Course Overview
Detailed Curricululm
Foundations of pre-algebra reasoning, number theory, fractions, equations, and proportional thinking. The last topic is the mid-year exam.
Commutative, associative, and distributive properties. Order of operations. Negative numbers, negation, subtraction, reciprocals, and division. (6.NS.B.3, 6.EE.A.3, 7.NS.A.1)
Squares and higher powers. Zero and negative exponents. Exponent laws. Scientific notation. (6.EE.A.1, 8.EE.A.1, 8.EE.A.3, 8.EE.A.4)
Multiples and divisibility tests. Prime numbers and prime factorization. LCM and GCD. Applications in problem solving. (6.NS.B.4, 4.OA.B.4)
Multiplying, dividing, and raising fractions to powers. Simplest form. Comparing, adding, and subtracting fractions. Mixed numbers. (5.NF.A.1, 5.NF.B.3, 5.NF.B.7, 6.NS.A.1)
Writing and evaluating expressions. Solving one-step and two-step linear equations. Translating word problems. Solving and graphing inequalities. (6.EE.A.2, 6.EE.B.5, 6.EE.B.7, 7.EE.B.3, 7.EE.B.4)
All four operations with decimals. Rounding. Converting between decimals and fractions. Repeating decimals. (5.NBT.B.7, 6.NS.B.3, 7.NS.A.2)
Understanding ratios. Multi-way ratios. Proportions and cross-multiplication. Unit conversions. Speed, distance, density, and cost-per-unit problems. (6.RP.A.1, 6.RP.A.2, 6.RP.A.3, 7.RP.A.1)
Percent of a quantity. Percent word problems. Percent increase and decrease. Compound percent change. Tax, discount, tip, and interest. (6.RP.A.3, 7.RP.A.3)
Comprehensive assessment of Session 1 concepts. Competition-style problem set. Review of key reasoning strategies.
Geometry, statistics, counting, and probability, completing the full pre-algebra picture. The last topic is the final exam.
Perfect squares and square roots. Square roots of non-square integers. Simplifying and performing arithmetic with square roots. (8.NS.A.2, 8.EE.A.2)
Measuring angles. Complementary, supplementary, and vertical angles. Parallel lines and transversals. Interior and exterior angles of polygons. (7.G.A.2, 7.G.B.5, 8.G.A.5)
Perimeter of polygons. Area of rectangles, parallelograms, triangles, and trapezoids. Composite figures. (6.G.A.1, 7.G.B.6)
Radius and diameter. Circumference and area. Arc length and sector area. Circles and π. (7.G.A.4, 7.G.B.4)
Understanding and applying the theorem. Pythagorean triples. Distance problems. Proofs of the Pythagorean Theorem. (8.G.B.6, 8.G.B.7, 8.G.B.8)
Properties of parallelograms, rectangles, rhombi, squares, trapezoids, and kites. Hierarchy of quadrilaterals. Area formulas. (5.G.B.3, 5.G.B.4, 6.G.A.1)
Mean, median, mode, range. Frequency tables, histograms, box plots, and stem-and-leaf plots. Interpreting and questioning data. (6.SP.A.2, 6.SP.A.3, 6.SP.B.4, 6.SP.B.5)
Fundamental Counting Principle. Permutations and combinations. Counting with restrictions. Casework and complementary counting. (7.SP.C.8)
Basic probability. Compound events. Independent vs. dependent events. Probability of “and” and “or.” Expected value. Geometric probability. (7.SP.C.5, 7.SP.C.6, 7.SP.C.7, 7.SP.C.8)
Collecting and organizing data. Analyzing trends. Random sampling. Making predictions. Identifying misleading statistics. (6.SP.A.1, 7.SP.A.1, 7.SP.A.2, 7.SP.B.3)
Comprehensive assessment of the full year. Competition-style problem set. Portfolio reflection and end-of-year review.
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