The Algebra Teacher's Guide to Reteaching Essential Concepts and Skills : 150 Mini-Lessons for Correcting Common Mistakes, Grades 6-12

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The Algebra Teacher's Guide to Reteaching Essential Concepts and Skills : 150 Mini-Lessons for Correcting Common Mistakes, Grades 6-12

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  • 製本 Paperback:紙装版/ペーパーバック版/ページ数 322 p.
  • 言語 ENG
  • 商品コード 9780470872826
  • DDC分類 372

Full Description


Easy to apply lessons for reteaching difficult algebra concepts Many students have trouble grasping algebra. In this book, bestselling authors Judith, Gary, and Erin Muschla offer help for math teachers who must instruct their students (even those who are struggling) about the complexities of algebra. In simple terms, the authors outline 150 classroom-tested lessons, focused on those concepts often most difficult to understand, in terms that are designed to help all students unravel the mysteries of algebra. Also included are reproducible worksheets that will assist teachers in reviewing and reinforcing algebra concepts and key skills. * Filled with classroom-ready algebra lessons designed for students at all levels * The 150 mini-lessons can be tailored to a whole class, small groups, or individual students who are having trouble * This practical, hands-on resource will help ensure that students really get the algebra they are learning

Table of Contents

About This Book                                    iii
About the Authors v
Acknowledgments vii
Section 1 Integers, Variables, And 1 (46)
Expressions
1.1 Using the Order of Operations 2 (2)
1.2 Simplifying Expressions That Have 4 (2)
Grouping Symbols
1.3 Simplifying Expressions with Nested 6 (2)
Grouping Symbols
1.4 Using Positive Exponents and Bases 8 (2)
Correctly
1.5 Simplifying Expressions with Grouping 10 (2)
Symbols and Exponents
1.6 Evaluating Expressions 12 (2)
1.7 Writing Expressions 14 (2)
1.8 Writing Expressions Involving 16 (2)
Grouping Symbols
1.9 Identifying Patterns by Considering 18 (2)
All of the Numbers
1.10 Writing Prime Factorization 20 (2)
1.11 Finding the Greatest Common Factor 22 (2)
1.12 Finding the Least Common Multiple 24 (2)
1.13 Classifying Counting Numbers, Whole 26 (2)
Numbers, and Integers
1.14 Finding Absolute Values and Opposites 28 (2)
1.15 Adding Integers with Different Signs 30 (2)
1.16 Subtracting Integers 32 (2)
1.17 Multiplying Two Integers 34 (2)
1.18 Multiplying More Than Two Integers 36 (2)
1.19 Using Integers as Bases 38 (2)
1.20 Dividing Integers 40 (2)
1.21 Finding Absolute Values of 42 (2)
Expressions
1.22 Finding Square Roots of Square 44 (3)
Numbers
Section 2 Rational Numbers 47 (40)
2.1 Classifying Counting Numbers, Whole 48 (2)
Numbers, Integers, and Rational Numbers
2.2 Simplifying Fractions 50 (2)
2.3 Rewriting Mixed Numbers as Improper 52 (2)
Fractions
2.4 Comparing Rational Numbers 54 (2)
2.5 Expressing Rational Numbers as 56 (2)
Decimals
2.6 Expressing Terminating DecimaLs as 58 (2)
Fractions or Mixed Numbers
2.7 Expressing Repeating Decimals as 60 (2)
Fractions or Mixed Numbers
2.8 Adding Rational Numbers 62 (2)
2.9 Subtracting Rational Numbers 64 (2)
2.10 Multiplying and Dividing Rational 66 (2)
Numbers
2.11 Expressing Large Numbers in 68 (2)
Scientific Notation
2.12 Evaluating Rational Expressions 70 (2)
