 James L. Day Middle School
 Compact 8
Triggs, Michelle
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Compact 8

Compact 8 Math
Compact 8 Class Information Letter
SEMESTER 1
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, twoway frequency tables, and listing
 Construct and interpret twoway 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 & sameside interior and exterior angles
 Identify more properties of triangles & quadrilaterals and use to solve for unknown measurements
 Write paragraph, twocolumn, and coordinate proofs for theorems about lines, angles, triangles, & parallelograms
Unit 3: Rigid Transformations & Congruence (Math 8 & Geometry)
 Understand the difference between rigid and nonrigid transformations
 Perform rotations, reflections, & translations
 Describe the effect of a transformation on a given twodimensional figure (congruent/notcongruent)
 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 twodimensional 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 angleangle 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 (306090 & 454590)
 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)
SEMESTER 2
Unit 4: Dilations, Similarity, & Trigonometry, cont. (Math 8 & Geometry)
 Perform dilations
 Describe the effect of a dilation on a given twodimensional 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 angleangle 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 (306090 & 454590)
 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 threedimensional 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