OST Grade 3 Math cheat sheet

Multiplication means equal groups: 4 × 6 is 4 groups of 6, so the product is 24.

Division undoes multiplication: 24 ÷ 6 = 4 because 4 × 6 = 24. The dividend is 24, the divisor is 6, the quotient is 4.

In a × b = c, a and b are factors and c is the product; a missing factor is found by dividing the product by the known factor.

Commutative property of multiplication: a × b = b × a, so 7 × 3 = 3 × 7.

Associative property: (a × b) × c = a × (b × c), so grouping does not change a product.

Distributive property: a × (b + c) = (a × b) + (a × c); 6 × 14 = 6 × 10 + 6 × 4 = 60 + 24 = 84.

Division facts: any nonzero number divided by itself is 1; any number divided by 1 is itself; 0 divided by any nonzero number is 0.

Two-step word problems: solve the inner operation first, then the outer one; check with an estimate before computing.

Rounding to estimate products: 4 × 19 ≈ 4 × 20 = 80, so an exact answer far from 80 signals an error.

Place values in a 4-digit number: 5,382 has 5 thousands, 3 hundreds, 8 tens, 2 ones; moving one place left multiplies a digit's value by 10.

Standard form 4,706 = expanded form 4,000 + 700 + 0 + 6 = word form four thousand seven hundred six.

Rounding rule: look at the digit to the right of the target place; 5 or more rounds up, 4 or less stays the same, then all digits to the right become 0.

Compare multi-digit numbers by digits from left to right; the first place where digits differ decides: 4,285 > 4,258 because 8 tens > 5 tens.

Addition and subtraction: line up digits by place value, regroup (carry or borrow) when a column reaches 10 or needs to borrow 10.

Multiply one-digit by two-digit: 3 × 47 = 3 × 40 + 3 × 7 = 120 + 21 = 141.

Division with remainders: 25 ÷ 4 = 6 R1 because 4 × 6 = 24 and 25 − 24 = 1; the remainder is always less than the divisor.

Multiplying a whole number by 10 appends a zero: 10 × 36 = 360; by 100 appends two zeros: 100 × 36 = 3,600.

A unit fraction 1/b is one equal part of a whole split into b parts; a/b means a copies of 1/b.

On a number line, 1/b is the distance from 0 to the first mark when the interval 0 to 1 is split into b equal parts.

Equivalent fractions: a/b = (a × n)/(b × n); 2/3 = 4/6 = 6/9, same point on the number line.

Compare fractions with the same numerator: the smaller denominator is larger, so 3/4 > 3/8. With the same denominator, compare numerators.

Compare fractions with unlike denominators by finding a common denominator: 2/3 and 3/5 become 10/15 and 9/15, so 2/3 > 3/5.

A fraction equals 1 when numerator equals denominator; a fraction greater than 1 has numerator greater than denominator and can be written as a mixed number.

Whole numbers as fractions: 3 = 3/1 = 6/2 = 9/3; n = (n × b)/b for any nonzero b.

Adding and subtracting fractions with the same denominator: add or subtract numerators, keep the denominator: 2/5 + 1/5 = 3/5.

Fractions on a ruler or number line: equal parts between whole numbers; a fraction at the same point as another is equivalent to it.

Elapsed time: subtract start time from end time, regrouping 1 hour as 60 minutes; 3:40 to 5:10 is 1 hour 30 minutes.

Telling time to the nearest minute: the minute hand moves 1 minute per small mark, 5 minutes per number; the hour hand moves between numbers as minutes pass.

Mass and volume: 1 kilogram = 1,000 grams; 1 liter = 1,000 milliliters; a paper clip is about 1 gram, a liter is about a water bottle.

Liquid volume and mass word problems: adding or subtracting requires the same unit; convert first, then compute.

Bar graphs and picture graphs: read the scale (each symbol or gridline may stand for 2, 5, or 10), then compare bars by subtraction.

Line plots: each X is one data value; the value with the most Xs is the most common; find how many more at one value than another by counting Xs.

Area of a rectangle = length × width; perimeter = 2 × (length + width).

Area by decomposing: split an L-shaped figure into rectangles, find each area, add them.

Perimeter of a polygon: add all side lengths; for a square, perimeter = 4 × side.

A quadrilateral has 4 sides and 4 angles; a square, rectangle, rhombus, and trapezoid are all quadrilaterals.

A square is a rectangle with 4 equal sides and 4 right angles; every square is a rectangle, but not every rectangle is a square.

A rhombus has 4 equal sides; a trapezoid has exactly one pair of parallel sides; a parallelogram has two pairs.

Equal shares: a shape split into parts of equal area has unit fractions; 3 of 4 equal parts is shaded = 3/4.

Partition shapes into halves, thirds, fourths, sixths, eighths by equal-area pieces; more parts mean smaller pieces.

Area of a rectangle can be found by counting unit squares or multiplying side lengths; a square with side 3 has area 9 square units.

A right angle measures 90 degrees; a rectangle's four corners are right angles, and its opposite sides are equal and parallel.

Shapes can share attributes: a shape can be both a rectangle and a rhombus (a square), so attribute lists can overlap.

