Pre-Algebra A. Syllabus. Course Overview. Course Goals. General Skills. Credit Value

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1 Syllabus Pre-Algebra A Course Overview Pre-Algebra is a course designed to prepare you for future work in algebra. In Pre-Algebra, you will strengthen your knowledge of numbers as you look to transition from numbers to variables. A variable is a letter or symbol used to represent a number. By pairing your foundational knowledge of numbers with new ideas on variables, you ll develop more sophisticated ways of solving a variety of real-world problems. Course Goals By the end of this course, you will be able to do the following: Perform operations on two- or three-digit numbers. Apply properties of operations. Simplify, compare, and perform operations on fractions. Identify the meaning of place value in the decimal system. Perform operations on decimal numbers. Compute percents and simplify ratios. Use knowledge of ratios to compute proportions. General Skills To participate in this course, you should be able to do the following: Complete basic operations with word processing software, such as Microsoft Word or Google Docs. Understand the basics of spreadsheet software, such as Microsoft Excel or Google Spreadsheets, but having prior computing experience is not necessary. Perform online research using various search engines and library databases. Communicate through and participate in discussion boards. For a complete list of general skills that are required for participation in online courses, refer to the Prerequisites section of the Plato Student Orientation document, found at the beginning of this course. Credit Value Pre-Algebra A is a 0.5-credit course EDMENTUM, INC.

2 Course Materials Notebook Basic Calculator Computer with Internet connection and speakers or headphones Microsoft Word or equivalent Microsoft Excel or equivalent Course Pacing Guide This course description and pacing guide is intended to help you keep on schedule with your work. Note that your course instructor may modify the schedule to meet the specific needs of your class. Unit 1: Whole Numbers Summary In this unit, you will perform the four operations (addition, subtraction, multiplication, and division) on whole numbers. You will explore the properties of whole numbers by comparing and ordering them, estimating, practicing special divisibility rules, and working with the commutative, associative, and distributive properties. You will also solve problems involving whole numbers and the operations. Day Activity/Objective Type Syllabus and Plato Student Orientation Review the Plato Student Orientation and Course Syllabus at the beginning of this course. Understanding Place Value: Thousands Work with place value for numbers through the hundred thousands. Understanding Place Value: Millions, Billions, and Beyond Work with place value for numbers through the hundred billions and beyond. Comparing and Ordering Whole Numbers Compare and order whole numbers with up to six digits. Estimation Basics Estimate by rounding. Estimation by Clustering Estimate by clustering. Adding Two 2-Digit Numbers: Sums Less Than 100 Add 2-digit numbers. Course Orientation 2

3 Adding Three or Four Numbers Add several numbers. Adding Two 2-Digit Numbers: Sums Greater Than 99 Add 2-digit numbers. Using the Identity Property of Addition Use the identity property and use the identity element 0, in addition and subtraction. Adding Multi-Digit Numbers Add multi-digit numbers one column at a time. Subtracting a 1-Digit Number from a 2-Digit Number Subtract from 2-digit numbers. Subtracting Two 2-Digit Numbers Subtract 2-digit numbers. Subtracting Multi-Digit Numbers with Regrouping Subtract multi-digit numbers one column at a time. Subtracting Multi-Digit Numbers with Consecutive Regrouping Subtract with multiple regrouping. Subtracting across Zeros Subtract from large numbers that contain zeros. Multiplying a 2-Digit Number by a 1-Digit Number Multiply a 2-digit number by a 1digit number. Multiplying a 3-Digit Number by a 1-Digit Number Multiply a 3-digit number by a 1digit number. Multiplying a 2-Digit Number by a 2-Digit Number Multiply two 2-digit numbers. Multiplying by a Multiple of 10 or 100 Multiply numbers when one of the factors is a multiple of 10 or 100. Multiplying a Multiple of 10 by a Multiple of 10 Multiply multiples of 10. Using the Identity Property of Multiplication Use the identity property and use the identity element, 1, in multiplication. 3

4 Dividing by a 1-Digit Number Divide by a 1-digit number. Dividing by a 2-Digit Number Divide by a 2-digit number. Dividing Multiples of 100 Divide a number that is a multiple of 10 or 100 by another multiple of 10. Special Divisibility Rules Use the divisibility rules for 2, 3, 4, 5, 6, and 10. Using the Commutative Property of Addition Use the commutative property of addition. Using the Associative Property of Addition Use the associative property of addition. Using the Commutative Property of Multiplication Use the commutative property of multiplication. Using the Associative Property of Multiplication Use the associative property of multiplication. Using the Distributive Property of Multiplication over Addition Use the distributive property of multiplication over addition. Solving Addition and Subtraction Story Problems Solve real-life problems using addition and subtraction. Solving Multiplication Story Problems Solve real-life problems using addition, subtraction, and multiplication. Solving Division Story Problems Solve real-life problems using addition, subtraction, and division. Posttest Unit 1 4

