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Real Number System Unit | Fractions, Decimals, Square Roots, and Real Numbers
Real Number System Unit | Fractions, Decimals, Square Roots, and Real Numbers
Real Number System Unit | Fractions, Decimals, Square Roots, and Real Numbers
Real Number System Unit | Fractions, Decimals, Square Roots, and Real Numbers
Real Number System Unit | Fractions, Decimals, Square Roots, and Real Numbers
Real Number System Unit | Fractions, Decimals, Square Roots, and Real Numbers
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What others say

"I used this product with math 8 (with MLs, IEP, 504, and gen ed) and accelerated 7th grade. Really helpful for the real number system! Great variety of question types and difficulty. Homework is short yet comprehensive. "
star
Katelyn S.
"Got me through my years as a middle school math teacher. Highly recommend Maneuvering the Middle products!!!"
star
Angela R.

Description

An 8 day CCSS-Aligned Real Number System Unit includes squares and square roots, rational vs. irrational numbers, classifying real numbers, and comparing and ordering real numbers.

Students will practice with both skill-based problems, real-world application questions, and error analysis to support higher level thinking skills. You can reach your students and teach the standards without all of the prep and stress of creating materials!

Standards: 8.NS.1, 8.NS.2, 8.EE.2; Texas Teacher? Grab the TEKS-Aligned Real Number System Unit. Please don’t purchase both as there is overlapping content.

Learning Focus:

  • approximate the value of an irrational number and locate the value on a number line
  • classify, compare, and order real numbers
  • convert between fractions and decimals and evaluate square roots

More details on what is included:

1. Unit Overviews

  • Streamline planning with unit overviews that include essential questions, big ideas, vertical alignment, vocabulary, and common misconceptions.
  • A pacing guide and tips for teaching each topic are included to help you be more efficient in your planning.

2. Student Handouts

  • Student-friendly guided notes are scaffolded to support student learning. 
  • Available as a PDF and the student handouts/homework/study guides have been converted to Google Slides™ for your convenience.

3. Independent Practice

  • Daily homework is aligned directly to the student handouts and is versatile for both in class or at home practice. 

4. Assessments

  • 1-2 quizzes, a unit study guide, and a unit test allow you to easily assess and meet the needs of your students.
  • The Unit Test is available as an editable PPT, so that you can modify and adjust questions as needed.

5. Answer Keys

  • All answer keys are included.

***Please download a preview to see sample pages and more information.***

How to use this resource:

  • Use as a whole group, guided notes setting
  • Use in a small group, math workshop setting
  • Chunk each student handout to incorporate whole group instruction, small group practice, and independent practice.
  • Incorporate our Real Number System Activity Bundle for hands-on activities as additional and engaging practice opportunities.

Time to Complete:

  • Each student handout is designed for a single class period. However, feel free to review the problems and select specific ones to meet your student needs. There are multiple problems to practice the same concepts, so you can adjust as needed.

Is this resource editable?

  • The unit test is editable with Microsoft PPT. The remainder of the file is a PDF and not editable.

Looking for hands-on classroom activities?

  • Check out the corresponding Real Number System Activity Bundle, which includes activities like scavenger hunts, find it and fix its, mazes and more to allow students to engage and practice the concepts. Win-win!

More 8th Grade Units:

Unit 1: Real Number System 

Unit 2: Exponents and Scientific Notation

Unit 3: Linear Equations

Unit 4: Linear Relationships

Unit 5: Functions

Unit 6: Systems of Equations

Unit 7: Transformations

Unit 8: Angle Relationships

Unit 9: Pythagorean Theorem

Unit 10: Volume
Unit 11: Scatter Plots and Data

More 8th Grade Activity Bundles:

Unit 1: Real Number System 

Unit 2: Exponents and Scientific Notation

Unit 3: Linear Equations

Unit 4: Linear Relationships

Unit 5: Functions

Unit 6: Systems of Equations

Unit 7: Transformations

Unit 8: Angle Relationships

Unit 9: Pythagorean Theorem

Unit 10: Volume
Unit 11: Scatter Plots and Data

Looking for more helpful teaching tips, ideas, and support? Check out Maneuveringthemiddle.com and join our online FB community MTM VIPS! 

Try out a FREE math resource! Grab your freebie here!

Licensing: 

This file is a license for ONE teacher and their students. Please purchase the appropriate number of licenses if you plan to use this resource with your team. Thank you!

