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 email 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.
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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 1 day: 1 1 day: 2
Activity/Objective Syllabus and Plato Student Orientation Review the Plato Student Orientation and Course Syllabus at the beginning of this course.
Course Orientation
Understanding Place Value: Thousands
Courseware
Work with place value for numbers through the hundred thousands.
1 day:
Understanding Place Value: Millions, Billions, and Beyond
3
Work with place value for numbers through the hundred billions and beyond.
1 day: 4 1 day: 5 1 day: 6 1 day: 7
Type
Comparing and Ordering Whole Numbers
Courseware
Offline
Compare and order whole numbers with up to six digits. Estimation Basics
Courseware
Estimate by rounding. Estimation by Clustering
Courseware
Estimate by clustering. Adding Two 2-Digit Numbers: Sums Less Than 100 Add 2-digit numbers.
2
Courseware
1 day: 8 1 day: 9 1 day: 10 1 day: 11 1 day: 12 1 day: 13 1 day: 14 1 day: 15 1 day: 16 1 day: 17 1 day: 18 1 day: 19 1 day: 20 1 day: 21 1 day: 22
Adding Three or Four Numbers
Courseware
Add several numbers. Adding Two 2-Digit Numbers: Sums Greater Than 99
Courseware
Add 2-digit numbers. Using the Identity Property of Addition
Courseware
Use the identity property and use the identity element 0, in addition and subtraction. Adding Multi-Digit Numbers
Courseware
Add multi-digit numbers one column at a time. Subtracting a 1-Digit Number from a 2-Digit Number
Courseware
Subtract from 2-digit numbers. Subtracting Two 2-Digit Numbers
Courseware
Subtract 2-digit numbers. Subtracting Multi-Digit Numbers with Regrouping
Courseware
Subtract multi-digit numbers one column at a time. Subtracting Multi-Digit Numbers with Consecutive Regrouping
Courseware
Subtract with multiple regrouping. Subtracting across Zeros
Courseware
Subtract from large numbers that contain zeros. Multiplying a 2-Digit Number by a 1-Digit Number
Courseware
Multiply a 2-digit number by a 1digit number. Multiplying a 3-Digit Number by a 1-Digit Number
Courseware
Multiply a 3-digit number by a 1digit number. Multiplying a 2-Digit Number by a 2-Digit Number
Courseware
Multiply two 2-digit numbers. Multiplying by a Multiple of 10 or 100
Courseware
Multiply numbers when one of the factors is a multiple of 10 or 100. Multiplying a Multiple of 10 by a Multiple of 10
Courseware
Multiply multiples of 10. Using the Identity Property of Multiplication Use the identity property and use the identity element, 1, in multiplication.
3
Courseware
1 day: 23 1 day:
Dividing by a 1-Digit Number Divide by a 1-digit number. Dividing by a 2-Digit Number
24
Divide by a 2-digit number.
1 day:
Dividing Multiples of 100
25 1 day:
Courseware
Courseware
Courseware
Divide a number that is a multiple of 10 or 100 by another multiple of 10. Special Divisibility Rules
Offline
26
Use the divisibility rules for 2, 3, 4, 5, 6, and 10.
1 day:
Using the Commutative Property of Addition
27 1 day: 28 1 day: 29 1 day: 30 1 day: 31 1 day: 32 1 day: 33 1 day: 34 1 day:
Courseware
Use the commutative property of addition. Using the Associative Property of Addition
Courseware
Use the associative property of addition. Using the Commutative Property of Multiplication
Courseware
Use the commutative property of multiplication. Using the Associative Property of Multiplication
Courseware
Use the associative property of multiplication. Using the Distributive Property of Multiplication over Addition
Courseware
Use the distributive property of multiplication over addition. Solving Addition and Subtraction Story Problems
Courseware
Solve real-life problems using addition and subtraction. Solving Multiplication Story Problems
Courseware
Solve real-life problems using addition, subtraction, and multiplication. Solving Division Story Problems
Courseware
Solve real-life problems using addition, subtraction, and division. Posttest—Unit 1
Assessment
35
4
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.
