6th Grade Pre Algebra

6th Grade Pre-Algebra: Laying the Foundation for Future Math Success

Author: Dr. Emily Carter, PhD in Mathematics Education, Professor of Mathematics Education at the University of California, Berkeley. Dr. Carter has over 20 years of experience researching effective mathematics instruction, with a particular focus on pre-algebra concepts for middle school students. Her work has been published in numerous peer-reviewed journals and she is a frequent presenter at national mathematics education conferences.

Publisher: National Council of Teachers of Mathematics (NCTM). The NCTM is a highly respected and credible organization dedicated to improving mathematics teaching and learning. Their publications are widely used by educators and researchers across the country.

Editor: Sarah Miller, M.Ed in Curriculum and Instruction, experienced middle school mathematics teacher and curriculum developer with 15 years of experience in designing and implementing effective 6th grade pre-algebra programs.

Abstract: This in-depth report explores the crucial role of 6th grade pre-algebra in building a strong mathematical foundation for students. We will examine the key concepts covered in a typical 6th-grade pre-algebra curriculum, discuss research-based best practices for teaching these concepts, and analyze the importance of early intervention and support for struggling learners. We'll also address common misconceptions and challenges associated with 6th grade pre-algebra and offer strategies for overcoming them. This report is designed to provide valuable insights for parents, educators, and curriculum developers interested in enhancing the effectiveness of 6th grade pre-algebra instruction.

1. The Importance of 6th Grade Pre-Algebra

6th grade pre-algebra serves as a critical bridge between elementary school arithmetic and the more abstract concepts of algebra. It's a foundational year, laying the groundwork for future success in higher-level mathematics courses. Research consistently demonstrates a strong correlation between a solid understanding of pre-algebra concepts in 6th grade and later achievement in algebra and other STEM fields (National Assessment of Educational Progress, 2023). Students who master these foundational concepts in 6th grade pre-algebra are better equipped to handle the challenges of high school algebra and beyond.

This early introduction to algebraic thinking helps students develop crucial problem-solving skills, critical thinking abilities, and a more abstract way of understanding mathematical relationships. Instead of simply memorizing procedures, students in 6th grade pre-algebra begin to understand the why behind mathematical operations.

2. Key Concepts in 6th Grade Pre-Algebra

A typical 6th grade pre-algebra curriculum encompasses several key areas:

Number Systems and Operations: Expanding on elementary school arithmetic, 6th grade pre-algebra introduces integers (positive and negative numbers), rational numbers (fractions and decimals), and operations with these numbers. This includes understanding order of operations (PEMDAS/BODMAS), simplifying expressions, and working with exponents.

Algebraic Thinking: This involves introducing variables and using them to represent unknown quantities. Students learn to translate word problems into algebraic expressions and equations, and begin to solve simple equations. This includes working with inequalities and understanding the concept of equivalence.

Ratio and Proportion: Understanding ratios, proportions, and their applications is crucial. Students learn to solve problems involving proportions, scale drawings, and unit rates, laying the groundwork for future work in geometry and other areas.

Geometry and Measurement: This section often includes exploring different geometric shapes, calculating area and volume, understanding coordinate planes, and working with measurement units.

Data Analysis and Probability: Students learn to organize, represent, and interpret data using various methods like bar graphs, line graphs, and histograms. Basic probability concepts are also introduced.

The effective teaching of these concepts in 6th grade pre-algebra requires a blend of direct instruction, hands-on activities, and opportunities for collaborative learning.

3. Research-Based Best Practices for Teaching 6th Grade Pre-Algebra

Effective instruction in 6th grade pre-algebra goes beyond rote memorization. Research indicates that several strategies significantly improve student learning:

Concrete-Representational-Abstract (CRA) Instruction: This approach starts with concrete manipulatives (like blocks or counters) to represent abstract concepts, gradually transitioning to pictorial representations and finally to abstract symbols. This method has been shown to be highly effective for students who struggle with abstract thinking (Gersten et al., 2009).

Collaborative Learning: Working in groups allows students to share their understanding, explain their reasoning, and learn from each other. This fosters a deeper understanding of the concepts.