2.13 Writing Ratios Correctly 72 (2)
2.14 Writing and Solving Proportions 74 (2)
2.15 Expressing Fractions as Percents 76 (2)
2.16 Expressing Percents as Fractions 78 (2)
2.17 Solving Percent Problems 80 (2)
2.18 Finding the Percent of Increase or 82 (2)
Decrease
2.19 Converting from One Unit of 84 (3)
Measurement to Another Using the
Multiplication Property of One
Section 3 Equations And Inequalities 87 (50)
3.1 Writing Equations 88 (2)
3.2 Solving Equations by Adding or 90 (2)
Subtracting
3.3 Solving Equations by Multiplying or 92 (2)
Dividing
3.4 Solving Two-Step Equations with the 94 (2)
Variable on One Side
3.5 Solving Equations Using the 96 (2)
Distributive Property
3.6 Solving Equations with Variables on 98 (2)
Both Sides
3.7 Solving Equations with Variables on 100(2)
Both Sides, Including Identities and
Equations That Have No Solution
3.8 Solving Absolute Value Equations 102(2)
3.9 Solving Absolute Value Equations That 104(2)
Have Two Solutions, One Solution, or No
Solution
3.10 Classifying Inequalities as True or 106(2)
False
3.11 Writing Inequalities 108(2)
3.12 Solving Inequalities with Variables 110(2)
on One Side
3.13 Rewriting Combined Inequalities as 112(2)
One Inequality
3.14 Solving Combined 114(2)
Inequalities--Conjunctions
3.15 Solving Combined 116(2)
Inequalities--Disjunctions
3.16 Solving Absolute Value Inequalities 118(2)
3.17 Solving Systems of Equations Using 120(2)
the Substitution Method
3.18 Solving Systems of Equations Using 122(2)
the Addition-or-Subtraction Method
3.19 Solving Systems of Equations Using 124(2)
Multiplication with the
Addition-or-Subtraction Method
3.20 Solving Systems of Equations Using a 126(2)
Variety of Methods
3.21 Solving Systems of Equations That 128(2)
Have One Solution, No Solution, or an
Infinite Number of Solutions
3.22 Using Matrices--Addition, 130(2)
Subtraction, and Scalar Multiplication
3.23 Identifying Conditions for 132(2)
Multiplying Two Matrices
3.24 Multiplying Two Matrices 134(3)
Section 4 Graphs Of Points And Lines 137(38)
4.1 Graphing on a Number Line 138(2)
4.2 Graphing Conjunctions 140(2)
4.3 Graphing Disjunctions 142(2)
4.4 Graphing Ordered Pairs on the 144(2)
Coordinate Plane
4.5 Completing T-Tables 146(2)
4.6 Finding the Slope of a Line, Given 148(2)
Two Points on the Line
4.7 Identifying the Slope and Y-Intercept 150(2)
from an Equation
4.8 Using Equations to Find the Slopes of 152(2)
Lines
4.9 Identifying Parallel and 154(2)
Perpendicular Lines, Given an Equation
4.10 Using the X-Intercept and the 156(2)
Y-Intercept to Graph a Linear Equation
4.11 Using Slope-Intercept Form to Graph 158(2)
the Equation of a Line
4.12 Graphing Linear Inequalities in the 160(2)
Coordinate Plane
4.13 Writing a Linear Equation, Given Two 162(2)
Points
4.14 Finding the Equation of the Line of 164(2)
Best Fit
4.15 Using the Midpoint Formula 166(2)
4.16 Using the Distance Formula to Find 168(2)
the Distance Between Two Points
4.17 Graphing Systems of Linear Equations 170(2)
When Lines Intersect
4.18 Graphing Systems of Linear Equations 172(3)
if Lines Intersect, Are Parallel, or
Coincide
Section 5 Monomials And Polynomials 175(48)
5.1 Applying Monomial Vocabulary 176(2)
Accurately
5.2 Identifying Similar Terms 178(2)
5.3 Adding Polynomials 180(2)
5.4 Subtracting Polynomials 182(2)
5.5 Multiplying Monomials 184(2)
5.6 Using Powers of Monomials 186(2)
