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:

5.NBT.6: Find whole-number quotients of whole numbers with up to four-digit dividends and two-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:

I can divide four digit numbers by two-digit divisors.

I can illustrate and explain a division problem using equations, arrays, and/or models.

Pre-Requisite Standard:

4.NBT.6: Find whole-number quotients and remainders with 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.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.

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. For some relationships, mathematical expressions and equations can be used to describe how members of one set are related to members of a second set.

Basic Facts and Algorithms: There is more than one algorithm for each of the operations with rational numbers. Some strategies for basic facts and 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.

Mathematical Processes: Doing mathematical involves a variety of processes including problem solving, reasoning, communicating, connecting, and representing.

Essential Questions:

What is the standard procedure for dividing with two-digit divisors?

Students will know...

Using basic facts and patterns can be helped in dividing by multiples of 10.

There is more than one way to estimate a quotient. Substituting compatible numbers is an efficient technique for estimating quotients.

An array/area model can be used to model the process for dividing whole numbers by 2-digit divisors.

Dividing with 2-digit divisors is just an extension of the steps for dividing with 1-digit divisors. Estimation and place value can help determine the placement of digits in the quotient.

Some real world quantities have a mathematical relationship; the value of one quantity can be found if you know the value of the other quantity. Patterns can sometimes be used to identify the relationship between quantities.

Dividing with 2-digit divisors is just an extension of the steps for dividing with 1-digit divisors. Estimation and place value can help determine the placement of digits in the quotient.

There is more than one way to estimate a quotient. Substituting compatible numbers is an efficient technique for estimating quotients. Dividing with multi-digit divisors is just an extension with 1 and 2-digit divisors. Estimation and place value can help determine the placement of digits in the quotient.

Students will be skilled at...

Finding the quotients of division problems whose dividends and divisors are multiples of 10, where the division involves a basic fact.

Using estimation to find approximate solutions to division problems with two-digit divisors using compatible numbers.

Using arrays and area models to model division.

Finding quotients with a two-digit divisor that is a multiple of ten.

Finding one-digit quotients where the divisor is a two-digit divisor.

Dividing a three-digit number by a two-digit number to find a two-digit quotient.

Solving problems involving division of numbers with 4 or 5 digits by 2-digit divisors with an estimate, or by using a calculator when the exact answer is needed.

Learning Activities:
5-1:Using basic facts and patterns can be helped in dividing by multiples of 10.
5-2:There is more than one way to estimate a quotient. Substituting compatible numbers is an efficient technique for estimating quotients.
5-3:An array/area model can be used to model the process for dividing whole numbers by 2-digit divisors.
5-4:Dividing with 2-digit divisors is just an extension of the steps for dividing with 1-digit divisors. Estimation and place value can help determine the placement of digits in the quotient.
5-5:Some real world quantities have a mathematical relationship; the value of one quantity can be found if you know the value of the other quantity. Patterns can sometimes be used to identify the relationship between quantities.
5-6:Dividing with 2-digit divisors is just an extension of the steps for dividing with 1-digit divisors. Estimation and place value can help determine the placement of digits in the quotient.
5-7:There is more than one way to estimate a quotient. Substituting compatible numbers is an efficient technique for estimating quotients. Dividing with multi-digit divisors is just an extension with 1 and 2-digit divisors. Estimation and place value can help determine the placement of digits in the quotient.

## Topic Five: Dividing by 2-Digit Divisors

## 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:I Can Statements:Pre-Requisite Standard:.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. For some relationships, mathematical expressions and equations can be used to describe how members of one set are related to members of a second set.Basic Facts and Algorithms:There is more than one algorithm for each of the operations with rational numbers. Some strategies for basic facts and 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.Mathematical Processes:Doing mathematical involves a variety of processes including problem solving, reasoning, communicating, connecting, and representing.Essential Questions:Students will know...Students will be skilled at...Assessment EvidencePerformance Assessment:Performance Assessment Task-5.NBT.6-Fruits and VegetablesOther Evidence:Learning PlanLearning Activities:5-1:Using basic facts and patterns can be helped in dividing by multiples of 10.

5-2:There is more than one way to estimate a quotient. Substituting compatible numbers is an efficient technique for estimating quotients.

5-3:An array/area model can be used to model the process for dividing whole numbers by 2-digit divisors.

5-4:Dividing with 2-digit divisors is just an extension of the steps for dividing with 1-digit divisors. Estimation and place value can help determine the placement of digits in the quotient.

5-5:Some real world quantities have a mathematical relationship; the value of one quantity can be found if you know the value of the other quantity. Patterns can sometimes be used to identify the relationship between quantities.

5-6:Dividing with 2-digit divisors is just an extension of the steps for dividing with 1-digit divisors. Estimation and place value can help determine the placement of digits in the quotient.

5-7:There is more than one way to estimate a quotient. Substituting compatible numbers is an efficient technique for estimating quotients. Dividing with multi-digit divisors is just an extension with 1 and 2-digit divisors. Estimation and place value can help determine the placement of digits in the quotient.

Resources:Problem of the Month:5.NBT.6: Through the GrapevineCenters:5.NBT.6: Division Strategy: Partial Quotients

5.NBT.6: Division the Partition

5.NBT.6: Division Strategy: Multiplying Up

5.NBT.6: Estimating Quotients

5.NBT.6: Creating and Solving a Division Problem

SmartBoard Resources:Division BingoSum Sense: Division

Division Challenge