Introduction - Learning Mathematics Through Reading and Writing Activities - Pre-Algebra Out Loud

Pre-Algebra Out Loud: Learning Mathematics Through Reading and Writing Activities (2013)

Introduction

Pre-Algebra Out Loud, like the other books in the Out Loud series, is based on the premise that students will perform better in mathematics if they learn to read mathematical content more efficiently, pinpoint and study the important content with better retention, and write well in several different formats about mathematical concepts.

Too often, students learn about mathematics only from watching the teacher do problems and repeating these examples. These activities are considered tried-and-true learning strategies, but if we want students to think deeply or to challenge themselves to truly get it, we must ask them to read, interpret (think), and write about the content in their own words.

Meant for use as a supplemental resource, Pre-Algebra Out Loud provides several successful classroom-tested reading and writing strategies and activities that can be used to help students learn math at a deep level. Some of these activities ask students to paraphrase math text, create word maps, and build and use graphic organizers and tables. Other reading and writing to learn pre-algebra activities include the creation of written problems, a math glossary, and biographies of mathematicians. The activities are meant to teach students how to read, think, and write mathematics efficiently, effectively, and accurately.

The following eight chapters focus on the main pre-algebra topics: the basic tools of algebra; exploring infinite sets; topics in integers; number theory; fractions, decimals, and percents; equations and inequalities; visualizing algebra by graphing; and geometry. Each chapter contains two mini-lessons, as well as activities and reproducible worksheets that you can copy and use in your classroom. All reading and writing activities and strategies have been classroom tested with successful results.

The topics and activities are aligned with the new Common Core State Standards (CCSS) Initiative, a concrete description of standard practice for teaching K--12 mathematics. This is “a state-led effort coordinated by the National Governors Association Center for Best Practices (NGA Center) and the Council of Chief State School Officers (CCSSO). The standards were developed in collaboration with teachers, school administrators, and experts, to provide a clear and consistent framework to prepare our children for college and the workforce” (Common Core Initiative, 2011). This practical and necessary initiative:

1. Make[s] sense of problems and persevere[s] in solving them.

2. Reason[s] abstractly and quantitatively.

3. Construct[s] viable arguments and critique[s] the reasoning of others.

4. Model[s] with mathematics.

5. Use[s] appropriate tools strategically.

6. Attend[s] to precision (know when and how to give exact answers).

7. Look[s] for and make[s] use of structure.

8. Look[s] for and express[es] regularity in repeated reasoning [Common Core Initiative, 2011].

These eight standards form the basic practice of mathematics. Tables I.1 to I.3 give the appropriate standards from the CCSS for the curriculum in grades 6 through 8 that is addressed in each chapter of this book. Since Pre-Algebra Out Loud is not meant to be a comprehensive textbook, only the CCSS standards that target the mini-lessons in each chapter are given. Most of the current pre-algebra textbooks explore the curriculum that meets all of the CCSS standards.

Because Pre-Algebra Out Loud is to be used to enhance your students' exploration of algebra, all of the lessons and activities that follow can be adjusted to fit your individual instructional needs in your sixth-, seventh-, or eighth-grade classroom.

Table I.1 Common Core Standards for Grade 6

Grade 6 Objectives

Chapters and Mini-Lessons

6.RP: Ratios and proportional relationships

Understand ratio concepts and use ratio reasoning to solve problems.

Mini-lesson 7.1

6.NS: Number System

Compute fluently with multi-digit numbers and find common factors and multiples.

Chapter Six; Mini-lessons 4.1, 5.2, 6.1, and 6.2

Apply and extend previous understandings of numbers to the system of rational numbers.

Mini-lessons 5.1 and 7.2

6.EE: Expressions and equations

Apply and extend previous understandings of arithmetic to algebraic expressions.

Mini-lessons 1.1 and 2.2

Reason about and solve one-variable equations and inequalities.

Chapter Two; Mini-lesson 1.2

Solve real-world and mathematical problems involving area, surface area, and volume.

Chapter Eight

Table I.2 Common Core Standards for Grade 7

Grade 7 Objectives

Chapters and Mini-Lessons

7.EE: Expressions and equations

Use properties of operations to generate equivalent expressions.

Chapter One; Mini-lesson 5.2

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Mini-lesson 2.1

7.G: Geometry

Draw, construct, and describe geometrical figures and describe the relationship between them.

Chapter Seven; Mini-lessons 8.1 and 8.2

Table I.3 Common Core Standards for Grade 8

Grade 8 Objectives

Chapters and Mini-Lessons

8.EE: Expressions and equations

Work with radicals and integer exponents.

Chapter Four; Mini-lesson 4.2

Understand the connections between proportional relationships, lines, and linear equations.

Chapter Three; Mini-lessons 3.1 and 3.2