Pinellas County Schools 2019-2020
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 Numbers
15
8/19 – 9/9
Remediation/Intervention
3
9/10 – 9/12
Unit 2: Linear Equations in One Variable
13
9/13 – 10/1
Remediation/Intervention
3
10/2 – 10/4
Cycle 1 Assessment (Review and Units 1 & 2)
1
10/7 (9/30 – 10/11)
Unit 3: Linear Equations in Two Variables
15
10/8 – 10/29
Remediation/Intervention
3
10/30 – 11/1
Unit 4: Functions
12
11/4 – 11/19
Remediation/Intervention
3
11/20-11/22
Unit 5: Triangles and Pythagorean Theorem (Split Unit)
7
12/2 – 1/21
Midterm Exam (& Review) Units 1-4 & 8.G.1.5
1
12/11 – 12/20
Unit 5: Triangles and Pythagorean Theorem (Split Unit)
9
12/2 – 1/21
Remediation/Intervention
3
1/22 – 1/24
Unit 6: Transformations, Congruence & Similarity
17
1/27 – 2/19
Remediation/Intervention
3
2/20 – 2/24
Unit 7: Volume
Spring Break 3/14 – 3/23
14
2/25 – 3/13
Remediation/Intervention
3
3/24 – 3/26
Unit 8: Scatter Plots and Data Analysis
12
3/27 – 4/14
Remediation/Intervention
3
4/15 – 4/17
FSA Grade 8 Math
2
5/4 – 5/29
Pinellas County Schools
GRADE 8 PRE-ALGEBRA
2019-2020
1 2 3 1 2 3 4
4 5 6 7 8 9 10 MAFS.8.NS.1.1 MAFS.8.EE.1.2 MAFS.8.G.1.5 MAFS.8.G.2.7 5 6 7 8 9 10 11
11 12 13 14 15 16 17
MAFS.8.NS.1.2 MAFS.8.EE.1.3 MAFS.8.G.2.6 MAFS.8.G.2.8 12 13 14 15 16 17 18
18 19 20 21 22 23 24
MAFS.8.EE.1.1 MAFS.8.EE.1.4 19 20 21 22 23 24 25
25 26 27 28 29 30 31 26 27 28 29 30 31
MAFS.8.G.1.1 MAFS.8.G.1.4
1 2 3 4 5 6 7
MAFS.8.EE.3.7 MAFS.8.G.1.2 MAFS.8.G.1.5 1
8 9 10 11 12 13 14
MAFS.8.G.1.3 MAFS.8.EE.2.6 2 3 4 5 6 7 8
15 16 17 18 19 20 21 9 10 11 12 13 14 15
22 23 24 25 26 27 28 16 17 18 19 20 21 22
29 30
MAFS.8.G.3.9 23 24 25 26 27 28 29
MAFS.8.EE.2.5 MAFS.8.EE.3.8
1 2 3 4 5
MAFS.8.EE.2.6 1 2 3 4 5 6 7
6 7 8 9 10 11 12
MAFS.8.SP.1.1 MAFS.8.SP.1.3 8 9 10 11 12 13 14
13 14 15 16 17 18 19
MAFS.8.SP.1.2 MAFS.8.SP.1.4 15 16 17 18 19 20 21
20 21 22 23 24 25 26
MAFS.8.F.1.1 MAFS.8.F.2.4 22 23 24 25 26 27 28
27 28 29 30 31
MAFS.8.F.1.2 MAFS.8.F.2.5 29 30 31
MAFS.8.F.1.3
1 2 1 2 3 4
3 4 5 6 7 8 9 5 6 7 8 9 10 11
10 11 12 13 14 15 16
MAFS.8.G.1.5 MAFS.8.G.2.7 12 13 14 15 16 17 18
17 18 19 20 21 22 23
MAFS.8.G.2.6 MAFS.8.G.2.8 19 20 21 22 23 24 25
24 25 26 27 28 29 30 26 27 28 29 30
1 2 3 4 5 6 7 1 2
8 9 10 11 12 13 14 3 4 5 6 7 8 9
15 16 17 18 19 20 21 10 11 12 13 14 15 16
22 23 24 25 26 27 28 17 18 19 20 21 22 23
29 30 31 24 25 26 27 28 29 30
31
1 2 3 4 5 6
January 2020
February 2020
March 2020
April 2020
Building Community in the Math Classroom
Re-Building Community in the Math Classroom
Unit 1: Real Numbers
Unit 2: Linear Equations in One Variable
Cycle 1 Assessment (on Units 1 & 2)
August 2019
September 2019
October 2019
November 2019
December 2019
Unit 3: Linear Equations in Two Variables
Unit 4: Functions
Unit 5: Triangles and Pythagorean Theorem
Midterm Exam (& Review) (on Units 3 & 4)
June 2020
May 2020
Dec. 11-Dec. 20
Unit 5: Triangles and Pythagorean Theorem
Unit 6: Transformations, Congruence & Similarity
Unit 7: Volume
Unit 8: Scatter Plots and Data Analysis
FSA Testing Window
May 4-29, 2019
INTERVENTION DAYS 9/10-9/12
INTERVENTION DAYS 1/22-1/24
INTERVENTION DAYS 2/20-2/24
INTERVENTION DAYS 3/24-2/26
INTERVENTION DAYS 4/15-4/17
INTERVENTION DAYS 11/20-11/22
INTERVENTION DAYS 10/30-11/1
INTERVENTION DAYS 10/2-10/4
Sept. 30-Oct. 11 (Take as early as possible)
Pinellas County Schools GRADE 8 PRE-ALGEBRA 2019-2020
Semester 1
Unit 1: Real Numbers
15 days: 8/19-9/9
INTERVENTION/REMEDIATION: 3 days, 9/10-9/12
Standards/Learning Goals:
Content Limits, Assessment Types, Calculator
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.
All irrational numbers excluding e.
Only rational numbers with repeating decimal
expansions up to thousandths may be used.
Calculator: NO
Editing Task Choice
Equation Editor
Hot Text
Matching Item
Multiple Choice
Multiselect
Open Response
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.,
. For example, by truncating the decimal expansion of
is
between 1 and 2, then between 1.4 and 1.5, and explain how to
continue on to get better approximations.
All real numbers excluding e.
Irrational expressions should only use one
operation.
Calculator: NO
Equation Editor
GRID
Multiple Choice
Multiselect
Open Response
MAFS.8.EE.1.1 Know and apply the properties of integer exponents
to generate equivalent numerical expressions. For example,
.
Exponents must be integers.
Bases must be whole numbers
Variables may not be used.
Calculator: NO
Equation Editor
GRID
Matching Item
Multiple Choice
Multiselect
MAFS.8.EE.1.2 Use square root and cube root symbols to represent
solutions to equations of the form
and
, where p is a
positive rational number. Evaluate square roots of small perfect
squares and cube roots of small perfect cubes. Know that
is
irrational.
Square roots and cube roots may be used to
represent solutions to equations.
Radicands may be rational or irrational.
Radicands may not include variables.
Calculator: NEUTRAL
Equation Editor
Matching Item
Multiple Choice
Multiselect
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 times
and the population of the world as 7 times
, and
determine that the world population is more than 20 times larger.
N/A
Calculator: NO
Editing Task Choice
Equation Editor
Hot Text
Multiple Choice
Open Response
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.
N/A
Calculator: NO
Editing Task Choice
Equation Editor
Hot Text
Matching Item
Multiple Choice
Open Response
Open Up Resources Lessons
Grade 8, Unit 7: Exponents and Scientific Notation
Pinellas County Schools GRADE 8 PRE-ALGEBRA 2019-2020
Lesson 1: Exponent Review
Lesson 2: Multiplying Powers of Ten
Lesson 3: Powers of Powers of 10
Lesson 4: Dividing Powers of 10
Lesson 5: Negative Exponents with Powers of 10
Lesson 6: What about Other Bases?
Lesson 7: Practice with Rational Bases
Lesson 8: Combining Bases
Lesson 9: Describing Large and Small Numbers Using Powers of 10
Lesson 10: Representing Large Numbers on the Number Line
Lesson 11: Representing Small Numbers on the Number Line
Lesson 12: Applications of Arithmetic with Powers of 10
Lesson 13: Definition of Scientific Notation
Lesson 14: Multiplying, Dividing, and Estimating with Scientific Notation
Lesson 15: Adding and Subtracting with Scientific Notation
Grade 8, Unit 8: Pythagorean Theorem and Irrational Numbers
Lesson 14: Decimal Representations of Rational Numbers
Lesson 15: Infinite Decimal Expansions
Decoded Standard
MAFS.8.NS.1.1
Students expand their knowledge of the Real Number System to include irrational numbers. A diagram shows the
relationship of the subsets:
see image on page 71 of the Common Core Mathematics Companion
An irrational number is a decimal whose expansion does not terminate or repeat. Irrational numbers cannot be written in
fraction form. Using decimal expressions, students compare rational numbers and irrational numbers to show that rational
number expansion repeat and irrational numbers expansions do not. The notation “…” means “continues indefinitely
without repeating.” For example,
is a ration number that repeats but does not repeat.
To convert a decimal expansion into a fraction:
Change
to a fraction
1. Let
2. Multiply both sides so that the repeating digits will be in front of the decimal. In this case, one digit repeats so
both sides are multiplied by 10, giving
3. Subtract the original equation from the new equation.
𝑥
4. Solve the equation by dividing both sides of the equation by 9.
5.
(Common Core Mathematics Companion, Pg. 71)
Instructional Resources
Formative Tasks
Mathematics Formative Assessments (MFAS)
Rational Numbers Identify rational numbers from a list of real
numbers.
Fraction to Decimal Conversion Given a fraction to convert
to a decimal; determine if the decimal repeats.
Decimal to Fraction Conversion Given several terminating
and repeating decimals to convert to fractions.
Lesson Resources
Engage NY
Grade 8, Module 7, Topic B, Lesson 8 Decimal
expansion
McGraw-Hill
Course 3, Chapter 1
Lesson 1
Pinellas County Schools GRADE 8 PRE-ALGEBRA 2019-2020
Illustrative Mathematics
Converting Decimal Representations of Rational
Numbers to Fraction Representations Convert repeating
decimals into fractions
Repeating or Terminating? Understand why terminating
decimal numbers can also be written as repeating decimals where the
repeating part is all 9’s.
