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This is math program designed to give students a firm mathematical understanding, both academically and spiritually. This curriculum consists of the Student Textbook and the Teacher's Guide. It is designed to be self-taught, so students should be able to read the material and complete assignments on their own, with a parent or teacher available for questions. The Teacher's Guide contains all the worksheets, quizzes, and tests, along with an answer key and suggested schedule.
Grades Covered
"This curriculum is aimed at grades 6-8, fitting into most math approaches the year or two years prior to starting high school algebra."Features
- Biblical Worldview: Discover how the very existence of the math concepts proclaims the faithfulness of God…and experience the joy of using math to explore God’s creation.
- Solid Foundation for High School Math and Real Life: Learn why the rules you’ve been memorizing work…and get practice applying those skills to real-life settings as you build problem-solving skills.
- History, Science, and Real-Life Connections: Find the height of a tree without leaving the ground, use negative numbers to describe the force on objects, explore historical multiplication methods, apply math to music, and much more!
" When we start with the Bible— God’s revealed Word to man — as our source of truth, it makes sense out of every area of life, including math. It gives us a framework for answering not only
what math is, but also where it came from and why it works." (Katherine A. Loop.)
Chapter 1: Introduction and Place Value..............
1.1 Math Misconceptions.....................................
1.2 What Is Math?...............................................
1.3 The Spiritual Battle in Math..................................................................
1.4 Numbers, Place Value, and Comparisons...................................................
1.5 Different Number Systems..............................................................................
1.6 Binary and Hexadecimal Place-value Systems..............................................
Chapter 2: Operations, Algorithms, and Problem Solving......................................
2.1 Addition and Subtraction..................................................................................
2.2 Applying Basic Addition and Subtraction to Time.......................................
2.3 Multi-digit Addition and Subtraction.............................................................
2.4 Keeping and Balancing a Checkbook Register..............................................
2.5 Different Addition and Subtraction Methods................................................
2.6 Problem Solving: An Introduction.................................................................
2.7 Chapter 1 and 2 Synopsis...........................................................................
Chapter 3: Mental Math and More Operations..........................................................
3.1 Mental Math.......................................................................................................
3.2 Rounding — Approximate Answers...............................................................
3.3 Multiplication......................................................................................................
3.4 Division...............................................................................................................
3.5Properties............................................................................................................
3.6 Conventions — Order of Operations............................................................
3.7 Chapter Synopsis..........................................................................................
Chapter 4: Multi-digit Multiplication and Division..............................................
4.1 Multi-digit Multiplication..............................................................................
4.2 The Distributive Property — Understanding Why.....................................
4.3 Multi-digit Division......................................................................................
4.4 More Multi-digit Division, Remainders, and Operations with Zero.........
4.5 More Problem-Solving Practice / Enter the Calculator.............................
4.6 Chapter Synopsis.........................................................................................
Chapter 5: Fractions and Factoring.........................................................................
5.1 Understanding Fractions..........................................................................
5.2 Mixed Numbers........................................................................................
5.3 Equivalent Fractions and Simplifying Fractions........................................
5.4 Understanding Factoring..............................................................................
5.5 Simplifying Fractions, Common Factors, and the Greatest Common Factor.124
5.6 Adding and Subtracting Fractions...............................................................
5.7 Least Common Denominator / Multiple...................................................
5.8 Chapter Synopsis and Expanding Our Worldview..............................
PRINCIPLES OF
MATHEMATICS
Chapter 6: More with Fractions.................................................................................
6.1 Multiplying Fractions.................................................................................
6.2 Working with Mixed Numbers......................................................................
6.3 Simplifying While Multiplying...................................................................
6.4 Reciprocal / Multiplicative Inverse and More.......................................
6.5 Dividing Fractions....................................................................................
6.6 Chapter Synopsis......................................................................................
Chapter 7: Decimals.................................................................................................
7.1 Introducing Decimals...................................................................................
7.2 Adding and Subtracting Decimals..............................................................
7.3 Multiplying Decimals......................................................................................
7.4 Dividing and Rounding with Decimals....................................................
7.5 Conversion and More with Decimals.......................................................
7.6 Chapter Synopsis............................................................................................
Chapter 8: Ratios and Proportions............................................................................
8.1 Ratios.................................................................................................................
8.2 Proportions......................................................................................................
8.3 Ratios and Proportions Containing Decimals..........................................
8.4 Scale Drawings and Models.......................................................................
8.5 Mental Math and Decimals.......................................................................
8.6 Chapter Synopsis.........................................................................................
Chapter 9: Percents.................................................................................................
