Grade 7 Advanced Mathematics Unit E: Real Numbers, Exponents, and Scientific Notation
Common Core State Standards
Unit Overview
Content
Standards
Know that there are numbers that are not rational, and approximate them by rational numbers.
Work with radicals and integer exponents.
Work from previous grades:
In 6th grade, students work with expressions containing exponents.
Highlighted Standards for
Mathematical Practice
MAFS.8.NS.1.1
MAFS.8.NS.1.2
MAFS.8.EE.1.1
MAFS.8.EE.1.2
MAFS.8.EE.1.3
MAFS.8.EE.1.4
Throughout 6th and 7th grade, students work with rational numbers including fractions, decimals, and
integers.
Textbook Resources
Florida Math
Florida Math
Unit A Real Numbers, Exponents, and Scientific Notation
Textbook Unit 1/ Chapter 1
*Interactive Whiteboard Ready presentation Is available for each lesson in the
chapter
*Online Tutors and Videos available for each section
Track your Common Core Progress:
Unit A page xvi
Unit 1/ Chapter 1
What tools do I need? Pg 4
MAFS.K12.MP.2.1 Reason
Abstractly and Quantitatively
MAFS.K12.MP.6.1 Attend to
Precision
MAFS.K12.MP.7.1 Look for and
make us of structure
Textbook Resources
Go Math
Unit 1 Real Numbers, Exponents, and Scientific Notation
Module 1: Real Numbers
1.1-1.3
Module 2: Exponents and Scientific Notation
2.1-2.4
Professional Development Video
Module 1 pg. 4, Module 2 pg. 30
Unit 1 Vocabulary Preview
Pg. 2
Math on the Spot **QR Reader for every example in the book for student use.
What do you already know? Pg 5
Are you ready? Pg 6
1.1-1.10
Continued on next page
Personal Math Trainer: online math trainer for every example in the book
This a working document that will continue to be revised and improved taking your feedback into consideration.
Pasco County Schools, 2014-2015
Grade 7 Advanced Mathematics Unit E: Real Numbers, Exponents, and Scientific Notation
Unit Project Video Unit Project Preview video Music to My Ears pg. 2
End of Unit Project: Music to my Ears pg. 103
Inquiry Lab:
Lesson 1-8 Scientific Notation using Graphing Technology Pg. 67, Lesson 1-9 Roots
and Non-Perfect Squares Pg. 79
Are you Ready (includes a personal math trainer video)
Module 1 pg. 4, Module 2 pg. 30
Reading Start Up: (includes a foldable example for module)
Module 1 pg. 5, Module 2 pg. 31
Unpacking the Standards: *includes a QR Scan Code for Smartphones
Module 1 pg. 6, Module 2 pg. 32
Problem Solving Investigation The Four-Step Plan pg. 39
Careers in Math: Astronomer page 1
College & Career Readiness Robotics Engineer pg. 97
End of Unit Performance Task: Astronomer pg. 62
Real-World Link Video
1-8 Roots pg. 71, 1-9 Estimate Roots pg. 81
Real World Video:
Module 1 pg. 3, Module 2 pg. 29
Example Videos:
Lesson 1-4 Power of a Power page 32 , Lesson 1-6 Scientific Notation pg. 53,
Lesson 1-8 Square Roots pg. 72, Lesson 1-9 Estimate Square and Cube Roots pg. 84
“Power Up” Performance Task: Planetary Play pg. 101
Ready to Go on? Module Quiz
Module 1 pg. 27, Module 2 pg. 57
Unit 1 Study Guide
Pg. 59
Foldables : cut out on page FL3 use on page 100
This a working document that will continue to be revised and improved taking your feedback into consideration.
Pasco County Schools, 2014-2015
Grade 7 Advanced Mathematics Unit E: Real Numbers, Exponents, and Scientific Notation
Mathematics Formative Assessment System Tasks
(Coming July)
The system includes tasks or problems that teachers can implement with their students,
and rubrics that help the teacher interpret students' responses. Teachers using MFAS
ask students to perform mathematical tasks, explain their reasoning, and justify their
solutions. Rubrics for interpreting and evaluating student responses are included so
that teachers can differentiate instruction based on students' strategies instead of
relying solely on correct or incorrect answers. The objective is to understand student
thinking so that teaching can be adapted to improve student achievement of
mathematical goals related to the standards. Like all formative assessment, MFAS is a
process rather than a test. Research suggests that well-designed and implemented
formative assessment is an effective strategy for enhancing student learning.
