FAST Grade 5 Practice

Big idea: Digits get their value from their place. In 7.409, the 4 is tenths, the 0 is hundredths, and the 9 is thousandths.

Compare decimals: Line up the decimal points and compare digit by digit from left to right.

Rounding: Look one place to the right. If it is 5 or more, round up.

Order matters: Parentheses first, then multiply/divide, then add/subtract.

Verbal expressions: “The quantity” usually means parentheses. Example: “3 times the quantity 9 minus 6” is 3 × (9 − 6).

Substitute: If n = 4, then 3n + 5 = 3 × 4 + 5 = 17.

Line up decimals: Ones under ones, tenths under tenths, hundredths under hundredths.

Add zeros if helpful: 4.5 can be written as 4.50.

Check with estimation: If 8.7 − 3.9, think about 9 − 4 = 5, so the answer should be close to 5.

Partial products: Break a number apart by place value. Example: 36 × 24 = 36 × 20 + 36 × 4.

Multiples of 10: Use place-value patterns. 48 × 100 = 4,800.

Word problems: Decide what one group has, then multiply by the number of groups.

Estimate first: 3.8 × 6 is close to 4 × 6 = 24.

Decimal placement: Multiply like whole numbers, then place the decimal so the answer makes sense.

Money problems: Cost of several items is usually price × number of items.

Division means equal groups: 156 ÷ 6 asks how many are in each of 6 equal groups.

Remainders matter: If packages are needed, round up when leftovers still need a package.

Check: Multiply the quotient by the divisor, then add the remainder.

Reason first: Estimate to know if the answer should be big or small.

Decimal divisor: If dividing by a decimal, make an equivalent problem by moving both decimals the same number of places.

Equal sections: Total length divided by number of equal parts gives the length of each part.

Same denominator: Add or subtract only the numerators (tops). Keep the denominator (bottom) the same. Example: 2/7 + 3/7 = 5/7.

Different denominators: Make equivalent fractions with a common denominator first.

Mixed numbers: Add or subtract the whole-number parts and fraction parts carefully.

Fraction × fraction: Multiply tops, multiply bottoms, then simplify. Example: 1/2 × 3/4 = 3/8.

“Of” means multiply: 1/3 of 12 means 1/3 × 12.

Mixed numbers: Change to an improper fraction before multiplying.

Whole number ÷ unit fraction: Ask how many unit-fraction pieces fit. Example: 3 ÷ 1/4 = 12.

Unit fraction ÷ whole number: Split one small fraction into equal parts. Example: 1/2 ÷ 3 = 1/6.

Draw it: Fraction division is easier when you picture equal pieces.

Know common conversions: 1 ft = 12 in, 1 lb = 16 oz, 1 L = 1,000 mL.

Same system only: Convert within customary or within metric.

Line plots: Each X is one measurement. Add the Xs or combine fractional measurements as asked.

Ordered pairs: (x, y) means move right first, then up.

Patterns: In a rule like 3n + 5, substitute each n value, multiply first, then add.

Data: Mean is the average, median is the middle, mode repeats most, and range is greatest minus least.

Volume: Volume measures how much space a solid figure takes up. Use cubic units.

Rectangular prism formula: V = length × width × height.

Missing dimension: Divide the volume by the two known dimensions.

Use defining attributes: Classify shapes by what is always true, not what only sometimes looks true.

Quadrilaterals: Rectangles have 4 right angles. Rhombuses have 4 equal sides. Squares have both.

3D shapes: Rectangular prisms have rectangular faces, edges, and vertices.