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4-N-1-6

Page history last edited by Tashe Harris 6 years, 2 months ago

4.N.1.6 Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g. , mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties).

In a Nutshell

Students will divide 3-digit whole number dividends by 1-digit whole number divisors. Students should be introduced to a variety of solution strategies, including mental math, partial quotients, repeated subtraction, and the standard algorithm, and should be encouraged to use the strategy or strategies which make the most sense to them. They should be able to appropriately apply the commutative, associative, and distributive properties and the principle of inverse operations to find and evaluate their solutions.

Student Actions	Teacher Actions
Develop strategies for problem solving (mental estimation strategies, standard algorithm, partial quotient, repeated subtraction, the commutative, associative, and distributive properties) and use corresponding multiple representations when solving problems involving division. Develop accurate and appropriate procedural fluency by correctly applying strategies and algorithms for solving division problems. Develop mathematical reasoning and the ability to communicate mathematically through comparing and contrasting solutions with peers, using correct division vocabulary (dividend, divisor, quotient, remainder).	Pose purposeful questions that guide students to make connections to prior knowledge regarding multiplication and division. Facilitate meaningful mathematical discourse among students to build shared understanding by asking them to explain their strategies and analyze the strategies of others. Implement tasks that promote reasoning and problem solving by presenting scenarios having multiple entry points, so students can use a variety of problem solving strategies. Use and connect multiple mathematical representations to model division problems. Build procedural fluency from the conceptual understanding of basic division facts and the relationship between multiplication and division.
Key Understandings	Misconceptions
Division equations (3-digit dividends by 1-digit divisors) can be accurately solved using one of several different division strategies. Prior knowledge of multiplication facts and an understanding of the properties of multiplication and division can be used to divide accurately and efficiently. By using inverse operations, it is possible to verify the accuracy of a quotient.	There is only one correct way to solve a problem. Division is commutative, as in 5 ÷ 3 = 3 ÷ 5 Division makes the answer smaller. For example, when you divide, the answer (quotient) is smaller than the starting amount (dividend). While this is true when dividing a whole number by a smaller whole number, it is not true when the divisor is greater than the dividend. The standard algorithm for division is a set of steps to be memorized.