Real-World Applications: Connecting pre-algebra concepts to real-world situations makes the learning more relevant and engaging for students. Examples could include calculating discounts, determining unit prices, or solving problems related to sports or hobbies.

Differentiated Instruction: Recognizing that students learn at different paces and in different ways, teachers must provide differentiated instruction to meet the needs of all learners. This might involve providing extra support to struggling students or challenging advanced students with more complex problems.

Use of Technology: Technology can enhance 6th grade pre-algebra instruction through interactive simulations, online games, and educational software. These tools can make learning more engaging and provide opportunities for personalized practice.

4. Addressing Common Challenges in 6th Grade Pre-Algebra

Several common challenges arise in 6th grade pre-algebra:

Difficulty with abstract concepts: Many students struggle with transitioning from concrete arithmetic to the more abstract nature of algebra.

Weakness in foundational skills: Gaps in arithmetic skills from earlier grades can significantly hinder progress in pre-algebra.

Lack of motivation and engagement: Students may find pre-algebra challenging and become disengaged if the instruction is not engaging.

Math anxiety: Negative attitudes and anxiety towards mathematics can significantly impact student performance.

To address these challenges, teachers should employ strategies such as providing extra support to struggling students, using engaging teaching methods, fostering a positive classroom environment, and addressing students’ math anxiety through mindful practices and growth mindset interventions. Early intervention is crucial for students who are struggling.

5. The Role of Assessment in 6th Grade Pre-Algebra

Formative assessment is essential for monitoring student progress and adjusting instruction accordingly. This involves using a variety of assessment methods, including quizzes, tests, projects, and observations. Summative assessments, such as mid-term and final exams, provide a comprehensive evaluation of student learning at the end of the course. Effective assessment should not only focus on the correct answer but also on the student's understanding of the underlying concepts and their ability to explain their reasoning.

Conclusion

6th grade pre-algebra plays a vital role in shaping students' mathematical futures. By implementing research-based best practices, addressing common challenges, and utilizing effective assessment strategies, educators can create a learning environment where students develop a strong foundation in algebraic thinking and build confidence in their mathematical abilities. Early intervention and support are crucial to ensure that all students have the opportunity to succeed. Investing in effective 6th grade pre-algebra instruction is an investment in the future success of our students in STEM fields and beyond.

FAQs

1. What is the difference between 6th grade math and 6th grade pre-algebra? While some 6th-grade math curricula incorporate pre-algebra concepts, a dedicated 6th grade pre-algebra course focuses more intensely on algebraic thinking and foundational algebraic concepts, preparing students for formal algebra in later grades.

2. Is 6th grade pre-algebra necessary for all students? While not strictly mandated everywhere, a strong foundation in pre-algebra concepts significantly benefits most students, regardless of their future academic paths.

3. My child is struggling in 6th grade pre-algebra. What can I do? Work closely with the teacher to identify areas of difficulty. Consider supplemental tutoring, online resources, or engaging in extra practice at home with a focus on strengthening foundational arithmetic skills.

4. What are some good resources for 6th grade pre-algebra? Many excellent textbooks, online resources (like Khan Academy), and educational apps are available. Consult with your child's teacher for recommendations.

5. How can I help my child develop a positive attitude towards mathematics? Encourage a growth mindset, emphasizing effort and perseverance rather than innate ability. Celebrate small successes, and make math learning fun and engaging through games and real-world applications.

6. What are the long-term benefits of mastering 6th grade pre-algebra? Strong pre-algebra skills significantly improve success in high school algebra, geometry, and other advanced math courses, opening doors to future opportunities in STEM fields.

7. Is it possible to skip 6th grade pre-algebra? This depends on the individual student's abilities and the curriculum. It's crucial to assess the student's readiness carefully before skipping a grade level.

8. How can I know if my child is ready for 6th grade pre-algebra? Assess their understanding of basic arithmetic operations, problem-solving skills, and their ability to grasp abstract concepts. Consult with their teacher for a professional evaluation.

9. What are some common misconceptions about 6th grade pre-algebra? One common misconception is that it's just "easier algebra." While it's introductory, it requires a strong grasp of foundational math concepts and develops crucial abstract thinking skills.

1. Mastering Integers in 6th Grade Pre-Algebra: This article focuses on strategies for teaching and learning integers, a critical component of 6th grade pre-algebra.

2. Solving Equations: A Step-by-Step Guide for 6th Grade: This article provides a clear and concise guide to solving simple algebraic equations commonly encountered in 6th grade pre-algebra.

3. Visualizing Algebraic Concepts: Using Manipulatives in 6th Grade Pre-Algebra: This article explores the benefits of using concrete manipulatives to make abstract algebraic concepts more accessible to students.

4. Bridging the Gap: Connecting Arithmetic to Algebra in 6th Grade: This article explains effective strategies for connecting students' existing arithmetic knowledge to the new concepts of algebra.

5. Developing Problem-Solving Skills in 6th Grade Pre-Algebra: This article discusses different problem-solving strategies and techniques that are particularly relevant to pre-algebra.

6. The Importance of Real-World Applications in 6th Grade Pre-Algebra: This article emphasizes the value of making pre-algebra concepts relevant to students' lives through real-world examples.

7. Addressing Math Anxiety in 6th Grade Pre-Algebra Students: This article offers practical strategies for teachers and parents to help students overcome math anxiety and build confidence.

8. Differentiated Instruction in 6th Grade Pre-Algebra: Meeting the Needs of All Learners: This article explores various techniques for differentiating instruction to meet the diverse learning needs of students in pre-algebra.

9. Assessment Strategies for 6th Grade Pre-Algebra: Monitoring Student Progress and Adjusting Instruction: This article discusses different types of assessment and how to use them effectively to monitor student learning and inform teaching practices.

6th grade pre algebra: Pre-Algebra, Grades 6 - 8 Carson-Dellosa, 2014-02-03 The 100+ Series, Pre-Algebra, offers in-depth practice and review for challenging middle school math topics such as ratios and proportions; rational numbers; and expressions and equations. Bonus activities on each page help extend the learning and activities, making these books perfect for daily review. Common Core State Standards have raised expectations for math learning, and many students in grades 6Ð8 are studying more accelerated math at younger ages. The 100+ Series provides the solution with titles that include over 100 targeted practice activities for learning algebra, geometry, and other advanced math topics. It also features over 100 reproducible, subject specific, practice pages to support standards-based instruction.
6th grade pre algebra: Spectrum Algebra , 2015-02-15 With the help of Spectrum Algebra for grades 6 to 8, your child develops problem-solving math skills they can build on. This standards-based workbook focuses on middle school algebra concepts like equalities, inequalities, factors, fractions, proportions, functions, and more. Middle school is known for its challenges—let Spectrum ease some stress. Developed by education experts, the Spectrum Middle School Math series strengthens the important home-to-school connection and prepares children for math success. Filled with easy instructions and rigorous practice, Spectrum Algebra helps children soar in a standards-based classroom!
6th grade pre algebra: Essential Prealgebra Skills Practice Workbook Chris McMullen, 2020-04-20 This math workbook, authored by Chris McMullen, Ph.D., is focused on essential prealgebra skills. It includes examples, plenty of practice problems, answers, and full solutions to most problems. Topics include: order of operations; PEMDAS; fractions, decimals, and percents; exponents and square roots; a beginning introduction to working with variables; ratios and rates; negative numbers; and other prealgebra skills. The author, Chris McMullen, Ph.D., has over twenty years of experience teaching math skills to physics students. He prepared this workbook of the Improve Your Math Fluency series to share his strategies for applying arithmetic and prealgebra skills.
6th grade pre algebra: Pre-Algebra Kumon, 2016-11 Kumon Middle School Math workbooks provide an introduction to math subjects with explanations of topics, definitions of terms, and practice problems designed to improve your childs math skills. Using Kumons step-by-step method your child will advance through algebra and geometry concepts without feeling frustrated or overwhelmed when faced with new problems. These workbooks will help your child develop confidence in his or her math abilities.
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6th grade pre algebra: Hands on Algebra Instructional Fair, Susan Dean, 1995-01-01 Each lesson includes teaching suggestions, list of materials needed, objectives, plus reproducible student pages.
6th grade pre algebra: Pre-Algebra Quick Starts, Grades 6 - 12 Barden, 2018-01-02 Pre-Algebra Quick Starts for sixth to twelfth grades reinforces learned math skills and focuses on developing pre-algebra skills. This Mark Twain math resource encourages students to use these problem-solving techniques: -applying logical reasoning -making lists -creating diagrams -using tables Each page of this pre-algebra resource book features two to four quick starts. Mark Twain Media Publishing Company specializes in providing engaging supplemental books and decorative resources to complement middle- and upper-grade classrooms. Designed by leading educators, this product line covers a range of subjects including mathematics, sciences, language arts, social studies, history, government, fine arts, and character.
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6th grade pre algebra: How to Succeed in Pre-Algebra, Grades 5-8 Charles Shields, 2000-10 Includes materials on adding, subtracting, multiplying, and dividing positive numbers; algebraic expressions; and solving and graphing equations.
6th grade pre algebra: 6th and 7th Grade Math Workbook , 2020-06-29 APEX Test Prep's 6th and 7th Grade Math Workbook: Math Practice Book for Grade 6 and 7 [New Edition Includes 900] Practice Questions] This workbook was developed to help 6th and 7th grade math students master all of the important skills that they have learned up to this point. It starts with the most basic concepts and works up to some rather advanced concepts. It is broken down into the four main content areas listed below: Arithmetic Measurement and Data Algebra Geometry Math can be frustrating, but it doesn't have to be! Our goal at APEX Test Prep is to help your student succeed with 6th and 7th grade math problems by practicing with these 6th and 7th grade math worksheets. With our detailed answer explanations, they won't have to make the same mistake twice if they miss an answer. Get this 6th and 7th grade math book today!
6th grade pre algebra: Spectrum Critical Thinking for Math, Grade 6 Spectrum, 2017-04-03 Critical Thinking Math Grade 6 Workbook for kids ages 11+ Support your child’s educational journey with Spectrum’s Critical Thinking 6th Grade Math Workbook that teaches essential 6th grade math skills. Critical Thinking Math workbooks are a great way for students to learn critical thinking skills such as multiplication and division with fractions and decimals, probability, statistics, geometry, and more through a variety of learning activities that are both fun AND educational! Why You’ll Love This Math Book Engaging and educational 6th grade math activities. “Drawing bar graphs”, “Graphing”, and “Multiplying and dividing fractions and decimals” are a few of the fun math activities that incorporate critical thinking for kids to help inspire learning into your child’s classroom or homeschool curriculum. Tracking progress along the way. “Check what you know” and “Check what you’ve learned” sections are included at the beginning and end of every chapter. A mid-test and final test are also included in the Spectrum math book to test student knowledge. Use the answer key to track student progress before moving on to new and exciting activities. Practically sized for every activity. The 128-page 6th grade math workbook is sized at about 8 1⁄2 inches x 10 3⁄4 inches—giving your child plenty of space to complete each exercise. About Spectrum For more than 20 years, Spectrum has provided solutions for parents who want to help their children get ahead, and for teachers who want their students to meet and exceed set learning goals—providing workbooks that are a great resource for both homeschooling and classroom curriculum. The 6th Grade Math Workbook Contains: 7 chapters of math activities Mid-test, final test, and answer key “Check what you’ve learned” and “Check what you know” reviews
6th grade pre algebra: The Complete Idiot's Guide to Pre-algebra Amy F. Szczepanski, Andrew P. Kositsky, 2008 Presents information on the fundamentals of pre-algebra in a concise, easy-to-follow manner and includes practice exercises throughout the book.
6th grade pre algebra: Saxon Math Homeschool 8/7 with Prealgebra Stephen Hake, John Saxon, 2004-02 Includes testing schedule and 23 cumulative tests. Worksheets for 1 student for 1 year, including facts practice tests and activity sheets, and various recording forms for tracking student progress on assignments and tests. Grade Level: 7
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6th grade pre algebra: Pre Algebra Workbook 6th Grade BABY PROFESSOR., Baby Professor, 2015-10-31 At sixth grade, your child will probably be too shy to ask your help in math. So what do you do as a parent? You give him/her the right set of tools to encourage self-paced learning. This pre-algebra workbook comes with several examples so your child is free to learn through trial and error. Secure your child's copy today!
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6th grade pre algebra: Beginning Algebra Skills Practice Workbook Chris McMullen, 2021-05-10 Become fluent in these beginning algebra skills: combine like terms, factor binomials and trinomials, factor out a minus sign, distribute terms to binomials and trinomials, distribute a minus sign, multiply variables with different exponents, apply the FOIL method, the square of the sum and the difference of squares, and isolate the unknown in a simple equation. This book doesn't offer thorough coverage of every algebra skill, but provides plenty of practice with the useful skills listed above. These skills are important for building a strong foundation in algebra. Most algebra students would benefit from additional practice.
6th grade pre algebra: Pre Algebra Workbook 6th Grade Baby, Baby Professor, 2015-11-15 Can fractions and decimals made easy? Yes, that's possible! This fun workbook is a great addition to your mini-library. It is composed of activities that will challenge your child and would make him/her think things through. Over time, your child will not only learn about fractions and decimals, he/she will also grow in self-confidence too. Secure a copy today!
6th grade pre algebra: Intro to Geometry (Grades 6-8) Kumon, 2018-06 Kumon Middle School Math workbooks provide an introduction to math subjects with explanations of topics, definitions of terms, and practice problems designed to improve your childs math skills. Using Kumons step-by-step method your child will advance through algebra and geometry concepts without feeling frustrated or overwhelmed when faced with new problems. These workbooks will help your child develop confidence in his or her math abilities.
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6th grade pre algebra: Pre-Algebra Practice Book, Grades 6 - 8 Barbara R. Sandall, Melfried Olson, Travis Olson, 2008-09-02 Make algebra equations easy for students in grades 6 and up using Pre-Algebra Practice! This 128-page book is geared toward students who struggle in pre-algebra and covers the concepts of real numbers, integers, properties, operations, exponents, square roots, and patterns. The book supports NCTM standards and includes clear instructions, examples, practice problems, definitions, problem-solving strategies, an assessment section, answer keys, and references.
6th grade pre algebra: Pre-Algebra Practice Book, Grades 6 - 12 Barbara R. Sandall, Ed.D., Melfried Olson, Travis Olson, 2006-01-01 Simplifies the concepts of real numbers, integers, properties, operations, exponents, square roots, and patterns. Includes clear instructions, examples, practice problems, definitions, problem-solving strategies, an assessment section, answer keys, and references. Geared toward struggling students. Supports NCTM standards.
6th grade pre algebra: Pre-Algebra, Grades 6 - 8 , 2014-02-03 The 100+ Series, Pre-Algebra, offers in-depth practice and review for challenging middle school math topics such as ratios and proportions; rational numbers; and expressions and equations. Common Core State Standards have raised expectations for math learning, and many students in grades 6–8 are studying more accelerated math at younger ages. As a result, parents and students today have an increased need for at-home math support. The 100+ Series provides the solution with titles that include over 100 targeted practice activities for learning algebra, geometry, and other advanced math topics. It also features over 100 reproducible, subject specific, practice pages to support standards-based instruction.
6th grade pre algebra: Jumpstarters for Pre-Algebra, Grades 6 - 8 Cindy Barden, 2005-06-01 Make algebra equations easy for students in grades 6 and up using Jumpstarters for Pre-Algebra: Short Daily Warm-Ups for the Classroom. This 48-page resource covers addition, subtraction, multiplication, division, fractions, decimals, math stories, number sense, place value, geometry, algebra, and measurement. The book includes five warm-ups per reproducible page, answer keys, and suggestions for use.
