GED/ABE Mathematics Book 1 (ABE/preGED)

Auston B Cron, Aug 30, 2015

[color=#c51414][b]G[/b]eneral [b]E[/b]ducational [b]D[/b]evelopment[/color] (GED) tests are a group of four subject tests which, when passed, certify that the test taker has American or Canadian high school-level academic skills. Here are some topics which can assist students in learning the mathematics covered on the GED/HiSET/TASC/GCSE [color=#c51414][b]G[/b]eneral [b]C[/b]ertificate of [b]S[/b]econdary [b]E[/b]ducation[/color]. Book 1 is a compilation of basic skills needed for success, but not tested. [b]Mostly PreGED/ABE Skills[/b] Book 2 has many activities which are tested. [b]Many GED Level Skills[/b] [b]GED/ABE Mathematics Book1[/b] [url]https://www.geogebra.org/m/j4UyPdKW[/url] [b]GED Mathematics Book 2[/b] [url]https://www.geogebra.org/m/mEs37yMj[/url] [b]GED Science[/b] [url]https://www.geogebra.org/m/kH5xMUpw[/url] [b]GED Slope[/b] [url]https://www.geogebra.org/m/cvAySD7E[/url] Thanks, Tim B. [b]Geometry Introduction[/b] [url]https://www.geogebra.org/m/dsGHMH8u[/url] [b]Nets of Solids[/b] (Surface Area and Volume Animations) [url]https://www.geogebra.org/m/gU22RUUA#material/J3Bmsxp3[/url] [b]GED MATH 2015-2021 Linear Algebra & Geometry [/b] [url]https://www.geogebra.org/m/ATn8TUCm[/url] [b]Basic Arithmetic Facts for GED[/b] [url]https://www.geogebra.org/m/x4qx9bz5[/url] [b]Prime Numbers Game[/b] [url]https://mathsbot.com/puzzles/findThePrimes[/url] [b]GeoGebra Math Activities[/b] [url]https://www.geogebra.org/math[/url] [b]GeoGebra Math Practice[/b] [url]https://www.geogebra.org/mathpractice/en[/url] [b]Graspable Math[/b] [url]https://activities.graspablemath.com/[/url]

