationships whose graph passes through the origin.

• Clarification 2: Instruction includes the representation of relationships using tables, graphs, equations and written descriptions.

• Items will present a relationship as a table, a graph, an equation, or a written description.

• For MA.8.AR.3.1, items presented as a written description must state that the relationship is linear and will require the student to identify whether it is proportional.

Calculator: NEUTRAL Context: BOTH

MA.8.AR.3.2 Given a table, graph or written description of a linear relationship, determine the slope. • Clarification 1: Problem types include cases where two points

are given to determine the slope. • Clarification 2: Instruction includes making connections of slope

to the constant of proportionality and to similar triangles represented on the coordinate plane.

• All values for x- and y-coordinates used to determine slope must be integers.

Calculator: NEUTRAL Context: MATHEMATICAL

MA.8.AR.3.3 Given a table, graph or written description of a linear relationship, write an equation in slope-intercept form.

• Items must state that the given table, graph, or written description represents a linear relationship.

• Tables must include at least two points. • Graphs must include at least two exact points

marked on the line and may be labeled with coordinates.

• Graphs must have integral y-intercepts. • All values for x- and y-coordinates used to

determine slope must be integers. Calculator: NEUTRAL Context: MATHEMATICAL

MA.8.AR.3.4 Given a mathematical or real-world context, graph a two-variable linear equation from a written description, a table or an equation in slope-intercept form.

• Graphs must have integral y-intercepts. • Coordinate points within tables and written

descriptions must be integers. Calculator: NEUTRAL Context: BOTH

MA.8.AR.3.5 Given a real-world context, determine and interpret the slope and 𝑦𝑦-intercept of a two-variable linear equation from a written description, a table, a graph or an equation in slope-intercept form. • Clarification 1: Problems include conversions with temperature

and equations of lines of fit in scatter plots.

• Items will require the student to find and interpret the slope, the y-intercept, or both.

• Items will not require the student to write an equation or graph a line on a given coordinate plane.

• Items that present a line of fit on a scatter plot must give the equation of the line of fit in slope-intercept form.

• Variables must be defined in context. Calculator: NEUTRAL Context: REAL-WORLD

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Essential Vocabulary Vocabulary Definition/Description

constant of proportionality a constant ratio or unit rate of two variable quantities; also called constant of variation

constant of variation a constant ratio or unit rate of two variable quantities; also called constant of proportionality

constant rate of change the rate of change between any two points in a linear relationship is the same or constant.

direct variation a relationship between two variable quantities with a constant ratio. linear relationship a relationship that has a straight-line graph. point-slope form an equation of the form y – y₁ = m (x – x₁), where m is the slope and (x₁, y₁) is a

given point on a nonvertical line. rise the vertical change between any two points on a line. run the horizontal change between any two points on a line. slope The rate of change between any two points on a line. The ratio of the rise, or

vertical change, to the run, or horizontal change. slope-intercept form an equation written in the form y = mx + b, where m is the slope and b is its y-

intercept. x-intercept the x-coordinate of the point where the line crosses the x-axis. y-intercept the y-coordinate of the point where the line crosses the y-axis.

MA.8.AR.3.1 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Determine if a linear relationship is also a proportional relationship.

MAFS.7.RP.1.2 Recognize and represent proportional relationships between quantities.

a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

MAFS.8.EE.2.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time.

Instructional Learning Objectives Instructional Resources Objective 1: Identify a linear relationship Objective 2: Identify a proportional relationship Objective 3: Understand a proportional relationship must pass through the origin Objective 4: Identify a nonlinear relationship Objective 5: Understand the difference between proportional and nonproportional Objective 6: Determine if the relationship of a table is linear or nonlinear.

Illustrative Mathematics This is a free resource for which teachers can sign up. Click here for the Grade 8 resources: Grade 8 For this standard, use the following lessons from Grade 8, Unit 3 in the IM Curriculum. Lesson 1 Lesson 2 Lesson 3 Lesson 4 IXL Identify proportional relationships by graphing (8-I.3) RXD

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Objective 7: Determine if the relationship of a graph is linear or nonlinear. Objective 8: Decide if an algebraic equation is linear or nonlinear.

Identify proportional relationships from graphs and equations (8-I.6) 45N Identify proportional relationships from tables (8-I.7) H8N EngageNY Module 1, Topic A, Lesson 5 Students decide whether two quantities are proportional to each other by graphing on a coordinate plane and observing whether the graph is a straight line through the origin. Module 1, Topic B, Lesson 10 Students consolidate their understanding of equations representing proportional relationships as they interpret what points on the graph of a proportional relationship mean in terms of the situation or context of the problem, including the point (0, 0). McGraw Hill Chapter 3: Lesson 1: Constant Rate of Change Lesson IQL 1: Inquiry Lab – Graphing Technology: Rate of Change Lesson 2: Slope Lesson 3: Equations in y=mx form

Sample Problems: 1. Is the linear relationship below proportional? Explain why or why not.

2. Below is a table of a linear relationship. Determine if the linear relationship is proportional and justify your

answer. X -1 5 6 8

Y -1 23 27 35

MA.8.AR.3.2 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Given a table, graph or written description of a linear relationship, determine the slope.

MAFS.8.EE.2.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time.

Instructional Learning Objectives Instructional Resources Objective 1: Understand slope to be the rate of change between two points Objective 2: Identify slope as the rate of change of a given function (whether as a table, graph, or written description) Objective 3: Determine the rate of change given a table of order points. Objective 4: Identify the slope of a table or graph given two points. Objective 5: Identify the slope as the unit rate and the y-intercept as initial value or starting point, when given a graph. Objective 6: Understand equivalent slopes given two different points on the same graphs.

Illustrative Mathematics This is a free resource for which teachers can sign up. Click here for the Grade 8 resources: Grade 8 For this standard, use the following lessons from Grade 8, Unit 3 in the IM Curriculum. Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 IXL Find the constant of proportionality from a table (8-I.1) ZCK Find the constant of proportionality from a graph (8-I.4) YMH Find the slope of a graph (8-Y.1) D7M Find the slope from two points (8-Y.2) 7LF EngageNY Grade 8, Module 4, Topic B, Lesson 11 Constant rate problems displayed in a graph and a table Grade 8, Module 4, Topic C, Lesson 15 Interpret slope as rate of change on a graph Grade 8, Module 4, Topic C, Lesson 16 Use triangles to explain slope; slope formula to find slope Grade 8, Module 4, Topic C, Lesson 17 Find slope of a line; Transform standard form to slope intercept form Grade 8, Module 4, Topic C, Lesson 19 Proof that any point on a line is a point on the graph of the equation of that line. Grade 8, Module 4, Topic C, Lesson 20 Any line is the graph of a linear equations MARS/Shell Defining Lines, by Points, Slopes, and Equations Find slopes and equations with ordered pairs; calculate and use slope and y-intercept to derive an equation. May involve similar triangles to help define slope. McGraw Hill

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Chapter 3: Lesson 1: Constant Rate of Change Lesson IQL 1: Inquiry Lab – Graphing Technology: Rate of Change Lesson 2: Slope Lesson 3: Equations in y=mx form Lesson 4: Slope-Intercept Form Lesson IQL: Inquiry Lab – Slope Triangles Chapter 7: Lesson 6: Slope and Similar Triangles

Sample Problems: 1) Given the following table, determine the slope of the linear function: 2) After Kanika’s first week of work she earned $201 (before taxes). Her friend, Sam, makes the same hourly

rate and earned $120.60 (before taxes) by working for 12 hours. By determining the rate per hour, how many hours did Kanika work?

3) The graph of a proportional relationship is shown below. Find the slope of the line.

X -1 5 6 8 Y -1 23 27 35

MA.8.AR.3.3 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Given a table, graph or written description of a linear relationship, write an equation in slope-intercept form.

MAFS.8.EE.2.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time. MAFS.8.EE.2.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

the equation y = mx + b for a line intercepting the vertical axis at b. MAFS.8.F.1.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

Instructional Learning Objectives Instructional Resources Objective 1: Identify slope intercept form as 𝑦𝑦 =𝑚𝑚𝑚𝑚 + 𝑏𝑏. Objective 2: Understand that m is the variable for slope. Objective 3: Understand that b is the variable for the y intercept. Objective 4: Identify and understand the y intercept. Objective 5: Understand that x is the independent variable and y is the dependent variable. Objective 6: Write an equation in slope- intercept form given a table. Objective 7: Write an equation in slope- intercept form given a graph. Objective 8: Write an equation in slope- intercept form from information in a real- world word problem.

IXL Write equations for proportional relationships from tables (8-I.2) S69 Write equations for proportional relationships from graphs (8-I.5) G7N Write a linear equation from a slope and y-intercept (8-Y.8) WHP Write a linear equation from a graph (8-Y.9) WHM Write a linear equation from a slope and a point (8-Y.10) VKP Write a linear equation from two points (8-Y.11) 2R9 Write a linear function from a table (8-Z.12) UYY Write linear functions: word problems (8-Z.15) YK6 McGraw Hill Chapter 3: Lesson 4: Slope-Intercept Form Chapter 4: Lesson 4: Linear Functions Chapter 7: Lesson 6: Slope and Similar Triangles EngageNY Grade 8, Module 4, Topic C, Lesson 15 Interpret slope as rate of change on a graph Grade 8, Module 4, Topic C, Lesson 16 Use triangles to explain slope; slope formula to find slope Grade 8, Module 4, Topic C, Lesson 17 Find slope of a line; Transform standard form to slope intercept form CPALMS Task Deriving Lines 1

Sample Problems: 1. Write the slope-intercept equation for the following graph:

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

2. Write the slope-intercept equation for the following table:

3. A local handyman charges a $250 service charge to work at your house. He then charges $55 an hour for

his time. Using C for total cost and h for hours, what would a slope-intercept equation model look like for this handyman’s charges?

