Georgia Milestones Math Grade 5 cheat sheet

Place value: in a multi-digit number each place is 10 times the place to its right; 7 in 7,432 means 7,000, and 0.7 is 1/10 of 7.

Powers of 10: multiplying by 10^n shifts digits n places left; dividing shifts them n places right, so 4.6 × 100 = 460 and 4.6 ÷ 100 = 0.046.

Decimal read/write: 0.36 = 36/100 = thirty-six hundredths; compare decimals by aligning place values, so 0.5 > 0.45 because 50 hundredths > 45 hundredths.

Rounding: to round 8.467 to the nearest hundredth, look at the thousandths digit (7 ≥ 5), so the result is 8.47.

Fraction equivalence: a/b = (a × n)/(b × n); 2/3 = 8/12. A fraction is simplified when the numerator and denominator share no common factor other than 1.

Multiply fractions: (a/b) × (c/d) = ac/bd; 2/3 × 3/4 = 6/12 = 1/2. Multiplying by a fraction less than 1 gives a product smaller than the starting number.

Divide with unit fractions: dividing by 1/n is the same as multiplying by n, so 4 ÷ 1/5 = 4 × 5 = 20.

Volume: V = length × width × height for a right rectangular prism; a prism 3 × 4 × 5 has volume 60 cubic units. Add volumes of non-overlapping parts to find a composite solid's volume.

Coordinate plane: the first coordinate is horizontal (x) and the second is vertical (y); point (3, 5) is 3 right and 5 up from the origin. Points on the same vertical line share the same x-coordinate.

Multi-digit multiplication: 24 × 36 = 24 × 30 + 24 × 6 = 720 + 144 = 864. Partial products can be added in any order.

Long division: 945 ÷ 7 = 135, since 7 × 100 = 700, 7 × 30 = 210, and 7 × 5 = 35, and 700 + 210 + 35 = 945.

Decimal operations: line up decimal points when adding or subtracting; when multiplying, the product has as many decimal places as the two factors combined (0.3 × 0.4 = 0.12).

Dividing decimals: make the divisor a whole number by shifting both decimals the same number of places, e.g., 4.5 ÷ 0.9 = 45 ÷ 9 = 5.

Order of operations: evaluate parentheses first, then multiplication and division left to right, then addition and subtraction left to right, so 2 + 3 × 4 = 14.

Numerical patterns: given the rule "add 6," the sequence 3, 9, 15, 21 continues with 27. Given ordered pairs, look for a rule relating the first value to the second.

Expressions: 3 × (8 + 2) can be read as "3 times the sum of 8 and 2"; interpret words such as sum, difference, product, and quotient as operation signals.

Measurement conversion: 1 km = 1,000 m, 1 m = 100 cm, 1 kg = 1,000 g, 1 L = 1,000 mL, 1 hour = 60 minutes. Convert by multiplying or dividing by the unit ratio.

Line plots with fractional data: each X represents one data value; find the total by adding all values, then divide by the number of X's for the mean.