Multiplication means equal groups: 4 × 6 is 4 groups of 6, so the product is 24.

Division undoes multiplication: 24 ÷ 6 = 4 because 4 × 6 = 24. The dividend is 24, the divisor is 6, the quotient is 4.

In a × b = c, a and b are factors and c is the product; a missing factor is found by dividing the product by the known factor.

Commutative property of multiplication: a × b = b × a, so 7 × 3 = 3 × 7.

Associative property: (a × b) × c = a × (b × c), so grouping does not change a product.

Distributive property: a × (b + c) = (a × b) + (a × c); 6 × 14 = 6 × 10 + 6 × 4 = 60 + 24 = 84.

Division facts: any nonzero number divided by itself is 1; any number divided by 1 is itself; 0 divided by any nonzero number is 0.

Two-step word problems: solve the inner operation first, then the outer one; check with an estimate before computing.

Rounding to estimate products: 4 × 19 ≈ 4 × 20 = 80, so an exact answer far from 80 signals an error.

Place values in a 4-digit number: 5,382 has 5 thousands, 3 hundreds, 8 tens, 2 ones; moving one place left multiplies a digit's value by 10.

Standard form 4,706 = expanded form 4,000 + 700 + 0 + 6 = word form four thousand seven hundred six.

Rounding rule: look at the digit to the right of the target place; 5 or more rounds up, 4 or less stays the same, then all digits to the right become 0.

Compare multi-digit numbers by digits from left to right; the first place where digits differ decides: 4,285 > 4,258 because 8 tens > 5 tens.

Addition and subtraction: line up digits by place value, regroup (carry or borrow) when a column reaches 10 or needs to borrow 10.

Multiply one-digit by two-digit: 3 × 47 = 3 × 40 + 3 × 7 = 120 + 21 = 141.

Division with remainders: 25 ÷ 4 = 6 R1 because 4 × 6 = 24 and 25 − 24 = 1; the remainder is always less than the divisor.

Multiplying a whole number by 10 appends a zero: 10 × 36 = 360; by 100 appends two zeros: 100 × 36 = 3,600.

A unit fraction 1/b is one equal part of a whole split into b parts; a/b means a copies of 1/b.

On a number line, 1/b is the distance from 0 to the first mark when the interval 0 to 1 is split into b equal parts.

Equivalent fractions: a/b = (a × n)/(b × n); 2/3 = 4/6 = 6/9, same point on the number line.

Compare fractions with the same numerator: the smaller denominator is larger, so 3/4 > 3/8. With the same denominator, compare numerators.

Compare fractions with unlike denominators by finding a common denominator: 2/3 and 3/5 become 10/15 and 9/15, so 2/3 > 3/5.

A fraction equals 1 when numerator equals denominator; a fraction greater than 1 has numerator greater than denominator and can be written as a mixed number.

Whole numbers as fractions: 3 = 3/1 = 6/2 = 9/3; n = (n × b)/b for any nonzero b.

Adding and subtracting fractions with the same denominator: add or subtract numerators, keep the denominator: 2/5 + 1/5 = 3/5.

Fractions on a ruler or number line: equal parts between whole numbers; a fraction at the same point as another is equivalent to it.

Elapsed time: subtract start time from end time, regrouping 1 hour as 60 minutes; 3:40 to 5:10 is 1 hour 30 minutes.

Telling time to the nearest minute: the minute hand moves 1 minute per small mark, 5 minutes per number; the hour hand moves between numbers as minutes pass.

Mass and volume: 1 kilogram = 1,000 grams; 1 liter = 1,000 milliliters; a paper clip is about 1 gram, a liter is about a water bottle.

Liquid volume and mass word problems: adding or subtracting requires the same unit; convert first, then compute.

Bar graphs and picture graphs: read the scale (each symbol or gridline may stand for 2, 5, or 10), then compare bars by subtraction.

Line plots: each X is one data value; the value with the most Xs is the most common; find how many more at one value than another by counting Xs.

Area of a rectangle = length × width; perimeter = 2 × (length + width).

Area by decomposing: split an L-shaped figure into rectangles, find each area, add them.

Perimeter of a polygon: add all side lengths; for a square, perimeter = 4 × side.

A quadrilateral has 4 sides and 4 angles; a square, rectangle, rhombus, and trapezoid are all quadrilaterals.

A square is a rectangle with 4 equal sides and 4 right angles; every square is a rectangle, but not every rectangle is a square.

A rhombus has 4 equal sides; a trapezoid has exactly one pair of parallel sides; a parallelogram has two pairs.

Equal shares: a shape split into parts of equal area has unit fractions; 3 of 4 equal parts is shaded = 3/4.

Partition shapes into halves, thirds, fourths, sixths, eighths by equal-area pieces; more parts mean smaller pieces.

Area of a rectangle can be found by counting unit squares or multiplying side lengths; a square with side 3 has area 9 square units.

A right angle measures 90 degrees; a rectangle's four corners are right angles, and its opposite sides are equal and parallel.

Shapes can share attributes: a shape can be both a rectangle and a rhombus (a square), so attribute lists can overlap.