http://www.cpalms.org/resource/mfas.aspx
Other Resources
http://map.mathshell.org/materials/stds.php?id=1620#standard1621
http://www.illustrativemathematics.org/8
https://www.georgiastandards.org/Common-Core/Pages/Math-6-8.aspx
http://www.engageny.org/resource/grade-8-mathematics
https://sites.google.com/a/nebo.edu/math-8-task-ideas/home/term-1
Repeating decimals
http://map.mathshell.org/materials/lessons.php?taskid=421#task421
Applying Properties of Exponents
http://map.mathshell.org/materials/lessons.php?taskid=573#task573
Exponent Rules WSHS music video
http://www.youtube.com/watch?v=QIZTruxt2rQ
Exponent Rules-Black Eyed Peas song music video
http://www.youtube.com/watch?v=hptchQB0YOY
This a working document that will continue to be revised and improved taking your feedback into consideration.
Pasco County Schools, 2014-2015
Grade 7 Advanced Mathematics Unit E: Real Numbers, Exponents, and Scientific Notation
Unit Scale (Multidimensional) (MDS)
The multidimensional, unit scale is a curricular organizer for PLCs to use to begin unpacking the unit. The MDS should not be used directly with students and is not for
measurement purposes. This is not a scoring rubric. Since the MDS provides a preliminary unpacking of each focus standard, it should prompt PLCs to further explore question #1,
“What do we expect all students to learn?” Notice that all standards are placed at a 3.0 on the scale, regardless of their complexity. A 4.0 extends beyond 3.0 content and helps
students to acquire deeper understanding/thinking at a higher taxonomy level than represented in the standard (3.0). It is important to note that a level 4.0 is not a goal for the
academically advanced, but rather a goal for ALL students to work toward. A 2.0 on the scale represents a “lightly” unpacked explanation of what is needed, procedural and
declarative knowledge i.e. key vocabulary, to move students towards proficiency of the standards.
4.0
In addition to displaying a 3.0 performance, the student must demonstrate in-depth inferences and applications that go beyond what was taught within these
standards. Examples:

3.0
2.0
1.0
Analyze the results of performing operations with varied forms of real numbers and justify which is more accurate and/or efficient
The Student will:
 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show
that the decimal expansion repeats eventually, and convert a decimal expansion, which repeats eventually into a rational number. (MAFS.8.NS.1.1)
 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., π²). (MAFS.8.NS.1.2)
 Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate
square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. (MAFS.8.EE.1.2)
 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² ×3-5=3-3=1/3³=1/27 (MAFS.8.EE.1.1)
 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. (MAFS.8.EE.1.3)
 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific
notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading).
Interpret scientific notation that has been generated by technology. (MAFS.8.EE.1.4)

The student will recognize or recall specific vocabulary, such as:
 Real number, rational number, irrational number, decimal expansion, square root, cube root, perfect square, exponent, power, base, scientific notation,
property
The student will perform basic processes, such as:
 Rational and irrational numbers are real numbers, and estimating their value helps us compare them
 There is a relationship between powers and square roots, and operations can be performed with them
 Scientific Notation is used to represent large and small quantities, and operations can be performed with these numbers
With help, partial success at 2.0 content but not at score 3.0 content
This a working document that will continue to be revised and improved taking your feedback into consideration.
Pasco County Schools, 2014-2015
Grade 7 Advanced Mathematics Unit E: Real Numbers, Exponents, and Scientific Notation
Sample of Unpacking the Standard: What do we want students to Know, Understand and Do (KUD):
The purpose of creating a Know, Understand, and Do Map (KUD) is to further the unwrapping of a standard beyond what the MDS provides and assist PLCs in answering question
#1, “What do we expect all students to learn?” It is important for PLCs to study the focus standards in the unit to ensure that all members have a mutual understanding of what
student learning will look and sound like when the standards are achieved. Additionally, collectively unwrapping the standard will help with the creation of the uni-dimensional
scale (for use with students). When creating a KUD, it is important to consider the standard under study within a K-12 progression and identify the prerequisite skills that are
essential for mastery.
Domain: Expressions and Equations
Cluster: Work with radicals and integer exponents (Major)
Standard: 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.
Understand
“Essential understandings,” or generalizations, represent ideas that are transferable to other contexts.
Understand that very large or very small numbers can be written in a different form.
Know
Declarative knowledge: Facts, vocab., information
Vocabulary: scientific notation
Know that a scientific calculator can be used to
perform scientific notation.
Do
Procedural knowledge: Skills, strategies and processes that are transferrable to other contexts.
Perform operations with numbers expressed in scientific notation. Use scientific notation to choose units of appropriate size
for very large or very small numbers.
Use a scientific calculator to interpret problems in scientific notation.
