Online Math 5 Classes: Fractions, Decimals, Ratios and Percent

Operations with whole numbers and place value, writing expressions and finding the unknown, multiplication by 1 and 2 digits and its properties, long division, missing digits, and money and multi-step word problems.

• Operations with Whole NumbersPractice with the four operations on whole numbers and place value to the hundred thousands, with standard, word and expanded forms. Problem-solving strategies include Guess the Number puzzles, working backwards and balance-scale problems.
• Writing Expressions and Finding the UnknownWriting expressions from words and situations, evaluating them (for example for x = 3), and finding the unknown with balance scales, bar models and operation chains. Missing-number calculations and shape puzzles recur.
• Multiplication by 1 Digit and Its PropertiesMultiplying 2-, 3- and 4-digit numbers by a 1-digit number, and the properties of multiplication. Number bonds for multiplication and division, "times as many" problems, and picture puzzles and equations with an unknown.
• Multiplication Facts and Long DivisionRecalling the multiplication table and the properties of multiplication, then long division by a 1-digit number, including division with a remainder. Word problems cover ages, money, and finding two numbers from their sum and difference.
• Long Division and Money Word ProblemsLong division with 3- and 4-digit dividends and multiplication by a 2-digit number (2-digit by 2-digit, then 3-digit by 2-digit). Money word problems cover daily and weekly pay, saving and comparing; two crosswords and mixed practice sets round out the week.
• Missing Digits and Multi-Step Word ProblemsFinding missing digits in subtraction and multiplication, long division with 3- and 4-digit dividends, and multi-step word problems, including money. A new skill is filtering the information a problem actually needs.

Multiples, factors, prime and composite numbers, factor trees, divisibility rules, GCF and LCM, and prime factorization with exponents.

• Multiplication and Division ProblemsThe vocabulary of multiplication and division (product, multiple, factor, dividend, divisor, quotient), prime and composite numbers, factor trees, and estimating a product or quotient to check that an answer is reasonable.
• Division with Remainder and Factor TreesDivisions with remainders (the remainder is always smaller than the divisor), factor trees for large numbers, then common factors and the GCF, and common multiples and the LCM, each with application problems.
• Factors and MultiplesDivisibility rules for 2, 3, 4, 5, 6 and 9, factor trees built with those rules, and the GCF and LCM again with applications such as cutting strings. Mental-math strategies (friendly grouping, compensation) are introduced.
• Factors, Multiples and PropertiesA review of factors, multiples, division and multiplication with the GCF, then smart calculation by grouping and compensation, and the distributive property of multiplication used for mental math.
• Factors, Multiples and DivisibilityEvery factor of a number listed in pairs, counting on in multiples, divisibility tests for 2, 3, 4, 5, 6, 9 and 10, and sorting numbers into prime and composite, each practiced in context.
• Prime Factorization, GCF and LCMPrime factorization with a factor tree, repeated primes written with exponents, and reading the GCF and the LCM off the factorizations. Mixed sets ask whether a problem needs the GCF or the LCM.

Splitting a factor and using a nearby round number to multiply in your head, area models, the commutative property, the order of operations (PEMDAS), and combining like terms in simple expressions.

• The Distributive Property of MultiplicationSplitting one factor to multiply the parts separately, using a nearby round number and correcting for the difference, and reading a two-part rectangle as one product or two. Mixed sets ask which split makes the arithmetic easiest.
• Distributive Property and Order of OperationsThe distributive property as a mental-math method (with addition and with subtraction), the commutative property, and the order of operations (PEMDAS). New: expressions and terms, like terms, and simplifying by combining them.

Fraction notation, equivalent fractions, comparing, adding and subtracting with like and unlike denominators, improper fractions and mixed numbers, multiplying and dividing fractions, and word problems.