Customer Service:

If you have any questions, please feel free to reach out for assistance.  We aim to provide quality resources to help teachers and students alike, so contact me before leaving feedback if you have a need. 

Maneuvering the Middle® Terms of Use

Products by Maneuvering the Middle®, LLC may be used by the purchaser for their classroom use only. This is a single classroom license only. All rights reserved. Resources may only be posted online in an LMS such as Google Classroom, Canvas, or Schoology. Students should be the only ones able to access the resources.  It is a copyright violation to upload the files to school/district servers or shared Google Drives. See more information on our terms of use here

If you are interested in a personalized quote for campus and district licenses, please click here

©Maneuvering the Middle® LLC, 2012-present

Report this resource to TPT
Reported resources will be reviewed by our team. Report this resource to let us know if this resource violates TPT's content guidelines.

Real Number System Unit | Fractions, Decimals, Square Roots, and Real Numbers

Maneuvering the Middle
27.3k Followers
$11.50

Highlights

Digital downloads
Grades icon
Grades
Standards icon
Standards
Pages
90
Answer Key
Included

What others say

"I used this product with math 8 (with MLs, IEP, 504, and gen ed) and accelerated 7th grade. Really helpful for the real number system! Great variety of question types and difficulty. Homework is short yet comprehensive. "
star
Katelyn S.
"Got me through my years as a middle school math teacher. Highly recommend Maneuvering the Middle products!!!"
star
Angela R.

Description

An 8 day CCSS-Aligned Real Number System Unit includes squares and square roots, rational vs. irrational numbers, classifying real numbers, and comparing and ordering real numbers.

Students will practice with both skill-based problems, real-world application questions, and error analysis to support higher level thinking skills. You can reach your students and teach the standards without all of the prep and stress of creating materials!

Standards: 8.NS.1, 8.NS.2, 8.EE.2; Texas Teacher? Grab the TEKS-Aligned Real Number System Unit. Please don’t purchase both as there is overlapping content.

Learning Focus:

  • approximate the value of an irrational number and locate the value on a number line
  • classify, compare, and order real numbers
  • convert between fractions and decimals and evaluate square roots

More details on what is included:

1. Unit Overviews

  • Streamline planning with unit overviews that include essential questions, big ideas, vertical alignment, vocabulary, and common misconceptions.
  • A pacing guide and tips for teaching each topic are included to help you be more efficient in your planning.

2. Student Handouts

  • Student-friendly guided notes are scaffolded to support student learning. 
  • Available as a PDF and the student handouts/homework/study guides have been converted to Google Slides™ for your convenience.

3. Independent Practice

  • Daily homework is aligned directly to the student handouts and is versatile for both in class or at home practice. 

4. Assessments

  • 1-2 quizzes, a unit study guide, and a unit test allow you to easily assess and meet the needs of your students.
  • The Unit Test is available as an editable PPT, so that you can modify and adjust questions as needed.

5. Answer Keys

  • All answer keys are included.

***Please download a preview to see sample pages and more information.***

How to use this resource:

  • Use as a whole group, guided notes setting
  • Use in a small group, math workshop setting
  • Chunk each student handout to incorporate whole group instruction, small group practice, and independent practice.
  • Incorporate our Real Number System Activity Bundle for hands-on activities as additional and engaging practice opportunities.

Time to Complete:

  • Each student handout is designed for a single class period. However, feel free to review the problems and select specific ones to meet your student needs. There are multiple problems to practice the same concepts, so you can adjust as needed.

Is this resource editable?

  • The unit test is editable with Microsoft PPT. The remainder of the file is a PDF and not editable.

Looking for hands-on classroom activities?

  • Check out the corresponding Real Number System Activity Bundle, which includes activities like scavenger hunts, find it and fix its, mazes and more to allow students to engage and practice the concepts. Win-win!

More 8th Grade Units:

Unit 1: Real Number System 

Unit 2: Exponents and Scientific Notation

Unit 3: Linear Equations

Unit 4: Linear Relationships

Unit 5: Functions

Unit 6: Systems of Equations

Unit 7: Transformations

Unit 8: Angle Relationships

Unit 9: Pythagorean Theorem

Unit 10: Volume
Unit 11: Scatter Plots and Data

More 8th Grade Activity Bundles:

Unit 1: Real Number System 

Unit 2: Exponents and Scientific Notation

Unit 3: Linear Equations

Unit 4: Linear Relationships

Unit 5: Functions

Unit 6: Systems of Equations

Unit 7: Transformations

Unit 8: Angle Relationships

Unit 9: Pythagorean Theorem

Unit 10: Volume
Unit 11: Scatter Plots and Data

Looking for more helpful teaching tips, ideas, and support? Check out Maneuveringthemiddle.com and join our online FB community MTM VIPS! 

