# Number 5.0

●      At Level 5, students identify complete factor sets for natural numbers and express these natural numbers as products of powers of primes (for example, 36 000 = 25 × 32 × 53).

●      They write equivalent fractions for a fraction given in simplest form (for example, 2/3 = 4/6 = 6/9 = … ).

●      They write the reciprocal of any fraction and calculate the decimal equivalent to a given degree of accuracy.

●      Students use knowledge of perfect squares when calculating and estimating squares and square roots of numbers (for example, 202 = 400 and 302 = 900 so √700 is between 20 and 30).

●      They evaluate natural numbers and simple fractions given in base-exponent form (for example, 54 = 625 and (2/3)2 = 4/9).

●      They know simple powers of 2, 3, and 5 (for example, 26 = 64, 34 = 81, 53 = 125).

●      They calculate squares and square roots of rational numbers that are perfect squares (for example, √0.81 = 0.9 and √9/16 = 3/4).

●       They calculate cubes and cube roots of perfect cubes (for example, 3√64 = 4).

●      Using technology they find square and cube roots of rational numbers to a specified degree of accuracy (for example, 3√200 = 5.848 to three decimal places).

●      Students express natural numbers base 10 in binary form, (for example, 4210 = 1010102), and add and multiply natural numbers in binary form (for example, 1012 + 112 = 10002 and 1012 × 112 = 11112).

●      Students use a range of strategies for approximating the results of computations, such as front-end estimation and rounding (for example, 925 ÷ 34 ≈ 900 ÷ 30 = 30).

●      Students use efficient mental and/or written methods for arithmetic computation involving rational numbers, including division of integers by two-digit divisors.

●      They use approximations to π in related measurement calculations (for example, π × 52 = 25π = 78.54 correct to two decimal places).

●      They use technology for arithmetic computations involving several operations on rational numbers of any size.