NVO Grade 4 Mathematics cheat sheet

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

Division undoes multiplication: 24 ÷ 6 = 4 because 4 × 6 = 24. The dividend is the total, the divisor is the group size or number of groups, and the quotient is the answer.

Multiplication and division facts through 12 × 12 should be recalled from memory; use known facts to derive unknown ones (if 6 × 7 = 42, then 6 × 8 = 42 + 6 = 48).

The four properties: commutative (3 × 5 = 5 × 3), associative ((2 × 3) × 4 = 2 × (3 × 4)), identity (n × 1 = n), and zero (n × 0 = 0).

Multiplicative comparison: '7 times as many as 5' means 7 × 5 = 35. The phrase 'times as many' signals multiplication, not addition.

A multi-step word problem is solved by identifying the hidden question first, then choosing operations in order; check the answer against the original question.

A number pattern follows a rule; to find the rule, compare consecutive terms. Example: 3, 6, 12, 24 follows 'multiply by 2.'

An equation with an unknown, such as 8 × n = 56, is solved by dividing: n = 56 ÷ 8 = 7.

Place value positions from right to left are ones, tens, hundreds, thousands, ten-thousands, hundred-thousands, millions; each place is 10 times the value of the place to its right.

A digit's value equals the digit times its place value: in 4,728 the 7 is worth 7 × 100 = 700.

Standard form is 45,302; expanded form is 40,000 + 5,000 + 300 + 2; word form is 'forty-five thousand, three hundred two.'

To compare multi-digit numbers, compare digits from the leftmost place; the first place where digits differ decides the comparison (>, <, or =).

Rounding rule: locate the target place, look at the digit to its right; 5 or more rounds up, 4 or less keeps the digit the same, and all digits to the right become zero.

Addition and subtraction are done by aligning place values and regrouping: 10 ones make 1 ten, 10 tens make 1 hundred; borrowing reverses this.

Multiplication by a one-digit number uses partial products: 3 × 246 = 3 × 200 + 3 × 40 + 3 × 6 = 600 + 120 + 18 = 738.

Division with remainders: 47 ÷ 5 = 9 remainder 2, and the check is 9 × 5 + 2 = 47. The remainder must be less than the divisor.

A fraction a/b means a equal parts out of b equal parts in the whole; the denominator b is the number of equal parts and the numerator a is how many are counted.

Equivalent fractions are made by multiplying or dividing numerator and denominator by the same nonzero number: 2/3 = 8/12 because both parts were multiplied by 4.

To compare fractions with the same denominator, compare numerators; with the same numerator, the larger denominator means smaller pieces (1/8 < 1/5).

Benchmark reasoning: a fraction is less than 1/2 if the numerator is less than half the denominator, and greater than 1/2 if it is more than half.

Adding or subtracting fractions with like denominators: add or subtract numerators and keep the denominator, then simplify (3/8 + 2/8 = 5/8).

To add fractions with unlike denominators, first rewrite both with a common denominator, such as 1/2 + 1/3 = 3/6 + 2/6 = 5/6.

A fraction times a whole number means repeated groups of that fraction: 3 × 2/5 = 6/5 = 1 1/5.

A mixed number such as 2 1/4 equals 9/4; multiply the whole number by the denominator, add the numerator, and place over the same denominator.

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

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

Capacity and weight: 1 cup = 8 fluid ounces, 1 pint = 2 cups, 1 quart = 2 pints, 1 gallon = 4 quarts; 1 pound = 16 ounces.

Time conversions: 1 minute = 60 seconds, 1 hour = 60 minutes, 1 day = 24 hours; elapsed time is found by counting forward or backward from the start time.

Area of a rectangle = length × width; perimeter = 2 × (length + width). Area is measured in square units, perimeter in linear units.

A line plot records data above a number line using X marks; the value with the most X marks is the most common measurement.

To convert from a larger unit to a smaller unit, multiply; to convert from a smaller unit to a larger unit, divide.

An angle is measured in degrees; a right angle is 90°, a straight angle is 180°, and a full turn is 360°. A protractor's inner and outer scales both start at 0°.

A line is straight and extends forever in both directions; a line segment has two endpoints; a ray has one endpoint and extends forever in one direction.

An angle is formed by two rays sharing an endpoint called the vertex; angles are classified as acute (< 90°), right (= 90°), obtuse (> 90° and < 180°), or straight (= 180°).

Two lines are parallel if they never meet and perpendicular if they meet at a right angle; intersecting lines cross at a single point.

Triangles are classified by angles (acute, right, obtuse) and by sides (equilateral: 3 equal sides; isosceles: 2 equal sides; scalene: 0 equal sides).

A line of symmetry divides a figure into two matching halves that fold onto each other; a square has 4 lines of symmetry, a rectangle has 2.

A quadrilateral has 4 sides and 4 angles; special types include the square (4 equal sides, 4 right angles), rectangle, rhombus, trapezoid, and parallelogram.

A right triangle has one 90° angle; the two sides forming it are perpendicular, and the side opposite the right angle is the longest side.