Table of Contents

  1. Introduction
    1. Isle of Math
  2. Place Value
    1. Practice Place Values
    2. Place Value
    3. Place Value for Decimals
    4. Expanding Decimal Numbers
    5. Place Value Cards - Input
    6. Place Value Cards - Random
    7. Two-digit whole numbers
    8. Three-digit whole numbers
    9. Place Value: Addition
    10. Place Value: Subtraction
    11. Numbers to Words (hundreds)
    12. Number To Words
    13. Words to Numbers
    14. Rounding Whole Numbers
    15. Scientific Notation-Section 4.1
    16. Scientific Notation
    17. Moving Place Value
  3. Arithmetic Skills
    1. Multiplication Practice
    2. Family of Addition/Multiplication Facts
    3. Integer Addition
    4. Integer Subtraction
    5. Integer Multiplication
    6. Integer Division
    7. Converting Decimals to Fraction
    8. Decimal Addition
    9. Decimal Subtraction
    10. Decimal Multiplication Practice
    11. Decimal Division
    12. Sieve of Eratosthenes
    13. Sieve of Eratosthenes
    14. Check if Number is Prime
    15. Prime Factors
    16. Prime Numbers Sieve Patterns
    17. Prime Numbers Sieve Patterns2
    18. Making Prime Factorization Trees
    19. Find the LCM
    20. Find G.C.F. by Listing Factors
    21. GCF and LCM
    22. Find the LCM(a,b,c)
    23. Factorization - Visual illustration of divisor pairs
    24. Fraction Addition and Subtraction
    25. Integer Base/Exponents
    26. Broken Hundreds Chart
    27. Number Line Construction Tool
    28. Addition of Integers
    29. Dynamic Inequalities on a Number Line
    30. Perfect Squares up to 15
    31. Perfect Squares up to 30
    32. Cubes up to 10
  4. Number Systems
    1. The Real Number System
    2. Venn Diagram Real Numbers
    3. Number Theory Sets
    4. Complex Number System
    5. Order of Operations
    6. Spiral of Pythagoras
    7. Multiplication is repeated Addition
    8. Division is Repeated Subtraction
    9. Subtraction is really Addition
    10. Divisibility Tests
    11. Integer Factors of Square Roots
    12. The Significance of a Negative Index (Power)
    13. The Universal Abacus
    14. sieve of eratosthenes
    15. Expressing Composite Numbers as a Product of Prime Numbers
    16. Rounding Decimals
    17. Identifying Prime Numbers
    18. Integers Representing Height
  5. Ratios, Proportion, Probability
    1. Comaparing Fractions
    2. Ordering Fractions
    3. Equivalent Fractions
    4. Ratios and Proportions Exploration 1.4
    5. Two fraction bars
    6. Fraction Comparison
  6. Percents
    1. Percentage Problem
    2. percent grid
    3. Fraction, Decimal, Percentage Equivalents
    4. dynamic percent grid
    5. percent mixture equation
  7. Fractions
    1. Writing Equivalent Fractions
    2. Fraction Flower
    3. Ordering Fractions
    4. Visualizing Equivalent Fractions Using Models
    5. Comparison of fractions (D Mentrard)
    6. Comparing Fractions Using a Benchmark
    7. Fraction Addition
    8. Fraction Bar - Subtraction
    9. Addition of Fractions (D Mentrard
    10. Fraction Addition and Subtraction
    11. Multiplication of Fractions (D Mentrard)
    12. Intuitive Sense of a Reciprocal
    13. Dividing Fractions Justification
    14. Dividing Fractions
    15. Proof without words: Division of fractions (D Mentrard)
    16. Fraction, Decimal, Percentage Equivalents
    17. Fractions and unit (part1) (D Mentrard)
    18. Additional fractions per unit (part 2)(D Mentrard)
    19. Differents views of a same fraction (D Mentrard)
    20. Dividing Proper Fractions
    21. Division of fractions
    22. Calculations with Fractions
    23. HELP in DRAWING Rational Numbers
    24. GCF and LCM
  8. GeoGebra Resource
    1. Measuring Angles with a Protractor
    2. 4Q Quiz: Measuring Angles with a Protractor
    3. Modeling Distributive Property
    4. Integers Representing Height
    5. Drawing Parallel, Perpendicular, and Intersecting Lines
    6. Comparing Fractions with Unlike Denominators Using Models
    7. Multiplying 2-Digit Numbers Using Partial Products
    8. Fraction Multiplication
    9. Changing Scale Factor
    10. Calculating Scale Factors of Similar Figures
    11. Factoring with Trees
    12. Additive Inverse
    13. Notation for Set Operations
    14. Common Multiples in a Hundreds Grid
    15. Tables, Graphs, and Linear Equations
    16. Exploring a Sequence of Transformations Level 3
  9. Math Definitions
    1. Square Numbers
    2. Definition of Square-Square Root
    3. Area of Rectangles and Squares
    4. Cube & Cube Root
    5. Composing Prisms by Stacking Cubes
    6. Squares and Cubes: Favorites of Mathematics
    7. Square and Cube Roots: Favorites of Mathematicians
    8. Exploring Scaled Figures Using Models
    9. Fundamental Theorem of Arithmetic
    10. Perimeter of Polygons
    11. Circumference
  10. Scientific Notation
    1. Expressing Numbers in Scientific Notation
    2. Calculating Sums and Differences in Scientific Notation
    3. Adding and Subtracting Numbers in Scientific Notation
    4. Multiplying Numbers in Scientific Notation
    5. Multiplication and Division with Multiples of Powers of Ten

1.

Introduction

  • 1. Isle of Math

1.1.

Isle of Math

Arithmetic: the branch of mathematics dealing with the properties and manipulation of numbers[br][br]The Isle of Mathematics floats in a Sea of Arithmetic. All special fields of mathematics are dependent on the "Laws of Arithmetic".
Geometry: earth measurements; a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space[br][br]Algebra: the language through which we describe patterns; it allows users to make general rules for arithmetic patterns; saves time for repetative processes[br][br]Trigonometry: a branch of mathematics that studies relationships involving lengths and angles of triangles.[br][br]Analytic Geometry: a branch of algebra that is used to model geometric objects - points, (straight) lines, and circles[br][br]Calculus: the mathematical study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations[br][br]More advanced chart: [url]http://meta.math.stackexchange.com/questions/6479/a-graph-map-of-math-se[/url]
Math Help Sheet Share My Lesson (Times Table, Signed Rules)
– Auston B Cron

2.

Place Value

I have added the work of some other contributors for completeness of the GED Math Book.

  • 1. Practice Place Values
  • 2. Place Value
  • 3. Place Value for Decimals
  • 4. Expanding Decimal Numbers
  • 5. Place Value Cards - Input
  • 6. Place Value Cards - Random
  • 7. Two-digit whole numbers
  • 8. Three-digit whole numbers
  • 9. Place Value: Addition
  • 10. Place Value: Subtraction
  • 11. Numbers to Words (hundreds)
  • 12. Number To Words
  • 13. Words to Numbers
  • 14. Rounding Whole Numbers
  • 15. Scientific Notation-Section 4.1
  • 16. Scientific Notation
  • 17. Moving Place Value

2.1.