9.1 Introducing Percents...................................................................................
9.2 FindinPercents..............................................................................................
9.3 More Finding Percentages / Multiplying and Dividing Percents.............
9.4 Adding and Subtracting Percents / Finding Totals.................................
9.5 Mental Percents...............................................................................................
9.6 Chapter Synopsis..........................................................................................
Chapter 10: Negative Numbers................................................................................
10.1 Understanding Negative Numbers.............................................................
10.2 Adding Negative Numbers........................................................................
10.3 Subtracting Negative Numbers.................................................................
10.4 Temperature and Negative Numbers......................................................
10.5 Absolute Value.............................................................................................
11.6 Multiplying and Dividing Negative Numbers......................................
10.7 Negative Mixed Numbers.......................................................................
10.8 Negative Fractions.....................................................................................
10.9 Chapter Synopsis......................................................................................
Chapter 11: Sets..........................................................................................................
11.1 Sets and Venn Diagrams............................................................................
11.2 Number Sets...............................................................................................
11.3 More on Sets......................................................................................
TABLE OF
CONTENTS
11.4 Ordered Sets (i.e., Sequences)...............................................................
11.5 Chapter Synopsis...................................................................................
Chapter 12: Statistics and Graphing......................................................................
12.1 Introduction to Statistics..........................................................................
12.2 Collecting Data — Sampling...................................................................
12.3 Organizing Data — Understanding Graphs.........................................
12.4 Organizing Data — Drawing Bar/Column Graphs.............................
12.5 Coordinates..............................................................................................
12.6 Organizing Data — Line Graphs............................................................
12.7 Organizing Data — Averages.................................................................
12.8 Organizing Data — More on Averages.......................................................
12.9 Chapter Synopsis.......................................................................................
Chapter 13: Naming Shapes: Introducing Geometry..............................................
13.1 Understanding Geometry.............................................................
13.2 Lines and Angles...........................................................................................
13.3 Polygons.........................................................................................................
13.4 Circles, Triangles, and Three-Dimensional Shapes............................
13.5 Fun with Shapes............................................................................................
13.6 Chapter Synopsis..........................................................................................
Chapter 14: Measuring Distance............................................................................
14.1 Chapters for Measuring Distance.............................................................
14.2 Conversions via Proportions.....................................................................
14.3 Different Conversion Methods.................................................................
14.4 Currency Conversions...............................................................................
14.5 Metric Conversions....................................................................................
14.6 Multistep Conversions................................................................................... Conversions Between U.S. Customary and Metric...............................
14.8 Time Conversions.........................................................................
14.9 Chapter Synopsis..........................................................................................
Chapter 15: Perimeter and Area of Polygons..........................................................
15.1 Perimeter.....................................................................................................
15.2 Formulas........................................................................................................
15.3 Area: Rectangles and Squares.......................................................................
15.4 Area: Parallelograms......................................................................................
15.5 Chapter Synopsis and the Basis of Math and Truth................................
Chapter 16: Exponents, Square Roots, and Scientific Notation..........................
16.1 Introducing Exponents..............................................................................
16.2 Understanding Square Roots....................................................................
16.3 Square Unit Conversions...........................................................................
16.4 Scientific Notation.......................................................................................
16.5 More Scientific Notation.............................................................................
16.6 Chapter Synopsis........................................................................................
910
PRINCIPLES OF
MATHEMATICS
Chapter 17: More Measuring: Triangles, Irregular Polygons, and Circles.............333
17.1 Area: Triangles.................................................................................
17.2 Area: More Polygons....................................................................................
17.3 Measuring Circles.......................................................................................
17.4 Irrational Numbers.....................................................................................
17.5 Chapter Synopsis and Pi in the Bible.......................................................
Chapter 18: Solid Objects and Volume...................................................................
18.1 Surface Area................................................................................................
18.2 Volume.........................................................................................................
18.3 Cubic Unit Conversion..............................................................................
18.4 Measuring Capacity in the U.S. Customary System...............................
18.5 Conversion to and from Cubic Units...........................................................
18.6 Measuring Capacity in the Metric System..............................................
18.7 Measuring Weight and Mass.......................................................................
18.8 Chapter Synopsis..........................................................................................
Chapter 19: Angles.......................................................................................
19.1 Measuring Angles............................................................................
19.2 More with Angles................................................................
19.3 Angles in Pie Graphs.....................................................................
19.4 Expanding Beyond...................................................
19.5 Chapter Synopsis and Faulty Assumptions.....................
Chapter 20: Congruent and Similar.............................................................
