In order to develop and use strategies to learn the multiplication facts through the twelves table, students should use concrete materials, a hundreds chart, and mental mathematics. Strategies to learn the multiplication facts include an understanding of multiples, properties of zero and one as factors, commutative property, and related facts. Investigating arithmetic operations with whole numbers helps students learn about the different properties of arithmetic relationships. These relationships remain true regardless of the whole numbers.
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Apply strategies, including place value and the properties of multiplication and/or addition when multiplying and dividing whole numbers. (a, b, c, d)
Create practical problems to represent a multiplication or division fact. (b)
As students work to solve multiplication and division problems, they naturally tend to utilize strategies that involve place value understanding and properties of the operations. Applying the commutative property of multiplication (e.g., 5 x 8 = 8 x 5) reduces in half the number of multiplication facts that students must learn. The distributive property of multiplication allows students to find the answer to a problem such as 6 x 7 by decomposing 7 into 3 and 4 (e.g., 6 x 7= 6 x (3 + 4)) allowing them to think about (6 x 3) + (6 x 4) = 18 + 24 = 42.
dividends do not exceed four digits.
The student will a) represent multiplication and division through 10 × 10, using a variety of approaches and models; b) create and solve single-step practical problems that involve multiplication and division through 10 × 10; c) demonstrate fluency with multiplication facts of 0, 1, 2, 5, and 10; and d) solve single-step practical problems involving multiplication of whole numbers, where one factor is 99 or less and the second factor is 5 or less.