5 Unit 2: Fractions Summary In this unit, you will perform the four basic operations on fractions, as well as find the factors, prime factors, and greatest common factors of numbers in order to perform those operations. You will also find reciprocals and simplify fractions, as well as compare and order fractions and solve problems involving fractions. Day Activity/Objective Type Fraction Notation: Numerator and Denominator Explore fraction notation. Proper Fractions and Improper Fractions Explore proper fractions and improper fractions. Finding Equivalent Fractions Find equivalent fractions. Finding Factors and Prime Factors Find the factors and the prime factors of whole numbers. Greatest Common Factors Find the greatest common factor of two whole numbers. Simplifying Fractions Find the simplest form of fractions. Finding Common Multiples and the Least Common Multiple Find the common multiples and the least common multiple (LCM) of two whole numbers. Working with Common Denominators and the Least Common Denominator Find the least common denominator and will use it to rename fractions. Comparing Fractions Compare fractions. Ordering Fractions Order fractions from least to greatest. Adding and Subtracting Fractions: Like Denominators Add and subtract fractions with like denominators. Adding and Subtracting Fractions: Unlike Denominators Add and subtract fractions with unlike denominators. 5

6 Multiplying Two Fractions Multiply fractions. Finding the Reciprocal Find reciprocals. Dividing a Fraction by a Fraction Divide a fraction by a fraction. Dividing Fractions Divide fractions. Solving Fraction Story Problems Solve real-life problems involving fractions using addition, subtraction, multiplication, and division. Posttest Unit 2 Unit 3: Decimals Summary This unit begins with decimal concepts such as place value and connections between decimals and fractions and whole numbers. You will perform the four basic operations on decimal numbers and explore repeating decimals, rational and irrational numbers, and mental math techniques with whole numbers and decimals. You will also solve word problems with decimal numbers. Day Activity/Objective Type Understanding Decimal Place Value: Tenths and Hundredths Represent mixed numbers and fractions through hundredths as decimal numbers. Understanding Decimal Place Value: Thousandths and Ten- Thousandths Read and write decimal numbers through the ten-thousandths place. Comparing and Ordering Decimals Compare and order decimal numbers less than one. Rounding Decimals Round decimal numbers. Relating Decimals, Fractions, and Mixed Numbers Write certain numbers as fractions or decimals. 6

7 Renaming a Fraction as a Decimal Rename a fraction as a decimal. Fractions and Repeating Decimals Convert between common repeating decimals and their fraction equivalents. Rational and Irrational Numbers Convert between common repeating decimals and their fraction equivalents. Adding and Subtracting Decimals Add and subtract decimal numbers. Multiplying Decimals Multiply decimal numbers. Dividing a 2-Digit Number by 10 or 100 Divide whole numbers by 10 and 100. Dividing Decimal Numbers Divide decimal numbers. Solving Decimal Story Problems Solve real-life problems involving fractions and decimals using addition, subtraction multiplication, and division. Mental Math with Whole Numbers and Decimals Mentally add, subtract, multiply, and divide whole numbers and some decimal numbers. Posttest Unit 3 7

8 Unit 4: Ratios and Proportions, Percents, and Measurement Summary This unit starts by introducing the concept of percent and how it relates to fractions and decimals. The concepts allow you to calculate percents (i.e., find the percent of a whole or decimal number), find percent increases and decreases, solve problems with percents, and use mental math with fractions and percents. You will explore ratios and proportions, find proportions, and work with scaling and proportion. You will also work with units of length, capacity, weight and mass, and convert between Celsius and Fahrenheit temperatures. Day Activity/Objective Type Understanding Percent Explore percents. Relating Fractions, Decimals, and Percents Change percents into decimals and fractions into percents. Finding a Percent of a Whole Number Find a percent of a whole number. Finding a Percent of a Decimal Number Find a percent of a decimal. Percent Increases and Decreases Find amounts after a percent increase or a percent decrease and the percent of an increase or decrease. Solving Problems with Percents Solve problems that involve percents. Mental Math with Fractions and Percents Use mental math to add, subtract, multiply, and divide two fractions, and find the percentage of a whole number when the percent ends in 0 or 5. Understanding Ratio Explore ratios. Equivalent Ratios Find equivalent ratios. Understanding Proportion Explore proportions. Solving Proportions Solve proportions. 8

9 2 days: Solving Ratio, Proportion, and Percent Story Problems Solve real-life problems using addition and subtraction. Solve real-life problems using multiplication and division. Solve real-life problems using fractions and decimals. Solve real-life problems using ratio, proportion, and percent. Scaling and Proportion, Part 1 Explore the difference between scaled drawings and representational diagrams, and identify an appropriate ratio for a scale drawing. Convert from one metric unit of length to another or from one customary unit of length to another. Convert between metric and customary units of length. Scaling and Proportion, Part 2 Use ratios to help find the actual size of an object. Length Match metric and customary units of length to various real-world circumstances. Capacity Match metric and customary units of capacity to various realworld circumstances. Convert from one metric unit of capacity to another or from one customary unit of capacity to another. Convert between metric and customary units of capacity. Weight and Mass Explore the differences between weight and mass. Convert between the common metric and customary units of weight and mass. Converting between Celsius and Fahrenheit Temperatures Convert between Celsius and Fahrenheit temperatures. Posttest Unit 4 Semester Review End-of-Semester Test Webtivity Webtivity Webtivity 9