4.

X -1 5 6 8 Y -1 23 27 35

MA.8.AR.3.4 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Given a mathematical or real-world context, graph a two-variable linear equation from a written description, a table or an equation in slope-intercept form.

MAFS.8.EE.2.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time. MAFS.8.EE.2.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

Instructional Learning Objectives Instructional Resources Objective 1: Graph a two-variable linear equation from an equation written in slope-intercept form given mathematical context. Objective 2: Graph a two-variable linear equation from a table given mathematical context.

IXL Graph proportional relationships (8-I.8) WHP Graph a line using slope (8-Y.5) FSV Graph a line from an equation in slope-intercept form (8-Y.6) W5E McGraw Hill

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Objective 3: Graph a two-variable linear equation from a written description given mathematical context. Objective 4: Graph a two-variable linear equation from an equation written in slope-intercept form given real-world context. Objective 5: Graph a two-variable linear equation from a table given real-world context. Objective 6: Graph a two-variable linear equation from a written description given real-world context.

Chapter 3: Lesson 3: Equations in y=mx form Lesson 4: Slope-Intercept Form Lesson IQL 6: Inquiry Lab – Graphing Technology: Model Linear Behavior Chapter 4: Lesson 1: Representing Relationships Lesson 3: Functions Lesson 4: Linear Functions Lesson PSI: Problem Solving Investigation – Make a Table Lesson 6: Construct Functions Chapter 7: Lesson 6: Slope and Similar Triangles EngageNY Grade 8, Module 6, Topic A, Lesson 1 Determine and interpret a linear function from a verbal description Grade 8, Module 6, Topic A, Lesson 2 Interpret slope and the initial value; describe the graph of the function based on its slope CPALMS Task Interpreting Slope

Sample Problems: 1. A kayak rental service charges a $20 transportation fee and $30 dollars an hour to rent a kayak. Write and

graph an equation representing the cost, y, of renting a kayak for x hours.

2. Graph the following linear equation: 𝑦𝑦 = −2

3𝑚𝑚 + 5

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

3.

MA.8.AR.3.5 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Given a real-world context, determine and interpret the slope and 𝑦𝑦-intercept of a two-variable linear equation from a written description, a table, a graph or an equation in slope-intercept form.

MAFS.8.EE.2.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time. MAFS.8.EE.2.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. MAFS.8.F.2.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Instructional Learning Objectives Instructional Resources Objective 1: Determine the slope and the y-intercept from a two-variable linear equation from a graph given real-world context. Objective 2: Determine the slope and the y-intercept from a two-variable linear equation from a table given real-world context.

Illustrative Mathematics This is a free resource for which teachers can sign up. Click here for the Grade 8 resources: Grade 8 For this standard, use the following lessons from Grade 8, Unit 3 in the IM Curriculum. Lesson 1

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Objective 3: Determine the slope and the y-intercept from a two-variable linear equation from a written description given real-world context.

Lesson 2 Lesson 3 Lesson 4 IXL Write and solve equations for proportional relationships (8-I.10) HPM Write linear functions: word problems (8-Z.15) YK6 McGraw Hill Chapter 3: Lesson 3: Equations in y=mx form Lesson 4: Slope-Intercept Form Lesson IQL 6: Inquiry Lab – Graphing Technology: Model Linear Behavior Chapter 4: Lesson 1: Representing Relationships Lesson 3: Functions Lesson 4: Linear Functions Lesson PSI: Problem Solving Investigation – Make a Table Lesson 6: Construct Functions EngageNY Grade 8, Module 6, Topic A, Lesson 3 Graph a line based on different characteristics (function, initial value, points CPALMS Task Stretching Statistics

Sample Problems: 1. The following equation models the cost of renting a booth at a holiday market and selling baked goods to

earn money: 𝑦𝑦 = 3.5𝑚𝑚 − 75. What is cost to rent the booth? How much does each baked good cost? How many baked goods would they have to sell to “break even” (earn at least $75)?

2. Raul bought a palm tree to plant at his house. He records the growth over many months and creates the

equation ℎ = 0.21𝑚𝑚 + 4.9, where h is the height of the palm tree in feet and m is the number of months. Interpret the slope and y-intercept from his equation.

3. To convert from Fahrenheit to Celsius, one formula we can use is𝐹𝐹 = 95𝐶𝐶 − 32. Using this model, interpret

the y intercept in terms of Fahrenheit and Celsius.

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Unit 8: Systems of Equations Standards Aligned Instruction 14 days January 5 – January 25

Intervention Days 2 days January 26 – January 27

The 2021-2022 school year we are transitioning from the Florida Mathematics Standards (MAFS) to the B.E.S.T. standards (MA).

In the unit guides we have identified which B.E.S.T. standard matches with which MAFS standard(s). Standards Content Limits

MA.8.AR.4.1 Given a system of two linear equations and a specific set of possible solutions, determine which ordered pairs satisfy the system of linear equations. Clarification 1: Instruction focuses on the understanding that a solution to a system of equations satisfies both linear equations simultaneously.

• Items must present the system of equations, and equations must be in slope-intercept form.

• Items must present possible solutions as integral ordered pairs.

Calculator: NEUTRAL Context: MATHEMATICAL

• MA.8.AR.4.2 Given a system of two linear equations represented graphically on the same coordinate plane, determine whether there is one solution, no solution or infinitely many solutions.

• Items may present the system of equations using slope-intercept form.

Calculator: NEUTRAL Context: MATHEMATICAL

MA.8.AR.4.3 Given a mathematical or real-world context, solve systems of two linear equations by graphing.

• Clarification 1: Instruction includes approximating non-integer solutions.

• Clarification 2: Within this benchmark, it is the expectation to represent systems of linear equations in slope-intercept for only.

• Clarification 3: Instruction includes recognizing that parallel lines have the same slope.

• System of equations must be given, and equations must be in slope-intercept form with integral y-intercepts.

• Items that require the student to graph and find the point of intersection will have the coordinates of the solution as integers.

• Given a system of equations and the graph, items may require the student to choose or select an approximate solution.

Calculator: NEUTRAL Context: MATHEMATICAL

Essential Vocabulary Vocabulary Definition/Description

Consistent system A type of system that has at least one solution

Dependent System A type of system that has infinitely many solution (its graph has only one visible line)

Elimination Method Method of solving a system in which two equations are added together in a manner that will eliminate one of the two variables.

Inconsistent System A type of system that does not have a solution

Independent System A system with exactly one solution (Its graph has two intersecting lines)

Linear equation An equation in the form 𝐴𝑥+𝐵𝑦=𝐶, with a graph that is a straight line.

Point of intersection The point at which two lines cross

Solution to a System The point of intersection for a system of equations

Substitution Method Method for solving a system of linear equations in which the equivalent expression of a variable is substituted for that variable into the other equation.

System of Equations A set of two or more equations that has a common set of solutions

MA.8.AR.4.1 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards

Given a system of two linear equations and a specific set of possible solutions, determine which ordered pairs satisfy the system of linear equations.

MAFS.8.EE.3.8 Analyze and solve pairs of simultaneous linear equations.

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

Instructional Learning Objectives Instructional Resources

Objective 1: Understand that the solution to a system of linear equations must make both equations true. Objective 2: Determine whether an ordered pair is a solution of a system of equations

McGraw Hill Chapter 3: Lesson IQL 3 – 7: Inquiry Lab: Graphing Technology – Systems of Equations Lesson 7: Solve Systems of Equations by Graphing Lesson IQL 3-8: Inquiry Lab: Analyze Systems of Equations IXL Is (x, y) a solution to the system of equations? N46 Illustrative Mathematics This is a free resource for which teachers can sign up. Click here for the Grade 8 resources: Grade 8 For this standard, use the following lessons from Grade 8, Unit 4 in the IM Curriculum. Unit 4, Lesson 10

Sample Problems:

1) From the set of points below, which one satisfies the system of equations stated here: {2𝑥 + 𝑦 = 6

3𝑥 + 𝑦 = 12}

a. (5, -3) b. (4,2) c. (2,3) d. (6, -6)

MA.8.AR.4.2 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards

Given a system of two linear equations represented graphically on the same coordinate plane, determine whether there is one solution, no solution or infinitely many solutions.

MAFS.8.EE.3.8 Analyze and solve pairs of simultaneous linear equations.

a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3𝑥 + 2𝑦 = 5 and 3𝑥 + 2𝑦 = 6 have no solution because 3𝑥 +2𝑦 cannot simultaneously be 5 and 6.

Instructional Learning Objectives Instructional Resources

Objective 1: Determine the coordinates of the point of intersection (solution) for a system of equations

McGraw Hill Chapter 3:

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Objective 2: Understand that a system of equations with one solution looks like two lines intersecting at one point Objective 3: Understand that a system of equations with no solution is a set of parallel lines Objective 4: Understand that a system of equations with infinitely many solutions is the same linear equation that may be written in different ways.

