# Compact 8

• Compact 8 Math

Compact 8 Class Information Letter

### Unit 1: Probability (Math 8 & Geometry)

• Learn and use appropriate vocabulary and notation
• Use counting strategies, such as Fundamental Counting Principle, factorials, permutations, and combinations
• Find simple, compound, geometric, and conditional probabilities using multiple approaches: formulae, tree diagrams, Venn diagrams, two-way frequency tables, and listing
• Construct and interpret two-way frequency tables.  Justify whether there is an association between the two sets of data
• Determine and justify whether events are independent or dependent and mutually exclusive or not
• Justify whether a given method is fair or not
• Analyze whether or not a decision is good using Bayes’ Theorem

### Unit 2:  Basics of Plane Geometry & Proofs (Math 8 & Geometry)

• Identify angle relationships & use to solve for unknown measurements
• Solve problems involving supplementary, complementary, vertical, and adjacent angles
• Understand and use facts about angle sum and exterior angles of triangles
• Construct congruent segments & angles and bisected segments & angles
• Use side relationships to determine whether a triangle is acute, right, or obtuse
• Use Pythagorean Theorem to find unknown lengths/distances
• Identify properties of triangles, such as the Triangle Inequality Theorem, and use to solve problems
• Introduce & use coordinate proofs to prove given statements
• Learn basic vocabulary related to logical reasoning
• Construct parallel & perpendicular lines and use parallel/perpendicular relationships to solve problems
• Understand and use facts about corresponding angles, alternate & same-side interior and exterior angles
• Identify more properties of triangles & quadrilaterals and use to solve for unknown measurements
• Write paragraph, two-column, and coordinate proofs for theorems about lines, angles, triangles, & parallelograms

### Unit 3:  Rigid Transformations & Congruence (Math 8 & Geometry)

• Understand the difference between rigid  and non-rigid transformations
• Perform rotations, reflections, & translations
• Describe the effect of a transformation on a given two-dimensional figure (congruent/not-congruent)
• Describe the sequence of transformations that would take one given figure to another
• Use criteria to prove two figures congruent
• Prove theorems relating to congruence

### Unit 4:  Dilations, Similarity, & Trigonometry (Math 8 & Geometry)

• Perform dilations
• Describe the effect of a dilation on a given two-dimensional figure (similar)
• Describe the sequence of transformations that would take one given figure to another
• Use criteria to prove two figures similar
• Understand and use facts about the angle-angle criterion for similarity of triangles
• Prove theorems relating to similarity
• Prove the Pythagorean Theorem
• Use Pythagorean Theorem to find unknown lengths/distances
• Use similarity to understand relationships with right triangles
• Derive trigonometric ratios for special right triangles (30-60-90 & 45-45-90)
• Define trigonometric ratios for acute angles in right triangles
• Understand the relationship of trigonometric ratios between complementary angles
• Use the properties of special right triangles to solve problems
• Derive & use trigonometric ratios to solve problems, such as those involving angles of elevation/depression
• Introduce vectors (If time permits – not on Unit CIA)

### Unit 4:  Dilations, Similarity, & Trigonometry, cont. (Math 8 & Geometry)

• Perform dilations
• Describe the effect of a dilation on a given two-dimensional figure (similar)
• Describe the sequence of transformations that would take one given figure to another
• Use criteria to prove two figures similar
• Understand and use facts about the angle-angle criterion for similarity of triangles
• Prove theorems relating to similarity
• Prove the Pythagorean Theorem
• Use Pythagorean Theorem to find unknown lengths/distances
• Use similarity to understand relationships with right triangles
• Derive trigonometric ratios for special right triangles (30-60-90 & 45-45-90)
• Define trigonometric ratios for acute angles in right triangles
• Understand the relationship of trigonometric ratios between complementary angles
• Use the properties of special right triangles to solve problems
• Derive & use trigonometric ratios to solve problems, such as those involving angles of elevation/depression
• Introduce vectors (If time permits – not on Unit CIA)

### Unit 5:  Geometric Modeling in 2 and 3 Dimensions (Math 8 & Geometry)

• Know & apply the following: area & circumference of circles; area, volume, surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms; volume of cones, cylinders, & spheres
• Use volume formulas for cylinders, pyramids, cones, & spheres to solve problems
• Use scale factors to determine length, area, and volume measures
• Modeling with and without constraints

### Unit 6:  Circles and Their Equations  (Geometry)

• Identify and describe relationships among inscribed angles, radii and chords & use to solve problems
• Graph and write equations for circles
• Derive the equation of a circle
• Prove theorems relating to circles
• Construct equilateral triangles, squares, & regular hexagons