Topic+Ten

= Topic Ten: Developing Fluency: Dividing by 1-Digit Divisors = Pacing (Duration of Unit):
 * ~ = Desired Results = ||
 * __Transfer:__

1. Makes sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. __//Use appropriate tools strategically.//__ 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||
 * __Established Goals:__
 * 4.NBT.6: Find whole-number quotients and remainderswith up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
 * 4.OA.3: Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

__ Pre-Requisite Standards: __
 * 3.OA.3: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities,e.g., by using drawings and equations with a symbol for the unknown number to represent the problem__.__
 * 3.OA.7: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 ´  5 = 40, one knows 40 ¸ 5 = 8) or properties of operations. By the end of grade 3, know from memory all products of two one-digit numbers.
 * 4.NBT.6: Find whole-number quotients and remainderswith up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

__ "I Can" Statements __
 * 4.NBT.6: "I can find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors."
 * 4.OA.3: " I can use what I know about addition, subtraction, multiplication and division to solve multi-step word problems involving whole numbers." ||
 * __Big Ideas:__
 * __Operation Meanings and Relationships__: There are multiple interpretations of addition, subtraction, multiplication, and division of rational numbers, and each operation is related to other operations.
 * Algorithms: There is more than one algorithm for each of the operations with rational numbers. Most algorithms for operations with rational numbers, both mental math and paper and pencil, use equivalence to transform calculations into simpler ones.
 * __Estimation__: Numbers can be approximated by numbers that are close. Numerical calculations can be approximated by replacing numbers with other numbers that are close and easy to compute mentally. Some measurements can be approximated using known referents as the unit in the measurement process.
 * __Practices, Processes, and Proficiencies:__ Mathematics content and practices can be applied to solve problems. || __Essential Questions:__
 * How can repeated subtraction be used to model division?
 * What is the standard procedures for dividing multi-digit numbers? ||
 * __Students will know...__


 * Repeated subtraction situations can be modeled and solved using division.
 * Repeated subtraction situations can be solved using a division algorithm different from the standard algorithm.
 * The sharing interpretation of division can be used to model the standard division algorithm.
 * The standard division algorithm breaks the calculation into simpler calculations using basic facts, place-value, the relationship between multiplication and division, and estimation.
 * The relationship between multiplication and division and estimation can be used to determine the place value of the largest digit in the quotient.

__Vocabulary:__ || __Students will be skilled at...__ __[|4.NBT.6: The Baker]__ || __Other Evidence:__ ||
 * Using repeated subtraction to model division.
 * Recording division as repeated subtraction.
 * Using place value to understand the algorithm of long division.
 * Using the standard algorithm to divide a two-digit number by a one-digit number.
 * Using the standard algorithm to divide 3-digit numbers by 1-digit numbers.
 * Using the standard algorithm to divide 3-digit numbers by 1- digit numbers and properly decide where to begin dividing. ||
 * ~ = Assessment Evidence = ||
 * __Performance Assessment:__
 * ~ = Learning Plan = ||
 * __Learning Activities:__

10-1: Repeated subtraction situations can be modeled and solved using division. 10-2: Repeated subtraction situations can be solved using a division algorithm different from the standard algorithm. 10-3: The sharing interpretation of division can be used to model the standard division algorithm. 10-4: The standard division algorithm breaks the calculation into simpler calculations using basic facts, place-value, the relationship between multiplication and division, and estimation. 10-5: The standard division algorithm breaks the calculation into simpler calculations using basic facts, place-value, the relationship between multiplication and division, and estimation. 10-6: The relationship between multiplication and division and estimation can be used to determine the place value of the largest digit in the quotient. ||
 * __Resources:__

__Problem of the Month:__ __ [|4.NBT.6: Diminishing Return] __

__ Center Activities: __ __[|Division Strategy: Partial Quotients]__ __[|Division Strategy Partial Quotients 2]__ || [|Remainders] [|Estimate the Quotient] [|Who has the largest quotient?] ||  ||
 * [|Division Strategy: Partition the Divdend]