Lesson IQL 3 – 7: Inquiry Lab: Graphing Technology – Systems of Equations Lesson 7: Solve Systems of Equations by Graphing Lesson IQL 3-8: Inquiry Lab: Analyze Systems of Equations IXL Find the number of solutions to a system of equations by graphing AGZ Better Lesson This is a free resource for teachers. In order to access the materials, you just have to sign up for a free account. Solve systems of linear functions by graphing Mathematics Assessment Project Classifying Solutions to Systems of Equations This lesson also assess their knowledge on determine a linear equation from a table, determining a function from a table, and their ability to graph a line. Illustrative Mathematics

This is a free resource for which teachers can sign up. Click here for the Grade 8 resources: Grade 8 For this standard, use the following lessons from Grade 8, Unit 4 in the IM Curriculum. Unit 4, Lesson 13 Unit 4, Lesson 14 (This lesson delves into solving systems algebraically)

Sample Problems:

1) Determine and describe the solution to the system of equations show below:

For the 2021-2022 school year, students may be expected to answer questions where they have to solve a system of equations algebraically. Below is an example that students may encounter.

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Example: Employee A makes $10 per hour and this can be modeled by the equation 𝑦 = 10𝑥. Where x is the number of hours worked and y is the money earned. Employee B is given a, one time, $200 starting bonus and earns $8 per hour.

a) What is the linear equation for Employee B? b) How many hours will each employee have to work before they make the same amount of money?

And what is that amount of money?

MA.8.AR.4.3 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards

Given a mathematical or real-world context, solve systems of two linear equations by graphing.

MAFS.8.EE.3.8 Analyze and solve pairs of simultaneous linear equations. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

Instructional Learning Objectives Instructional Resources

Objective 1: Determine the coordinates of the point of intersection (solution) for a system of equations Objective 2: Understand that a system of equations with one solution looks like two lines intersecting at one point Objective 3: Understand that a system of equations with no solution is a set of parallel lines Objective 4: Understand that parallel lines have the same slope Objective 5: Understand that a system of equations with infinitely many solutions is the same linear equation that may be written in different ways. Objective 6: Solve system of equations by graphing. Objective 7: Determine whether a given system has one solution, no solution, or infinitely many solutions Objective 8: Solve application problems by graphing a system of equations

McGraw Hill Chapter 3: Lesson IQL 3 – 7: Inquiry Lab: Graphing Technology – Systems of Equations Lesson 7: Solve Systems of Equations by Graphing Lesson IQL 3-8: Inquiry Lab: Analyze Systems of Equations IXL Solve a system of equations by graphing WV5 Solve a system of equations by graphing: word problems W9J Better Lesson This is a free resource for teachers. In order to access the materials, you just have to sign up for a free account. Solve systems of linear equations by graphing This lesson does require students to create a linear equation in slope intercept form. All the information is given, but not in the strict format of y = mx +b. Real-life Systems 1 Real-life Systems 2 Illustrative Mathematics This is a free resource for which teachers can sign up. Click here for the Grade 8 resources: Grade 8 For this standard, use the following lessons from Grade 8, Unit 4 in the IM Curriculum. Unit 4, Lesson 11 Unit 4, Lesson 12 Unit 4, Lesson 15 (This lesson requires students to write the equations for the system from a real-world context)

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Unit 4, Lesson 16 (a rigorous lesson that depends upon student knowledge of solving systems algebraically and graphically)

Sample Problems:

1) A system of equations is given the follow description: Equation A has a slope of 2/3 and a y intercept of 4.

Equation B is 𝑦 = −3

2𝑥 + 17

Graph the two equations to determine the solution to the system of equations.

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Unit 9: Triangles & Angles Standards Aligned Instruction 12 days January 28 – February 14 Intervention Days 2 days February 15 – February 16

The 2021-2022 school year we are transitioning from the Florida Mathematics Standards (MAFS) to the B.E.S.T. standards (MA).

In the unit guides we have identified which B.E.S.T. standard matches with which MAFS standard(s). Standards Content Limits

MA.8.GR.1.4 Solve mathematical problems involving the relationships between supplementary, complementary, vertical or adjacent angles.

• Angle measures may be expressed as numerical values or algebraic expressions.

• Items including an algebraic expression for representing an unknown angle must determine the unknown angle measure.

Calculator: NEUTRAL Context: MATHEMATICAL

MA.8.GR.1.5 Solve problems involving the relationships of interior and exterior angles of a triangle • Clarification 1: Problems include using the Triangle Sum

Theorem and representing angle measures as algebraic expressions.

• Angle measures may be expressed as numerical values or algebraic expressions.

• Items including an algebraic expression for representing an unknown angle must determine the unknown angle measure.

Calculator: NEUTRAL Context: MATHEMATICAL

MA.8.GR.1.6 Develop and use formulas for the sums of the interior angles of regular polygons by decomposing them into triangles. • Clarification 1: Problems include representing angle measures as

algebraic expressions.

• Angle measures may be expressed as numerical values or algebraic expressions.

• Items including an algebraic expression for representing an unknown angle must determine the unknown angle measure.

Calculator: NEUTRAL Context: MATHEMATICAL

Essential Vocabulary Vocabulary Definition/Description

Adjacent angles Two angles that share a common vertex and common side Alternate exterior angles A pair of congruent angles on the outside of two parallel lines but on opposite

sides of a transversal Alternate interior angles A pair of congruent angles on the inside of two parallel lines but on opposite

sides of a transversal Congruent Equal in measure Complementary angles Two angles whose sum is 90o Corresponding angles Angles that are congruent and are in the same relative position as another angle

somewhere else in the figure. Corresponding angles in plane geometry are created when transversals cross two lines.

Decompose To breaking something into parts, that together are the same as the original. Exterior angles An angle formed by one side of a polygon ad the extension of an adjacent side Interior angles Angles within a plane figure Parallel lines Lines in a plane that will never intersect Regular polygons A many sided, closed, simple figure created with congruent lines and angles Same side interior angles A pair of angles on the inside of two parallel lines and on the same side of a

transversal Supplementary angles Two angles whose sum is 180o Transversal lines A line that intersects two or more lines Triangle Sum Theorem The sum of the interior angles of any triangle is 180 degrees Vertical angles Nonadjacent angles with equal measure located across a common vertex

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

MA.8.GR.1.4 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Solve mathematical problems involving the relationships between supplementary, complementary, vertical or adjacent angles.

MAFS.7.G.2.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure

Instructional Learning Objectives Instructional Resources Objective 1: Solve equations to find a variable using properties of supplementary angles. Objective 2: Solve equations to find a variable using properties of complementary angles. Objective 3: Solve equations to find a variable using properties of vertical angles. Objective 4: Solve equations to find a variable using properties of adjacent angles. Objective 5: Solve equations to find a variable using properties of a combination of angle properties.

McGraw-Hill Course 2 This topic is currently found in Course 2, the 7th grade McGraw Hill book IXL Identify complementary, supplementary, vertical, adjacent, and congruent angles Find measures of complementary, supplementary, vertical, and adjacent angles KHAN Academy Complimentary and supplementary angles video Vertical angles video Practice with angles Open Up Resources This is a free resource for teachers. An account is free to make and then you have access to lesson and resources. Grade 7, Unit 7 Lesson 2: Adjacent Angles Lesson 3: Nonadjacent Angles Lesson 4: Solving for Unknown Angles Lesson 5: Using Equations to Solve for Unknown Angles EngageNY Grade 7 Module 6 Topic A Lesson 1 Students solve for unknown angles in word problems and in diagrams involving complementary and supplementary angles. Grade 7 Module 6 Topic A Lesson 2 Students solve for unknown angles in word problems and in diagrams involving complementary, supplementary, vertical, and adjacent angles. Grade 7 Module 6 Topic A Lesson 3 Students solve for unknown angles in word problems and in diagrams involving all learned angle facts. Grade 7 Module 6 Topic A Lesson 4 Students solve for unknown angles in word problems and diagrams.

Sample Problems:

1. Write and solve an equation to find m∠PQT.

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

2. Write and solve an equation to find x. Show your work.

3. 4.

MA.8.GR.1.5 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Solve problems involving the relationships of interior and exterior angles of a triangle

MAFS.8.G.1.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

Instructional Learning Objectives Instructional Resources

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Objective 1: Solve equations using properties of interior angles of a triangle. Objective 2: Solve equations using properties of exterior angles of a triangle. Objective 3: Utilize the triangle sum theorem to find missing interior or exterior angle measures.

