Unit 1: Number Sense and Logical Reasoning
1. Number Theory
2. Number Line
3. Composite Numbers and Prime Factorization
4. Rational and Irrational Numbers
5. Absolute
6. Divisibility Theorem and Patterns
7. Least Common Factor and its application
8. Greatest Common Factor and its application
9. Set properties
10. Connection with Word Problems
11. Binary Numbering Systems
12. Logical Reasoning and Problem Solving
Unit 2: Rational, Irrational Numbers and Operations (Integers, Fractions, Decimals, Mixed numbers)
1. Arithmetic Operations Properties
2. Inequality Properties
3. Closure Properties
4. Inverse Additive and Multiplication
5. Convert Numbers from Decimals to Fraction
6. Overview of Irrational Numbers
7. Compare and Order: Fractions, Mixed Numbers, Decimals, and Irrational
8. Estimate and compute with Fractions (including simplification of fractions, integers, decimals, and mixed numbers
9. Algebra connection with word problem
Unit 3: Exponents and Square Roots
1. Exponent Overview
2. Exponent Properties
3. Evaluate and Simplify Exponents
4. Exponent Patterns – Negative Base and Exponents, Even and Odd
5. Variable Exponents and Base
6. Square Root Properties
7. Perfect Square Roots and Estimate Square Roots
8. Scientific Notations
9. Algebra connection with word problems – Geometry, work, mixture, rate
Unit 5: Expressions and Equations
1. Simplification: simplify algebraic expressions
2. Word Problem: translate word problems into equations
3. Combining Like Terms
4. Substitution: see if equation is right with a given value
5. Solving One step linear equations
6. Solving two step linear equations
7. Inequalities – Number Line, one step and two step linear inequalities
Unit 6: Linear Functions
1. Overview of Functions - Range and Domain
2. Function Table and Venn Diagram
3. Build functions using tables and word problems
4. Evaluate Functions and Covert to Table
5. Graph Linear Functions
6. Build Equation from Graph
7. X and Y-Intercepts
8. Evaluate Slope (Rate of Change) from Graph and Table
9. Solve Linear Equations Algebraically – Substitution and Elimination Method
10. Solve Linear Equations with Graph
11. Solution Sets – Parallel and Intersection Lines
12. Connect Linear Equations with Applications – Speed, Money, Work
13. Multistep Word Problems
Unit 4: Ratios and Proportions
1. Ratios and Proportions Properties
2. Connect Ratios with Fractions
3. Equivalent Ratios, Compare Ratios
4. Direct Proportions and Inverse Proportions
a. Connect with Ratios
b. Convert Ratios to Proportions
5. Connect with applications –
a. Geometry, Units, Lengths
b. Unit Rates (speed, acceleration, …)
c. Scale Drawings
d. Reading Maps
e. Measuring quantities - Compare and Convert Metric Units
6. Ratios and Proportion with Variables
7. Overview of Rate and Work
8. Multistep Word Problems – Speed, Work, Money, Mixture, Time, Work, etc
Unit 5: Percentage
1. Percentage Concepts
2. Connect Percentage with Ratios and Proportions
3. Percentage of Change (Order of Deviation)
4. Compare and Order – Percentage, Ratios and Proportions
5. Connect Percentage of Change with Linear Equations
6. Word Problems
Unit 6: Geometry
1. Plane Properties (Points, Cartesian Coordinate Plane)
2. Lines, Line Segments, and Rays
3. Parallel, Perpendicular, Intersecting Lines
4. Polygon Properties - Convex and Concave Figures
5. Relationship of Angles for Line, Triangle, Circle
6. Congruence and Similar Figures (Complementary, Supplementary, Congruent, Vertical, and Adjacent, Bisect Angles)
7. Relationship of Angles by Intersecting Lines, and two parallel lines cut by a traversal lines
8. Triangle Properties (Include Triangle Inequality Theorem)
9. Triangle Classifications
10. Pythagorean Theorem
11. Interior and Exterior Angles - Regular Polygons
12. Connect Ratios and Proportions to find side and angle for similar Figures
13. Quadrilaterals Classifications
14. Circle Properties
15. Parts of Circle – Arc, Chord, Radius, Diameter Measurements
16. Perimeter – Polygons, Circle
17. Area – Polygons, and Circle
18. Solid Shapes – Three dimensional
19. Volume and Surface Area – Different Shapes (Cone, Prism, Cylinder, Sphere, Rectangular, etc)
20. Front, Side, and Top - Views
21. Transformations – Reflections, Translations, Rotations, Symmetry
Unit 7: Data Analysis, Statistics, and Probability
1. Create and Read Tabular and Graphical Representations of Data
a. Venn Diagrams
b. Circular or Pie Graph
c. Histograms
d. Line Graphs or Linear Graphs
e. Stem-and-Leaf Plots
2. Mean, Median, Mode, Range (data interpretations and compare different set of data)
3. Arithmetic Average and Weighted Average
4. Sets, Counting, Combination and Probability
a. Counting events
b. Combinations
c. Independent and dependent Events and Probabilities