Online Math 6 Classes: Ratios, Percent, Signed Numbers and First Algebra

Decimal operations, exponent notation and the order of operations, then divisibility rules, prime factorization, GCF and LCM.

• Decimals and Order of OperationsDecimal place value and all four operations with decimals, including dividing by a decimal, then exponent notation and the order of operations.
• Divisibility, Prime Factorization, GCF and LCMDivisibility rules (with 7, 8 and 11 as harder extras), prime and composite numbers, prime factorization in exponent form, then the GCF and LCM and which one a situation asks for.

Adding, subtracting, multiplying and dividing fractions and mixed numbers, with reciprocals, then converting between fractions, decimals and percents.

• Fraction Addition and SubtractionEquivalent fractions and simplifying with the GCF, then a common denominator from the LCM to add and subtract fractions and mixed numbers, regrouping when needed.
• Fraction Multiplication and ReciprocalsMultiplying fractions and mixed numbers (simplifying first), a fraction of an amount, predicting whether a product gets bigger or smaller, and writing reciprocals.
• Fraction DivisionDivision as "how many fit", dividing by unit fractions and whole numbers, keep-⁠change-flip for any two fractions or mixed numbers, and reading the leftover in a word problem.
• Fractions, Decimals and PercentsConverting between fractions, decimals and percents in every direction, telling whether a decimal stops or repeats, and comparing numbers written in different forms.

Negatives, opposites and absolute value, the four operations on integers, then signed fractions and decimals with the order of operations, and the properties of exponents.

• Negatives, Opposites and Absolute ValueNegative numbers in real situations and on a number line, opposites and the three jobs of the minus sign, absolute value as a distance, and ordering signed numbers.
• Adding and Subtracting IntegersAdding integers with zero pairs, rewriting every subtraction as adding the opposite, working chains of three or four signed terms, and finding a change as NEW minus OLD.
• Multiplying and Dividing IntegersThe sign rules for multiplying and dividing integers and why two negatives make a positive, powers of negative numbers, and averages and rates with negatives.
• Signed Rationals and Order of OperationsThe same sign rules applied to fractions and decimals, deciding the sign first, then the order of operations with signed numbers, fractions included.
• Properties of ExponentsThe product, quotient and power rules for exponents, then zero and negative exponents evaluated exactly, ending with simplifying expressions that use all three rules.

Ratios and tape diagrams, unit rates and metric conversions, proportions by scale factor or cross products, then similar figures and indirect measurement.

• Ratios and Ratio Word ProblemsReading and simplifying ratios, part-⁠to-⁠part versus part-⁠to-⁠whole, tables of equivalent ratios, and tape diagrams for sharing an amount and working backwards from one share or a difference.
• Unit Rates and Measurement ConversionUnit rates and what their units mean, comparing offers on the same unit rate, and converting metric units (and hours to minutes) by treating a conversion as a rate.
• Proportions and Cross ProductsDeciding whether a relationship is proportional, solving proportions by scale factor and by cross products with the units labeled, and applying them to shadows and scale drawings.
• Similar Figures and Scale FactorWhat makes figures similar, scale factors and missing lengths found with proportions, measuring a tree or building from its shadow, and how area changes when lengths are scaled.

The coordinate plane, graphing linear relationships, slope and y = mx + b, then the three percent types and percent change.

• The Coordinate Plane and Reading GraphsPlotting points in all four quadrants, reading real graphs (including one that goes down), and finding horizontal and vertical distances as absolute values, with rectangles on the grid.
• Graphing Linear RelationshipsMoving between tables, ordered pairs and lines, telling linear from non-⁠linear and proportional from linear only, and graphing a situation from its starting value and its step.
• Slope as Rate of Change and Slope-Intercept Form
• Percent - The Three TypesThe percent bar and the three percent questions: finding the part, the percent and the whole, with benchmark percents for mental work and the link to proportions.
• Percent Change and ApplicationsPercent increase and decrease, one-⁠step multipliers, discounts, tax, tips, commission, interest and markup, working back from a sale price, and why two changes in a row do not add.

Variables and evaluating expressions, the laws of operations and combining like terms, then the distributive property and factoring.

• Variables and Evaluating ExpressionsWhat a variable, term, coefficient and constant are, translating words into expressions (watching word order), and evaluating by substitution, including negative values, two variables and formulas.
• Laws of Operations and Combining Like TermsThe commutative, associative, identity and inverse laws and where they do not hold, then like terms: combining them in long chains with signs, with more than one variable, and in perimeters.
• The Distributive Property and FactoringMultiplying out parentheses (also to make mental arithmetic easier), distributing a negative, factoring out the GCF, and expanding two sets of parentheses in one expression.

One- and two-⁠step equations, multi-step equations and variables on both sides, equations with fractions and decimals, then inequalities.

• One- and Two-⁠Step EquationsWhat it means to solve an equation, inverse operations on a balance scale for one- and two-⁠step equations, negative coefficients and negative answers, and writing an equation from words.
• Multi-Step Equations and Variables on Both SidesExpanding parentheses and combining like terms before solving, collecting x-terms when the variable is on both sides, equations with no solution or every number, and comparing two plans.
• Equations with Fractions and DecimalsFraction coefficients, clearing every denominator by multiplying by the LCD, choosing between the two routes, numerators grouped by the fraction bar, and clearing decimals the same way.
• Inequalities - Solving and GraphingWriting inequalities from phrases such as "at least", graphing solution sets with open or closed dots, solving like an equation, reversing the sign for a negative, and constraint problems.

Angle relationships, triangle and polygon angle sums, quadrilaterals and area, then circles, volume and surface area.

• Angles and Angle RelationshipsNaming angles and reading a protractor, complementary and supplementary angles, angles round a point and on a line, vertical angles, and equations for unknown angles.
• Triangles and Polygon Angle SumsThe 180° angle sum of a triangle, classifying triangles by angles and by sides, impossible angle combinations, the exterior angle, and the angle sum of any polygon by cutting it into triangles.
• Quadrilaterals and the Area of PolygonsThe five quadrilaterals and how they overlap, the area of parallelograms, triangles and trapezoids using the perpendicular height, perimeter versus area, and composite figures.
• Circles, Solids and the Cumulative FinalCircles in terms of π, volume of prisms and cylinders with V = B × h, volume and capacity, surface area from nets, then a final drill, final word problems and a look back over the year's eight units.