Topic+Nine

= Topic Nine: Number Sense: 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.

__Pre-Requisite Standards:__
 * 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.OA.2: Multiply or divide to solve word problems involving multiplicative comparison //, // e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison // . //
 * 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.

__"I Can" Statements__ 4.NBT.6: "I can find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors." ||
 * __Big Ideas:__
 * __Patterns, Relations, and Functions:__ Relationships can be described and generalizations made for mathematical situations that have numbers or objects that repeat in predictable ways.
 * __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.
 * __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.
 * __Practices, Processes, and Proficiencies:__ Mathematics content and practices can be applied to solve problems. || __Essential Questions:__


 * What are different meanings of division?
 * How can mental math and estimation be used to divide? ||
 * __Students will know...__
 * Basic facts and place-value patterns can be used to divide multiples of 10 and 100 by one-digit numbers.
 * Substituting compatible numbers is an efficient technique for estimating quotients.
 * Mentally multiplying by different powers of ten will help you arrive at an estimate for a quotient of a multi-digit division problem.
 * The remainder when dividing must be less than the divisor. The nature of the question asked determines how to interpret and use the remainder.
 * Some real-world problems involving joining equal groups, separating equal groups, or comparison can be solved using multiplication; others can be solved using division.
 * Information in a problem can often be shown using a picture or diagram and used to understand and solve the problem. Some problems can be solved by writing and completing a number sentence or equation.

__Vocabulary:__ remainder || __Students will be skilled at...__
 * Using basic facts and patterns of zeros to solve division problems with 3-digit dividends and 1-digit divisors.
 * Using compatible numbers and rounding to estimate quotients.
 * Estimating quotients of multi-digit division problems using multiplication facts and place-value concepts.
 * Dividing whole numbers by 1-digit divisors resulting in quotients with remainders.
 * Using words and models to represent multiplication and division problems accurately.
 * Drawing pictures and writing related number sentences to solve problems. ||
 * ~ = Assessment Evidence = ||
 * __Performance Assessment:__

__[|MARS Performance Task 4.NBT.6: The Baker]__ || __Other Evidence:__ ||
 * ~ = Learning Plan = ||
 * __Learning Activities:__

9-1: Basic facts and place-value patterns can be used to divide multiples of 10 and 100 by one-digit numbers. 9-2: Substituting compatible numbers is an efficient technique for estimating quotients. 9-3: Mentally multiplying by different powers of ten will help you arrive at an estimate for a quotient of a multi-digit division problem. 9-4: The remainder when dividing must be less than the divisor. The nature of the question asked determines how to interpret and use the remainder. 9-5: Some real-world problems involving joining equal groups, separating equal groups, or comparison can be solved using multiplication; others can be solved using division. 9-6: Information in a problem can often be shown using a picture or diagram and used to understand and solve the problem. Some problems can be solved by writing and completing a number sentence or equation. ||
 * __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]