Prerequisite skills: What prior knowledge (foundational skills) do students need to have mastered to be successful with this standard?
Know the meanings of base, exponent, power, integer rules, order of operations.
Learning Goals:
Add, subtract, multiply, and divide expressions with scientific notation.
Moving Beyond: Extend the properties of exponents to rational exponents. (MAFS.9-12. RN.1.1)
This a working document that will continue to be revised and improved taking your feedback into consideration.
Pasco County Schools, 2014-2015
Grade 7 Advanced Mathematics Unit E: Real Numbers, Exponents, and Scientific Notation
Sample Uni-Dimensional, Lesson Scale:
The uni-dimensional, lesson scale unwraps the cognitive complexity of a focus standard for the unit, using student friendly language. The purpose is to articulate distinct levels of
knowledge and skills relative to a specific topic and provide a roadmap for designing instruction that reflects a progression of learning. The sample performance scale shown
below is just one example for PLCs to use as a springboard when creating their own scales for student-owned progress monitoring. The lesson scale should prompt teams to
further explore question #2, “How will we know if and when they’ve learned it?” for each of the focus standards in the unit and make connections to Design Question 1,
“Communicating Learning Goals and Feedback” (Domain 1: Classroom Strategies and Behaviors). Keep in mind that a 3.0 on the scale indicates proficiency and includes the
actual standard. A level 4.0 extends the learning to a higher cognitive level. Like the multidimensional scale, the goal is for all students to strive for that higher cognitive level,
not just the academically advanced. A level 2.0 outlines the basic declarative and procedural knowledge that is necessary to build towards the standard.
Standard: 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.
Learning Progression
Score
4.0
3.5
3.0
2.5
2.0
1.0
I can…
 Performing multiple operations with numbers that
are expressed in scientific notation.
Sample Tasks
Simplify. Write your answer in scientific notation.
I can do everything at a 3.0, and I can demonstrate partial success at score 4.0.
I can…
 Perform operations with numbers expressed in
scientific notation including decimals.

Interpret scientific notation from the calculator or
other forms of technology.
I can do everything at a 2.0, and I can demonstrate partial success at score 3.0.
I can…
Write
 Write, compare, and order numbers in standard
form and scientific notation.
 Use my scientific calculator to simplify scientific
notation.
I need prompting and/or support to complete 2.0 tasks.
the number either in standard form or scientific notation.
This a working document that will continue to be revised and improved taking your feedback into consideration.
Pasco County Schools, 2014-2015
Grade 7 Advanced Mathematics Unit E: Real Numbers, Exponents, and Scientific Notation
Sample High Cognitive Demand Tasks:
These task/guiding questions are intended to serve as a starting point, not an exhaustive list, for the PLC and are not intended to be prescriptive. Tasks/guiding questions simply
demonstrate one way to help students learn the skills described in the standards. Teachers can select from among them, modify them to meet their students’ needs, or use them
as an inspiration for making their own. They are designed to generate evidence of student understanding and give teachers ideas for developing their own activities/tasks and
common formative assessments. These guiding questions should prompt the PLC to begin to explore question #3, “How will we design learning experiences for our students?”
and make connections to Marzano’s Design Question 2, “Helping Students Interact with New Knowledge”, Design Question 3, “Helping Students Practice and Deepen New
Knowledge”, and Design Question 4, “Helping Students Generate and Test Hypotheses” (Domain 1: Classroom Strategies and Behaviors).
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., π²).
MAFS Mathematical Content Standard(s)
Design Question 1; Element 1
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.
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.
CCSS Mathematical Practice(s)
MAFS.K12.MP.2.1 Reason abstractly and quantitatively
Design Question 1; Element 1
MAFS.K12.MP.6.1 Attend to Precision
Marzano’s Taxonomy
Level 3 Analysis
Teacher Notes
Misconceptions: Students will multiply the base by the exponents. Students may have difficulty finding the square root of a
number in scientific notation. Students may forget to use order of operations.
Questions to develop mathematical thinking,
possible misconceptions/misunderstandings,
how to differentiate/scaffold instruction,
anticipate student problem solving strategies
This a working document that will continue to be revised and improved taking your feedback into consideration.
Pasco County Schools, 2014-2015
Grade 7 Advanced Mathematics Unit E: Real Numbers, Exponents, and Scientific Notation
Task
*These tasks can either be teacher created or
modified from a resource to promote higher
order thinking skills. Please cite the source for
any tasks.
http://www.doe.k12.de.us/assessment/files/Math_Grade_8.pdf
This a working document that will continue to be revised and improved taking your feedback into consideration.
Pasco County Schools, 2014-2015