• FractionsFraction notation, fractions on a number line and the fraction wall, equivalent fractions, comparing, a fraction of a number, and adding and subtracting fractions with the same denominator, with word problems.
• Fractions with Unlike DenominatorsAdding and subtracting fractions with different denominators, and comparing and ordering fractions (same denominator, same numerator, different denominators). Also simplifying fractions with divisibility rules and by combining like terms.
• Improper Fractions and Mixed NumbersImproper fractions and mixed numbers, converting between them in both directions, and adding and subtracting mixed numbers with like denominators. New: multiplying a fraction or mixed number by a whole number.
• Multiplying FractionsFinding a fraction of a whole number, multiplying two fractions (and why the rule works), simplifying before multiplying, and multiplying mixed numbers. New: predicting whether a product will be bigger or smaller than the starting number.
• Dividing FractionsDividing fractions by counting how many small pieces fit in a larger amount, finding the reciprocal, and dividing by a fraction by multiplying by its reciprocal. Also dividing mixed numbers and reading a leftover part in the story.
• Fractions Word ProblemsA practice week on fractions with unlike denominators: comparing, adding and subtracting them, mixed numbers and improper fractions, and word problems. Many brain teasers and puzzles, such as fraction cards and number machines.

Decimal place value, comparing, then adding, subtracting, multiplying and dividing decimals, and converting between fractions and decimals.

• Decimals Addition and SubtractionDecimal place value from whole numbers to thousandths, tenths and hundredths as decimals and fractions, comparing decimals and placing them on a number line, then adding and subtracting decimals, with word problems.
• Decimals Multiplication and DivisionA review of decimal place value, comparing, adding and subtracting, then new: multiplying decimals by counting decimal places, and dividing decimals by shifting the point or with long division. Word problems and puzzles throughout.
• Decimals Division and Mixed ProblemsReviews adding, subtracting and multiplying decimals, then more dividing: by 0.1, 0.01, 0.2 and 0.3, and with long division. New: mixed fraction and decimal problems, better-buy questions and magic squares.
• Fractions and DecimalsConverting fractions and mixed numbers to decimals and decimals to fractions, dividing a decimal by a decimal and by a whole number, and evaluating expressions. Word problems cover sum and difference, length, area and perimeter.

Numbers below zero on a number line, opposites, comparing and ordering, and adding and subtracting by moving right and left, with temperature, depth and money-owed problems.

• Negative NumbersReading and placing numbers below zero on a number line, opposites, comparing and ordering negative numbers, and adding and subtracting by moving right and left. Problems use temperature, depth and money owed.

Ratios and tape diagrams, ratios with metric and time units, proportions, unit rates and changing ratios.

• RatiosWriting ratios both ways round (a ratio is not a fraction), simplifying and building equivalent ratios, three-part ratios, and drawing a tape diagram to share a total in a given ratio.
• Ratios with Time and Metric UnitsConverting between metric units by moving digits and between units of time, then matching the units before writing a ratio, and reading matching pairs off a double number line.
• ProportionsDeciding whether two quantities are in proportion at all, finding the scale factor between two equivalent ratios, and solving for the missing quantity. New: writing the units beside the rows so a proportion is set up the same way round on both sides.
• Proportions and Unit RatesUnit rates: the price of one, comparing two offers by unit price, and solving a rate problem by finding one first. Rates that are not prices and reading a rate off a double number line are included.
• Changing RatiosWhat stays the same when a ratio changes: working out the new ratio after people join, leave or move across, and finding a total from the difference between the parts or from one part on its own.

Percent, decimal and fraction forms, percentages of a quantity, sale prices, increases and "what percent" problems, then a year-end review of ratios, proportions and percentages with a checkpoint.

• PercentagesA percent as a fraction over one hundred, moving between percent, decimal and fraction, the four percentages worth knowing by heart (50%, 25%, 10%, 1%), and finding a percentage of a quantity two ways.
• Percentages in PracticePercentages applied to money: sale prices in one step, prices after an increase, finding what percent one number is of another, and why two percentages do not add. Multi-step money problems close the week.
• Year-End Review - Ratios, Proportions and PercentagesA year-end review of ratios, proportions and percentages as one idea: the errors named over the last eight weeks, three sets (one per topic), a set with no method given, and a checkpoint.