Decoded Standard
MAFS.8.NS.1.2
Students compare irrational numbers and locate them on a number line by finding their rational
approximations. Find rational approximations by creating lists of numbers by answering the following question:
Between which two numbers will you find
? Since
= 1 and
=4, it is between 1 and 2. To be more
precise, it is closer to 1 or 2? Systematically square 1.1, 1.2, 1.3, 1.4….. 1.9. Between which two numbers do
you find 2? Repeat the process until the degree of precision you are seeking.
Instructional Resources
Formative Tasks
Mathematics Formative Assessments (MFAS)
Approximating Irrational Numbers Plot the square root
of eight on three number lines, scaled to progressively more
precision.
Locating Irrational Numbers Graph three different
irrational numbers on number lines.
Comparing Irrational Numbers Estimate the value of
several irrational numbers using a calculator and order them on a
number line.
The Irrational Beauty of the Golden Ratio Find and
interpret lower and upper bounds of an irrational expression using a
calculator.
Illustrative Mathematics
Comparing Rational and Irrational Numbers
Compare rational and irrational numbers without a calculator
Irrational Numbers on the Number Line Label
irrational numbers on a number line
Engaging Tasks
Decimal Approximations of Roots - Open Middle
Rational and Irrational Roots - Open Middle
Number 18 – Which One Doesn’t Belong
Lesson Resources
Engage NY
Grade 8, Module 7, Topic B, Lesson 11 Decimal
expansion of roots
Grade 8, Module 7, Topic B, Lesson 12 Decimal
expansions of fractions
Grade 8, Module 7, Topic B, Lesson 13 Compare and
order rational approximations
MARS/Shell
Rational and Irrational Numbers 2 Understand the
properties of rational and irrational number.
McGraw-Hill
Course 3, Chapter 1
Lesson 9; Lesson 10
Decoded Standard
MAFS.8.EE.1.1
Students learn how to compute using integer exponents building on their earlier experiences with adding and subtracting
integers. For any non-zero real numbers a and b and integers n and m, the properties of integer exponents are as follows:
1.
=
2.
3.
4.
5.
6.
(Common Core Mathematics Companion, Pg. 118)
Pinellas County Schools GRADE 8 PRE-ALGEBRA 2019-2020
Formative Tasks
Mathematics Formative Assessments (MFAS)
Exponents Tabled Complete a table of powers of three and
provide an explanation of zero powers.
Multiplying and Dividing Integer Exponents Apply the
properties of integer exponents to generate equivalent numerical
expressions.
Illustrative Mathematics
Raising to the zero and negative powers Use the
quotient rule of exponents to help explain how to define the
expression c
k
Engaging Tasks
How Can We Make Stronger Passwords Determine
how long it will take to crack your password.
Lesson Resources
Engage NY
Grade 8, Module 1, Topic A, Lesson 1 Understanding
exponential notation
Grade 8, Module 1, Topic A, Lesson 2 Simplifying
exponential expressions
Grade 8, Module 1, Topic A, Lesson 3 Powers of powers
Grade 8, Module 1, Topic A, Lesson 4 Base raised to
the zero power
Grade 8, Module 1, Topic A, Lesson 5 Negative
exponents
Grade 8, Module 1, Topic A, Lesson 6 Integer exponents
MARS/Shell
Applying Properties of Exponents Apply the properties of
exponents by a matching activity.
McGraw-Hill
Course 3, Chapter 1
Lesson 3, 4 and 5
Decoded Standard
MAFS.8.EE.1.2
Students learn that squaring and cubing numbers are the inverse operations to finding square and cube roots. This
standard works with perfect squares and perfect cubes, and students will begin to recognize those numbers. Equations
should include rational numbers such as
=
and
=
and fractions where both the numerator and denominator are
perfect squares or cubes:
=
=
x =
Square roots can be positive or negative because 2 x 2 = 4 and -2 x -2 = 4= 4.
(Common Core Mathematics Companion, Pg. 119)
Instructional Resources
Formative Tasks
Mathematics Formative Assessments (MFAS)
The Root of the Problem Evaluate perfect square roots and
perfect cube roots.
Dimension Needed Solve problems involving square roots and
cube roots.
Roots and Radicals Use square root and cube root symbols to
represent the real solutions of each equation. Then evaluate any
square roots of perfect squares and cube roots of perfect cubes.
Indicate if any of your solutions are irrational.
Lesson Resources
Engage NY
Grade 8, Module 7, Topic A, Lesson 2 Square and cube
roots
McGraw-Hill
Course 3, Chapter 1
Lesson 8
Decoded Standard
MAFS.8.EE.1.3
This standard emphasizes scientific notation. Students write very large and very small numbers in scientific notation using
positive and negative exponents. For example 123,000 written in scientific notation is 1.23 x
, and 0.008 written in
scientific notation is 8 x
. When mastered, students use the skill to determine how many times larger (or smaller) one
number written in scientific notation is than another. To compare, if the exponent increases by 1, the value increases 10
Pinellas County Schools GRADE 8 PRE-ALGEBRA 2019-2020
times. In the example of the U.S. and world populations, the exponent increased by 1, and the 7 is a little more than 2
times 3. So 2 x 10 makes for 20 times larger.
(Common Core Mathematics Companion, Pg. 120)
Instructional Resources
Formative Tasks
Mathematics Formative Assessments (MFAS)
Estimating Extreme Values Estimate each value described
below by writing it in the form
where a is a single digit
number and n is an integer.
How Many Times Given pairs of numbers written in
exponential form to compare them multiplicatively.
Compare Numbers Given pairs of numbers written in scientific
notation compare them multiplicatively.
Order Matters Given pairs of numbers written in the form of an
integer times a power of 10. Then compare the numbers in each pair
using the inequality symbols.
Illustrated Mathematics
Ant and Elephant Compare very small and very large quantities
using metric system
Lesson Resources
Engage NY
Grade 8, Module 1, Topic B, Lesson 1 Powers of 10
Grade 8, Module 1, Topic B, Lesson 2 Translating
scientific notation and standard form
Grade 8, Module 1, Topic B, Lesson 13 Comparing
numbers in scientific notation
MARS/Shell
Applying Properties of Exponents Estimating length
using scientific notation.
McGraw-Hill
Course 3, Chapter 1
Lesson 6 (supplement to express how many times larger)
Decoded Standard
MAFS.8.EE.1.4
This standard builds on previous standards as now students use what they know about scientific notation and properties
of integer exponents to solve problems. Quantities in the problems can be expressed in scientific notation and decimal
form. Students focus on the size of the measurement to determine which units are appropriate for the context such as
millimeters for very small quantities. This standard also calls for students to use technology and be able to interpret the
scientific notation used. The teacher needs to check the class calculators to be familiar with the notation used by those
particular calculators as the notation used by calculators to express scientific notation is not standard.
(Common Core Mathematics Companion, Pg. 121)
Instructional Resources
Formative Tasks
Mathematics Formative Assessments (MFAS)
Mixed Form Operations Given word problems with numbers
in both standard and scientific notation to solve problems using
various operations.
Sums and Differences in Scientific Notation Add and
subtract numbers given in scientific notation in real-world contexts.
Scientific Multiplication and Division Multiply and
divide numbers given in scientific notation in real-world contexts.
Scientific Calculator Display Given examples of calculator
displays and asked to convert the notation in the display to both
scientific notation and standard form.
Engaging Tasks
Scientific Notation – Math Mistakes
Lesson Resources
Engage NY
Grade 8, Module 1, Topic B, Lesson 9 Operations with
numbers in scientific notation
Grade 8, Module 1, Topic B, Lesson 10 Operations
with numbers in scientific notation
Grade 8, Module 1, Topic B, Lesson 11 Operations
with numbers in scientific notation
Grade 8, Module 1, Topic B, Lesson 12 Measurement
McGraw-Hill
Course 3, Chapter 1
Lesson 7
Pinellas County School GRADE 8 PRE-ALGEBRA 2019-2020
Semester 1
Unit 2: Linear Equations in One Variable
13 days: 9/13-10/1
INTERVENTION/REMEDIATION: 3 days, 10/2-10/4
Standards/Learning Goals:
Content Limits, Assessment Types,
Calculator
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 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.
Numbers in items must be rational
numbers.
Calculator: YES
Equation Editor
GRID
Matching Item
Multiple Choice
Multiselect
Open Response
Open Up Resources Lessons
Grade 8, Unit 2: Dilations, Similarity, and Introducing Slope
Lesson 10: Meet Slope
Lesson 11: Writing Equations for Lines
Lesson 12: Using Equations for Lines
Grade 8, Unit 3: Linear Relationships
Lesson 1: Understanding Proportional Relationships
Lesson 2: Graphs of Proportional Relationships
Lesson 3: Representing Proportional Relationships
Lesson 4: Comparing Proportional Relationships
Lesson 5: Introduction to Linear Relationships
Lesson 6: More Linear Relationships
Lesson 7: Representations of Linear Relationships
Lesson 8: Translating to
Lesson 9: Slopes Don’t Have to be Positive
Lesson 10: Calculating Slope
Lesson 11: Equations of All Kinds of Lines
Decoded Standard
MAFS.8.EE.3.7
This standard has students solving linear equations. It is explained by 8.EE.3.7a and b. It is best to teach a and b together
so that they are not considered isolated skills.
These standards provide the foundation for all future work with linear equations. Students solve equations that have one,
zero, or infinitely many solutions and relate those solutions to the context. If the solution is in the form , there is only
one solution. If , there are infinitely many solutions. If results (where a and b are different numbers), there are
no solutions.
Linear equations can have fractions and decimals as coefficients and can be solved by expanding expressions with the
distributive property and/or collecting like terms. (Common Core Mathematics Companion, Pg. 128)
Instructional Resources
Formative Tasks
Mathematics Formative Assessments (MFAS)
Counting Solutions Worksheet includes three equations
where students identify whether there is one solution, no
solution, or infinitely many solutions.
Lesson Resources
Engage NY
Grade 8, Module 4, Topic A, Lesson 3 Solving equations with
variables on both sides
Pinellas County School GRADE 8 PRE-ALGEBRA 2019-2020
Equation Prototypes Worksheet includes three
questions where students are to create equations with one
solution, no solution, and infinitely many solutions.
Linear Equations I Students are to solve one linear
equation with only one variable that involves rational numbers
(fractions).
Linear Equations II Students are to solve one linear
equation with only one variable that involves rational
coefficients (decimals) and distributive property.