McGraw-Hill Course 3 Chapter 5, lessons 1-3 Parallel lines inquiry lab Triangle inquiry lab IXL Find missing angles in triangles JFJ Find missing angles in triangles using ratios 59G Triangle Angle-Sum Theorem 6Q6 Exterior Angle Theorem FMP Identify Alternate Interior and Exterior Angles 8NW Parallel lines and transversals, naming angles ZLF Parallel lines and transversal finding the measure of angles V99 KHAN Academy Finding angles in triangles Angels, Parallel Lines and Transversals Open Up Resources This is a free resource for teachers. An account is free to make and then you have access to lesson and resources. Lesson 14: Alternate Interior Angles Lesson 15: Adding the Angles in a Triangle Lesson 16: Parallel Lines and the Angles in a Triangle

EngageNY Grade 8, Module 2, Topic C, Lesson 13 Informal arguments about Angle Sum Theorem for triangles Grade 8, Module 2, Topic C, Lesson 14 Informal proof of angle sum theorem. Find missing angle measures and prove their answer is correct. Mathematics Formative Assessments (MFAS) Justifying the Triangle Sum Theorem Provide proof using a triangle. Same Side Interior Angles Given same side interior angles, describe relationship and provide justification when not required to find angle measurement. Justifying Angle Relationships Describe the relationship between alternate interior angle and provide justification. Justifying the Exterior Angle Theorem Justify when it is not required to find angle measurement. Engaging Tasks Transversals, Tape and Stickies Place sticky notes in their assigned location based on a description

Better Lessons

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Use the Relationships of Vertical Angles, Adjacent Angles, and Supplementary Angles to Find the Measure of Missing Angles Understand the Traits of and Identify a Transversal Line and the Corresponding Angles it Creates

Sample Problems:

What is the measure of angle x? Find the measure of angles a, b, c, d & x

1. Identify congruent angles and justify your answers. 2. If the measure of angle 1 is 115o, find the measure of angles 2 through 8.

3.

4.

MA.8.GR.1.6 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Develop and use formulas for the sums of the interior angles of regular polygons by decomposing them into triangles.

No current matching MAFS Standard, extension of MAFS.G.1.5

Instructional Learning Objectives Instructional Resources Objective 1: Determine the number of triangles a regular polygon can be made from

McGraw-Hill Course 3, Volume 1 Chapter 4

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Objective 2: Determine the interior angle sum of any regular polygon Objective 3: Determine an equation/formula to determine the interior angle sum of any regular polygon.

IXL Find missing angles in quadrilaterals I (8-O.10) Find missing angles in quadrilaterals II (8-O.11) Interior angles of polygons (8-O.13) KHAN Academy Sum of interior angles of polygons Sum of exterior angles of polygons Practice angles of polygons Youtube Interior and Exterior angles of polygons https://www.youtube.com/watch?v=BG1HpadfiKw https://www.youtube.com/watch?v=T6hCjnqwV2g

Sample Problems: 1. What is the measure of one interior angle of a regular hexagon? 2. What is the measure of one exterior angle of a regular hexagon? 3. Complete the table to determine the number of sides, number of triangles and the interior angle sum

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Unit 10: Pythagorean Theorem Standards Aligned Instruction 5 days February 17 – February 24 Intervention Days 2 days February 25 – February 28

The 2021-2022 school year we are transitioning from the Florida Mathematics Standards (MAFS) to the B.E.S.T. standards (MA).

In the unit guides we have identified which B.E.S.T. standard matches with which MAFS standard(s). Standards Content Limits

MA.8.GR.1.1 Apply the Pythagorean Theorem to solve mathematical and real-world problems involving unknown side lengths in right triangles. • Clarification 1: Instruction includes exploring right triangles with

natural-number side lengths to illustrate the Pythagorean Theorem.

• Clarification 2: Within this benchmark, the expectation is to memorize the Pythagorean Theorem.

• Clarification 3: Radicands are limited to whole numbers up to 225.

• Items will not present triangles on a coordinate plane.

• Items will not require the student to simplify square roots of non-perfect squares.

• Non-perfect square roots may be represented in radical form or as an approximation.

Calculator: NEUTRAL Context: BOTH

MA.8.GR.1.2 Apply the Pythagorean Theorem to solve mathematical and real-world problems involving the distance between two points in a coordinate plane. • Clarification 1: Instruction includes making connections between

distance on the coordinate plane and right triangles. • Clarification 2: Within this benchmark, the expectation is to

memorize the Pythagorean Theorem. It is not the expectation to use the distance formula.

• Clarification 3: Radicands are limited to whole numbers up to 225.

• Items will not require the student to simplify square roots of non-perfect squares.

• Non-perfect square roots may be represented in radical form or as an approximation.

Calculator: NEUTRAL Context: BOTH

MA.8.GR.1.3 Use the Triangle Inequality Theorem to determine if a triangle can be formed from a given set of sides. Use the converse of the Pythagorean Theorem to determine if a right triangle can be formed from a given set of sides.

• Limit real-world context to simple situations using the converse of the Pythagorean Theorem.

Calculator: NEUTRAL Context: BOTH

Essential Vocabulary Vocabulary Definition/Description

Leg the sides adjacent to the right angle Hypotenuse the longest side of a right triangle, opposite the right angle Right Angle Angle that measures 90° Adjacent Side Any two sides of a polygon with a common vertex Opposite Side the side across from a given angle

MA.8.GR.1.1 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Apply the Pythagorean Theorem to solve mathematical and real-world problems involving unknown side lengths in right triangles.

MAFS.8.G.2.6 Explain a proof of the Pythagorean Theorem and its converse. MAFS.8.G.2.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

real-world and mathematical problems in two and three dimensions.

Instructional Learning Objectives Instructional Resources Objective 1: Find the length of a missing leg of a right triangle Objective 2: Find the length of the hypotenuse of a right triangle Objective 3: Find the distance between 2 points on the coordinate plane

McGraw-Hill Course 3 Chapter 5 Inquiry Lab: Proofs about Pythagorean Theorem Open Up Resources Grade 8, Unit 8: Pythagorean Theorem and Irrational Numbers Lesson 7: A Proof of the Pythagorean Theorem Lesson 8: Finding Unknown Side Lengths EngageNY Grade 8, Module 2, Topic D, Lesson 15: Know the Pythagorean Theorem, show an informal proof of the theorem and use it to find the length of a hypotenuse. Grade 8, Module 7, Topic C, Lesson 15 Explain the proof of the Pythagorean Theorem. IXL Pythagorean theorem: find the length of the hypotenuse (8-R.1) Pythagorean theorem: find the missing leg length (8-R.2) Pythagorean theorem: find the missing leg or hypotenuse length (8-R.3) Pythagorean theorem: find the perimeter (8-R.4) Pythagorean theorem: word problems (8-R.5) Khan Academy Pythagorean Theorem Introduction Introduction to Pythagorean Theorem 2

Sample Problems:

1) Triangle ABC is a right triangle. The lengths of the legs are 60cm and 80cm. What is the length, in centimeters, of the hypotenuse?

2) Triangle ABC is a right triangle. The lengths of one leg is 80cm and the hypotenuse is 120cm. What is

the length, in centimeters, of the other leg?

3) A right pyramid is shown. The base has a side length, b, of 30cm. The height, h, is 10cm. What is the length in centimeters, of I?

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

MA.8.GR.1.2 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Apply the Pythagorean Theorem to solve mathematical and real-world problems involving the distance between two points in a coordinate plane.

MAFS.8.G.2.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. MAFS.8.G.2.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Instructional Learning Objectives Instructional Resources Objective 1: Find the length of a segment from two points on the coordinate plane.

McGraw-Hill Course 3, Chapter 5 Lesson 6 Lesson 7 Open Up Resources Grade 8, Unit 8: Pythagorean Theorem and Irrational Numbers Lesson 11: Finding Distances in the Coordinate Plane EngageNY Grade 8, Module 2, Topic D, Lesson 16: Use Pythagorean Theorem to find missing side lengths. Grade 8, Module 7, Topic C, Lesson 17: Use the Pythagorean Theorem to determine the distance between two points on a coordinate plane. Grade 8, Module 7, Topic C, Lesson 18: Apply the Pythagorean Theorem to real world and mathematical problems in two dimensions IXL Find the distance between two points (8-N.4) Khan Academy Finding Distance with Pythagorean Theorem

Sample Problems:

1) What is the distance, in units, between A(-1,3) and B(3,5)?

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

2)

3) Two points are on the coordinate plan shown. What is the distance between A(-5,3) and B(-3,5)

MA.8.GR.1.3 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Use the Triangle Inequality Theorem to determine if a triangle can be formed from a given set of sides. Use the converse of the Pythagorean Theorem to determine if a right triangle can be formed from a given set of sides.

MAFS.8.G.2.6 Explain a proof of the Pythagorean Theorem and its converse.

Instructional Learning Objectives Instructional Resources Objective 1: Determine if three side lengths can form a right triangle by applying the Pythagorean Theorem. Objective 2: Recognize Pythagorean Triples Objective 3: Identify the hypotenuse given all three side lengths (not including the image)

Open Up Resources Grade 8, Unit 8: Pythagorean Theorem and Irrational Numbers Lesson 9: The Converse Lesson 10: Applications of the Pythagorean Theorem EngageNY Grade 8, Module 7, Topic C, Lesson 16 Explain the proof of the converse of the Pythagorean Theorem. IXL Converse of the Pythagorean theorem: is it a right triangle? (8-R.6)

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Triangle inequality (8) Khan Academy Triangle Inequality Theorem Right Triangle Side Lengths

Sample Problems:

1) Select all the sets of numbers that can form a right triangle. a) 1, 2, 3 b) 3.2, 7, 8 c) 5, 12, 13 d) 3.6, 4.7, 5.2 e) 6, 8, 10

2) Select three side lengths that can form a right triangle.

a) 5 b) 6 c) 8 d) 10 e) 11 f) 12

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Unit 11: Transformations, Congruence & Similarity Standards Aligned Instruction 9 days March 1 – March 11 Intervention Days 2 days March 22 – March 23

Spring Break is March 12 – March 21

The 2021-2022 school year we are transitioning from the Florida Mathematics Standards (MAFS) to the B.E.S.T. standards (MA).

