AA
ADDITION AND SUBTRACTION
Advanced Addition and Subtraction of Whole Numbers (Revision)
The student can estimate answers and solve addition and subtraction tasks involving whole numbers mentally by choosing appropriately from a broad range of advanced mental strategies, e.g.,63 – 39 = 63 – 40 + 1 = 24 (roundingand compensating) or 39 +20 + 4 = 63,so 63 – 39 = 24 (reversibility) or 64 – 40 = 24 (equal additions)
e.g., 324 – 86 = 300 – 62 = 238 (standard place value partitioning) or 324–100 + 14 = 238 (roundingand compensating).
MULTIPLICATION AND DIVISION
Derived Multiplication (Revision)
The student uses a combination of known facts and mental strategies to derive answers to multiplication and division problems, e.g., 4 x 8 = 2 x 16 = 32 (doubling and halving), e.g., 9 x 6 is (10 x 6) – 6 = 54 (rounding and compensating), e.g., 63 ÷ 7 = 9 because 9 x 7= 63 (reversibility).
PROPORTIONS AND RATIOS
Fraction of a Number by Addition and Multiplication
The student uses repeated halving or known multiplication and division facts to solve problems that involve finding fractions of a set or region, renaming improper fractions, and division with remainders,
e.g., 1/3 of 36, 3 x 10 = 30, 36 – 30 = 6, 6 ÷ 3 = 2, 10 + 2 = 12
e.g., 16/3 =5 1/3 (using 5 x 3 = 15)
e.g., 8 pies shared among 3 people (8 ÷ 3) by giving each person 2 pies and dividing the remaining 2 pies into thirds (answer:2 + 1/3 + 1/3 =2 2/3).
The student uses repeated replication to solve simple problems involving ratios and rates, e.g. 2:3 ➝ 4:6 ➝ 8:12 etc.