Multiplication means equal groups: 4 × 6 is 4 groups of 6, so the product is 24.

Division undoes multiplication: 24 ÷ 6 = 4 because 4 × 6 = 24. The dividend is 24, the divisor is 6, the quotient is 4.

In a × b = c, a and b are factors and c is the product; a missing factor is found by dividing the product by the known factor.

Commutative property of multiplication: a × b = b × a, so 7 × 3 = 3 × 7.

Associative property: (a × b) × c = a × (b × c), so grouping does not change a product.

Distributive property: a × (b + c) = (a × b) + (a × c); 6 × 14 = 6 × 10 + 6 × 4 = 60 + 24 = 84.

Division facts: any nonzero number divided by itself is 1; any number divided by 1 is itself; 0 divided by any nonzero number is 0.

Two-step word problems: solve the inner operation first, then the outer one; check with an estimate before computing.

Rounding to estimate products: 4 × 19 ≈ 4 × 20 = 80, so an exact answer far from 80 signals an error.

Place values in a 4-digit number: 5,382 has 5 thousands, 3 hundreds, 8 tens, 2 ones; moving one place left multiplies a digit's value by 10.

Standard form 4,706 = expanded form 4,000 + 700 + 0 + 6 = word form four thousand seven hundred six.

Rounding rule: look at the digit to the right of the target place; 5 or more rounds up, 4 or less stays the same, then all digits to the right become 0.

Compare multi-digit numbers by digits from left to right; the first place where digits differ decides: 4,285 > 4,258 because 8 tens > 5 tens.

Addition and subtraction: line up digits by place value, regroup (carry or borrow) when a column reaches 10 or needs to borrow 10.

Multiply one-digit by two-digit: 3 × 47 = 3 × 40 + 3 × 7 = 120 + 21 = 141.

Division with remainders: 25 ÷ 4 = 6 R1 because 4 × 6 = 24 and 25 − 24 = 1; the remainder is always less than the divisor.

Multiplying a whole number by 10 appends a zero: 10 × 36 = 360; by 100 appends two zeros: 100 × 36 = 3,600.

A unit fraction 1/b is one equal part of a whole split into b parts; a/b means a copies of 1/b.

On a number line, 1/b is the distance from 0 to the first mark when the interval 0 to 1 is split into b equal parts.

Equivalent fractions: a/b = (a × n)/(b × n); 2/3 = 4/6 = 6/9, same point on the number line.

Compare fractions with the same numerator: the smaller denominator is larger, so 3/4 > 3/8. With the same denominator, compare numerators.

Compare fractions with unlike denominators by finding a common denominator: 2/3 and 3/5 become 10/15 and 9/15, so 2/3 > 3/5.

A fraction equals 1 when numerator equals denominator; a fraction greater than 1 has numerator greater than denominator and can be written as a mixed number.

Whole numbers as fractions: 3 = 3/1 = 6/2 = 9/3; n = (n × b)/b for any nonzero b.

Adding and subtracting fractions with the same denominator: add or subtract numerators, keep the denominator: 2/5 + 1/5 = 3/5.

Fractions on a ruler or number line: equal parts between whole numbers; a fraction at the same point as another is equivalent to it.

Elapsed time: subtract start time from end time, regrouping 1 hour as 60 minutes; 3:40 to 5:10 is 1 hour 30 minutes.

Telling time to the nearest minute: the minute hand moves 1 minute per small mark, 5 minutes per number; the hour hand moves between numbers as minutes pass.

Mass and volume: 1 kilogram = 1,000 grams; 1 liter = 1,000 milliliters; a paper clip is about 1 gram, a liter is about a water bottle.

Liquid volume and mass word problems: adding or subtracting requires the same unit; convert first, then compute.

Bar graphs and picture graphs: read the scale (each symbol or gridline may stand for 2, 5, or 10), then compare bars by subtraction.

Line plots: each X is one data value; the value with the most Xs is the most common; find how many more at one value than another by counting Xs.

Area of a rectangle = length × width; perimeter = 2 × (length + width).

Area by decomposing: split an L-shaped figure into rectangles, find each area, add them.

Perimeter of a polygon: add all side lengths; for a square, perimeter = 4 × side.

A quadrilateral has 4 sides and 4 angles; a square, rectangle, rhombus, and trapezoid are all quadrilaterals.

A square is a rectangle with 4 equal sides and 4 right angles; every square is a rectangle, but not every rectangle is a square.

A rhombus has 4 equal sides; a trapezoid has exactly one pair of parallel sides; a parallelogram has two pairs.

Equal shares: a shape split into parts of equal area has unit fractions; 3 of 4 equal parts is shaded = 3/4.

Partition shapes into halves, thirds, fourths, sixths, eighths by equal-area pieces; more parts mean smaller pieces.

Area of a rectangle can be found by counting unit squares or multiplying side lengths; a square with side 3 has area 9 square units.

A right angle measures 90 degrees; a rectangle's four corners are right angles, and its opposite sides are equal and parallel.

Shapes can share attributes: a shape can be both a rectangle and a rhombus (a square), so attribute lists can overlap.