In the unit guides we have identified which B.E.S.T. standard matches with which MAFS standard(s). Standards Content Limits

MA.8.GR.2.1 Given a preimage and image generated by a single transformation, identify the transformation that describes the relationship. • Clarification 1: Within this benchmark, transformations are

limited to reflections, translations or rotations of images. • Clarification 2: Instruction focuses on the preservation of

congruence so that a figure maps onto a copy of itself.

• Items will not use the coordinate plane. • Items must use prime notation in given figures. Calculator: NEUTRAL Context: MATHEMATICAL

MA.8.GR.2.2 Given a preimage and image generated by a single dilation, identify the scale factor that describes the relationship. • Clarification 1: Instruction includes the connection to scale

drawings and proportions. • Clarification 2: Instruction focuses on the preservation of

similarity and the lack of preservation of congruence when a figure maps onto a scaled copy of itself, unless the scaling factor is 1.

• Items will not ask the student to find the lengths of missing sides using a scale factor.

• Items will not use the coordinate plane. • Items must use prime notation in given figures. Calculator: NEUTRAL Context: MATHEMATICAL

MA.8.GR.2.3 Describe and apply the effect of a single transformation on two-dimensional figures using coordinates and the coordinate plane. • Clarification 1: Within this benchmark, transformations are

limited to reflections, translations, rotations or dilations of images.

• Clarification 2: Lines of reflection are limited to the x-axis, y-axis or lines parallel to the axes.

• Clarification 3: Rotations must be about the origin and are limited to 90°, 180°, 270° or 360°.

• Clarification 4: Dilations must be centered at the origin.

• Rotation must state the direction of rotation with the angle of rotation.

• Transformations will not be given as ordered pair rules.

Calculator: NEUTRAL Context: MATHEMATICAL

MA.8.GR.2.4 Solve mathematical and real-world problems involving proportional relationships between similar triangles.

• Given dimensions of figures in items must be the same unit.

Calculator: NEUTRAL Context: BOTH

Essential Vocabulary Vocabulary Definition/Description

Axis/axes A fixed reference line for the measurement of coordinates Congruent Having the exact same shape AND same size. Coordinate plane A two-dimension surface formed by two number lines. One number line is

horizontal and is called the x-axis. The other number line is vertical number line and is called the y-axis. The two axes meet at a point called the origin.

Coordinate point A pair of numbers that define a point’s exact location on a two-dimensional plane (i.e. a coordinate plane).

Dilation A transformation that enlarges or reduces a figure.

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Line of reflection A line that is equidistant between the pre-image and the new image. Origin The point where the reference axes in a coordinate system meet. The values of

coordinates are normally defined as zero. Preimage The original figure before the transformation Prime notation Marks used to distinguish a figure from the pre-image (original) For example: x’

which we say out loud as “x prime.” Proportion A number sentence or an equation that states that two ratios are equal.

Proportions are usually written in one of these two ways: a : b = c : d or a / b = c / d in which a, b, c, and d are real numbers and b does not equal 0 and d does not equal 0.

Reflection A transformation where a figure is “flipped” over a line and creates a mirror image.

Rotation A transformation in which a figure is turned around a fixed point. Scale factor The ratio of the lengths of two corresponding sides of two similar polygons. Similar If one image can be obtained from another be a sequence of transformations

and dilations, the images are similar. Figures with the same shape AND proportional lengths.

Transformation An operation that maps a geometric figure, the pre-image, onto a new figure, the image.

Translation A transformation that slides a figure from one position to another without turning.

MA.8.GR.2.1 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Given a preimage and image generated by a single transformation, identify the transformation that describes the relationship.

MAFS.8.G.1.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. MAFS.8.G.1.1 Verify experimentally the properties of rotations, reflections, and translations:

a. Lines are taken to lines, and line segments to line segments of the same length.

b. Angles are taken to angles of the same measure.

c. Parallel lines are taken to parallel lines. Instructional Learning Objectives Instructional Resources

Objective 1: Identify transformations given the preimage and image. Objective 2: Described relationships between preimages and images. Objective 3: Identify rotation, reflection and translations.

McGraw-Hill Course 3, Chapter 6 Inquiry Lap: Transformations Lesson 1, 2, and 3 Course 3, Chapter 7 Lesson 1

IXL Identify reflections, rotations, and translations UYL Translations: graph the image XUS

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Objective 4: Identify congruence between preimages and images.

Reflections over the x- and y-axes: graph the image 74Z Reflections: graph the image NBM Rotations: graph the image AC9 Describe a sequence of transformations XPK Congruence statements and corresponding parts LPP Side lengths and angle measures of congruent figures DSQ Open Up Resources Grade 8, Unit 1: Rigid Transformations and Congruence Lessons 1-6 Engage NY Grade 8, Module 2, Topic A, Lesson 1 Rigid Motion Grade 8, Module 2, Topic A, Lesson 2 Translations Grade 8, Module 2, Topic A, Lesson 3 Parallel Lines Grade 8, Module 2, Topic A, Lesson 4 Reflections Grade 8, Module 2, Topic A, Lesson 5 Rotations Illustrative Mathematics This is a free resource for which teachers can sign up. Click here for the Grade 8 resources: Grade 8  For this standard, use the following lessons from Grade 8, Unit 3 in the IM Curriculum.   Unit 3, Lesson 1- Moving in the Plane Unit 3, Lesson 2- Identifying the Transformation Unit 3, Lesson 3- Identifying the transformation using coordinate planes

Sample Problems:

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Which transformation best describes the movement from the pre-image to the image? Which transformation has occurred between the two figures below?

MA.8.GR.2.2 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Given a preimage and image generated by a single dilation, identify the scale factor that describes the relationship.

MAFS.8.G.1.3 Describe the effects of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. MAFS.8.G.1.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. MAFS.7.G.1.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

Instructional Learning Objectives Instructional Resources Objective 1: Identify scale factors for dilations from preimage to image. Objective 2: Describe the relationship between a preimage and image.

McGraw-Hill Course 3, Chapter 6 Lesson 1 (Translation) Lesson 2 (Reflections) Lesson 3 (Rotations)

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Lesson 4 (Dilations) Course 3, Chapter 7 Lesson 3: Similarity and Transformations Illustrative Mathematics This is a free resource for which teachers can sign up. Click here for the Grade 8 resources: Grade 8  For this standard, use the following lessons from Grade 8, Unit 2 & 3 in the IM Curriculum.   Unit 2, Lesson 1- Making the connection Scale Drawings and Dilations Unit 2, Lesson 2- Intro to Dilations Unit 2, Lesson 3- Dilations with no Grid Unit 2, Lesson 4- Dilations on a Coordinate Plane Unit 2, Lesson 6- Similar Figures Unit 3, Lesson 7- Understanding Corresponding Sides and Angles Unit 3, Lesson 11- Identifying Congruent Figures

Open Up Resources Grade 8, Unit 1: Rigid Transformations and Congruence Lessons 7-10 Unit 2 address the concepts of dilation and similarity. Unit 2 Use lessons 1 – 9 and 13

IXL Dilations: scale factor and classification 8NK Dilations: find the coordinates UV9 Dilations: graph the image 9T4 Engage NY Grade 8, Module 3, Topic A, Lesson 6 Dilations using Coordinates

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Sample Problems:

1. What is the scale factor between ΔPQR and ΔP’Q’R’?

2. Determine the scale factor from the similar figures below:

3.

4.

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

MA.8.GR.2.3 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Describe and apply the effect of a single transformation on two-dimensional figures using coordinates and the coordinate plane.

MAFS.8.G.1.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. MAFS.8.G.1.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

Instructional Learning Objectives Instructional Resources Objective 1: Perform single transformations on a preimage using a translation, reflection, rotation or dilation. Objective 2: Graph preimage and image on a coordinate plane. Objective 3: Identify coordinates of the image after the transformation has been applied.

McGraw-Hill Course 3, Chapter 6 Lesson 1: Translations Lesson 2: Reflections Lesson 3: Rotations Inquiry Lab: Dilations Lesson 4: Dilations 21st Century Career: In Computer Animation Course 3, Chapter 7 Lesson 4 Open Up Resources Units 1 and 2 address the concepts of rigid transformations, dilation, and similarity. Unit 1 Use lessons 1 – 10 Unit 2 Use lessons 1 – 9 and 13 IXL Translations: graph the image XUS Translations: find the coordinates RUP Reflections over the x- and y-axes: graph the image 74Z Reflections over the x- and y-axes: find the coordinates 5UM Rotations: graph the image AC9 Rotations: find the coordinates HHS Dilations: graph the image 9T4 Dilations: find the coordinates UV9 Engage NY Grade 8, Module 2, Topic B, Lesson 7 Sequencing transformations that enjoy the same properties as a single translation with respect to lengths of segments and angle degrees. Grade 8, Module 3, Topic B, Lesson 8 Sequence of Transformations that lead to Similarity Illustrative Mathematics This is a free resource for which teachers can sign up. Click here for the Grade 8 resources: Grade 8 

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

For this standard, use the following lessons from Grade 8, Unit 3 in the IM Curriculum.   Unit 3, Lesson 4- Determine the Transformation Part 1 Unit 3, Lesson 5- Determine the Transformation Part 2 Unit 3, Lesson 6- Determine the Transformation Part 3 Unit 3, Lesson 8- Identify That Pattern

Sample Problems:

Reflect the figure below over the y axis Rotate Figure WIPS 90° counterclockwise

MA.8.GR.2.4 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Solve mathematical and real-world problems involving proportional relationships between similar triangles.

