Fundamentals of Geometry and Algebra
Course Overview
Students enhance computational and problem-solving skills while learning topics in algebra, geometry, probability,
and statistics. They solve expressions and equations in the context of perimeter, area, and volume problems while further
developing computational skills with fractions and decimals. The study of plane and solid figures includes construction
and transformations of figures. Also in the context of problem solving, students add, subtract, multiply, and divide positive
and negative integers and solve problems involving ratios, proportions, and percents, including simple and compound
interest, rates, discount, tax, and tip problems. They learn multiple representations for communicating information, such as
graphs on the coordinate plane, statistical data and displays, as well as the results of probability and sampling experiments.
They investigate patterns involving addition, multiplication, and exponents, and apply number theory and computation to
mathematical puzzles.
Course Outline
Area: Multiplication Equations
• Semester 1 Introduction
• Foundations for Unit 3
• Foundations for Unit 1
• Units of Area
• On the Number Line
• Areas of Rectangles
• Order of Operations
• Special Quadrilaterals
• Number Properties
• Areas of Triangles
• Translating Between Words and Math
• Figures Made Up of Triangles and Parallelograms
• Translating Mixed Operations
• Unknown Side Lengths: Division
• Problem-Solving Strategies
• Unknown Side Lengths: Square Roots
• Estimation and Reasonableness
•Precision
Distance: Addition Equations
Working with Rational Numbers
• Foundations for Unit 4
• Equivalent Fractions
• Representing Rational Numbers
• Foundations for Unit 2
• Comparing Rational Numbers
• Units of Distance
• Perimeters with Fractions
• Polygons and Perimeter
• Areas with Fractions
• Addition and Subtraction Equations
• Dividing Fractions
• Applications of Addition and Subtraction Equations
• Solving Problems with Fraction Division
• Negative Numbers
• Absolute Value and Distance
• Addition and Subtraction with Negative Numbers
• Solving Addition Equations with Negative Numbers
Solids
• Foundations for Unit 5
• Cubes and Cube Roots
• Volumes of Prisms
• Nets of Solids
• Surface Area: Prisms and Pyramids
• Properties of Volume and Surface Area
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• Identifying Information in Word Problems
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Problem Solving
The Second Dimension
• Foundations for Unit 6
• Foundations for Unit 11
• Ratios as Comparisons
• Points on a Coordinate Plane
•Percent
• Using Points to Solve Problems
• Finding Percents of Numbers
• Equations with Two Variables
•Discount
• Scatter Plots
• Tax and Tip
• Interpreting Scatter Plots
•Proportions
• Solving Proportions
• Reducing and Enlarging
Angles and Circles
Rates
• Foundations for Unit 12
• Rates as Comparisons
• Unit Rates
• Solving Unit-Rate Problems
• Foundations for Unit 7
• Average-Speed Problems
• Angle Pairs
• Constant-Rate Problems
• Finding Angle Measures
• Direct Variation
• Regular Polygons
• Interpreting Direct Variation
• Parts of a Circle
•Circumference
• Areas of Circles
•Cylinders
Probability
Working with Positives and Negatives
• Foundations for Unit 13
• Adding and Subtracting Signed Numbers
• Net Gains and Losses
• Multiplying Signed Numbers
• Foundations for Unit 8
• Dividing Signed Numbers
•Counting
• Properties of Signed Numbers
•Probability
•Inequalities
• Experimental Probability
• Theoretical Probability
• The Law of Large Numbers
• Independent and Dependent Events
• Complementary Events
Statistics
Making and Moving Figures
• Foundations for Unit 14
• Folded-Paper Construction
• Compass and Straightedge Construction
•Translation
•Reflection
• Semester 2 Introduction
•Rotation
• Foundations for Unit 10
• Translating with Coordinates
• Circle Graphs
• Reflecting with Coordinates
• More Statistical Graphs
• Figures on a Coordinate Plane
•Histograms
• Measures of Center
• Box-and-Whisker Plots
• Measures of Variation
•Outliers
• Samples and Bias
• Sampling Strategies
• Statistical Claims
Patterns, Primes, and Puzzles
• Foundations for Unit 15
• Addition Patterns
• Multiplication Patterns
•Exponents and Patterns
• Compound Interest
• Primes and Composites
• Figuring Out Math Puzzles
• Creating Math Puzzles
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• Simple Interest
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Comparisons: Ratios
Lesson Time and Scheduling
Total lessons: 180 (151 lessons + 29 Your Choice days)
Lesson time: 60 minutes
Standard Curriculum Items
• Fundamentals of Geometry and Algebra:
A Reference Guide and Problem Sets
• Fundamentals of Geometry and Algebra
Learning Coach Guide
• Fundamentals of Geometry and Algebra
Student Guide
Additional Curriculum Items
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•Protractor