5.7 Multiplying a Polynomial by a Monomial 188(2)
5.8 Multiplying Two Binomials 190(2)
5.9 Multiplying Two Polynomials 192(2)
5.10 Dividing Monomials 194(2)
5.11 Dividing Polynomials 196(2)
5.12 Finding the Greatest Common Factor 198(2)
of Two or More Monomials
5.13 Factoring Polynomials by Finding the 200(2)
Greatest Monomial Factor
5.14 Factoring the Difference of Squares 202(2)
5.15 Factoring Trinomials if the Last 204(2)
Term Is Positive
5.16 Factoring Trinomials if the Last 206(2)
Term Is Negative
5.17 Factoring by Grouping 208(2)
5.18 Factoring Trinomials if the Leading 210(2)
Coefficient Is an Integer Greater Than 1
5.19 Factoring the Sums and Differences 212(2)
of Cubes
5.20 Solving Quadratic Equations by 214(2)
Factoring
5.21 Solving Quadratic Equations by 216(2)
Finding Square Roots
5.22 Solving Quadratic Equations Using 218(2)
the Quadratic Formula
5.23 Using the Discriminant 220(3)
Section 6 Rational Expressions 223(28)
6.1 Using Zero and Negative Numbers as 224(2)
Exponents
6.2 Using the Properties of Exponents 226(2)
That Apply to Division
6.3 Using the Properties of Exponents 228(2)
That Apply to Multiplication and Division
6.4 Identifying Restrictions on the 230(2)
Variable
6.5 Simplifying Algebraic Fractions 232(2)
6.6 Adding and Subtracting Algebraic 234(2)
Fractions with Like Denominators
6.7 Finding the Least Common Multiple of 236(2)
Polynomials
6.8 Writing Equivalent Algebraic Fractions 238(2)
6.9 Adding and Subtracting Algebraic 240(2)
Fractions with Unlike Denominators
6.10 Multiplying and Dividing Algebraic 242(2)
Fractions
6.11 Solving Proportions 244(2)
6.12 Solving Equations That Have 246(2)
Fractional Coefficients
6.13 Solving Fractional Equations 248(3)
Section 7 Irrational And Complex Numbers 251(22)
7.1 Simplifying Radicals 252(2)
7.2 Multiplying Radicals 254(2)
7.3 Rationalizing the Denominator 256(2)
7.4 Dividing Radicals 258(2)
7.5 Adding and Subtracting Radicals 260(2)
7.6 Multiplying Two Binomials Containing 262(2)
Radicals
7.7 Using Conjugates to Simplify Radical 264(2)
Expressions
7.8 Simplifying Square Roots of Negative 266(2)
Numbers
7.9 Multiplying Imaginary Numbers 268(2)
7.10 Simplifying Complex Numbers 270(3)
Section 8 Functions 273(43)
8.1 Determining if a Relation Is a 274(2)
Function
8.2 Finding the Domain of a Function 276(2)
8.3 Finding the Range of a Function 278(2)
8.4 Using the Vertical Line Test 280(2)
8.5 Describing Reflections of the Graph 282(2)
of a Function
8.6 Describing Vertical Shifts of the 284(2)
Graph of a Function
8.7 Describing Horizontal and Vertical 286(2)
Shifts of the Graph of a Function
8.8 Describing Dilations of the Graph of 288(2)
a Function
8.9 Finding the Composite of Two Functions 290(2)
8.10 Finding the Inverse of a Function 292(2)
8.11 Evaluating the Greatest Integer 294(2)
Function
8.12 Identifying Direct and Indirect 296(2)
Variation
8.13 Describing the Graph of the 298(2)
Quadratic Function
8.14 Using Rational Numbers as Exponents 300(2)
8.15 Using Irrational Numbers as Exponents 302(2)
8.16 Solving Exponential Equations 304(2)
8.17 Using the Compound Interest Formula 306(2)
8.18 Solving Radical Equations 308(2)
8.19 Writing Logarithmic Equations as 310(2)
Exponential Equations
8.20 Solving Logarithmic Equations 312(2)
8.21 Using the Properties of Logarithms 314(2)
Common Core State Standards for Mathematics 316