Linear Equations III Students are to solve a linear
equation in one variable with rational coefficients and variables
on both sides of the equation.
Engaging Tasks
Linear Equations with One Solutions Create a
linear equation with one solution – Open Middle
One Solution, No Solutions, Infinite Solutions
– Open Middle
Solving Equations – Math Mistakes
Solving Systems Algebraically – Math Mistakes
Number 17 – Which One Doesn’t Belong
Grade 8, Module 4, Topic A, Lesson 4 Solving equations with
rational coefficients and variables on both sides
Grade 8, Module 4, Topic A, Lesson 6 Solving equations with
rational coefficients, distributive property and variables on both sides
Grade 8, Module 4, Topic A, Lesson 7 Understanding the
conditions for a=a, a=b and x=a
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.)
Classifying Solutions to Systems of Equations . Tasks require
students to classify solutions that are represented graphically and use
substitution to complete a table of values for linear equations.
McGraw-Hill
Course 3, Chapter 2
Inquiry Lab: Equations with Variables on Each Side; Lesson 4 and 5
Pinellas County Schools GRADE 8 PRE-ALGEBRA 2019-2020
Semester 1
Unit 3: Linear Equations in Two Variables
15 days: 10/8-10/29
INTERVENTION/REMEDIATION: 3 days, 10/30-11/1
Standards/Learning Goals:
Content Limits, Assessment Types, Calculator
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 graph to a distance-time
equation to determine which of two moving objects has greater
speed.
Numbers in items must be rational numbers
Calculator: YES
Equation Editor
GRID
Matching Item
Multiple Choice
Multiselect
Open Response
MAFS.8.EE.2.6 Use similar triangles to explain why the slope m is
the same distance between 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.
All triangles must be right triangles and on a
coordinate grid.
Numbers in items must be rational numbers.
Functions must be linear.
Calculator: YES
Editing Task Choice
Equation Editor
GRID
Hot Text
Matching Item
Multiple Choice
Multiselect
Open Response
Table Item
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.
c. 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.
Numbers in items must be rational numbers.
Coefficients of equations in standard form must
be integers.
Items written for MAFS.8.EE.3.8a must include the
graph or the equations.
Equations in items written for MAFS.8.EE.3.8a
must be given in slope-intercept form.
Calculator: YES
Editing Task Choice
Equation Editor
GRID
Hot Text
Matching Item
Multiple Choice
Open Response
Open Up Resources Lessons
Grade 8, Unit 3: Linear Relationships
Lesson 12: Solutions to Linear Equations
Lesson 13: More Solutions to Linear Equations
Grade 8, Unit 4: Linear Equations and Linear Systems
Lesson 1: Number Puzzles
Lesson 2: Keeping the Equation Balanced
Lesson 3: Balanced Moves
Lesson 4: More Balanced Moves
Lesson 5: Solving Any Linear Equation
Lesson 6: Strategic Solving
Lesson 7: All, Some, or No Solutions
Pinellas County Schools GRADE 8 PRE-ALGEBRA 2019-2020
Lesson 8: How Many Solutions?
Lesson 9: When Are They the Same
Lesson 10: On or Off the Line?
Lesson 11: On Both of the Lines
Lesson 12: Systems of Equations
Lesson 13: Solving Systems of Equations
Lesson 14: Solving More Systems
Lesson 15: Writing Systems of Equations
Lesson 16: Solving Problems with Systems of Equations
Decoded Standard
MAFS.8.EE.2.5
Students build on their work from Grade 6 with unit rates and their work with proportional relationships in Grade 7 to
compare graphs, tables, and equations of liner (proportional) relationships. Students identify the unit rate as slope in
graphs, tables, and equations to compare proportional relationships presented using different representations. For
example, compare the unit rate in a problem about a phone bill presented in graphic form on a Cartesian plane to a phone
bill from a different company where the unit rate can be found represented in an equation or table. (Common Core
Mathematics Companion, Pg. 123)
Instructional Resources
Formative Tasks
Mathematics Formative Assessments (MFAS)
Interpreting Slope Using a worksheet, graph a proportionate
relationship (from a table of values), find and interpret slope.
Proportional Paint Interpret a graph through a worksheet
including three questions (identify unit rate, find slope, and describe
how they are related).
Compare Slopes Identify, describe, and compare the slopes of two
proportional relationships given the graph of one and the equation of
the other.
Illustrative Mathematics
Who has the best job? Compare the rate of change of two
functions displayed as a table and an equation.
Peaches and Plums Reason about the relative costs per pound of
the two fruits without actually knowing what the costs are.
Lesson Resources
Engage NY
Grade 8, Module 4, Topic B, Lesson 11 Constant rate
problems displayed in a graph and a table
MARS/Shell
Buying cars Students will create, compare, and evaluate different
representations of functions.
Defining Lines by Points, Slopes and Equations Find
slopes and equations using graphs and use slopes and y intercepts to
derive equations
McGraw-Hill
Course 3, Chapter 3
Lesson 1
Decoded Standard
MAFS.8.EE.2.6
Students gain additional knowledge about slope in this standard as they use similar triangles to explain how the slope m of
a line is the same between any two points on a given non-vertical line. Students understand positive/negative slopes, 0
slope, and undefined slopes. Through the use of similar triangles, teachers lead students to derive the general equation
(𝑦 = 𝑚𝑥 + 𝑏) of a line and discover that m is the slope and b is the y-intercept. (Common Core Mathematics Companion,
Pg. 124)
The similarity portion of this standard will be addressed in Unit 6.
Instructional Resources
Formative Tasks
Mathematics Formative Assessments (MFAS)
Slope Triangles Use similar triangles to explain why the slope is
the same regardless of the points used to calculate it (worksheet uses
proportionality of line segments to help students visualize concept).
Deriving Lines II Students are asked to derive one general
equation of a line (using the slope formula) with a y-intercept of (0,b).
Lesson Resources
Engage NY
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
Pinellas County Schools GRADE 8 PRE-ALGEBRA 2019-2020
Illustrative Mathematics
Slopes between points on a line Help students
understand why the calculated slope will be the same for any two points
on a given line.
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
Grade 8, Module 4, Topic C, Lesson 23 Solving systems
with equations in different forms
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
Course 3, Chapter 3
Lesson 4
Decoded Standard
MAFS.8.EE.3.8
This standard has students solving simultaneous linear equations. It is explained by 8.EE.3.8a-c. It is best to consider a, b,
and c together as they are not isolated skills.
Students will understand that points of intersection are the solutions to pairs of simultaneous linear equations (also known
as systems of linear equations). Students will solve systems graphically, algebraically, and by inspection. Examples in this
standard are in real-world contexts and mathematical problems. (Common Core Mathematics Companion, Pg. 129)
Instructional Resources
Formative Tasks
Mathematics Formative Assessments (MFAS)
Identify the Solution Two graphs are given; students are to
identify the solutions of the system and justify their answer.
Solving Systems of Linear Equations Three problems are
given; students are asked to solve each algebraically (equations are
written in both standard form and slope-intercept form).
Solving Systems of Linear Equations by Graphing
Solve one system of equation problem graphically (written in slope-
intercept form), write the solution as an ordered pair and explain why it
is the solution.
How Many Solutions? Determine the number of solutions for
each of the four systems of linear equations without solving (standard
form and slope-intercept form) and justify the answer.
Writing System Equations Two word problems are given.
Students are asked to write a system of linear equations that could be
used to solve them.
System Solutions One word problem (real world context) with
both equations provided. Students are to solve the system of linear
equations (elimination or substitution).
Engaging Tasks
Candy and Chips Solve the system to determine the cost of a new
order of chips and candy.
Solutions of Two Linear Equations Given a graphic, provide
4 points that represent 2 distinct lines
Lesson Resources
Engage NY
Grade 8, Module 4, Topic D, Lesson 24 Intro to Systems of
Equations
Grade 8, Module 4, Topic D, Lesson 25 Solving systems by
graphing
Grade 8, Module 4, Topic D, Lesson 26 Solving systems
with parallel lines
Grade 8, Module 4, Topic D, Lesson 27 Solving systems
with no solution
Grade 8, Module 4, Topic D, Lesson 28 Solving systems by
elimination and substitution
MARS/Shell
Solving Real Life Problems: Baseball Jerseys Tasks
require students to select appropriate mathematical methods to
interpret and evaluate data generated and identify a break-even point.
McGraw-Hill
Course 3, Chapter 3
Lesson 7
Pinellas County Schools GRADE 8 PRE-ALGEBRA 2019-2020
Create a System of Equations, Given 1 Equation and
the Solution Write linear equations so that the solution of the
system of that line and equation is a particular point.
System of Equations, Special Case Infinitely Many
Solutions Fill in the boxes so that there are infinitely many solutions
to the system
Systems of Equations, Special Case No Solution Fill in
the boxes so that there is no solution to the system
Solve Linear Equations with Special Cases Complete each
equation with the given number of solutions
Pinellas County Schools GRADE 8 PRE-ALGEBRA 2019-2020
Semester 1
Unit 4: Functions
12 days: 11/4-11/19
INTERVENTION/REMEDIATION: 3 days, 11/20-11/22
Standards/Learning Goals:
Content Limits, Assessment Types, Calculator
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.
Function notation may not be used.
Nonlinear functions may be included for
identifying a function.
Calculator: NEUTRAL
Editing Task Choice
Equation Editor
GRID
Hot Text
Multiple Choice
Multiselect
Open Response
Table Item
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.
Function notation is not used.
Functions must be linear.
Calculator: YES
Editing Task Choice
Equation Editor
GRID
Hot Text
Matching Item
Multiple Choice
Multiselect
Open Response
Table Item
MAFS.8.F.1.3 Interpret the equation as defining a
linear function, whose graph is a straight line; give examples of
functions that are not linear. For example, the function
giving the area of a square as a function of its side length is not
linear because its graph contains the points
,
which are not on a straight line.
Function notation may not be used.
Calculator: YES
Editing Task Choice
Equation Editor
GRID
Hot Text
Matching Item
Multiple Choice
Multiselect
Open Response
Table Item
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.
Function notation may not be used.
Functions must be linear.
Rate of change must be simple fractions up to
tenths.
Calculator: NEUTRAL
Equation Editor
GRID
Matching Item
Multiple Choice
Multiselect
Open Response
Table Item
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
Linear or nonlinear relationships may use any of
the four quadrants.
Graph descriptions move from left to right.
Functional relationships must be continuous.