20.1 Congruent...........................................................................
20.2 Corresponding Parts — Applying Congruency....................
20.3 Exploring Similar Shapes.................................................................
20.4 Angles in Triangles and AA Similarity................................
20.5 Similar Triangles in Action — Finding the Height of a Tree.
20.6 Chapter Synopsis and A Peek Ahead.....................................................
Chapter 21: Review.................................................................................
21.1 Arithmetic Synopsis............................................................
21.2 Geometry Synopsis..............................................................
21.3 Life of Johannes Kepler......................................................
21.4 Course Review..........................................................................
Appendix A............................................................................................
1.1 Math Misconceptions.....................................
1.2 What Is Math?...............................................
1.3 The Spiritual Battle in Math..................................................................
1.4 Numbers, Place Value, and Comparisons...................................................
1.5 Different Number Systems..............................................................................
1.6 Binary and Hexadecimal Place-value Systems..............................................
Chapter 2: Operations, Algorithms, and Problem Solving......................................
2.1 Addition and Subtraction..................................................................................
2.2 Applying Basic Addition and Subtraction to Time.......................................
2.3 Multi-digit Addition and Subtraction.............................................................
2.4 Keeping and Balancing a Checkbook Register..............................................
2.5 Different Addition and Subtraction Methods................................................
2.6 Problem Solving: An Introduction.................................................................
2.7 Chapter 1 and 2 Synopsis...........................................................................
Chapter 3: Mental Math and More Operations..........................................................
3.1 Mental Math.......................................................................................................
3.2 Rounding — Approximate Answers...............................................................
3.3 Multiplication......................................................................................................
3.4 Division...............................................................................................................
3.5Properties............................................................................................................
3.6 Conventions — Order of Operations............................................................
3.7 Chapter Synopsis..........................................................................................
Chapter 4: Multi-digit Multiplication and Division..............................................
4.1 Multi-digit Multiplication..............................................................................
4.2 The Distributive Property — Understanding Why.....................................
4.3 Multi-digit Division......................................................................................
4.4 More Multi-digit Division, Remainders, and Operations with Zero.........
4.5 More Problem-Solving Practice / Enter the Calculator.............................
4.6 Chapter Synopsis.........................................................................................
Chapter 5: Fractions and Factoring.........................................................................
5.1 Understanding Fractions..........................................................................
5.2 Mixed Numbers........................................................................................
5.3 Equivalent Fractions and Simplifying Fractions........................................
5.4 Understanding Factoring..............................................................................
5.5 Simplifying Fractions, Common Factors, and the Greatest Common Factor.124
5.6 Adding and Subtracting Fractions...............................................................
5.7 Least Common Denominator / Multiple...................................................
5.8 Chapter Synopsis and Expanding Our Worldview..............................
PRINCIPLES OF
MATHEMATICS
Chapter 6: More with Fractions.................................................................................
6.1 Multiplying Fractions.................................................................................
6.2 Working with Mixed Numbers......................................................................
6.3 Simplifying While Multiplying...................................................................
6.4 Reciprocal / Multiplicative Inverse and More.......................................
6.5 Dividing Fractions....................................................................................
6.6 Chapter Synopsis......................................................................................
Chapter 7: Decimals.................................................................................................
7.1 Introducing Decimals...................................................................................
7.2 Adding and Subtracting Decimals..............................................................
7.3 Multiplying Decimals......................................................................................
7.4 Dividing and Rounding with Decimals....................................................
7.5 Conversion and More with Decimals.......................................................
7.6 Chapter Synopsis............................................................................................
Chapter 8: Ratios and Proportions............................................................................
8.1 Ratios.................................................................................................................
8.2 Proportions......................................................................................................
8.3 Ratios and Proportions Containing Decimals..........................................
8.4 Scale Drawings and Models.......................................................................
8.5 Mental Math and Decimals.......................................................................
8.6 Chapter Synopsis.........................................................................................
Chapter 9: Percents.................................................................................................
9.1 Introducing Percents...................................................................................
9.2 FindinPercents..............................................................................................
9.3 More Finding Percentages / Multiplying and Dividing Percents.............
9.4 Adding and Subtracting Percents / Finding Totals.................................
9.5 Mental Percents...............................................................................................
9.6 Chapter Synopsis..........................................................................................
Chapter 10: Negative Numbers................................................................................
