There are 3 rows of apples If 18 apples are arranged If 18 apples are arranged with 6 apples in each row. into 3 equal rows, how into equal rows of 6 How many apples are many apples will be in apples, how many rows there? each row? will there be? Arrays, Area Area example. What is the Area example. A rectangle Area example. A rectangle area of a 3 cm by 6 cm has area 18 square has area 18 square rectangle? centimeters. If one side is centimeters. If one side is 3 cm long, how long is a 6 cm long, how long is a side next to it? side next to it? A blue hat costs $6. A red A red hat $18 and A red hat costs $18 and a hat costs 3 times as much that is 3 times as much as blue hat costs $6. How as the blue hat. How a blue hat costs. How many times as much does much does the red hat much does a blue hat the red hat cost as the cost? cost? blue hat? Measurement example. A Measurement example. A Measurement example. A Compare rubber band is 6 cm long. rubber band is stretched rubber band was 6 cm How long will the rubber to be 18 cm long and that long at Now it is band be when it is is 3 times as long as it was stretched to be 18 cm stretched to be 3 times as at first. How long was the long. How many times as long? rubber band at first? long is the rubber band now as it was at first? General a b = ? a ? = p and p a = ? ? b = p and p b = ? Table 3. The properties of operations. Here a, b and c stand for arbitrary numbers in a given number system. The properties of operations apply to the rational number system, the real number system, and the complex number system. Associative property of addition (a + b) + c = a + (b + c) Commutative property of addition a + b = b + a 0 0 + = Additive identity property of 0 a + = a a Existence of additive inverses For every a there exists so that a + (–a) = (–a) + a = 0. –a Associative property of multiplication (a b) c = a (b c)
Arrays, Area There are 3 rows of apples with 6 apples in each row. How many apples are there? Area example. What is the area of a 3 cm by 6 cm rectangle? If 18 apples are arranged into 3 equal rows, how many apples will be in each row? Area example. A rectangle has area 18 square centimeters. If one side is 3 cm long, how long is a side next to it? If 18 apples are arranged into equal rows of 6 apples, how many rows will there be? Area example. A rectangle has area 18 square centimeters. If one side is 6 cm long, how long is a side next to it? Compare A blue hat costs $6. A red hat costs 3 times as much as the blue hat. How much does the red hat cost? Measurement example. A rubber band is 6 cm long. How long will the rubber band be when it is stretched to be 3 times as long? A red hat $18 and that is 3 times as much as a blue hat costs. How much does a blue hat cost? Measurement example. A rubber band is stretched to be 18 cm long and that is 3 times as long as it was at first. How long was the rubber band at first? A red hat costs $18 and a blue hat costs $6. How many times as much does the red hat cost as the blue hat? Measurement example. A rubber band was 6 cm long at Now it is stretched to be 18 cm long. How many times as long is the rubber band now as it was at first? General a b = ? a ? = p and p a = ? ? b = p and p b = ? Table 3. The properties of operations. Here a, b and c stand for arbitrary numbers in a given number system. The properties of operations apply to the rational number system, the real number system, and the complex number system. Associative property of addition Commutative property of addition Additive identity property of 0 Existence of additive inverses Associative property of multiplication (a + b) + c = a + (b + c) a + b = b + a a + 0 = 0 + a = a For every a there exists –a so that a + (–a) = (–a) + a = 0. (a b) c = a (b c)
REVISED%20Math%20Content%20Standards.docx