Pinellas County Schools GRADE 8 PRE-ALGEBRA 2019-2020
graph that exhibits the qualitative features of a function that has
been described verbally.
Calculator: NEUTRAL
Editing Task Choice
Equation Editor
GRID
Hot Text
Matching Item
Multiple Choice
Multiselect
Open Response
Table Item
Open Up Resources Lessons
Grade 8, Unit 5: Functions and Volume
Lesson 1: Inputs and Outputs
Lesson 2: Introduction to Functions
Lesson 3: Equations for Functions
Lesson 4: Tables, Equations, and Graphs of Functions
Lesson 5: More Graphs of Functions
Lesson 6: Even More Graphs of Functions
Lesson 7: Connecting Representations of Functions
Lesson 8: Linear Functions
Lesson 9: Linear Models
Lesson 10: Piecewise Linear Functions
Decoded Standard
MAFS.8.F.1.1
This standard is the students’ introduction to functions and involves the definition of function as a rule that assigns to each
input exactly one output. Students are not required to use or recognize function notation at this grade but will be able to
identify functions using tables, graphs, and equations. A relationship is not a function when there is more than one y-value
associated with any x-value. Using the definition, an example of a table that does not represent a function is as follows:
See tables on page 139 of the Common Core Mathematics Companion
(Common Core Mathematics Companion, Pg. 139)
Instructional Resources
Pinellas County Schools GRADE 8 PRE-ALGEBRA 2019-2020
Formative Tasks
Mathematics Formative Assessments (MFAS)
What is a Function? Definition including important properties.
Identifying Algebraic Functions Determine if each of three
equations represents a function.
Recognizing Functions Determine whether or not each of two
graphs represent functions.
Tabulating Functions Determine whether or not tables of
ordered pairs represent functions.
Illustrative Mathematics Assessment Tasks
Foxes and Rabbits Illustrates examples of functions as well as
relationships that are not functions.
US Garbage, Version 1 Describing a linear function.
Introduction to Linear Functions Explore the differences
between linear and non-linear functions.
Engaging Tasks
Figure This! Double or Not Would you rather work 7 days at
$20 per day or be paid $2 for the first day and have your salary double
every day for a week?
25 Billion Apps When should you start bombarding the App Store
with purchases if you want to win?
Tables of Values: Not a Function Create a table of values
that is not a function
Tables of Values: Function Create a table of values that is a
function
Lesson Resources
Engage NY
Grade 8, Module 5, Topic A, Lesson 2 Expressing
functions by rule, and when input is used with the formula, the
outcome is the output.
Grade 8, Module 5, Topic A, Lesson 6 Determine if a
function is linear and interpret the equation y=mx+b as a linear
function
McGraw-Hill
Course 3, Chapter 4
Lesson 2
Decoded Standard
MAFS.8.F.1.2
For this standard students will compare the properties of functions. One property of functions is slope. When students are
given two different functions, each represented in a different form (algebraically, graphically, in a table, or by a verbal
description), students should be able to determine which function has the greater slope. An example follows:
Ruth starts with a $50 gift card for Walmart. She spends $5.50 per week to buy cat food. Let y be the amount left on the
card and x represent the number of weeks.
x
y
0
50
1
44.5
2
39.00
3
33.50
4
28.00
Boyce rents bikes for $5 an hour. He also collects a non-refundable fee of $10.00 for a rental to cover wear and tear. Write
the rule for the total cost (c) of renting a bike as a function of the number of hours (h) rented.
Solution: Ruth’s story is an example of a function with a negative slope. The amount of money left on the card decreases
each week. The graph has a negative slope of -5.5, which is the amount the card balance decreases every time Ruth buys
cat food.
Boyce’s bike rental is an example of a function with a positive slope. This function has a positive slope of 5, which is the
amount to rent a bike for an hour. An equation for Boyce’s bikes could be .
(Common Core Mathematics Companion, Pg. 140)
Pinellas County Schools GRADE 8 PRE-ALGEBRA 2019-2020
Instructional Resources
Formative Tasks
Mathematics Formative Assessments (MFAS)
Innovative Functions Compare the rates of change of two functions
presented in different forms (an expression and a table) within a real-
world context.
Speed Reading Compare the rates of change of two functions
presented in different forms (an expression and a table) within a real-
world context.
Competing Functions Recognize and compare the initial values of
two functions represented in different ways.
This House is Mine! Compare a specific value of two functions given
in different forms (a graph and a verbal description) within a real-world
context.
Illustrative Mathematics Assessment Tasks
Battery Charging Verbal and numerical descriptions of battery life as
a function of time.
Engaging Tasks
Comparing Functions Generate five ordered pairs that represent
a linear function that has a greater rate of change than the graph.
Lesson Resources
Engage NY
Grade 8, Module 5, Topic A, Lesson 7 Compare 2
functions in different way
McGraw-Hill
Course 3, Chapter 4
Lesson 2
Decoded Standard
MAFS.8.F.1.3
In this standard students become familiar with the equation as defining a linear function that will graph as a
straight line. Students distinguish between linear (functions that graph into a straight line) and nonlinear functions
(functions that do not graph into a straight line such as a curve). Note that standard form and point-slope for are not
studied in this grade. (Common Core Mathematics Companion, Pg. 141)
Instructional Resources
Formative Tasks
Mathematics Formative Assessments (MFAS)
What Am I? Describe a linear function, its graph, and the meaning
of its parameters.
Explaining Linear Functions Describe defining properties of
linear functions.
Nonlinear Functions Provide an example of a nonlinear function
and explain why it is nonlinear.
Linear or Nonlinear? Identify a function as either linear or
nonlinear and to justify their decision.
Illustrative Mathematics Assessment Tasks
Function Rules Connect a function described by a verbal rule with
corresponding values in a table.
Lesson Resources
Engage NY
Grade 8, Module 5, Topic A, Lesson 8 Determine
whether an equation is linear or non-linear by examining the rate
of change
MARS/Shell
Meal Out Use equations to solve a problem with a restaurant
check.
Linear Graphs Match equations with linear graphs.
McGraw-Hill
Course 3, Chapter 4
Lesson 4
Decoded Standard
MAFS.8.F.2.4
Students identify the rate of change (slope) and y-intercept (initial value) from tables, graphs, equations, and verbal
descriptions of linear relationships. The y-intercept is the y-value when the x-value is 0. Interpretation of slope and the
initial value of the function is accomplished using real-world situations. (Common Core Mathematics Companion, Pg. 143)
Instructional Resources
Formative Tasks
Mathematics Formative Assessments (MFAS)
Lesson Resources
Engage NY
Pinellas County Schools GRADE 8 PRE-ALGEBRA 2019-2020
Construction Function Construct a function to model a linear
relationship between two quantities given two ordered pairs in context.
Profitable Functions Write a function to model a linear
relationship given its graph.
Trekking Functions Construct a function to model a linear
relationship between two quantities given a table of values.
Smart TV Determine the rate of change and initial value of a linear
function given a table of values, and interpret the rate of change and
initial value in terms of the situation it models.
Drain the Pool Determine the rate of change and initial value of a
linear function when given a graph, and to interpret the rate of change
and initial value in terms of the situation it models.
Illustrative Mathematics Assessment Tasks
Video Streaming Model of a linear function.
High School Graduation Estimating approximate time name
called using a linear function.
Baseball Cards Interpreting linear functions.
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.
Grade 8, Module 6, Topic A, Lesson 3 Graph a line
based on different characteristics (function, initial value, points
MARS/Shell
Lines and Linear Functions Interpret speed as the slope
of a linear graph and translate between the equation of a line and
its graphical representation.
Interpreting Time-Distance Graphs Interpret
distance–time graphs as if they are pictures of situations rather
than abstract representations of them.
McGraw-Hill
Course 3, Chapter 4
Lesson 1
Decoded Standard
MAFS.8.F.2.5
Given a graph, students will provide a verbal description of the function, including whether the graph is linear or nonlinear
or where the function is increasing or decreasing. Given a function’s verbal description, students will be able to sketch the
graph displaying qualitative properties of that function. The quantitative features of the graph are not displayed (specific
quantities on the axes). (Common Core Mathematics Companion, Pg. 144)
Instructional Resources
Formative Tasks
Mathematics Formative Assessments (MFAS)
Jet Fuel Describe the relationship between two linearly related
quantities.
Population Trend Describe the relationship between two
quantities in a nonlinear function.
Graph the Ride Given a verbal description of the relationship
between two quantities and are asked to sketch a graph to model the
relationship.
Bacterial Growth Graph Given a verbal description of the
relationship between two quantities and are asked to sketch a graph to
model the relationship.
Illustrative Mathematics Assessment Tasks
Tides Interpreting the graph of a function in terms of the relationship
between quantities that it represents.
Distance Interpret two graphs that look the same but show very
different quantities.
Bike Race Interpret two distance-time graphs in terms of the context
of a bicycle race.
Engaging Tasks
Joules Three Acts Math - Do you think Joules will work as advertised?
Lesson Resources
Engage NY
Grade 8, Module 6, Topic A, Lesson 4 Describe and
sketch qualitatively function relationships.
Grade 8, Module 6, Topic A, Lesson 5 Qualitatively
sketch and describe function relationship
MARS/Shell
Modeling Situation with Linear Equations Explore
relationships between variables in everyday situations.
McGraw-Hill
Course 3, Chapter 4
Lesson 9
Pinellas County Schools GRADE 8 PRE-ALGEBRA 2019-2020
Split Across Semester
1 & 2
Unit 5: Triangles and Pythagorean
Theorem
16 days: 12/2-12/10 and
1/8-1/21
INTERVENTION/REMEDIATION: 3 days, 1/22-1/24
Winter Break is 12/21 – 1/6
Standards/Learning Goals:
Content Limits, Assessment Types, Calculator
MAFS.8.G.1.5 Use informal arguments to establish facts about the
angle sum & exterior angle of triangles and about the angle created
when parallel lines are cut by a transversal. 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.
Do not include shapes beyond triangles.
Calculator: NEUTRAL
Equation Editor
GRID
Multiple Choice
Multiselect
Open Response
MAFS.8.G.2.6 Explain a proof of the Pythagorean Theorem and its
converse.
For the converse, use only perfect roots.
Calculator: YES
Editing Task Choice
Equation Editor
GRID
Hot Text
Multiple Choice
Multiselect
Open Response
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.
If the triangles is part of a 3-dimensional figure, a
graphic of the 3-dimensional figure must be
included.
No coordinate plane items should be included.
Points on the coordinate grid must be where grid
lines intersect.
Calculator: YES
Editing Task Choice
Equation Editor
GRID
Hot Text
Matching Item
Multiple Choice
Multiselect
MAFS.8.G.2.8 Apply the Pythagorean Theorem to find the distance
between two points in a coordinate system.
Graphics of 3-dimensional figures can be included.
Dimensions must be given as rational numbers.
Figures must not be composite.
Calculator: YES
Editing Task Choice
Equation Editor
GRID
Hot Text
Multiple Choice
Multiselect
Open Up Resources Lessons
Grade 8, Unit 1: Rigid Transformations and Congruence
Lesson 14: Alternate Interior Angles
Lesson 15: Adding the Angles in a Triangle
Lesson 16: Parallel Lines and the Angles in a Triangle
Grade 8, Unit 8: Pythagorean Theorem and Irrational Numbers
Lesson 1: The Areas of Squares and Their Side Lengths
Lesson 2: Side Lengths and Areas
Lesson 3: Rational and Irrational Numbers
Lesson 4: Square Roots on the Number Line
Pinellas County Schools GRADE 8 PRE-ALGEBRA 2019-2020
Lesson 5: Reasoning About Square Roots
Lesson 6: Finding Side Lengths of Triangles
Lesson 7: A Proof of the Pythagorean Theorem
Lesson 8: Finding Unknown Side Lengths
Lesson 9: The Converse
Lesson 10: Applications of the Pythagorean Theorem
Lesson 11: Finding Distances in the Coordinate Plane
Decoded Standard
MAFS.8.G.1.5
Students are expected to make informal arguments while exploring facts about the sum of the angles of a triangle, exterior
angles of triangles, angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similar
triangles. The example demonstrates how these facts are interrelated. Note that formal two-column proofs are not
expected at this grade.
See image on page 184 of the Common Core Mathematics Companion.
(Common Core Mathematics Companion, Pg. 184)
Instructional Resources
Formative Tasks
Mathematics Formative Assessments (MFAS)
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.
What is the Triangle Relationship? Describe the
relationship between similar triangles.
Justifying the Triangle Sum Theorem Provide proof
using a triangle.
Illustrative Mathematics
Congruence of Alternate Interior Angles via
Rotations Experiment with rigid motions to help visualize
why alternate interior angles (made by a transverse
connecting two parallel lines) are congruent.
Find the Angle The task is an example of a direct but non-
trivial problem in which students have to reason with angles
and angle measurements (and in particular, their knowledge
of the sum of the angles in a triangle) to deduce information
from a picture.
Engaging Tasks
Transversals, Tape and Stickies Place sticky notes in their
assigned location based on a description
Lesson Resources
Engage NY
Grade 8, Module 2, Topic C, Lesson 12 Understand
equivalent angle relationships when lines are parallel. Understand
angle relationships related to translations and rotations. Present
informal arguments about angles formed from parallel lines cut by a
transversal.
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.
Grade 8, Module 3, Topic B, Lesson 10 Informal proof of
Angle-Angle criterion and whether or not triangles are similar
MARS/Shell
Identifying Similar Triangles Categorize diagrams of pairs
of triangles based on their similarity.
McGraw-Hill
Course 3, Chapter 5
Lesson 3 (review vocabulary pg. 372)
Decoded Standard
MAFS.8.G.2.6
There are many proofs of the Pythagorean Theorem. Students will work through one to understand the meaning of 𝑎
2
+
𝑏
2
= 𝑐
2
and its converse. The converse statement is as follows.: If the square of one side o a triangle is equal to the sum of
the squares of the other two sides, then the triangle is a right triangle. (Common Core Mathematics Companion, Pg. 186)
Pinellas County Schools GRADE 8 PRE-ALGEBRA 2019-2020
Instructional Resources
Formative Tasks
Mathematics Formative Assessments (MFAS)
Pythagorean Squares Demonstrate knowledge of the
square root and right triangle in the Pythagorean theorem.
Explaining a Proof of the Pythagorean Theorem
Proof of similar triangles.
Converse of the Pythagorean Theorem Teacher
scenario to prove that the teacher is correct and prove that
triangles are congruent.
Engaging Tasks
How can we correct the Scarecrow How can we correct
the Scarecrow’s statement so it is mathematically precise?
Lesson Resources
Engage NY
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.
Grade 8, Module 7, Topic C, Lesson 16 Explain the
proof of the converse of the Pythagorean Theorem.
MARS/Shell
The Pythagorean Theorem: Square Areas Use the
area of right triangles to deduce the areas of other shapes.
McGraw-Hill
Course 3, Chapter 5
Inquiry Lab: Proofs about Pythagorean
Theorem
Decoded Standards
MAFS.8.G.2.7
Students solve problems where they must apply the Pythagorean Theorem. Problems may be real-world or mathematical,
and they may involve two- and three-dimensional situations. (Common Core Mathematics Companion, Pg. 187)
Instructional Resources
Formative Tasks
Mathematics Formative Assessments (MFAS)
New Television Using the measurement given, show if the
TV can fit in the space provided.
How Far to School Use the Pythagorean theorem to find
distance.
Three Dimensional Diagonal Apply the Pythagorean
theorem to a rectangular prism’s diagonal.
Pyramid Height Find the height of a pyramid.
Illustrative Mathematics
Running on the Football Field Reason how to use the
Pythagorean Theorem to find the distance ran by Ben Watson
and Champ Bailey.
Area of a Trapezoid Decompose the given trapezoid into
other polygons and use the Pythagorean Theorem to find the
unknown side-lengths of a trapezoid in order to determine the
area.
Spiderbox Visualize and apply the Pythagorean Theorem to
determine the length of a spider’s path around the outside of a
box.
Engaging Tasks
Viewmongous TV Is the 80” TV double, triple or quadruple the
viewing area of a 55’ TV?
Pythagorean Theorem Problems Math Mistakes
examines several student errors with utilizing the Pythagorean
Theorem.
Lesson Resources
Engage NY
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
McGraw-Hill
Course 3, Chapter 5
Lesson 6
Pinellas County Schools GRADE 8 PRE-ALGEBRA 2019-2020
Decoded Standards
MAFS.8.G.2.8
Use the Pythagorean Theorem to find the distance between two points. Problems can best be modeled in a coordinate
system. (Common Core Mathematics Companion, Pg. 188)
Instructional Resources
Formative Tasks
Mathematics Formative Assessments (MFAS)
Distance Between Two Points Find the distance between
two points on a coordinate grid.
Distance on the Coordinate Plane Find the distance
between two points on a coordinate plain.
Coordinate Plane Triangle Graph the given coordinates and
find the lengths of each side of the triangle.
Calculate Triangle Sides Graph the given coordinates to find
the lengths of each side of the triangle.
Engaging Tasks
Where’s the Nearest Toys R Us? Determine how store
locators measure distance and calculate several distances.
Pythagorean Theorem Problems Math Mistakes
examines several student errors with utilizing the Pythagorean
Theorem
Lesson Resources
Engage NY
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
McGraw-Hill
Course 3, Chapter 5
Lesson 7
Pinellas County Schools GRADE 8 PRE-ALGEBRA 2019-2020
Semester 2
Unit 6: Transformations, Congruence and
Similarity
17 days: 1/27-2/19
INTERVENTION/REMEDIATION: 3 days, 2/20-2/24
Standards/Learning Goals:
Content Limits, Assessment Types,
Calculator
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.
Assessed though MAFS.8.G.1.2,
MAFS.8.G.1.4
Calculator: NEUTRAL
Editing Task Choice
Equation Editor
GRID
Hot Text
Matching Item
Multiple Choice
Multiselect
Open Response
Table Item
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.
The coordinate plane should not be used
until (8.G.1.3).
Limit sequences to no more than two
transformations.
A pre-image and image should not include
apostrophe notation as this would give away
the identification of similarity and
congruence.
No reference to the definition of
congruence or symbols relating to the
definition should be used (HS Geometry).
Calculator: NEUTRAL
Editing Task Choice
Equation Editor
GRID
Hot Text
Matching Item
Multiple Choice
Multiselect
Open Response
Table Item
MAFS.8.G.1.3 Describe the effect of dilations, translations, rotations,
and reflections on two-dimensional figures using coordinates.
Coordinate values of x and y must be
integers.
The number of transformations should be
no more than two.
In items that require the student to draw a
transformed figure using a dilation or a
rotation, the center of the transformation
must be given.
Calculator: NEUTRAL
Editing Task Choice
Equation Editor
GRID
Hot Text
Multiple Choice
Multiselect
Open Response
Table Item
Pinellas County Schools GRADE 8 PRE-ALGEBRA 2019-2020
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.
Items should not include the coordinate
plane as the coordinate plane is needed in
8.G.1.3.
Limit the sequence to no more than two
transformations.
2-dimensional figures are limited to no more
than 7 sides.
A pre-image or image should not include
apostrophe notation as this would give away
the identification of similarity and
congruence.
No reference to the definition of
congruence or symbols relating to the
definition should be used (HS Geometry).
Calculator: NEUTRAL
Editing Task Choice
Equation Editor
GRID
Hot Text
Matching Item
Multiple Choice
Multiselect
Open Response
Table Item
MAFS.8.G.1.5 Use informal arguments to establish facts about the
angle sum and exterior angle of triangles, about the angle 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.
Do not include shapes beyond triangles.
Calculator: NEUTRAL
Equation Editor
GRID
Multiple Choice
Multiselect
Open Response
MAFS.8.EE.2.6 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 𝑦 = 𝑚𝑥 for a line through the
origin and the equation 𝑦 = 𝑚𝑥 + 𝑏 for a line intercepting the vertical
axis at b.
All triangles must be right triangles and on a
coordinate grid.
Numbers in items must be rational numbers.
Functions must be linear.
Calculator: YES
Editing Task Choice
Equation Editor
GRID
Hot Text
Matching Item
Multiple Choice
Multiselect
Open Response
Table Item
Open Up Resources Lessons
Grade 8, Unit 1: Rigid Transformations and Congruence
Lesson 1: Moving in the Plane
Lesson 2: Naming the Moves
Lesson 3: Grid Moves
Lesson 4: Making the Moves
Lesson 5: Coordinate Moves
Lesson 6: Describing Transformations
Lesson 7: No Bending or Stretching
Pinellas County Schools GRADE 8 PRE-ALGEBRA 2019-2020
Lesson 8: Rotation Patterns
Lesson 9: Moves in Parallel
Lesson 10: Composing Figures
Lesson 11: What is the Same?