Practice Place Values

Bilingual Practice of place value using sliders...
Practice Place Values
[url=http://tube.geogebra.org/m/2000837] Suri — November 7, 2015 - 2:10 AM[/url]
– Auston B Cron

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3.

Arithmetic Skills

Basic Skills Practice for multiplication, integers, and more. Several lesson allow you to change the [b]Max value[/b] by clicking on it and typing a new Max value. Great tool to learn Multiplication Tables :[url]http://mathsbot.com/activities/timesTables[/url] Sieve of Eratosthenes [url]http://mathsbot.com/activities/sieveOfEratosthenes[/url]

  • 1. Multiplication Practice
  • 2. Family of Addition/Multiplication Facts
  • 3. Integer Addition
  • 4. Integer Subtraction
  • 5. Integer Multiplication
  • 6. Integer Division
  • 7. Converting Decimals to Fraction
  • 8. Decimal Addition
  • 9. Decimal Subtraction
  • 10. Decimal Multiplication Practice
  • 11. Decimal Division
  • 12. Sieve of Eratosthenes
  • 13. Sieve of Eratosthenes
  • 14. Check if Number is Prime
  • 15. Prime Factors
  • 16. Prime Numbers Sieve Patterns
  • 17. Prime Numbers Sieve Patterns2
  • 18. Making Prime Factorization Trees
  • 19. Find the LCM
  • 20. Find G.C.F. by Listing Factors
  • 21. GCF and LCM
  • 22. Find the LCM(a,b,c)
  • 23. Factorization - Visual illustration of divisor pairs
  • 24. Fraction Addition and Subtraction
  • 25. Integer Base/Exponents
  • 26. Broken Hundreds Chart
  • 27. Number Line Construction Tool
  • 28. Addition of Integers
  • 29. Dynamic Inequalities on a Number Line
  • 30. Perfect Squares up to 15
  • 31. Perfect Squares up to 30
  • 32. Cubes up to 10

3.1.

Multiplication Practice

Small tool for students to practice multiplication tables. I recommend learning through the 16's. It is useful for factoring fractions and quadratic expressions. You can [b]change Max value[/b] by clicking on it and typing a new Max value.
[url=http://forum.geogebra.org/viewtopic.php?f=20&t=42797&p=158133#p158133]Idea implements ccambre answer[/url]
– Auston B Cron

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4.

Number Systems

Learning about Numbers: 1) Counting 2) Whole 3) Integers 4) Rational Numbers (includes Fractions and Repeating Decimals) 5) Irrational Numbers (Non-repeating Decimals) 6) Real Numbers 7) Non-Real Numbers (Imaginary) 8) Complex Numbers

  • 1. The Real Number System
  • 2. Venn Diagram Real Numbers
  • 3. Number Theory Sets
  • 4. Complex Number System
  • 5. Order of Operations
  • 6. Spiral of Pythagoras
  • 7. Multiplication is repeated Addition
  • 8. Division is Repeated Subtraction
  • 9. Subtraction is really Addition
  • 10. Divisibility Tests
  • 11. Integer Factors of Square Roots
  • 12. The Significance of a Negative Index (Power)
  • 13. The Universal Abacus
  • 14. sieve of eratosthenes
  • 15. Expressing Composite Numbers as a Product of Prime Numbers
  • 16. Rounding Decimals
  • 17. Identifying Prime Numbers
  • 18. Integers Representing Height

4.1.

The Real Number System

Here we will study the Real Number System. The vocabulary in this lesson will be used in every mathematics class.
Students are expected to know these concepts and vocabulary words for daily use.
– Auston B Cron

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5.

Ratios, Proportion, Probability

  • 1. Comaparing Fractions
  • 2. Ordering Fractions
  • 3. Equivalent Fractions
  • 4. Ratios and Proportions Exploration 1.4
  • 5. Two fraction bars
  • 6. Fraction Comparison

5.1.

Comaparing Fractions

Can you find equivalent fractions with a common denominator that make it easy to compare the size of the [color=#1551b5]blue[/color] and [color=#0a971e]green[/color] fractions?
Comaparing Fractions
Source Neil Dickson [url=https://tube.geogebra.org/material/simple/id/1732919]Comparing Fractions[/url]
– Auston B Cron, Neil

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6.

Percents

  • 1. Percentage Problem
  • 2. percent grid
  • 3. Fraction, Decimal, Percentage Equivalents
  • 4. dynamic percent grid
  • 5. percent mixture equation

6.1.

