Number and Operations
Number and Operations is the largest domain on this Grade 5 mathematics assessment. Questions ask you to read, compare, compute with, and explain whole numbers through millions, decimals through thousandths, and fractions, then choose an operation that fits a context.
Place value and rounding
- In a whole number, each place is ten times the place to its right. In 4,207,316 the 2 is worth 200,000; the 7 is worth 7,000.
- In decimals, 0.407 means 407 thousandths; 0.47 means 47 hundredths, so 0.47 > 0.407.
- To round, find the target place and look one place to the right: 5 or more rounds up.
Whole-number computation
- Multiply multi-digit numbers by decomposing or using the standard algorithm; keep columns aligned by place.
- Divide with partial quotients or long division. A remainder must be interpreted: 43 ÷ 5 = 8 R3 can mean 8 full groups with 3 left, or 8 3/5.
Fractions
- Equivalent fractions multiply numerator and denominator by the same nonzero number.
- Compare by common denominators or benchmarks such as 1/2.
- Add or subtract only after denominators match. Multiply a fraction by a whole number by multiplying the numerator.
Decimals and order of operations
- Line up decimal points for addition and subtraction. For multiplication, multiply as whole numbers, then place the decimal using the total number of decimal places.
- Work inside parentheses or brackets first, then × and ÷ left to right, then + and − left to right.
Worked example
3/4 + 5/6. The least common denominator is 12: 3/4 = 9/12 and 5/6 = 10/12. Add numerators: 19/12. Rewrite as 1 7/12. Check with benchmarks: each fraction is less than 1, and the sum is a little more than 1.5, which fits.
Traps that cost marks
- Adding denominators: 3/4 + 5/6 is not 8/10.
- Lining up decimals by the last digit instead of the decimal point.
- Rounding too early in a multi-step problem.
- Ignoring what the remainder means in a division context.
- Forgetting that a fraction times a whole number can be renamed as a mixed number.