Lesson 12: Congruent Polygons
Lesson 13: Congruence
Grade 8, Unit 2: Dilations, Similarity, and Introducing Slope
Lesson 1: Projecting and Scaling
Lesson 2: Circular Grid
Lesson 3: Dilations with no Grid
Lesson 4: Dilations on a Square Grid
Lesson 5: More Dilations
Lesson 6: Similarity
Lesson 7: Similar Polygons
Lesson 8: Similar Triangles
Lesson 9: Side Length Quotients in Similar Triangles
Decoded Standard
MAFS.8.G.1.1 – students need multiple opportunities to explore the transformation of figures
Eighth graders add rotations, reflections, and translations to their study of transformations from Grade 7 dilations.
Students verify through experimentation with figures on a coordinate plane that lines are taken to lines and line
segments to line segments of the same length; angles are taken to angles of the same measure, and parallel lines are
taken to parallel lines. This standard is an introduction, and students should spend time exploring these transformations.
See image on page 178 of the Common Core Mathematics Companion.
(Common Core Mathematics Companion, Pg. 178)
Instructional Resources
Formative Tasks
Mathematics Formative Assessments (MFAS)
Segment Transformations Translation, rotation, and
reflection
Angle Transformations Students will need rulers and
transparent paper. Students experimentally verify the properties of
angle transformations.
Parallel Line Transformations Students experimentally
verify properties of parallel lines transformation.
Engaging Tasks
How did they make Ms. Pac-Man Describe Ms. Pac-
Man’s movements with academic vocabulary
How do Skytypers Write Messages? Use transformation
applications to create skytyping messages and translate it into a set
of coordinates.
Naming Coordinates, Feedback and Revision Revise
a student error involving translating a quadrilateral
Best Reflection Students compare 4 images with their
reflection to determine which one is the best.
Pool Bounce Determine where each shot will hit using
reflections.
Transformations – Shortest Sequence What’s the fewest
number of transformations needed to take pre-image ABCT to
A’B’C’D’.
Lesson Resources
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
MARS/Shell
Representing and Combining Transformations
Combining rigid transformations
McGraw-Hill
Course 3, Chapter 6
Inquiry Lab: Transformations
Lesson 1, 2 and 3
Course 3, Chapter 7
Lesson 1
Pinellas County Schools GRADE 8 PRE-ALGEBRA 2019-2020
Decoded Standard
MAFS.8.G.1.2
Students use what they previously learned about transformations to determine congruency between figures. Congruent
figures share the same size and shape. When given two congruent figures, students describe the sequence of
transformations that occurred to create the congruent figure. Note that dilations cannot be used for congruent figures.
(Common Core Mathematics Companion, Pg. 180)
Instructional Resources
Formative Tasks
Mathematics Formative Assessments (MFAS)
Proving Congruence Students are asked to explain
congruence in terms of rigid motions.
Rigid Motion 1 Students are asked to describe the motion and
determine if the shapes are congruent. Translation
Rigid Motion II-Reflection Describe a rigid motion to
demonstrate two polygons are congruent.
Rigid Motion III Describe a rigid motion to demonstrate two
polygons are congruent.
Multistep Congruence Describe a sequence of rigid motions
to demonstrate the congruence of two polygons.
Illustrative Mathematics
Cutting a Rectangle Into Two Shows the congruence of
two triangles in a particular geometric context arising by cutting a
rectangle in half along the diagonal.
Congruent Triangles Develop an understanding of rigid
motions in the context of demonstrating congruence and reflections
refined by orientation.
Engaging Tasks
Naming Coordinates, Feedback and Revision Revise
a student error involving translating a quadrilateral
Best Reflection Students compare 4 images with their
reflection to determine which one is the best.
Transformations – Shortest Sequence What’s the fewest
number of transformations needed to take pre-image ABCT to
A’B’C’D’.
Transformations – Three Sequences List three
sequences of transformations that take pre-image ABCT to image
A’B’C’D’
Lesson Resources
Engage NY
Grade 8, Module 2, Topic B, Lesson 10
Mapping one figure onto another
Grade 8, Module 2, Topic C Lesson 11
Congruence through Rigid Motion
MARS/Shell
Transforming 2D Figures Describe in words the
transformation that maps an object to a transformed image. Given
a geometric figure and a rotation, reflection or translation, draw
the transformed figure (or the original figure if the image is given.)
Describe transformations as algebraic functions that take points in
the plane as inputs and give other points as outputs.
McGraw-Hill
Course 3, Chapter 7
Lesson 2
Decoded Standard
MAFS.8.G.1.3
Students continue looking at two-dimensional figures on the coordinate plane, concentrating on the coordinates of the
resulting figure after transformations, including dilations learned in Grade 7.
(Common Core Mathematics Companion, Pg. 181)
Instructional Resources
Pinellas County Schools GRADE 8 PRE-ALGEBRA 2019-2020
Formative Tasks
Mathematics Formative Assessments (MFAS)
Translation Coordinates Two problems both require
students to graph a two-dimensional figure’s translation and identify
the new coordinates.
Rotation Coordinates Two problems both require students to
graph a two-dimensional figure’s rotation and identify the new
coordinates.
Reflection Coordinates Two problems both require students
to graph a two-dimensional figure’s reflection and identify the new
coordinates.
Engaging Tasks
How do Skytypers Write Messages? Use transformation
applications to create skytyping messages and translate it into a set
of coordinates.
Naming Coordinates, Feedback and Revision Revise
a student error involving translating a quadrilateral
Transformations – Shortest Sequence What’s the fewest
number of transformations needed to take pre-image ABCT to
A’B’C’D’.
How did they make Ms. Pac-Man Describe Ms. Pac-
Man’s movements with academic vocabulary
Lesson Resources
Engage NY
Grade 8, Module 3, Topic A, Lesson 6
Dilations using Coordinates
MARS/Shell
Representing and Combining Transformations
Students will recognize and visualize transformations of 2D shapes.
They will translate, reflect and rotate shapes, and combine these
transformations.
McGraw-Hill
Course 3, Chapter 6
Lesson 1 (Translations), Lesson 2 (Reflections), Lesson 3
(Rotations) and Lesson 4 (Dilations)
Decoded Standard
MAFS.8.G.1.4
With this standard, students move from congruence to similarity. Students develop the understanding that similar
figures can be created by a series of transformations, including rotations, reflections, dilations, and translation, and can
identify those transformations given an image and a pre-image.
See image on page 182 of the Common Core Mathematics Companion.
(Common Core Mathematics Companion, Pg. 182)
Instructional Resources
Formative Tasks
Mathematics Formative Assessments (MFAS)
Proving Similarity Explain similarity in terms of
transformations
Similarity I Describe a sequence of transformations to show that
two polygons are similar.
Similarity II Describe a sequence of transformations to show that
two polygons are similar.
Similarity III Describe a sequence of transformations that
demonstrates two polygons are similar.
Illustrative Mathematics
Are they Similar? Provide experience applying transformations
to show that two polygons are similar.
Creating Similar Triangles Provide experience applying
transformations to show that two polygons are similar.
Engaging Tasks
Right Triangles – Trapezoids What question comes to mind
for the given image?
Lesson Resources
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
McGraw-Hill
Course 3, Chapter 7
Lesson 4
Decoded Standard
MAFS.8.G.1.5
Pinellas County Schools GRADE 8 PRE-ALGEBRA 2019-2020
Students are expected to make informal arguments while exploring facts about the sum of the angles of a triangle,
exterior angles of triangles, angles created when parallel lines are cut by a transversal, and the angle-angle criterion for
similar triangles. The example demonstrates how these facts are interrelated. Note that formal two-column proofs are
not expected at this grade.
See image on page 184 of the Common Core Mathematics Companion.
(Common Core Mathematics Companion, Pg. 184)
Instructional Resources
Formative Tasks
Mathematics Formative Assessments (MFAS)
Same Side Interior Angles Describe and justify the
relationship between same side interior angles.
Justifying Angle Relationships Describe and justify the
relationship between corresponding angles and alternate interior
angles
Justifying the Exterior Angle Theorem Apply the
Exterior Angle of a Triangle Theorem and provide an informal
justification
What is the Triangle Relationship? Describe the
relationship between two triangles given that two pairs of
corresponding angles are congruent, and provide an informal
justification of the relationship (similarity).
Justifying the Triangle Sum Theorem Provide an
informal justification of the Triangle Sum Theorem
Illustrative Mathematics
Rigid motions and congruent angles Given parallel lines
cut by a transversal, prove congruence between angle pairs.
A Triangle’s Interior Angles Given parallel lines with a
triangle drawn with its transversals, prove that a+b+c = 180
Find the Missing Angle Find the measure of a missing angle
between parallel lines
Congruence of Alternate Interior Angles via
Rotations Explain why rotating a pair of parallel lines cut by a
transversal demonstrates that angles are congruent.
Street Intersections Apply facts about angles in order to
calculate angle measures in the context of a map.
Lesson Resources
Engage NY
Grade 8, Module 2, Topic C, Lesson 12
Angle Relationships of Parallel Lines
Grade 8, Module 2, Topic C, Lesson 13
Angle Sum Theorem Triangles
Grade 8 Module 2, Topic C, Lesson 14
Missing Angle Measures Triangles
McGraw-Hill
Course 3, Chapter 7
Lesson 5
Decoded Standard
MAFS.8.EE.2.6
Students gain additional knowledge about slope in this standard as they use similar triangles to explain how
the slope m of a line is the same between any two points on a given non-vertical line. Students understand
positive/negative slopes, 0 slope, and undefined slopes. Through the use of similar triangles, teachers lead
students to derive the general equation (𝑦 = 𝑚𝑥 + 𝑏) of a line and discover that m is the slope and b is the y-
intercept. (Common Core Mathematics Companion, Pg. 124)
Instructional Resources
Formative Tasks
Mathematics Formative Assessments (MFAS)
Slope with similar Triangles Use similar triangles to explain
why the slope is the same regardless of the points used to calculate
it.
Deriving Lines I- Using the slope formula Derive the
general equation of a line containing the origin.
Deriving Lines II Using the slope formula Derive the
general equation of a line with a y-intercept of (0, b)
Lesson Resources
Engage NY
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.