Try out a FREE math resource! Grab your freebie here!

Licensing: 

This file is a license for ONE teacher and their students. Please purchase the appropriate number of licenses if you plan to use this resource with your team. Thank you!

Customer Service:

If you have any questions, please feel free to reach out for assistance.  We aim to provide quality resources to help teachers and students alike, so contact me before leaving feedback if you have a need. 

Maneuvering the Middle® Terms of Use

Products by Maneuvering the Middle®, LLC may be used by the purchaser for their classroom use only. This is a single classroom license only. All rights reserved. Resources may only be posted online in an LMS such as Google Classroom, Canvas, or Schoology. Students should be the only ones able to access the resources.  It is a copyright violation to upload the files to school/district servers or shared Google Drives. See more information on our terms of use here

If you are interested in a personalized quote for campus and district licenses, please click here

©Maneuvering the Middle® LLC, 2012-present

Report this resource to TPT
Reported resources will be reviewed by our team. Report this resource to let us know if this resource violates TPT's content guidelines.

Reviews

4.9
Rated 4.88 out of 5, based on 655 reviews
655
ratings
5
600
4
53
3
2
2
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Mostly used with 8th grade
Reviews
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56
187
15
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1
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7th
8th
9th
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What customers are saying
Met expectations
100%
Is a great value
100%
Is standards-aligned
100%
All verified TPT purchases
PERFECT for Beginning of Year
Rated 5 out of 5
April 23, 2026
Met expectations
Great value
Standards-aligned
I used this product with math 8 (with MLs, IEP, 504, and gen ed) and accelerated 7th grade. Really helpful for the real number system! Great variety of question types and difficulty. Homework is short yet comprehensive.
Class with Katelyn
(TPT Seller)
167 reviews • Indiana
Grades taught: 6th, 7th, 8th
Student populations: Autism, Emerging bilinguals, Learning difficulties, Mild to severe disabilities
Great Supplemental Activities
Rated 5 out of 5
April 9, 2026
Met expectations
Great value
Standards-aligned
This is a great supplemental bundle of activities.
Tammy Gilbert
(TPT Seller)
1,651 reviews • South Dakota
Grades taught: 7th, 8th
A Must-Have for Middle Schoolers!
Rated 5 out of 5
March 21, 2026
Met expectations
Standards-aligned
Got me through my years as a middle school math teacher. Highly recommend Maneuvering the Middle products!!!
Angela R.
25 reviews
Grades taught: 9th, 10th, 11th, 12th
Excellent resource
Rated 5 out of 5
March 19, 2026
Met expectations
Great value
Standards-aligned
Great unit. Lots of good practice. Very well organized.
Educational Odyssey
(TPT Seller)
932 reviews • Tennessee
Grades taught: 8th
Cute and effective notes
Rated 5 out of 5
February 23, 2026
Very cute intro to the real number system that worked well for my students.
Katherine T.
64 reviews
Grades taught: 7th
Great Resource for Teaching Real Numbers
Rated 5 out of 5
February 13, 2026
Met expectations
Great value
Standards-aligned
I used this resource in my math workshop class to assist students during our real numbers unit in math class. It was great to help them learn and reinforce their learning during this unit.
Jessica K.
134 reviews • Alaska
Grades taught: 9th, 10th
Student populations: Autism, Learning difficulties, Mild to severe disabilities
Well-Organized and Easy to Use Real Number Unit
Rated 5 out of 5
February 10, 2026
Met expectations
Great value
Standards-aligned
This unit was very helpful for keeping everything in one place. The lessons flow nicely. It saved me time and made planning much easier.
Alcira V.
360 reviews
Grades taught: 8th
Excellent resource
Rated 5 out of 5
January 1, 2026
Met expectations
Great value
Standards-aligned
This resource was exactly s described. I highly recommend.
Kelly R.
51 reviews
Grades taught: 6th, 7th, 8th

Questions & Answers

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Standards

to see state-specific standards (only available in the US).
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.
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). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
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.
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