OST Grade 4 Math cheat sheet

Multiplication is repeated addition: 4 × 6 means 4 groups of 6, equal to 6 + 6 + 6 + 6 = 24.

Division undoes multiplication: 24 ÷ 6 = 4 because 4 × 6 = 24. Quotient × divisor = dividend.

A multiplication equation a × b = c has two division facts: c ÷ a = b and c ÷ b = a.

Multiplicative comparison: '7 times as many as 5' means 7 × 5 = 35; 'how many times as many' means divide the larger by the smaller.

Multi-step word problems: solve parentheses first, then multiply/divide left to right, then add/subtract left to right.

Factors of a whole number divide it evenly with remainder 0; multiples are products of that number and 1, 2, 3, ...

A number is prime if it has exactly two factors, 1 and itself (2, 3, 5, 7, 11, ...); 1 is neither prime nor composite.

Patterns: find the rule by comparing consecutive terms; a rule such as 'add 6' or 'multiply by 3' must fit every pair of terms.

Check an answer by estimating first (round factors) and by using the inverse operation.

Place value: in 4,582 the 5 is worth 500, the 8 is worth 80, and the 2 is worth 2; each place is 10 times the place to its right.

Expanded form: 4,582 = 4,000 + 500 + 80 + 2; word form: four thousand five hundred eighty-two.

Rounding: look at the digit to the right of the target place; 5 or more rounds up, 4 or less stays the same.

Compare multi-digit numbers by digits from left to right; the first place where digits differ decides the comparison (>, <, =).

Standard algorithm for addition/subtraction: line up places, regroup when a column exceeds 9 or when subtracting from a smaller digit.

Multiply a multi-digit number by a one-digit number by multiplying each place value, then adding partial products.

Multiplication by 10, 100, 1,000: append that many zeros to the whole-number factor (e.g., 47 × 100 = 4,700).

Division with remainders: remainder = dividend − (quotient × divisor); the remainder must be less than the divisor.

Area model: split a factor into place-value parts, multiply each part, and add the partial products.

Equivalent fractions: multiply or divide numerator and denominator by the same nonzero number (1/2 = 2/4 = 3/6).

Compare fractions with the same numerator: the smaller denominator makes the larger fraction (3/5 > 3/8).

Compare fractions with the same denominator: compare numerators only.

Benchmark fractions 0, 1/2, and 1 help order fractions: a fraction with numerator less than half the denominator is less than 1/2.

Add or subtract fractions with like denominators by combining numerators and keeping the denominator.

A fraction a/b with a > b is greater than 1 and can be written as a mixed number: 7/4 = 1 3/4.

Multiply a fraction by a whole number: multiply the numerator by the whole number (3 × 2/5 = 6/5).

Decimal–fraction link: 0.3 = 3/10, 0.25 = 25/100 = 1/4; compare decimals by place value.

A fraction with denominator 10 or 100 can be written as a decimal: 7/100 = 0.07.

Customary length conversions: 1 foot = 12 inches, 1 yard = 3 feet = 36 inches, 1 mile = 5,280 feet.

Metric length conversions: 1 kilometer = 1,000 meters, 1 meter = 100 centimeters, 1 centimeter = 10 millimeters.

Capacity and mass: 1 gallon = 4 quarts = 8 pints = 16 cups; 1 kilogram = 1,000 grams; 1 liter = 1,000 milliliters.

Time: 1 hour = 60 minutes, 1 minute = 60 seconds; elapsed time = end time − start time.

Perimeter of a rectangle = 2 × (length + width); perimeter of any polygon = sum of all side lengths.

Area of a rectangle = length × width; area is measured in square units.

Unknown side: width = area ÷ length; length = perimeter ÷ 2 − width.

Line plot: each X stands for one data value; the value with the most X's is the mode.

Angle measure: a right angle is 90°, a straight angle is 180°; adjacent angles add to the whole angle.

A point is a location; a line extends forever in both directions; a ray has one endpoint and extends forever one way.

Parallel lines never meet and stay the same distance apart; perpendicular lines meet at a 90° right angle.

Acute angle < 90°, right angle = 90°, obtuse angle > 90° and < 180°, straight angle = 180°.

Triangles: equilateral has 3 equal sides, isosceles has 2 equal sides, scalene has no equal sides.

Triangles by angles: acute (all angles < 90°), right (one 90° angle), obtuse (one angle > 90°).

Quadrilaterals: parallelogram (both pairs of opposite sides parallel), rectangle (4 right angles), rhombus (4 equal sides), square (4 right angles and 4 equal sides), trapezoid (exactly one pair of parallel sides).

A line of symmetry folds a figure onto itself; a square has 4 lines of symmetry, a rectangle has 2.

Angle measure is additive: if a 120° angle is split into a 45° part, the other part measures 120° − 45° = 75°.