10.1 Understanding Negative Numbers.............................................................
10.2 Adding Negative Numbers........................................................................
10.3 Subtracting Negative Numbers.................................................................
10.4 Temperature and Negative Numbers......................................................
10.5 Absolute Value.............................................................................................
11.6 Multiplying and Dividing Negative Numbers......................................
10.7 Negative Mixed Numbers.......................................................................
10.8 Negative Fractions.....................................................................................
10.9 Chapter Synopsis......................................................................................
Chapter 11: Sets..........................................................................................................
11.1 Sets and Venn Diagrams............................................................................
11.2 Number Sets...............................................................................................
11.3 More on Sets......................................................................................
TABLE OF
CONTENTS
11.4 Ordered Sets (i.e., Sequences)...............................................................
11.5 Chapter Synopsis...................................................................................
Chapter 12: Statistics and Graphing......................................................................
12.1 Introduction to Statistics..........................................................................
12.2 Collecting Data — Sampling...................................................................
12.3 Organizing Data — Understanding Graphs.........................................
12.4 Organizing Data — Drawing Bar/Column Graphs.............................
12.5 Coordinates..............................................................................................
12.6 Organizing Data — Line Graphs............................................................
12.7 Organizing Data — Averages.................................................................
12.8 Organizing Data — More on Averages.......................................................
12.9 Chapter Synopsis.......................................................................................
Chapter 13: Naming Shapes: Introducing Geometry..............................................
13.1 Understanding Geometry.............................................................
13.2 Lines and Angles...........................................................................................
13.3 Polygons.........................................................................................................
13.4 Circles, Triangles, and Three-Dimensional Shapes............................
13.5 Fun with Shapes............................................................................................
13.6 Chapter Synopsis..........................................................................................
Chapter 14: Measuring Distance............................................................................
14.1 Chapters for Measuring Distance.............................................................
14.2 Conversions via Proportions.....................................................................
14.3 Different Conversion Methods.................................................................
14.4 Currency Conversions...............................................................................
14.5 Metric Conversions....................................................................................
14.6 Multistep Conversions................................................................................... Conversions Between U.S. Customary and Metric...............................
14.8 Time Conversions.........................................................................
14.9 Chapter Synopsis..........................................................................................
Chapter 15: Perimeter and Area of Polygons..........................................................
15.1 Perimeter.....................................................................................................
15.2 Formulas........................................................................................................
15.3 Area: Rectangles and Squares.......................................................................
15.4 Area: Parallelograms......................................................................................
15.5 Chapter Synopsis and the Basis of Math and Truth................................
Chapter 16: Exponents, Square Roots, and Scientific Notation..........................
16.1 Introducing Exponents..............................................................................
16.2 Understanding Square Roots....................................................................
16.3 Square Unit Conversions...........................................................................
16.4 Scientific Notation.......................................................................................
16.5 More Scientific Notation.............................................................................
16.6 Chapter Synopsis........................................................................................
910
PRINCIPLES OF
MATHEMATICS
Chapter 17: More Measuring: Triangles, Irregular Polygons, and Circles.............333
17.1 Area: Triangles.................................................................................
17.2 Area: More Polygons....................................................................................
17.3 Measuring Circles.......................................................................................
17.4 Irrational Numbers.....................................................................................
17.5 Chapter Synopsis and Pi in the Bible.......................................................
Chapter 18: Solid Objects and Volume...................................................................
18.1 Surface Area................................................................................................
18.2 Volume.........................................................................................................
18.3 Cubic Unit Conversion..............................................................................
18.4 Measuring Capacity in the U.S. Customary System...............................
18.5 Conversion to and from Cubic Units...........................................................
18.6 Measuring Capacity in the Metric System..............................................
18.7 Measuring Weight and Mass.......................................................................
18.8 Chapter Synopsis..........................................................................................
Chapter 19: Angles.......................................................................................
19.1 Measuring Angles............................................................................
19.2 More with Angles................................................................
19.3 Angles in Pie Graphs.....................................................................
19.4 Expanding Beyond...................................................
19.5 Chapter Synopsis and Faulty Assumptions.....................
Chapter 20: Congruent and Similar.............................................................
20.1 Congruent...........................................................................
20.2 Corresponding Parts — Applying Congruency....................
20.3 Exploring Similar Shapes.................................................................
20.4 Angles in Triangles and AA Similarity................................
20.5 Similar Triangles in Action — Finding the Height of a Tree.
20.6 Chapter Synopsis and A Peek Ahead.....................................................
Chapter 21: Review.................................................................................
21.1 Arithmetic Synopsis............................................................
21.2 Geometry Synopsis..............................................................
21.3 Life of Johannes Kepler......................................................
21.4 Course Review..........................................................................
Appendix A............................................................................................
References:
