Table of Contents. Daily Skill Builders: Pre-Algebra. Table of Contents

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2 Table of Contents Table of Contents Introduction to the Teacher...iv NCTM Standards Matrix for Grades Activity # Skill Fractions and Mixed Numbers 1. Factors.... Determining Factors.... Divisibility.... Prime and Composite Numbers.... Prime Factorization Using Factoring to Find the Greatest Common Factor Using Prime Factorization to Find the Greatest Common Factor Least Common Multiple Equivalent Fractions Simplifying Improper Fractions Writing Whole Numbers as Fractions Writing Mixed Numbers as Fractions Writing Fractions in Lowest Terms Adding Fractions With Like Denominators Adding Fractions With Unlike Denominators Subtracting Fractions With Like Denominators Subtracting Fractions With Unlike Denominators Adding and Subtracting Fractions in Word Problems Multiplying Fractions Dividing Fractions Finding a Fraction of a Whole Number Canceling in Fractions Review Adding and Subtracting Fractions/ Test Taking Review Multiplying and Dividing Fractions/ Test Taking... 1 Decimals. Rounding Decimals Changing Fractions to Decimals Multiplying and Dividing by 10; 100; 1,000; etc., Scientific Notation Adding and Subtracting Decimals Multiplying Decimals Dividing Decimals by Whole Numbers Dividing Decimals by Decimals Review Decimals/Test Taking Review Decimals/Test Taking Integers and Variable Expressions. Integers and Absolute Value Comparing Numbers Ordering Numbers Adding Integers Subtracting Integers Multiplying Integers Dividing Integers.... Order of Operations.... Variable Expressions.... Evaluating Variable Expressions.... Exponents Multiplying and Dividing Exponents Negative Exponents Order of Operations Writing Variable Expressions for Real World Problems Properties of Numbers Commutative Property Associative Property Distributive Property Properties of Zero and One... 9 Equations and Inequalities. Combining Like Terms Simplifying Variable Expressions Solving Equations by Subtracting Solving Equations by Adding Solving Equations by Adding or Subtracting Problem Solving With Equations Solving Equations by Dividing Solving Equations by Multiplying Solving Equations by Dividing or Multiplying. 6. Problem Solving Using Equations Solving Two-Step Equations Solving Two-Step Equations Problem Solving by Writing and Solving Equations Problem Solving Using Equations/ Test Practice Simplifying and Solving Equations Simplifying and Solving Equations Formulas Formulas Inequalities Graphing Inequalities Graphing Inequalities Solving Inequalities by Adding and Subtracting Solving Inequalities by Dividing or Multiplying Review Solving Inequalities/Test Taking... 1 Graphing in the Coordinate Plane 79. Graphing in the Coordinate Plane... ii

3 Table of Contents Table of Contents (cont.) 80. Graphing in the Coordinate Plane Equations With Two Variables Graphing Linear Equations Graphing Linear Equations Slope Finding Slope From a Graph Negative Slope and Zero Slope Finding Slope Using Two Points Graphing Linear Equations Using Slope Finding x- and y-intercepts Equations in Slope-Intercept Form Writing an Equation for a Line Changing Equations to Slope-Intercept Form Review Graphing Linear Equations/ Test Taking Review Graphing Linear Equations/ Test Taking Graphing Inequalities Systems of Linear Equations Graphing Systems of Linear Equations Systems of Linear Equations With No Solution... 1 Ratios, Proportions, and Percents 99. Ratios Rates Equivalent Ratios Proportions Using Proportions Changing Percents to Fractions Changing Percents to Decimals Changing Decimals to Percents Changing Fractions to Percents Calculating Percents From a Graph Percent Problems Percent Problems Percent Problems Word Problems With Percents Percent of Change Review Percents/Test Taking... 9 Rational Numbers and Irrational Numbers 11. Comparing Rational Numbers Adding Rational Numbers Subtracting Rational Numbers Multiplying Rational Numbers Dividing Rational Numbers Solving Equations With Rational Numbers Solving Equations With Rational Numbers Solving Equations With Rational Numbers Square Roots Square Roots Adding and Subtracting Square Roots Multiplying and Dividing Square Roots Approximate Square Roots Square Roots and Rational Numbers Review Square Roots/Test Taking Review Square Roots/Test Taking Square Roots and Equations The Pythagorean Theorem Using the Pythagorean Theorem Square Roots and Formulas Polynomials 1. Polynomials Evaluating Polynomials Combining Like Terms in Polynomials Adding Polynomials Problem Solving With Addition of Polynomials Subtracting Polynomials Multiplying Polynomials Powers of Monomials Multiplying Polynomials by Monomials Evaluating Products of Polynomials and Monomials Dividing Polynomials by Monomials Multiplying Binomials Problem Solving Using Polynomials Problem Solving Using Polynomials Problem Solving With Polynomials Problem Solving With Polynomials Reviewing Adding and Subtracting Polynomials/ Test Taking Reviewing Multiplying and Dividing Polynomials/ Test Taking Probability and Odds 1. Patterns and Sequences Patterns and Sequences The Counting Principle Factorials Probability Independent and Dependent Events Computing Probabilities Odds Using a Sample to Make Predictions Using a Sample to Make Decisions... 8 Answer Key... 8 iii

4 Introduction to the Teacher Introduction to the Teacher Both the No Child Left Behind Act and standardized testing require students to meet certain proficiency standards. These Daily Skill Builders are designed to provide students with the opportunity to review or gain extra practice with the skills they are learning in their regular curriculum. They were written with the NCTM National Standards in mind. A matrix correlating the activities with the standards they address is included on pages 1. Suggestions for Use: Each activity page is divided into two reproducible sections that can be cut apart and used separately. Activities could be used in class as a warm-up, a review of a topic covered earlier in the year, as extra practice on a topic currently being studied, in a learning center for review or extra practice, or as a homework assignment. Organization: Activities are arranged by topic and skill level and are progressively more difficult within each topic area. Activities are designed to cover most areas that are addressed in an average pre-algebra curriculum. The Table of Contents indentifies the skills that each activity covers. Since standardized testing is an important component of education, review activities provide practice in standardized test-taking formats. This helps students become familiar and comfortable with the format and provides test-taking practice. Topics Covered: Topics covered in the Daily Skill Builders: Pre-Algebra book include: Fractions and Mixed Numbers Decimals Integers and Variable Expressions Equations and Inequalities Graphing in the Coordinate Plane Ratios, Proportions, and Percents Rational Numbers and Irrational Numbers Polynomials Probability and Odds iv

5 ACTIVITY 1 Factors If a number divides evenly into another number, then it is a factor of that number. Example: The numbers 1,,,, 6, and 1 will all go into 1 evenly, so they are factors of 1. Answer yes or no to the following. 1. Is 6 a factor of 0?. Is a factor of?. Is a factor of 8?. Is a factor of 18?. Is a factor of 19? 6. Is 11 a factor of 11? Circle the numbers that are factors of the first number. 7. 8: : : : : : : : ACTIVITY Determining Factors For each number, find all of the factors. Example: 0 1,,,, 10,

6 (cont.) ACTIVITY Divisibility Tests for Divisibility: A number is divisible by if the last digit is an even number. A number is divisible by if the digits add up to any multiple of (e.g.,, 6, 9, ). A number is divisible by if the last digit is 0 or. A number is divisible by 10 if the last digit is 0. Circle the numbers in this row that are 1. divisible by : divisible by : divisible by : divisible by 10: Bonus: Which of these numbers is divisible by and? ACTIVITY Prime and Composite Numbers A number is prime if it is a whole number greater than 1 that has only 1 and itself as factors. A number is composite if it is a whole number greater than 1 that has at least one other factor besides 1 and itself. In this grid, circle all the prime numbers and underline all the composite numbers