Percentage Problem

Percentage is one of life's continual problem. Everyone uses them daily, sometimes without knowing it. There are basically 3 unique percentage problems, all are presented here:[br]1) Find the percent of a number. (Usually calculator ready.)[br]2) Find what a number is when you are given the % and the whole.[br]3) Find what percent a number is of another number.[br]The second two require a little algebra to work. Here this algebra has been set to be a proportion which solves easily with all 3 types.
This [url=http://highered.mheducation.com/sites/0809222329/student_view0/chapter6/ged_practice_quiz.html]Practice Test[/url] was used to assist in creating this worksheet.
– Auston B Cron

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7.

Fractions

  • 1. Writing Equivalent Fractions
  • 2. Fraction Flower
  • 3. Ordering Fractions
  • 4. Visualizing Equivalent Fractions Using Models
  • 5. Comparison of fractions (D Mentrard)
  • 6. Comparing Fractions Using a Benchmark
  • 7. Fraction Addition
  • 8. Fraction Bar - Subtraction
  • 9. Addition of Fractions (D Mentrard
  • 10. Fraction Addition and Subtraction
  • 11. Multiplication of Fractions (D Mentrard)
  • 12. Intuitive Sense of a Reciprocal
  • 13. Dividing Fractions Justification
  • 14. Dividing Fractions
  • 15. Proof without words: Division of fractions (D Mentrard)
  • 16. Fraction, Decimal, Percentage Equivalents
  • 17. Fractions and unit (part1) (D Mentrard)
  • 18. Additional fractions per unit (part 2)(D Mentrard)
  • 19. Differents views of a same fraction (D Mentrard)
  • 20. Dividing Proper Fractions
  • 21. Division of fractions
  • 22. Calculations with Fractions
  • 23. HELP in DRAWING Rational Numbers
  • 24. GCF and LCM

7.1.

Writing Equivalent Fractions

Rewrite equivalent fractions using smaller or larger denominators.
– GeoGebra Content Team

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8.

GeoGebra Resource

Selected applications from the GEOGEBRA RESOURCE!

  • 1. Measuring Angles with a Protractor
  • 2. 4Q Quiz: Measuring Angles with a Protractor
  • 3. Modeling Distributive Property
  • 4. Integers Representing Height
  • 5. Drawing Parallel, Perpendicular, and Intersecting Lines
  • 6. Comparing Fractions with Unlike Denominators Using Models
  • 7. Multiplying 2-Digit Numbers Using Partial Products
  • 8. Fraction Multiplication
  • 9. Changing Scale Factor
  • 10. Calculating Scale Factors of Similar Figures
  • 11. Factoring with Trees
  • 12. Additive Inverse
  • 13. Notation for Set Operations
  • 14. Common Multiples in a Hundreds Grid
  • 15. Tables, Graphs, and Linear Equations
  • 16. Exploring a Sequence of Transformations Level 3

8.1.

Measuring Angles with a Protractor

Move the LARGE POINTS to move the protractor around. Measure the colored angle you see here and enter its value in the input box (upper right).
– Tim Brzezinski

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9.

Math Definitions

  • 1. Square Numbers
  • 2. Definition of Square-Square Root
  • 3. Area of Rectangles and Squares
  • 4. Cube & Cube Root
  • 5. Composing Prisms by Stacking Cubes
  • 6. Squares and Cubes: Favorites of Mathematics
  • 7. Square and Cube Roots: Favorites of Mathematicians
  • 8. Exploring Scaled Figures Using Models
  • 9. Fundamental Theorem of Arithmetic
  • 10. Perimeter of Polygons
  • 11. Circumference

9.1.

Square Numbers

• a number which can be represented in the shape of a square.[br]• a number that results from multiplying an integer by itself.[br]• also called a perfect square.
[url=https://www.mathsisfun.com/definitions/square-number.html ]Square Numbers[br][/url][br]Picture from Twitter: Miss Konstantine @GiftedBA
– Auston B Cron

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10.

Scientific Notation

  • 1. Expressing Numbers in Scientific Notation
  • 2. Calculating Sums and Differences in Scientific Notation
  • 3. Adding and Subtracting Numbers in Scientific Notation
  • 4. Multiplying Numbers in Scientific Notation
  • 5. Multiplication and Division with Multiples of Powers of Ten

10.1.

Expressing Numbers in Scientific Notation

Discover the connection between standard notation and scientific notation in this activity.
Putting It All Together
Answer these open ended questions on your own or with others to form deeper math connections.
What is the place value of the digit 1 in the number [math]\textsf{1.2\times10^3}[/math]?
A number in scientific notation has a negative number as the exponent of 10. What do you know about the number?
Numbers in scientific notation are in the format [math]\textsf{a\times10^b}[/math]. What are the requirements of the coefficient [math]\textsf{a}[/math]?
– GeoGebra Content Team

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Information