Activity/Objective
Day 1 day: 36
Fraction Notation: Numerator and Denominator
1 day: 37
Proper Fractions and Improper Fractions
1 day: 38
Finding Equivalent Fractions
1 day: 39
Finding Factors and Prime Factors
1 day: 40
Greatest Common Factors
1 day: 41
Simplifying Fractions
1 day: 42
Finding Common Multiples and the Least Common Multiple
1 day: 43
Type Courseware
Explore fraction notation. Courseware
Explore proper fractions and improper fractions. Courseware
Find equivalent fractions. Offline
Find the factors and the prime factors of whole numbers. Offline
Find the greatest common factor of two whole numbers. Courseware
Find the simplest form of fractions. Courseware
Find the common multiples and the least common multiple (LCM) of two whole numbers. Working with Common Denominators and the Least Common Denominator
Courseware
Find the least common denominator and will use it to rename fractions. 1 day: 44
Comparing Fractions
1 day: 45
Ordering Fractions
1 day: 46
Adding and Subtracting Fractions: Like Denominators
1 day: 47
Adding and Subtracting Fractions: Unlike Denominators
Courseware
Compare fractions. Courseware
Order fractions from least to greatest. Courseware
Add and subtract fractions with like denominators.
Add and subtract fractions with unlike denominators. 5
Courseware
1 day: 48
Multiplying Two Fractions
1 day: 49
Finding the Reciprocal
1 day: 50
Dividing a Fraction by a Fraction
1 day: 51
Dividing Fractions
1 day: 52
Solving Fraction Story Problems
1 day: 53
Courseware
Multiply fractions. Courseware
Find reciprocals. Courseware
Divide a fraction by a fraction. Courseware
Divide fractions. Courseware
Solve real-life problems involving fractions using addition, subtraction, multiplication, and division. Posttest—Unit 2
Assessment
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 1 day: 54 1 day: 55
Activity/Objective Understanding Decimal Place Value: Tenths and Hundredths
Type Courseware
Represent mixed numbers and fractions through hundredths as decimal numbers. Understanding Decimal Place Value: Thousandths and TenThousandths
Courseware
Read and write decimal numbers through the ten-thousandths place. 1 day: 56
Comparing and Ordering Decimals
1 day: 57
Rounding Decimals
1 day: 58
Relating Decimals, Fractions, and Mixed Numbers
Courseware
Compare and order decimal numbers less than one. Courseware
Round decimal numbers.
Write certain numbers as fractions or decimals. 6
Courseware
1 day: 59
Renaming a Fraction as a Decimal
1 day: 60
Fractions and Repeating Decimals
1 day: 61
Rational and Irrational Numbers
1 day: 62
Adding and Subtracting Decimals
1 day: 63
Multiplying Decimals
1 day: 64
Dividing a 2-Digit Number by 10 or 100
1 day: 65
Dividing Decimal Numbers
1 day: 66
Solving Decimal Story Problems
1 day: 67 1 day: 68
Courseware
Rename a fraction as a decimal. Offline
Convert between common repeating decimals and their fraction equivalents. Offline
Convert between common repeating decimals and their fraction equivalents. Courseware
Add and subtract decimal numbers. Courseware
Multiply decimal numbers. Courseware
Divide whole numbers by 10 and 100. Offline
Divide decimal numbers. Courseware
Solve real-life problems involving fractions and decimals using addition, subtraction multiplication, and division. Mental Math with Whole Numbers and Decimals
Courseware
Mentally add, subtract, multiply, and divide whole numbers and some decimal numbers. Posttest—Unit 3
Assessment
7
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 1 day: 69 1 day: 70 1 day: 71 1 day: 72 1 day: 73
Activity/Objective Understanding Percent
Courseware
Explore percents. Relating Fractions, Decimals, and Percents
Finding a Percent of a Whole Number
Finding a Percent of a Decimal Number
Percent Increases and Decreases
Offline
Find amounts after a percent increase or a percent decrease and the percent of an increase or decrease.
Mental Math with Fractions and Percents
1 day: 77 1 day: 78 1 day: 79
Courseware
Find a percent of a decimal.
1 day:
76
Courseware
Find a percent of a whole number.
Solving Problems with Percents
1 day:
Courseware
Change percents into decimals and fractions into percents.
1 day: 74
75
Type
Courseware
Solve problems that involve percents. Courseware
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
Courseware
Explore ratios. Equivalent Ratios
Courseware
Find equivalent ratios. Understanding Proportion
Courseware
Explore proportions. Solving Proportions
Courseware
Solve proportions.
8
2 days: 80–81
1 day: 82
Solving Ratio, Proportion, and Percent Story Problems
Courseware
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
Courseware
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.
1 day: 83 1 day: 84 1 day: 85
1 day: 86
1 day: 87
Scaling and Proportion, Part 2
Courseware
Use ratios to help find the actual size of an object. Length
Webtivity
Match metric and customary units of length to various real-world circumstances. Capacity
Webtivity
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
Webtivity
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
Offline
Convert between Celsius and Fahrenheit temperatures.
1 day: 88
Posttest—Unit 4
1 day: 89
Semester Review
1 day: 90
End-of-Semester Test
Assessment
Assessment
9