7 ACTIVITY Prime Factorization Every composite number can be factored into a product of prime numbers. This is called prime factorization. To give the prime factorization of a composite number, first list the number as the product of any two numbers. Then, if either or both of those numbers is not prime, factor them. Continue until there are no more factors that are not prime. Example: Find the prime factorization of 1: 1 x 6 ( is prime, but 6 is not.) Factor 6: x (Both are prime.) Therefore, the prime factorization of 1 is x x. Find the prime factorization for each number. (cont.) ACTIVITY 6 Using Factoring to Find the Greatest Common Factor The Greatest Common Factor (GCF) of two numbers is the largest number that is a factor of both numbers. One way to find the Greatest Common Factor of two numbers is to list all the factors of each number, and then find the factors they have in common and see which is the largest. Example: Find the GCF of 1 and 18 Factors of 1: 1,,,, 6, 1 Factors of 18: 1,,, 6, 9, 18 Factors in common: 1,,, 6 6 is the largest, so it is the GCF. Use the method described to find the greatest common factor of these number pairs and 6. 1 and 8 Factors of 0: Factors of 1: Factors of 6: Factors of 8: Common factors: GCF: Common factors: GCF:. 16 and. and 8 Factors of 16: Factors of : Factors of : Factors of 8: Common factors: GCF: Common factors: GCF:

8 ACTIVITY 7 Using Prime Factorization to Find the Greatest Common Factor Another way to find the Greatest Common Factor of two numbers is to first find the prime factorization of both numbers, list all the prime factors the numbers have in common, then multiply the common prime numbers together to get the GCF. Use prime factorization to find the GCF of each of these number pairs. GCF 1. 1 and 0. 1 and Prime factors of 1: Prime factors of 1: Prime factors of 0: Prime factors of : Prime factors in common: Prime factors in common: Multiply common factors: Multiply common factors:. 18 and. 1 and 0 Prime factors of 18: Prime factors of 1: Prime factors of : Prime factors of 0: Prime factors in common: Prime factors in common: Multiply common factors: Multiply common factors: (cont.) ACTIVITY 8 Least Common Multiple The Least Common Multiple (LCM) of two or more numbers is the lowest number that each is a factor of (except 0). To find the Least Common Multiple, begin listing the multiples of both numbers until you find the first one they have in common (the lowest multiple). LCM Example: and Multiples of :, 6, 9, 1, 1, 18, 1 Multiples of :, 10, 1, 0, LCM: 1 Find the LCM of these pairs of numbers: 1. and 6. and 7 Multiples of : Multiples of : Multiples of 6: Multiples of 7: LCM: LCM:. and 8. and 9 Multiples of : Multiples of : Multiples of 8: Multiples of 9: LCM: LCM: 6

$(cont.) ACTIVITY 9 Equivalent Fractions Complete to get an equivalent fraction. 1 1.... 6 18 16 8. 6. 7. 8. 1 0 8 16$

9 (cont.) ACTIVITY 9 Equivalent Fractions Complete to get an equivalent fraction ACTIVITY 10 Simplifying Improper Fractions Simplify these improper fractions IMPROPER PROPER 1 6 7

10 ACTIVITY 11 Writing Whole Numbers as Fractions To write a whole number as a fraction, write the number over the denominator 1, and then multiply both the numerator and the denominator by the same number. Example: Change to fifths. Change to halves Change to the indicated number. x to fifths. 8 to fourths 6. to ninths (cont.) 7. 7 to thirds 8. to sixths 9. to tenths ACTIVITY 1 Writing Mixed Numbers as Fractions To write a mixed number as a fraction, multiply the whole number by the denominator, and add the numerator. This number becomes the numerator and is placed over the original denominator. Example: Change to a fraction. Whole number () x denominator () 8 + numerator () 11 Then place 11 over the denominator (). Change each mixed number to a fraction

$ACTIVITY 1 Writing Fractions in Lowest Terms To write a fraction in lowest terms, divide both the numerator and the denominator by their Greatest Common Factor.$

11 ACTIVITY 1 Writing Fractions in Lowest Terms To write a fraction in lowest terms, divide both the numerator and the denominator by their Greatest Common Factor. Example: Write each fraction in lowest terms. (cont.) ACTIVITY 1 Adding Fractions With Like Denominators To add fractions with like denominators, add the numerators, write the sum over the denominator, and then reduce the fraction to lowest terms if necessary. Example: Add and put in simplest form

$ACTIVITY 1 Adding Fractions With Unlike Denominators To add fractions with unlike denominators, find the Least Common Multiple, change to equivalent fractions, and then add. (cont.) Example: +?$

