NA3-1: Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.

Elaboration on this Achievement Objective

This means students will use a range of mental strategies based on partitioning and combining to solve addition and subtraction problems with multi-digit whole numbers and simple decimals (tenths). These strategies include standard place value, for example 603 – 384 = box. as 60 – 38 tens less one (219), rounding and compensating, for example 923 – 587 = box. as 923 – 600 + 13 = box. , and reversing (applying inverse), for example 923 – 587 = box. as 587 + box. = 923. Students should also connect known multiplication facts to solve multiplication and division problems, for example 13 x 6 = box. as 10 x 6 + 3 x 6 = box. (distributive property), 14 x 9 = box. as 2 x (7 x 9) = box. (associative property) and 36 ÷ 9 = box. using 4 x 9 = 36 (inverse). This multiplicative understanding allows students at Level Three to find fractions of quantities, for example two-thirds of 24 as 24 ÷ 3 x 2 = 16, find simple equivalent fractions related to doubling and halving, for example 3/4 = 6/8 , to add and subtract fractions with the same denominators, for example 3/4 + 3/4 = 6/4 = 1 2/4, and to convert improper fractions to mixed numbers, for example 17/3 = 5 2/3. Students should know the decimals and percentage conversions of simple fractions (halves, quarters, fifths, tenths) and use these to solve simple percentage of amount problems, for example 50% is fifty out of one hundred. 50% is one half so 50% of 18 is 9 or five is half of ten. Level Three corresponds to the Advanced Additive stage of the number framework.