MAFS.7.G.1.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. MAFS.8.EE2.6 Use similar triangles to explain why the slope m is the same between two distinct points on a non-vertical line in the coordinate plane; derive the equation 𝑦𝑦 = 𝑚𝑚 for a line through the origin and the

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

equation 𝑦𝑦 = 𝑚𝑚+𝑏𝑏 for a line intercepting the vertical axis at b. MAFS.8.G.1.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

Instructional Learning Objectives Instructional Resources Objective 1: Find distance using similar triangles. Objective 2: Proof proportional relationships in similar triangles. Objective 3: Explain why slopes of similar triangles are congruent.

McGraw-Hill Chapter 7: Lesson 5: Similar Triangles and Indirect Measurement Lesson 6: Slope and Similar Triangle Lesson 8: Area and Perimeter of Similar Figures 21st Century Career: In Car Design Illustrative Mathematics This is a free resource for which teachers can sign up. Click here for the Grade 8 resources: Grade 8  For this standard, use the following lessons from Grade7 Unit 1, Grade 8, Unit 2 & 3 in the IM Curriculum.   Grade 7 Unit 1, Lesson 2- Corresponding Parts and Scale Factors Grade 7 Unit 1, Lesson 3- Making Scaled Copies Grade 7 Unit 1, Lesson 4- Scaled Relationships Grade 7 Unit 1, Lesson 5- Finding the Scale Factor Grade 7 Unit 1, Lesson 7- Scale Drawings Grade 7 Unit 1, Lesson 9- Creating Scale Drawings Grade 8 Unit 2, Lesson 5- More Dilation Practice Grade 8 Unit 2, Lesson 6- Similar Figures Grade 8 Unit 3, Lesson 12- Congruent Polygons Grade 8 Unit 3, Lesson 13- Congruency Open Up Resources Unit 2 address the concepts of dilation and similarity. Unit 2 Use lessons 1 – 9 and 13 IXL Side lengths of similar triangles QSK Similar triangles and indirect measurement 88W Similar and congruent figures U85 Side lengths and angle measures of similar figures 79Y EngageNY Grade 8, Module 4, Topic C, Lesson 16 Use similar triangles to explain slope and calculate the slope between two distinct points on a non-vertical line.

Sample Problems: 1.) During a Tampa Bay Lightning game one player, Johnson, passes the puck to his teammate, Stamkos, by

bouncing the puck off the wall of the rink. The path of the puck creates two line segments that form

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

hypotenuses for each of two similar right triangles, with the height of each triangle the distance from one of the players to the wall of the rink. If Johnson is 12 feet from the wall and Stamkos is 3 feet from the wall. How far did the puck travel from the wall of the rink to Stamkos if the distance traveled from Johnson to the wall was 16 feet?

2.)

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Unit 12: Volume (only for the 21-22 school year) Standards Aligned Instruction 7 days March 24 – April 1 Intervention Days 2 days April 4 – April 5

The 2021-2022 school year we are transitioning from the Florida Mathematics Standards (MAFS) to the B.E.S.T. standards (MA).

In the unit guides we have identified which B.E.S.T. standard matches with which MAFS standard(s). Standards Content Limits

MAFS.8.G.3.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

For the 2021-2022 school year, students will still be tested on MAFS.8.G.3.9. However, it is not correlated with any of the new BEST Benchmarks. Therefore, this is the last school year to teach this MAFS standard in full.

Essential Vocabulary Vocabulary Definition/Description

Cone A solid (3-dimensional) object that has a circular base joined to a point by a curved side. The point is called a vertex.

Cylinder A solid object with two identical flat ends that are circular and one curved side. Height The distance from top of bottom of a figure. The height and the base ALWAYS

create a right angle (90°). Radius The distance from the center of a circle to a point on the circle. Plural is radii. Slant height The distance up the side of a pyramid, cone, etc, to the apex (point at the top). Sphere A 3-dimensional object shaped like a ball. Every point on the surface is the same

distance from the center. Surface area The total area of the surface of a three-dimensional object. Volume The amount of 3-dimensional space something takes up - also called Capacity.

For example, how much water a water bottle can hold.

MAFS.8.G.3.9 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards No correlating BEST Benchmark. This standard has two distinct parts. First, students learn the volume formulas for cones, cylinders, and spheres. Then they apply this knowledge to solve real-world and mathematical problems. The formulas should be taught through experiments where students figure out the formulas. (Common Core Mathematics Companion, Pg. 190)

MAFS.8.G.3.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Instructional Learning Objectives Instructional Resources Objective 1: Understand the meaning of volume. Objective 2: Distinguish between volume and surface area Objective 3: Identify the height, radius, and/or slant height of a 3-D object.

McGraw-Hill Course 3, Chapter 8 Lesson 1 (Cylinders) Lesson 2 (Cones – skip ex. 3) Lesson 3 (Spheres – skip ex. 4) Open Up Resources

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Objective 4: Know the formula for the volume of a cylinder, of a cone, and of a sphere. Objective 5: Apply the formula for the volume of a cylinder, of a cone, and of a sphere. Objective 6: Interpret word problems to determine which formula to use. Objective 7: Understand the relationship between a cylinder and a cone.

Lesson 11: Filling Containers Lesson 12: How Much Will Fit? Lesson 13: The Volume of a Cylinder Lesson 14: Finding Cylinder Dimensions Lesson 15: The Volume of a Cone Lesson 16: Finding Cone Dimensions Lesson 17: Scaling One Dimension Lesson 18: Scaling Two Dimensions Lesson 19: Estimating a Hemisphere Lesson 20: The Volume of a Sphere Lesson 21: Cylinders, Cones, and Spheres MAFS Tasks Cone Formula Write the formula for the volume of a cone, explain what each variable represents, and label the variables on a diagram. Cylinder Formula Write the formula for the volume of a cylinder, explain what each variable represents, and label the variables on a diagram. Sphere Formula Write the formula for the volume of a sphere, explain what each variable represents, and label the variables on a diagram. Sugar Cone Solve a problem that requires calculating the volume of a cone.

Platinum Cylinder Solve a problem that requires calculating the volume of a cylinder. Burning Sphere Solve a problem that requires calculating the volume of a sphere. Illustrative Mathematics Assessment Tasks Comparing Snow Cones Find the volume of a cone. Glasses Use volume formulas for cylinders, cones and spheres. Flower Vases Use volume formulas for cylinders, cones and spheres. EngageNY Grade 8, Module 5, Topic B, Lesson 10 Volume of Cylinders and Cones; Solve real-world volume problems Grade 8, Module 5, Topic B, Lesson 11 Volume of Spheres; Solve real-world volume problems IXL Volume of cylinders 9F3 Volume of cones YYR Volume of spheres QX7

Sample Problems:

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Unit 13: Statistics Standards Aligned Instruction 8 days April 6 – April 18 Intervention Days 2 days April 19 – April 20

The 2021-2022 school year we are transitioning from the Florida Mathematics Standards (MAFS) to the B.E.S.T. standards (MA).

In the unit guides we have identified which B.E.S.T. standard matches with which MAFS standard(s). Standards Content Limits

MA.8.DP.1.1 Given a set of real-world bivariate numerical data, construct a scatter plot or a line graph as appropriate for the context. • Clarification 1: Instruction includes recognizing similarities and

differences between scatter plots and line graphs, and on determining which is more appropriate as a representation of the data based on the context.

• Clarification 2: Sets of data are limited to 20 points.

• Data sets will include between 5 and 20 points, inclusive.

• Items will state whether a scatter plot or line graph is to be constructed based on the intent of the given context.

Calculator: NEUTRAL Context: REAL-WORLD

MA.8.DP.1.2 Given a scatter plot within a real-world context, describe patterns of association. • Clarification 1: Descriptions include outliers; positive or negative

association; linear or nonlinear association; strong or weak association.

• Items will not require the student to determine strong vs. weak association.

• Items will use wording of association exclusively when describing as linear, nonlinear, positive, or negative.

Calculator: NEUTRAL Context: REAL-WORLD

MA.8.DP.1.3 Given a scatter plot with a linear association, informally fit a straight line. • Clarification 1: Instruction focuses on the connection to linear

functions. • Clarification 2: Instruction includes using a variety of tools,

including a ruler, to draw a line with approximately the same number of points above and below the line.

• Items will not require the student to write or determine the equation of a line of fit.

Calculator: NEUTRAL Context: BOTH

MAFS.8.SP.1.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.

For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?

• Clarifications: Numbers in items must be rational numbers. Data given should include the grand total of the survey. Tables must not include more than two columns (plus category and total) and two rows (plus category and total).

This standard has been moved to Algebra 1 in the BEST Benchmarks, but still needs to be taught until the 2022-2023 school year.

Essential Vocabulary Vocabulary Definition/Description

Bivariate data Data for two variables (usually two types of related data). Example: Ice cream sales and the temperature of the day

Clustering When numerous points of data seem to be “gathered” around a particular value

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Correlation When two sets of data are strongly linked together we say they have a high correlation. Correlation can have a value:

• 1 is a perfect positive correlation • 0 is no correlation

- 1 is a perfect negative correlation Data A collection of facts, such as numbers, words, measurements, observations or

even just descriptions of things. Dependent variable The "output" value of a function. (It is called dependent because its value

depends on what you put into the function.) Independent variable An "input" value of a function. Line graph A graph with points connected by lines to show how something changes in

value: • as time goes by • or as something else changes.

Line of best fit A line on a graph showing the general direction that a group of points seem to follow.

Linear A pattern, or equation, that demonstrates, or results, in a straight line. Negative association (correlation)

As on data value increases, the other data set decreases in a set of bivariate data.

Non-linear A pattern, or equation, that does not show, or result, in a straight line Outlier Values that lie outside the other values. Think outliers = “lie out”side Positive association (correlation)

As on data value increases, so does the other in a set of bivariate data.

Scatter plot A graph of plotted points that show the relationship between two sets of data. Strong association (correlation)

The value of the correlation is near to 1 or -1, but not near 0 which indicates no association.

Weak association (correlation)

The value of the correlation gets closer to 0 (think between -0.5 and 0.5) and indicates a weak association/correlation between the two sets of data.

MA.8.DP.1.1 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Given a set of real-world bivariate numerical data, construct a scatter plot or a line graph as appropriate for the context.

MAFS.8.SP.1.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

Instructional Learning Objectives Instructional Resources Objective 1: Understand independent and dependent variables Objective 2: Understand how to construct a scatter plot within a context Objective 3: Understand the relationship of the bivariate data presented Objective 4: Construct a line graph to represent the given bivariate data

McGraw-Hill Course 3, Chapter 9: Lesson 1 EngageNY Grade 8, Module 6, Topic B, Lesson 6 Constructing Scatter Plots

Open Up Resources Grade 8, Unit 6: Associations in Data Lesson 1: Organizing Data Lesson 2: Plotting Data

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Objective 5: Appropriate label a scatter plot/line graph Objective 6: Using bivariate data construct a scatter plot Objective 7: Using bivariate data construct a line graph

Lesson 3: What a Point in a Scatter Plot Means Mathematics Formative Assessments (MFAS) Bungee Cord Data: Construct a scatterplot corresponding to a given set of data.

IXL CC.5 Create line graphs ERM CC.15 Create scatter plots AVL Khan Academy Constructing a scatterplot Bivarate date scatter plots and line graphs Virtual Nerd How do you make a scatter plot? Other Engaging Tasks Creating correlating and non-correlating graphs

Sample Problems: 1.) Jaylyn is collecting data about the relationship between grades in English and grades in mathematics. He represents the data using a scatter plot because he is interested if there is an association between the two variables without thinking of either one as an independent or dependent variable. Is Jaylyn’s reasoning correct? 2.) Samantha is collecting data on her weekly quiz grade in her social studies class. She represents the data using a line graph with time as the independent variable. Is Samantha’s reasoning correct? 3.) The table shows the numbers of students on a basketball team and the number of free throws each student made during practice. Using the graph below, construct a scatter plot. 4.) Tory is collecting information about dinosaurs, their length, and their respective weight. From the table of collected information, construct a scatter plot.

Length (feet)

28 50 79 100 100

Weight (tons)

9 9 33 50 60

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

MA.8.DP.1.2 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Given a scatter plot within a real-world context, describe patterns of association.

MAFS.8.SP.1.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

Instructional Learning Objectives Instructional Resources Objective 1: Identify negative and positive association Objective 2: Identify clusters Objective 3: Identify outliers Objective 4: Identify linear and non-linear associations Objective 5: Understand outliers, clusters, negative and positive association Objective 6: Recognize an association given a scatter plot Objective 7: Describe the associations given on a scatter plot

McGraw-Hill Course 3, Chapter 9: Lesson 1 IXL CC.16 Identify trends with scatter plots GZE CC.17 Make predictions with scatter plots CM7 DD.8 Outliers in scatter plots RP8

Khan Academy Interpreting Scatter Plots Exploring bivariate numerical data

EngageNY Grade 8, Module 6, Topic B, Lesson 7 Patterns in Scatter Plots

Open Up Resources Grade 8, Unit 6: Associations in Data Lesson 5: Describing Trends in Scatter Plots Lesson 7: Observing More Patterns in Scatter Plots Lesson 8: Analyzing Bivariate Data Lesson 9: Looking for Associations Lesson 10: Using Data Displays to Find Associations

Mathematics Formative Assessments (MAFS) Sleepy Statistics Describe the association between scores on the Epworth Sleepiness Scale and scores on the math test. Population Density Describe the relationship between population and land area. Infectious Statistics Describe the association between the passage of time and the number of bacteria. Cheesy Statistics Describe the association between time spent watching advertisements and the percent of each group willing to buy the company’s cheese crackers.

Illustrative Mathematics Assessment Tasks Birds’ Eggs Identify a correlation and use it to make interpolative predictions. Texting and Grades I Describe the relationship between number of text messages sent and GPA.

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Virtual Nerd What’s positive correlation?

Sample Problems: 1.) What type of association is shown in the scatter plot? A. a negative linear association B. a positive linear association C. a negative nonlinear association D. no association

2.) Which of the following patterns applies to the scatter plot shown? Select all that apply. A. Strong negative association B. Strong positive association C. No association D. Linear association E. Nonlinear association F. Outlier

3.) The scatter plot at right shows the average traffic

volume and average vehicle speed on a certain freeway for 50 days in 2018. Write a statement that best describes the relationship between average traffic volume and average vehicle speed.

4.) Which graph best shows a positive correlation between the number of hours studied and the test scores?

MA.8.DP.1.3 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Given a scatter plot with a linear association, informally fit a straight line. The BEST Benchmark does not explicitly state that students need to create/write the line of best fit, however it needs to be covered for the next two

MAFS.8.SP.1.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

school years as we are still tested on the MAFS standards.

Instructional Learning Objectives Instructional Resources Objective 1: Gather the points from a scatter plot Objective 2: Understand slope Objective 3: Determine the slope from a linear association Objective 4: Determine which line is a line of best fit Objective 5: Determine slope given two points from a scatter plot Objective 6: Write an equation of the line of best fit

McGraw-Hill Course 3, Chapter 9: Lesson 2 Engage NY Grade 8, Module 6, Topic B, Lesson 8 Informally fit a line to data in scatter plot Grade 8, Module 6, Topic C, Lesson 9 Informally fit a line to data in scatter plot Grade 8, Module 6, Topic C, Lesson 11 Scatter plots; Fit line to data; Interpret slope

Open Up Resources Grade 8, Unit 6: Associations in Data Lesson 4: Fitting a Line to Data Lesson 6: The Slope of a Fitted Line Mathematics Formative Assessments (MFAS) Two Scatterplots - Compare how well each line fits its set of data. Explain your reasoning. Three Scatterplots - Informally assess three lines fitted to data to determine which fit is the best. Line of Good Fit I - Fit a line to model the relationship between two quantitative variables and to assess how well that line fits the data. Line of Good Fit II - See description above. Illustrative Mathematics Assessment Tasks Hand Span and Height - Construct and Interpret Scatter plots by generating and recording data. Animal Brains - Create scatterplots and think critically about associations and outliers in data as well as informally fit a trend line to data. Laptop Battery Charge - Find and use a linear model answer this question. IXL DD.9 Scatter plots: line of best fit ZQ6

Khan Academy Estimating Lines of Best Fit Exploring bivariate numerical data Virtual Nerd How do you use a scatter plot to find a line of fit? How do you write and use a prediction equation? Engaging Task

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Line of Best Fit: Create 4 points that could generate a line of best fit with the equation y=-x+8.

Sample Problems: 1.) The table shows the number of Calories burned when walking laps around a track. Construct a scatter plot of the data and then draw a line of best represents the data.

2.) Which graph shows a line of best fit for the scatter plot?

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

3.) For which scatter plot would the line of best fit be represented by the equation 𝑦𝑦 = 1 2𝑥𝑥 + 2?

MAFS.8.SP.1.4 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards This MAFS standard has been moved up to Algebra 1 in the BEST Benchmarks. As such, it still has to be taught for the next two school years.

MAFS.8.SP.1.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.

Instructional Learning Objectives Instructional Resources Objective 1: Understand bivariate data can be displayed as a two-way table or a Venn diagram Objective 2: Accurate calculate percentages for relative frequencies Objective 3: Construct a two-way table Objective 4: Calculate relative frequencies (by row and column) Objective 5: Interpret data from a two-way table Objective 6: Interpret relative frequencies to determine and association between the two sets of data

McGraw-Hill Course 3, Chapter 9: Lesson 3 Khan Academy Two Way Tables IXL EE.4 Find probabilities using two-way frequency tables CRV Engage NY Grade 8, Module 6, Topic D, Lesson 13: Two-way tables, row and column relative frequencies Grade 8, Module 6, Topic D, Lesson 14: Association between two categorical values

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Mathematics Formative Assessments (MAFS) School Start Time: Interpret data given in a two-way table. Music and Sports: Construct a two-way frequency table given a set of raw data. Sibling and Pets: Interpret data given in a two-way table Two-Way Relative Frequency Table: Convert raw data to relative frequencies by both rows and columns given a two-way frequency table.

Illustrative Mathematics Assessment Tasks What’s your favorite Subject? Calculate appropriate relative frequencies using the given data Music and Sports: Investigate the association between whether a student plays a sport and whether he or she pays a musical instrument

MARS/Shell Testing a new product: Assess how well students can organize, represent and analyze bivariate categorical data in an appropriate way

Sample Problems: 1. There are 150 children at a summer camp and 71 signed up for swimming. There were a total of 62 children

that signed up for canoeing and 28 of them also signed up for swimming. Construct a two-way table summarizing the data.