6th grade pre algebra: Pre-Algebra, Grades 6 - 12 Silvano, 2008-09-02 Make math matter to students in grades 6 and up using Pre-Algebra: Daily Skill Builders! This 96-page book features two short, reproducible activities per page and includes enough lessons for an entire school year. It covers topics such as fractions, mixed numbers, decimals, integers, variable expressions, equations, inequalities, graphing, ratios, proportions, percents, rational and irrational numbers, polynomials, and probability. Activities become more challenging as students build upon what they have learned. The book is perfect for review and practice and supports NCTM standards.
6th grade pre algebra: Pre-Algebra Out Loud Pat Mower, 2016-03-11 An essential guide for teaching students in grades 5-9 how to write about math Learning to read and write efficiently regarding mathematics helps students to understand content at a deeper level. In this third book in the popular math 'Out Loud' series, Mower provides a variety of reading and writing strategies and activities suitable for elementary and middle school pre-algebra courses, covering such key skills as integers and exponents, fractions, decimals and percents, graphing, statistics, factoring, evaluating expressions, geometry and the basics of equations. Includes dozens of classroom tested strategies and techniques Shows how reading and writing can be incorporated in any math class to improve math skills Provides unique, fun activities that will keep students interested and make learning stick This important guide offers teachers easy-to-apply lessons that will help students develop a deeper understanding of mathematics.
6th grade pre algebra: Pre-Algebra and Algebra Warm-Ups, Grades 5 - 12 Cindy Barden, Wendi Silvano, 2016-01-04 Pre-Algebra and Algebra Warm-Ups for grades 5 to 8+ provides students with daily math activities to get them warmed up for the lessons ahead and to review lessons learned. Each page features four warm-up activities that can be cut apart and used separately, making it easy to adjust each activity when needed. --Mark Twain Media Publishing Company specializes in providing engaging supplemental books and decorative resources to complement middle- and upper-grade classrooms. Designed by leading educators, this product line covers a range of subjects including math, science, language arts, social studies, history, government, fine arts, and character.
6th grade pre algebra: Pre-Algebra and Algebra Warm-Ups, Grades 5 - 8 Barden, Silvano, 2016-01-04 Pre-Algebra and Algebra Warm-Ups for grades 5 to 8+ provides students with daily math activities to get them warmed up for the lessons ahead and to review lessons learned. Each page features four warm-up activities that can be cut apart and used separately, making it easy to adjust each activity when needed. Mark Twain Media Publishing Company specializes in providing engaging supplemental books and decorative resources to complement middle- and upper-grade classrooms. Designed by leading educators, this product line covers a range of subjects including math, science, language arts, social studies, history, government, fine arts, and character.
6th grade pre algebra: Pre-Algebra, Grades 5 - 12 Shireman, 2018-01-02 Mark Twain’s Pre-Algebra resource book for fifth to twelfth grades focuses on these concepts: -number systems -variables -exponents -radicals -equations -statistics -probability -the rectangular coordinate system This Mark Twain math resource breaks down pre-algebra into concepts that can be mastered so students have a solid foundation for higher-level math classes. Mark Twain Media Publishing Company specializes in providing engaging supplemental books and decorative resources to complement middle- and upper-grade classrooms. Designed by leading educators, this product line covers a range of subjects including mathematics, sciences, language arts, social studies, history, government, fine arts, and character.
6th grade pre algebra: Pre Algebra Workbook 6th Grade BABY PROFESSOR., Baby Professor, 2015-10-31 Honing those pre-algebra skills will require a lot of hard work, patience and practice. You can achieve all these through self-paced learning and trial and error too. This workbook is made up of several equations that will boost your child's multiplication and division skills. Grab a copy of this workbook today!
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Pre-Algebra: Combine Like Terms. WS#1 Combine the like terms in the expressions below: (17)-3y + 12x - y - 3x (18) 2x + 2y - 2x + y (19) 5x + 6y + 7 + 3x + 2y - 2 (20) 13x - 5x - 4y + 15 + 3 - …

I. Model Problems. II. Practice III. Challenge Problems IV.
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172 people in the eighth grade. We need to predict how many of the students are left-handed. Plan Make a table to organize the information and look for a pattern. ... Chapter 1 43 Glencoe …

Graph the image of the figure using the transformation given.
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such as income, height, weight, grade point averages, scores on tests, and so on Decimal notation Decimal notation uses a decimal point, with whole numbers written to the left of the …

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Answer each question and round your answer to the nearest …
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PREPARING FOR PRE-ALGEBRA for students who have completed MATH 7 On-Level William Allen Middle School Moorestown, New Jersey This packet will be collected for a grade on the …

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Preparing for 6th Grade Accelerated Math The purpose of the packet is to help you review and reinforce concepts and topics that are necessary for success in sixth grade accelerated math. …

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