Online Math 4 Classes: Multi-Digit Operations, Fractions and Decimals

Place value to the ten thousands, expanded form, comparing and rounding, then adding and subtracting multi-digit numbers (including across zeros) and one- and two-step word problems.

• Place Value and Number SensePlace value through the ten thousands and regrouping, expanded form and number words, comparing and ordering whole numbers, and rounding to the nearest hundred or thousand.
• Adding and Subtracting Multi-Digit NumbersAdding with regrouping and subtracting across zeros in numbers up to six digits, then checking each answer by estimating to the nearest thousand and asking whether it is reasonable.
• Addition and Subtraction Word ProblemsOne- and two-step word problems: drawing a tape diagram, finding the hidden first step, and choosing add or subtract by whether the whole is known, not by words like 'more'. Also extra information and problems that cannot be solved.

Multiplying by 10, 100 and 1,000, then by one-digit and two-digit numbers with area models and the column method, plus the distributive property and mental shortcuts.

• Multiplication PatternsMultiplying by 10, 100 and 1,000 by moving the digits left, multiplying multiples of ten by counting zeros, and estimating a product by rounding each factor to one leading digit.
• Multiplying by a One-Digit NumberMultiplying a two-digit, then a three- or four-digit number by a one-digit number with carrying, with the area model showing why it works, and equal-groups word problems.
• The Distributive Property and Area ModelsSplitting a factor into tens and ones (the distributive property) and drawing it as an area model, plus mental shortcuts for multiplying by 9, 99 and 5.
• Multiplying Two-Digit by Two-DigitMultiplying two-digit by two-digit numbers: first the area model with four parts, then the standard column method with its second row, then multi-step word problems.

Dividing by a one-digit number with the standard algorithm and a check by multiplying, then remainders: what they mean, estimating a quotient, and how a remainder is used in a word problem.

• Dividing by a One-Digit NumberDivision as equal sharing and as making groups, the standard algorithm worked from the left (including a zero in the answer), and checking a quotient by multiplying back.
• Division with RemaindersWhat a remainder means and how to find the quotient and remainder, including longer dividends, checking by multiplying and adding, and estimating a quotient.
• Interpreting Remainders in Word ProblemsOne division can have three different answers: round up when you need one more, drop the remainder when only full groups count, or report the remainder when it is what the question asks.

Factors, multiples, and prime and composite numbers, then divisibility rules, factor trees, prime factorization, and the GCF and LCM with word problems that need one or the other.

• Factors, Multiples, Prime and Composite NumbersFinding all the factors of a number in pairs, multiples and common multiples, and telling prime numbers from composite numbers by counting factors.
• Divisibility Rules, Factor Trees, GCF and LCMDivisibility rules for 2, 3, 5, 6, 9 and 10, factor trees and prime factorization, then the greatest common factor and least common multiple and which one a word problem needs.

Exponents and the order of operations, letters for unknowns with expressions and like terms, multi-step word problems, and number patterns with rules and input and output tables.

• Order of OperationsWhy an order is needed, exponents and powers of 10, then the order itself: parentheses, exponents, multiply and divide, add and subtract, working left to right within each rank.
• Problems with UnknownsUsing a letter for an unknown number, evaluating expressions, combining like terms, writing a number sentence from a story, and finding the unknown by undoing operations.
• Multi-Step Word ProblemsMulti-step word problems: finding the hidden first step, writing the small questions in order, and checking the answer against the question for what was asked, sensible size and units.
• Number Patterns and RulesContinuing number patterns, stating a rule in words, and input and output tables, including two-step rules, finding the rule from a table and working backwards through it.

Fractions as parts of a whole and on a number line, comparing, equivalent fractions and simplifying, adding and subtracting with like and then unlike denominators, mixed numbers, and a fraction times a whole number.

• Understanding and Comparing FractionsA fraction as equal parts of a whole, fractions on a number line (including fractions more than 1), and comparing fractions with the same bottom, the same top, or the benchmarks 0, 1/2 and 1.
• Equivalent FractionsMaking equivalent fractions by multiplying top and bottom, simplifying by dividing both by the same number, and comparing fractions by rewriting them with the same denominator.
• Adding and Subtracting Fractions with Like DenominatorsAdding and subtracting fractions with like denominators, simplifying answers, and word problems where the fractions are parts of the same whole.
• Improper Fractions and Mixed NumbersWriting improper fractions as mixed numbers and back again, with a number-line picture, then adding and subtracting mixed numbers.
• Multiplying a Fraction by a Whole NumberMultiplying a fraction by a whole number as repeated addition, then the shortcut of multiplying the top only, with recipe and measurement problems.

• Tenths, Hundredths and ThousandthsDecimal place value to the thousandths, reading and writing decimals, tenths and hundredths as fractions, and decimals on a number line.
• Comparing and Ordering DecimalsComparing decimals place by place, ordering a set by giving every decimal the same number of places, and rounding to the nearest tenth.
• Adding and Subtracting DecimalsAdding and subtracting decimals by lining up the decimal points, with money problems and measurement problems where the units must match first.
• Multiplying and Dividing DecimalsMultiplying and dividing decimals by 10, 100 and 1,000, a decimal times a whole number, a decimal times a decimal, and a decimal divided by a whole number.
• Fractions and Decimals TogetherWriting tenths and hundredths as fractions and decimals, converting by rewriting over 10 or 100, four conversions to know by heart, and comparing a fraction with a decimal.

Metric and customary units, multi-step measurement, elapsed time and line plots, perimeter and area, lines and symmetry, and angles.

• Measurement Units and ConversionMetric units of length, mass and capacity, customary units, and converting within one system: multiply when going to a smaller unit, divide when going to a bigger one.
• Measurement Problems and Line PlotsMulti-step measurement problems that need a unit conversion first, elapsed time, and reading line plots with a scale in fractions of an inch.
• Perimeter and AreaPerimeter and area of a rectangle, telling them apart by their units, and working backwards to a missing side from a given perimeter or area.
• Lines, Angles and SymmetryPoints, lines, rays and segments, parallel and perpendicular lines, and lines of symmetry found by folding.
• Measuring Angles and Cumulative ReviewClassifying angles, measuring with a protractor, adding angle measures to find a missing angle, then a cumulative review of the whole year in two sets of mixed questions.