McGraw-Hill
Course 3, Chapter 7
Lesson 6
Pinellas County Schools GRADE 8 PRE-ALGEBRA 2019-2020
Semester 2
Unit 7: Volume
14 days: 2/25-3/13
INTERVENTION/REMEDIATION: 3 days, 3/24-3/26
Spring Break is 3/14-3/23
Standards/Learning Goals:
Content Limits, Assessment Types, Calculator
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.
Graphics of three-dimensional figures can be
included.
Dimensions must be given as rational numbers.
Figures must not be composite
Calculator: YES
Equation Editor
Multiple Choice
Multiselect
Open Up Resources Lessons
Grade 8, Unit 5: Functions and Volume
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
Decoded Standard
MAFS.8.G.3.9
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)
Instructional Resources
Formative Tasks
Mathematics Formative Assessments (MFAS)
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.
Lesson Resources
Engage NY
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
McGraw-Hill
Course 3, Chapter 8
Lesson 1 (Cylinders), Lesson 2 (Cones – skip ex. 3), and
Lesson 3 (Spheres – skip ex. 4)
Pinellas County Schools GRADE 8 PRE-ALGEBRA 2019-2020
Pinellas County Schools GRADE 8 PRE-ALGEBRA 2019-2020
Semester 2
Unit 8: Scatter Plots and Data Analysis
12 days: 3/27-4/14
INTERVENTION/REMEDIATION: 3 days, 4/15-4/17
Standards/Learning Goals:
Content Limits, Assessment Types, Calculator
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.
Numbers in items must be rational numbers.
Calculator: NEUTRAL
GRID
Multiple Choice
Multiselect
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.
Numbers in items must be rational numbers.
Trend/association is based on visual inspection.
Line of best fit must be informally assessed.
Trend/association must be linear.
Calculator: NEUTRAL
GRID
Multiple Choice
Multiselect
Open Response
MAFS.8.SP.1.3 Use the equation of a linear model to solve problems
in the context of bivariate measurement data, interpreting the slope
an intercept. For example, in a linear model for a biology
experiment, interpret a slop of 1.5 cm/hr. as meaning that an
additional hour of sunlight each day is associated with an additional
1.5cm in mature plant height.
Numbers in items must be simple rational
numbers (e.g., ½, ¼, to the 10
th
).
Data are required for all items.
In all items requiring a line of best fit, the equation
of that line should be given.
Calculator: NEUTRAL
Equation Editor
Multiple Choice
Multiselect
Open Response
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 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?
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).
Calculator: YES
Equation Editor
GRID
Multiple Choice
Multiselect
Table Item
Open Up Resources Lessons
Grade 8, Unit 6: Associations in Data
Lesson 1: Organizing Data
Lesson 2: Plotting Data
Lesson 3: What a Point in a Scatter Plot Means
Lesson 4: Fitting a Line to Data
Lesson 5: Describing Trends in Scatter Plots
Lesson 6: The Slope of a Fitted Line
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
Pinellas County Schools GRADE 8 PRE-ALGEBRA 2019-2020
Decoded Standard
MAFS.8.SP.1.1
Students study scatter plots of bivariate data by constructing and interpreting them in terms of patterns they can see. They
look for the patterns of clustering, outliers, positive or negative association, and linear or nonlinear association. Examples
of scatter plots below show positive and negative associations, clustering, and an outlier.
See the image on page 238 of the Common Core Mathematics Companion
(Common Core Mathematics Companion, Pg. 238)
Instructional Resources
Formative Tasks
Mathematics Formative Assessments (MFAS)
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.
Bungee Cord Data Construct a scatterplot corresponding to a
given set of data.
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.
Engaging Tasks
Positive Correlation Create a set of points that have specific
characteristics
Interpreting Graphs Where Up Isn’t Good Interpret
data on a scatterplot that appears unconventional.
Lesson Resources
Engage NY
Grade 8, Module 6, Topic B, Lesson 6
Constructing Scatter Plots
Grade 8, Module 6, Topic B, Lesson 7
Patterns in Scatter Plots
Grade 8, Module 6, Topic C, Lesson 11
Scatter plots; Fit line to data; Interpret slope
McGraw-Hill
Course 3, Chapter 9
Lesson 1
Decoded Standard
MAFS.8.SP.1.2
Students focus on linear patterns of association in scatter plots and understand that linear models (straight lines) are
commonly used to model linear relationships. Then they begin to informally fit a straight line to the data and learn to
assess its fit by judging the closeness of the line to the data points. The most appropriate line is the one that comes closest
to most data points. The use of linear regression is not expected at this grade. (Common Core Mathematics Companion,
Pg. 239)
Instructional Resources
Formative Tasks
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.
Lesson Resources
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
McGraw-Hill
Pinellas County Schools GRADE 8 PRE-ALGEBRA 2019-2020
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.
Engaging Tasks
Line of Best Fit Create 4 points that could generate a line of
best fit with the equation y=-x+8.
Course 3, Chapter 9
Lesson 2
Decoded Standard
MAFS.8.SP.1.3
Students practice solving contextual linear problems. The problems involve situations using bivariate measurement data
such as those collected in a biology experiment. This standard connects with what students have learned about models of
linear equations, slope, and intercept. (Common Core Mathematics Companion, Pg. 240)
Instructional Resources
Formative Tasks
Mathematics Formative Assessments (MFAS)
Tuition Use this equation to predict the average tuition cost at a
public university.
Stretching Statistics Explain the significance of a point and the
y-intercept.
Foot Length Interpret the slope and intercept of a linear function
that models the relationship between foot length and height.
Developmental Data Explain the significance of the slope of
the equation in terms of a problem’s context.
Illustrative Mathematics Assessment Tasks
US Airports, Assessment Variation Use a linear function
to model a relationship between two quantities.
Chicken and Steak, Variation 1 Presents a real world
situation that can be modeled with a linear function best suited for
an instructional context
Lesson Resources
Engage NY
Grade 8, Module 6, Topic C, Lesson 10
Interpret slope and initial value
Grade 8, Module 6, Topic C, Lesson 11
Scatter plots; Fit line to data; Interpret slope
McGraw-Hill
Course 3, Chapter 9
Lesson 2
Decoded Standard
MAFS.8.SP.1.4
This standard asks students to switch from using numerical data to categorical data and use frequencies to answer
questions about possible associations (linear/nonlinear, positive/negative/no association). Students construct and
interpret tables that display categorical data on two different variables from the same subjects. A two-way table is a table
that shows categorical data classified in two different ways. An example of a two-way table that records possible data
from the example in the standard about chores and curfews may be the following:
CURFEW
CHORES
YES
NO
YES
44
20
NO
20
44
One interpretation of the chart is that of the students who answered yes, they had a curfew, 44 had chores and 20 did not.
Of the students who answered no, they did not have a curfew, 20 had chores and 44 did not. From this sample, there
Pinellas County Schools GRADE 8 PRE-ALGEBRA 2019-2020
appears to be a positive correlation between having a curfew and having chores. (Common Core Mathematics Companion,
Pg. 214)
Instructional Resources
Formative Tasks
Mathematics Formative Assessments (MFAS)
Two-Way Relative Frequency Table Convert raw data to
relative frequencies by both rows and columns given a two-way
frequency table.
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.
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 plays a musical
instrument.
Lesson Resources
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
MARS/Shell
Testing a New Product Assess how well students are able
to organize, represent and analyze bivariate categorical data in
an appropriate way.
McGraw-Hill
Course 3, Chapter 9
Lesson 3
MS Math Scoring Criteria (Grade 8 Math)
Number and Quantity: Reason, describe, and analyze quantitatively, using units and number systems to solve
problems.
Scoring Criteria
Performance
Indicators
Emerging
Progressing
Meets
Exceeds
G. Students will
know that there
are numbers
that are not
rational, and
approximate
them by
rational
numbers
[8.NS.1.1,
8.NS.1.2]
i. Students can
find the square
roots of small
perfect squares.
i. Students can identify
square roots of non-
square numbers and pi
as irrational numbers;
identify rational or
irrational numbers and
convert familiar
rational numbers with
one repeating digit to
fraction form.
i. Students can place
irrational numbers on
a number line;
identify irrational
decimal expansions
as approximations;
identify rational and
irrational numbers
and convert less
familiar rational
numbers to fraction
form.
i. Students can use
approximations
of irrational
numbers to
estimate the
value of an
expression;
compare and
order rational
and irrational
numbers without
a number line.
Algebra: Create, interpret, use, and analyze expressions, equations and inequalities.
Scoring Criteria
Performance
Indicators
Emerging
Progressing
Meets
Exceeds
F. Students will
work with
radicals and
integer
exponents.
[8.EE.1.1, 8.EE.1.2,
8.EE.1.3, 8.EE.1.4]
i. Students can
identify numbers
in scientific
notation as being
a very large
number (positive
exponent) or a
very small number
(negative
exponent).
i. Students can apply
the properties of
natural number
exponents to
generate equivalent
numerical
expressions.
ii. Students can
evaluate square
roots and solve
mathematical
equations in the
form 𝑥
2
= 𝑝, where
p is a positive
rational number and
is a small perfect
square; knows that
square root 2 is
irrational.
iii. Students can use
numbers expressed
in the form of a
single digit times an
integer power of 10
to express very large
numbers.
iv. Students can
represent very large
and very small
i. Students can apply
the properties of
integer exponents
to generate
equivalent
numerical
expressions.
ii. Students can use
square root and
cube root symbols
to represent
solutions to
mathematical
equations in the
form 𝑥
2
= 𝑝 and
𝑥
3
= 𝑝, where p is a
positive rational
number; evaluate
cube roots of small
perfect cubes.
iii. Students can use
numbers expressed
in the form of a
single digit times an
integer power of 10
to express very
small numbers.
iv. Students can
perform operations
i. Students can use
multiple properties
of integer
exponents within
an expression;
analyze the
reasonableness of
the result of using
the properties of
integer exponents.
ii. Students can write
and solve
equations
representing real-
world situations
using square root
and cube root
symbols; justify
how square roots
and cube roots
relate to each
other and to their
radicands.
iii. Students can
express how many
times as much a
number written in
the form of a
single digit times
MS Math Scoring Criteria (Grade 8 Math)
quantities in
scientific notation
and use units of
appropriate sixe for
measurements of
very large or very
small quantities.
with numbers
expressed in
scientific notation,
including problems
where both decimal
and scientific
notation are used;
interpret scientific
notation generated
by technology.
an integer power
of 10 is than
another number
written in the
same form.
iv. Students can
perform
operations and
interpret values
written in scientific
notation within a
real-world context;
analyze the
process and
solution to given
problems using
scientific notation.
