Online Math 3 Classes: Multiplication, Division and Fractions

Expanded form, skip counting, the commutative and associative properties of addition, sum and difference, fact families, stacking, and adding and subtracting 9, 10 and 11. Multiplication facts start through skip counting, and even and odd numbers close the unit.

• Standard and Expanded Form, Multiplication through AdditionClass 1 covers standard and expanded form, skip counting with 5s to 9s and the commutative property of multiplication. Class 2 introduces multiplication as repeated addition, adds and subtracts 9, 10 and 11, and ends with word problems and number riddles.
• Properties of Addition and Skip Counting by 3 and 4Class 1 teaches addends and sum, the commutative property of addition and skip counting by 3, with input-output rules and word problems. Class 2 reviews them and adds the associative property and skip counting by 4, ending with Guess the Number riddles.
• Skip Counting by 4, 5 and 10 and the Addition-Subtraction ConnectionClass 1 practices skip counting by 4, forwards and backwards, and multiplication by 4. Class 2 covers skip counting by 5 and 10, adding and subtracting 10, fact families and checking a subtraction with addition.
• Sum and Difference, Strategies and Stacking AdditionClass 1 defines sum and difference and teaches stepping to the nearest ten, with word problems that use the terms. Class 2 adds two-digit numbers by stacking, introduces magic squares and returns to input-output tables and expanded form.
• Adding and Subtracting 9, Even and Odd NumbersClass 1 teaches adding and subtracting 9 and keeps practicing stacking, Guess the Number riddles and skip-counting puzzles. Class 2 teaches even and odd numbers and how they behave when added and subtracted, with word problems.

Multiplication as repeated addition and the commutative property, area and perimeter of the rectangle, multiplying by whole tens, parentheses, the order of operations and multiplication tricks for 2, 4, 5, 8, 9 and 10.

• The Concept of Multiplication and Sharing ProblemsClass 1 explains multiplication as repeated addition, groups and arrays, the commutative property and sharing problems. Class 2 continues with multiplication input-output tables and multiplication word problems.
• Area and Perimeter of the RectangleClass 1 reviews area as unit squares and links it to multiplication. Class 2 introduces perimeter, then finds a missing side of a rectangle from its area and works out the perimeter.
• Computing Area and Perimeter, Multiplying by Whole TensClass 1 computes the area of a rectangle by multiplying length by width and the perimeter by adding all sides, then finds a missing side. Class 2 reviews multiplying by whole tens, with word problems and more missing-side problems.
• Parentheses, Order of Operations and Multiplication TricksClass 1 introduces parentheses and turns words into expressions, with multiplication tricks for 2, 4, 5 and 10. Class 2 teaches the order of operations (parentheses, then multiply and divide, then add and subtract) and tricks for 8 and 9.

Part + part = whole, the idea of an unknown and equations such as X + 5 = 23, then telling time and elapsed time.

• Part plus Part equals Whole and the Idea of an UnknownClass 1 introduces part + part = whole and the unknown, with equations such as X + 5 = 23 and X − 12 = 65. Class 2 solves for X in more forms and in word problems, and has students write a word problem for an equation.
• Telling Time, Elapsed Time and UnknownsClass 1 teaches reading the hour and minute hands and finding elapsed time, with more equations with unknowns. Class 2 covers elapsed-time word problems, multiplying by 5 to read minutes, and tables with two-step rules such as 2 × P + 4.
• Multiplying by 6 and 7, Order of Operations and Elapsed TimeClass 1 practices multiplication by 6 and 7, the order of operations (P.E.M.D.A.S.) and elapsed time. Class 2 adds word problems, converting days, hours, minutes and seconds, finding two numbers from their sum and difference, and multi-step problems.

Division as sharing and as groups, fact families, division terminology, division word problems and the divisibility rules for 2, 3, 4, 5, 6 and 10.

• Introduction to Division and Fact FamiliesClass 1 introduces division as sharing and as groups, its link to multiplication facts, fact families and division word problems. Class 2 names dividend, divisor and quotient and practices true-or-false division sentences and word problems.
• Division Word Problems and Divisibility RulesClass 1 continues division word problems, including finding a missing side from the area, and reviews clock time. Class 2 teaches the divisibility rules for 2, 5 and 10 and practices fact families and input-output tables that divide.
• Divisibility Rules for 2, 3, 4, 5, 6 and 10Class 1 reviews the rules for 2 and 10 and teaches divisibility by 4 and by 3. Class 2 reviews 3 and 5, teaches divisibility by 6 and sorts a list of numbers by each rule. Both classes include division word problems.
• Factors and Multiples, Metric Units and DivisibilityClass 1 covers multiplying and dividing by 10 and 100, division patterns, and the terms factor, product and multiple. Class 2 teaches metric units and prefixes, then reviews division terms, the distributive property and the divisibility rules in one table.