2. Using the table below, calculate the relative frequencies by ROW.

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

Unit 14: Probability Standards Aligned Instruction 5 days April 21 – April 27 Intervention Days 2 days April 28 – April 29

The 2021-2022 school year we are transitioning from the Florida Mathematics Standards (MAFS) to the B.E.S.T. standards (MA).

In the unit guides we have identified which B.E.S.T. standard matches with which MAFS standard(s). Standards Content Limits

MA.8.DP.2.1 Determine the sample space for a repeated experiment. • Clarification 1: Instruction includes recording sample spaces

for repeated experiments using organized lists, tables or tree diagrams.

• Clarification 2: Experiments to be repeated are limited to tossing a fair coin, rolling a fair die, picking a card randomly from a deck with replacement, picking marbles randomly from a bag with replacement and spinning a fair spinner.

• Clarification 3: Repetition of experiments is limited to two times except for tossing a coin.

• Items may present sample spaces as an organized list, a table, or a tree diagram.

• Items including a deck of cards are not limited to a standards 52-card deck, and can include, but are not limited to, cards containing names, letters of the alphabet, a variety of colors, or the like.

• Items including a fair die are not limited to a standard 6-sided die and can include a variety of sides.

• Items including a fair die are not limited to including consecutive sequential numbers and can include repeated or not repeated, colors shapes, words, numbers, or the like.

Calculator: NEUTRAL Context: REAL-WORLD

MA.8.DP.2.2 Find the theoretical probability of an event related to a repeated experiment. • Clarification 1: Instruction includes representing probability as

a fraction, percentage or decimal. • Clarification 2: Experiments to be repeated are limited to

tossing a fair coin, rolling a fair die, picking a card randomly from a deck with replacement, picking marbles randomly from a bag with replacement and spinning a fair spinner.

• Clarification 3: Repetition of experiments is limited to two times except for tossing a coin.

• Items may present sample spaces as an organized list, a table, or a tree diagram.

• Items including a deck of cards are not limited to a standards 52-card deck, and can include, but are not limited to, cards containing names, letters of the alphabet, a variety of colors, or the like.

• Items including a fair die are not limited to a standard 6-sided die and can include a variety of sides.

• Items including a fair die are not limited to including consecutive sequential numbers and can include repeated or not repeated, colors shapes, words, numbers, or the like.

Calculator: NEUTRAL Context: REAL-WORLD

MA.8.DP.2.3 Solve real-world problems involving probabilities related to single or repeated experiments, including making predictions based on theoretical probability. • Clarification 1: Instruction includes making connections to

proportional relationships and representing probability as a fraction, percentage or decimal.

• Clarification 2: Experiments to be repeated are limited to tossing a fair coin, rolling a fair die, picking a card randomly from a deck with replacement, picking marbles randomly from a bag with replacement and spinning a fair spinner.

• Clarification 3: Repetition of experiments is limited to two times except for tossing a coin.

Example: If Gabriella rolls a fair die 300 times, she can predict that she will roll a 3 approximately 50 times since the theoretical probability is 1/6. Example: Sandra performs an experiment where she flips a coin three times. She finds the theoretical probability of landing on exactly one head as 3/8. If she performs this experiment 50 times (for a total of

• Probability will be represented using a fraction, percent, or decimal.

• Items including a deck of cards are not limited to a standards 52-card deck, and can include, but are not limited to, cards containing names, letters of the alphabet, a variety of colors, or the like.

• Items including a fair die are not limited to a standard 6-sided die and can include a variety of sides.

• Items including a fair die are not limited to including consecutive sequential numbers and can include repeated or not repeated, colors shapes, words, numbers, or the like.

• Descriptions representing an experiment are not limited to the repetition of two trials.

Calculator: NEUTRAL Context: REAL-WORLD

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

150 flips), predict the number of repetitions of the experiment that will result in exactly one of the three flips landing on heads.

Essential Vocabulary Vocabulary Definition/Description

Compound Event (click for video)

Two or more simple events. (tossing a coin and rolling a die)

Experimental probability Find the experimental probability of an event by repeating an experiment many times using the ratio P(event)= 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 𝑜𝑜𝑜𝑜 𝑡𝑡𝑡𝑡𝑛𝑛𝑛𝑛𝑡𝑡 𝑛𝑛𝑒𝑒𝑛𝑛𝑛𝑛𝑡𝑡 𝑜𝑜𝑜𝑜𝑜𝑜𝑛𝑛𝑛𝑛𝑡𝑡

𝑡𝑡𝑜𝑜𝑡𝑡𝑡𝑡𝑡𝑡 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 𝑜𝑜𝑜𝑜 𝑡𝑡𝑛𝑛𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡

Fair coin, fair die etc. A coin or die where all outcomes are equally likely. If a coin had two heads it would not be a fair coin.

Repeated experiment To repeat an experiment over and over (rolling a dice, flipping a coin, picking marbles)

Sample Space (click for video)

The set of all possible outcomes in an experiment.

Theoretical probability When all outcomes of an action are equally likely, P(event) = 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 𝑜𝑜𝑜𝑜 𝑜𝑜𝑡𝑡𝑒𝑒𝑜𝑜𝑛𝑛𝑡𝑡𝑛𝑛𝑡𝑡𝑛𝑛 𝑜𝑜𝑛𝑛𝑡𝑡𝑜𝑜𝑜𝑜𝑛𝑛𝑛𝑛𝑡𝑡 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 𝑜𝑜𝑜𝑜 𝑝𝑝𝑜𝑜𝑡𝑡𝑡𝑡𝑡𝑡𝑛𝑛𝑡𝑡𝑛𝑛 𝑜𝑜𝑛𝑛𝑡𝑡𝑜𝑜𝑜𝑜𝑛𝑛𝑛𝑛𝑡𝑡

Tree diagram Diagram that helps calculate the number of all possible outcomes of an event.

MA.8.DP.2.1 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Determine the sample space for a repeated experiment.

MAFS.7.SP.3.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

b. Represent sample spaces for compound events using methods such as organized lists, tables, and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.

Instructional Learning Objectives Instructional Resources Objective 1: Represent sample spaces by using an organized list. (Click on hyperlink for video) Objective 2: Represent a sample space by using a tree diagram. Objective 3: Represent a sample space using a table. Objective 4: Determine the possible outcomes of repeated experiments using fair coins, fair die, and fair spinners and randomly picking a card. Objective 5: Find probabilities of compound events using the sample space.

McGraw-Hill Course 2, Chapter 9 (Current 7th grade book) Lesson 3 Probability of Compound Events IXL EE.6 Compound events: find the number of outcomes P5R

Khan Academy Sample Spaces for Compound Events Die Rolling Probability Count Outcomes using Tree Diagrams Virtual Nerd Using Tree diagrams to count the number of outcomes in a sample space Nearpod

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Representing Sample Spaces Fishtank Learning Probability Open Educational Resources Compound Events and Sample Spaces Open Up Resources This is a free resource for teachers. An account is free to make and then you have access to lesson and resources. 7th Grade - Unit 8, Lesson 8: Keeping track of all possible outcomes

Sample Problems: What is the sample space of flipping a coin 3 times? Show your answer as a table, list or tree diagram.

MA.8.DP.2.2 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Find the theoretical probability of an event related to a repeated experiment.

MAFS.7.SP.3.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

Instructional Learning Objectives Instructional Resources Objective 1: Find the probability of a repeated event with replacement. Objective 2: Express the probability as a fraction, decimal or a percent

McGraw-Hill Course 2, Chapter 9 (Current 7th grade book) Inquiry Lab – Independent events Lesson 7 – Independent events IXL Probability of simple events Probability of compound events Khan Academy Probability of a compound event Open Up Resources This is a free resource for teachers. An account is free to make and then you have access to lesson and resources. 7th Grade - Unit 8, Lesson 9 Multi-step experiments Better Lessons Compound probability

Sample Problems: 1) A coin is tossed three times. Find the probability of getting at least two heads.

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

2) A die is thrown twice. What is the probability both numbers are prime? 3) A card is drawn from a deck of cards then replaced, then a second card is drawn from the deck. What is the

probability that both cards are Aces?

MA.8.DP.2.3 Connections between B.E.S.T. and Florida Standards

B.E.S.T. Florida Standards Solve real-world problems involving probabilities related to single or repeated experiments, including making predictions based on theoretical probability.

MAFS.7.SP.3.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but the probably not exactly 200 times. MAFS.7.SP.3.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

c. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

MAFS.7.SP.3.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

Instructional Learning Objectives Instructional Resources Objective 1: Use theoretical probability to predict the outcome of an experiment. Objective 2: Solve real world problems involving probability.

McGraw-Hill Course 2, Chapter 9 (Current 7th grade book) Lesson 2 IXL Make predictions (38C) Khan Academy Making predictions with probability

Pinellas County Schools GRADE 8 PRE-ALGEBRA 2021-2022

EngageNY Estimating probability Module 5, Topic B, Lesson 8 Estimating probability Module 5, Topic B, Lesson 9

Sample Problems: 1. If Matteo rolls a fair die 300 times, how many times will he roll a 3? 2. The theoretical probability for flipping a coin three times and landing on exactly one head is 3/8. If you

flipped your coin 150 times, theoretically, how many times you would land on exactly one head?