G. Students will
understand the
connections
between
proportional
relationships,
lines, and linear
equations.
[8.EE.2.5, 8.EE.2.6]
i. Students can
graph a
proportional
relationship given
a table.
ii. Students can
identify the slope
of a line when
given an equation
in slope-intercept
form.
i. Students can graph
proportional
relationships,
interpreting the unit
rate as the slope.
ii. Students can
determine the slope
of a line given a
graph.
i. Students can
identify the unit
rate as the slope;
compare two
different
proportional
relationships
represented in
different ways.
ii. Students can
explain, using
similar triangles,
why the slope is the
same between any
two distinct points
on a nonvertical line
in the coordinate
plane; derive the
equation 𝑦 = 𝑚𝑥
for a line through
the origin.
i. Students can
generate a model
of a proportional
relationship given
specific quantities.
ii. Students can
derive the
equation 𝑦 =
𝑚𝑥 + 𝑏 for a line
intercepting the
vertical axis at b;
compare and
contrast situations
in which similar
triangles would or
would not yield
the same slope
between two
distinct points on a
nonvertical line in
the coordinate
plane.
H. Students will
analyze and
solve linear
equations and
pairs of
simultaneous
linear
equations.
[8.EE.3.7, 8..EE.3.8]
i. Students can use
substitution with
an equation or
pair of equations
and a data set to
determine if any
number(s) from
the data set
makes the
equation true.
i. Students can solve
linear equations with
integer coefficients
and variables on one
side.
ii. Students can
interpret
mathematical or
real-world problems
given the graph, of a
system of two linear
equations in two
variables.
i. Students can solve
multistep linear
equations in one
variable with
rational coefficients
using the
distributive
property or
collecting like terms
on a given side;
identify linear
equations as having
solution of one,
i. Students can
justify why an
equation has one
solution, infinitely
many solutions, or
no solution; create
examples of
equations that
have one solution,
infinitely many
solutions, or no
solution.
MS Math Scoring Criteria (Grade 8 Math)
infinitely many, or
none by
transforming the
given equation into
simpler forms by
inspection.
ii. Students can solve
mathematical and
real-world systems
of two linear
equations in two
variables with
integer coefficients
by inspection,
algebraically by
multiplying only one
of the equations by
an integer.
ii. Students can solve
and analyze a
system of
equations in two
variables with
integer and
benchmark
fraction
coefficients; solve
and analyze
problems involving
two linear
equations in two
variables with
rational
coefficients or
constants.
Functions: Use various forms of functions to interpret and analyze a variety of contexts.
Scoring Criteria
Performance
Indicators
Emerging
Progressing
Meets
Exceeds
A. Students will
define,
evaluate, and
compare
functions.
[8.F.1.1, 8.F.1.2,
8.F.1.3]
i. Students can
define the terms
function, linear,
nonlinear, and
slope.
i. Students can identify,
from a graph, if a
relation is a function.
ii. Students can
compare properties
(i.e., slope, y-
intercept, values) of
two linear functions
represented in a
different way (graph
and equation in slope
intercept form).
iii. Students can
determine whether a
function is linear or
nonlinear from a
graph.
i. Students can use a
table or graph to
demonstrate
understanding that a
function is a rule
that assigns to each
input exactly one
output and that the
graph of a function
is the set of ordered
pairs consisting of an
input and the
corresponding
output.
ii. Students can
compare properties
(i.e., slope, y-
intercept, values) of
two linear functions
each represented in
a different way
(algebraically,
graphically,
numerically in
tables, or verbal
description).
iii. Students can
interpret the
i. Students can
explain, given a
rule, why it is a
function or not a
function; create a
rule, given a table
or graph, and
explain why it is or
is not a function.
ii. Students can
compare two
linear functions
and justify
whether two
functions each
represented in a
different way
(algebraically,
graphically,
numerically in
tables, or verbal
description) are
equivalent or not
by comparing
properties; create
a function, based
on given criterion,
MS Math Scoring Criteria (Grade 8 Math)
equation 𝑦 = 𝑚𝑥 +
𝑏 as defining a linear
function whose
graph is a straight
line.
in comparison to a
given function.
iii. Students can
determine
whether a
function is linear
or nonlinear (table
or equation); give
real-world
examples of
functions that are
linear or
nonlinear.
B. Students will
use functions to
model
relationships
between
quantities.
[8.F.2.4, 8.F.2.5]
i. Students can
determine the
rate of change
given points on a
coordinate plane.
i. Students can
determine the rate of
change from two (x ,
y) values or from a
graph.
ii. Students can
describe qualitatively
the functional
relationship between
two quantities by
analyzing some
features of a graph to
be linear and
nonlinear.
i. Students can
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;
construct a function
to model a linear
relationship
between two
quantities.
ii. Students can
describe
qualitatively the
functional
relationship
between two
quantities by
analyzing a graph
(e.g, where the
function is
increasing or
decreasing, linear or
nonlinear).
i. Students can
interpret the rate
of change and
initial value of a
linear function in
terms of a verbal
description of the
linear function;
analyze a set of
values in either a
table or graph to
determine
changes to be
made to make the
relationship linear.
ii. Students can
sketch a graph
that exhibits given
qualitative
features of a
function; interpret
qualitative
features of a
function in a
context.
Geometry: Understand geometric concepts and constructions, prove theorems, and apply appropriate results
to solve problems.
Scoring Criteria
Performance
Indicators
Emerging
Progressing
Meets
Exceeds
D. Students will
understand
congruence and
similarity using
physical
i. Students can
define/explain the
terms translation,
rotation,
i. Students can
describe a rigid
transformation
between two
congruent figures
i. Students can
describe a sequence
of up to two rigid
transformations
i. Students can use
properties of rigid
and non-rigid
transformations to
understand the
MS Math Scoring Criteria (Grade 8 Math)
models,
transparencies,
or geometry
software.
[8.G.1.1, 8.G.1.2,
8.G.1.3, 8.G.1.4,
8.G.1.5]
reflection, and
dilation.
that exhibit the
congruence between
them.
ii. Students can
describe the effect of
a reflection or
translation on two-
dimensional figures
using coordinates.
between two
congruent figures.
ii. Students can
describe the effect
of a dilation,
translation,
rotation, or
reflection on two-
dimensional figures
using coordinates
and coordinate
notation.
iii. Students can
identify a sequence
of transformations
and a dilation that
results in similarity.
relationship
between
transformations
and congruence.
ii. Students can
describe the effect
of up to two rigid
transformations on
two-dimensional
figures using
coordinates;
describe the effect
of two
transformations,
including at least
one dilation, on
two-dimensional
figures using
coordinates and
coordinate
notation.
iii. Students can
describe a
sequence of
transformations
and a dilation that
results in
similarity.
E. Students will
understand and
apply the
Pythagorean
Theorem.
[8.G.2.6, 8.G.2.7,
8.G.2.8]
i. Students can recall
the equation for the
Pythagorean
Theorem.
i. Students can use the
Pythagorean Theorem
and apply to right
triangles.
ii. Students can calculate
hypotenuse length
using the Pythagorean
Theorem, given a
picture of a right
triangle or the lengths
of the two legs.
i. Students can model
and explain the proof
of the Pythagorean
Theorem and its
converse using a
pictorial
representation.
ii. Students can calculate
unknown side lengths
using the Pythagorean
Theorem; apply the
Pythagorean Theorem
to find the distance
between two points in
a coordinate system
with the right triangle
drawn.
i. Students can apply
the Pythagorean
Theorem to a real-
world situation in
two and three
dimensions to
determine unknown
side lengths or the
distance between
two points in a
coordinate system.
ii. Students can find
multiple leg lengths
given a hypotenuse
of an isosceles
triangle or find
multiple leg lengths
when two triangles
with the same
hypotenuse are
given; apply the
Pythagorean
Theorem in
multistep problems;
find the coordinates
of a point which is a
given distance
MS Math Scoring Criteria (Grade 8 Math)
(nonvertical and
nonhorizontal) from
another point.
F. Students will
solve real-world
and
mathematical
problems
involving
volume of
cylinders,
cones, and
spheres.
[8.G.3.9]
i. Students can
identify three
dimensional figures
as cones, cylinders
or spheres.
i. Students can recall the
formulas for finding the
volume of cones,
cylinders and spheres.
i. Students can use the
formulas for the
volume of cones,
cylinders, and spheres
to solve real-world
and mathematical
problems.
i. Students can explain
and justify the
relationship between
formulas for the
volume of cones,
cylinders, or spheres;
explain the
derivation of the
formulas for cones,
cylinders, and
spheres.
Statistics and Probability: Interpret and apply statistics and probability to analyze data, reach and justify
conclusions, and make inferences.
Scoring Criteria
Performance
Indicators
Emerging
Progressing
Meets
Exceeds
F. Students will
investigate
patterns of
association in
bivariate data.
[8.SP.1.1, 8.SP.1.2,
8.SP.1.3, 8.SP.1.4]
i. Students can
construct a scatter
plot and describe
the pattern as
positive, negative,
or no relationship.
ii. Students can
identify a straight
line used to describe
a linear association
on a scatter plot.
iii. Students can
identify the slope
and y-intercept of a
linear model on a
scatter plot, given
an equation.
iv. Students can
interpret a two-way
table by row or
column.
i. Students can
conduct and
interpret scatter
plots for bivariate
measurement data
to investigate
patterns of
association
between
quantities.
ii. Students can draw
a straight line on a
scatter plot that
closely fits the data
points.
iii. Students can
interpret the slope
and intercept,
given context.
iv. Students can
complete a two-
way table of
categorical data.
i. Students can
describe patterns
such as outliers
and nonlinear
associations.
ii. Students can
judge how well
the trend line fits
the data;
compare more
than one trend
line for the same
scatter plot and
justify the best
one.
iii. Students can use
the equations of
a linear model to
solve problems in
the context of
bivariate
measurement
data; create and
use a linear
model based on a
set of bivariate
data to solve a
problems
involving slope
and intercept.
iv. Students can
construct and/or
MS Math Scoring Criteria (Grade 8 Math)
interpret a two-
way table to
summarize data;
describe and/or
compare relative
frequencies.