Fractions on the number line, improper fractions and mixed numbers, equivalent fractions, adding, subtracting, comparing and simplifying, fractions of a set, and decimals as tenths and hundredths.

• Introduction to FractionsClass 1 introduces fractions as equal parts, numerator and denominator, number lines, improper fractions and mixed numbers. Class 2 covers fractions in real life, same-denominator addition and subtraction, and converting mixed and improper fractions.
• Fractions into Decimals and Lines of SymmetryClass 1 puts fractions on the number line, solves and makes up fraction word problems, and introduces decimals as another way to write a fraction. Class 2 simplifies fractions, converts decimals and fractions both ways and draws lines of symmetry.
• Equivalent FractionsClass 1 explains equivalent fractions with the pizza question and with bars and circles. Class 2 teaches the rule for making equivalent fractions, reviews mixed and improper fractions, and adds and subtracts same-denominator fractions in word problems.
• Adding and Subtracting Fractions with Different DenominatorsClass 1 shows why equivalent fractions matter, then adds and subtracts fractions with different denominators using a common denominator. Class 2 practices finding equivalent fractions and gives more addition and subtraction, with sums written as mixed numbers.
• Comparing and Simplifying FractionsClass 1 reviews adding and subtracting fractions, then teaches comparing fractions with different denominators and fraction word problems. Class 2 teaches simplifying fractions, with more comparing, word problems and fractions of an hour.
• Fractions on the Number Line, Decimals and SymmetryClass 1 has fractions on the number line and fraction word problems; class 2 has decimals as tenths and hundredths, fractions and decimals both ways, and lines of symmetry.
• Fractions of a SetClass 1 introduces finding a fraction of a set by dividing, and 2/3 of a number by finding one part first. Class 2 continues with fractions of a set in word problems and adds fractions, writing the sum as a mixed number.
• Fractions of a Set, Mixed Numbers and DecimalsClass 1 continues fractions of a set, including word problems and working backwards, and shows how many halves, thirds or quarters a mixed number holds. Class 2 continues them and reviews decimals: tenths, hundredths, money and the number line.
• Mixed Numbers and Fraction ReviewClass 1 practices fraction word problems, two-step fractions of a set and conversions between mixed numbers and improper fractions. Class 2 reviews the whole fraction toolkit, then adds and subtracts mixed numbers.

Rounding to the nearest 10 and 100 and comparing fractions with numerator 1, then the distributive property, stacked multiplication and area models for two-digit numbers times one-digit and two-digit numbers.

• Rounding, Estimating and Comparing FractionsClass 1 teaches rounding to the nearest 10 and 100 and compares fractions with numerator 1 on number lines. Class 2 adds rounding puzzles and word problems, filling in + or × to make expressions true, and more comparing of fractions.
• Distributive Property and Stacked MultiplicationClass 1 reviews the distributive property and teaches stacked multiplication of a two-digit by a one-digit number, then area models. Class 2 uses area models for two-digit by two-digit products and adds area and perimeter puzzles.

Review of the order of operations, equations, divisibility rules, perimeter and area, then compound areas, units of length, expressions, age problems and number sense.

• More Review of Operations, Equations and DivisibilityA second review week with new problems. Class 1 adds longer order-of-operations expressions and word problems that turn into equations. Class 2 adds the divisibility rule for 9, a two-step input-output rule and balancing equations.
• Perimeter, Area and Division ReviewClass 1 reviews perimeter, including shapes with missing sides and regular polygons, and the divisibility rules. Class 2 reviews perimeter and area by drawing rectangles, working backwards from the area and the order of operations.
• Compound Areas and Units of MeasurementClass 1 finds the area of compound shapes and teaches customary units of length with conversions between inches and feet. Class 2 converts feet and yards, then teaches metric units and prefixes, and ends with adding and subtracting 9, 10 and 11.
• Expressions, Age Problems and Number SenseClass 1 writes and evaluates expressions with variables, reviews fractions, and solves number-sense problems about consecutive numbers. Class 2 solves age problems and more number-sense questions, including Kangaroo-style ones.
• FUN Class - the Best Problems of the YearA FUN class. Class 1 gathers favorite problems: missing numbers and digits, inserting + or −, patterns, listing numbers. Class 2 has magic squares, comparing with <, > or =, an optional sum-and-difference trick, a look back at the year and a review game.