12 ACTIVITY 1 Adding Fractions With Unlike Denominators To add fractions with unlike denominators, find the Least Common Multiple, change to equivalent fractions, and then add. (cont.) Example: +? 1 and 6 have 1 as the LCM. stays the same Change to 8 Add: Add and put in simplest form ACTIVITY 16 Subtracting Fractions With Like Denominators To subtract fractions with like denominators, subtract the numerators, put the difference over the denominator, and reduce to lowest terms if necessary. Example: Subtract and put in simplest form /10 - /10/

13 Answer Keys Answer Keys Activity 1 (page ) 1. yes. no. no. yes. no 6. yes 7., 8.,, , ,, 8, ,, , 8 1., 1.,, 10, 1 Activity (page ) 1. 1,,,, 6, 8, 1,. 1,,,, 6, 10, 1, 0. 1,,, 6, 9, 18. 1,,. 1,,,, 6, 9, 1, 18, ,,, 9, 1, 7. 1,,,, 8, 10, 0, , ,, 7, ,,,, 6, 1 Activity (page ) Divisible by : 8, 10, 0, 6,, 8 Divisible by : 9, 7,,, 18,, 780 Divisible by :, 70, 90, 8, 110, 89 Divisible by 10: 80, 60, 0, 70, 0, 0 Bonus: 6 Activity (page ) The following numbers should be circled:,,, 7, 11, 1, 17, 19,, 9, 1, 7, 1,, 7. The rest of the numbers should be underlined. Activity (page ) Activity 6 (page ) 1. Factors of 0: 1,,,, 10, 0 Factors of 6: 1,,,, 6, 9, 1, 18, 6 Common Factors: 1,, GCF:. Factors of 1: 1,, 7, 1 Factors of 8: 1,,, 7, 1, 8 Common Factors: 1, 7 GCF: 7. Factors of 16; 1,,, 8, 16 Factors of : 1,,, 6, 7, 1, 1, Common Factors: 1, GCF:. Factors of : 1,,,, 6, 8, 1, Factors of 8: 1,,,, 6, 8, 1,, 8 Common Factors: 1,,,, 6, 8, 1, GCF: Activity 7 (page 6) 1. Prime factors of 1:, Prime factors of 0:,, Prime factors in common:, GCF: 6. Prime factors of 1:, 7 Prime factors of :, 7 Prime factors in common: 7 GCF: 7. Prime factors of 18:, Prime factors of :, Prime factors in common:, GCF: 6. Prime factors of 1:, Prime factors of 0:, Prime factors in common: GCF: Activity 8 (page 6) 1. Multiples of :, 8, 1, 16, 0, Multiples of 6: 6, 1, 18, LCM: 1. Multiples of :,, 6, 8, 10, 1, 1, 16, 18, 0, Multiples of 7: 7, 1, 1 LCM: 1. Multiples of :, 6, 9, 1, 1, 18, 1,, 7 Multiples of 8: 8, 16,, LCM:. Multiples of :, 10, 1, 0,, 0,, 0,, 0 Multiples of 9: 9, 18, 7, 6,, LCM: Activity 9 (page 7) Activity 10 (page 7) 1. 1!g.!f.. #g @d 8. $g 9. 6@j 10. 8!f 11. 7!j 1. 8!s Wq Pp Activity 11 (page 8) 1. *s. AwS. Sw:. Dt:. DrS 6. SoJ 7. SeA 8. SyF 9. Activity 1 (page 8) 1. #s. &d. ArD. AtJ. Du: 6. SiA 7. SuF 8. Se: 9. SrS Activity 1 (page 9) 1.!s. ^j.!s.!g.!k 7.!d 8.!l Activity 1 (page 9) 1. %k aqs 6. aua 7. $g atk Qq Qt Qq Qt Activity 1 (page 10) 1. %h. %k.. 1 rjp. 6. aeh 7. *l 8. #f 9. 1!s#k Activity 16 (page %k 6. aqs 7.!f 8.!s!g 9.!f 8

Are You Ready? Simplify Fractions

Are You Ready? Simplify Fractions SKILL 10 Simplify Fractions Teaching Skill 10 Objective Write a fraction in simplest form. Review the definition of simplest form with students. Ask: Is 3 written in simplest form? Why 7 or why not? (Yes,