Key Concept: Area models can be used to separate factors of a multiplication equation into simpler parts and the products of those parts can be added to find the solution.

Topic Overview | Standards Alignment | #### Common Core

4.NBT.A.1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represent in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concept of place value and division.

4.NBT.A.2 Read and write multi-digit numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons.

4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.#### Georgia

MGSE4.NBT.1 Recognize that in a multi-digit whole number, a digit in any one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

MGSE4.NBT.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

MGSE4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. IEP Goals

This topic introduces students to the area model as a strategy for solving multi-digit mutliplication problems. The topic begins by linking previous understanding of computing area to using the area model in representing multi-digit multiplication. Students see partial products presented in the procedure as they complete the model. They summarize their solutions in an equation.

4.NBT.A.2 Read and write multi-digit numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons.

4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

MGSE4.NBT.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

MGSE4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

1. Given a set of 10 multiplication equations, in which one of the factors is a multiple of 10 and previous guided practice with models, the student will accurately solve at least 90% of the problems by the end of the third quarter.

2. Given multiplication expressions with a single-digit multiplier and a starting value less than 10,000 the student will use their understanding of place value to separate the starting value, so that they can solve for the product with at least 85% accuracy upon completion of the IEP.

3. Given multiplication equations with two-digit factors and guided practice, students will use an area model to correctly solve 4/5 problems by the end of the marking period.

2. Given multiplication expressions with a single-digit multiplier and a starting value less than 10,000 the student will use their understanding of place value to separate the starting value, so that they can solve for the product with at least 85% accuracy upon completion of the IEP.

3. Given multiplication equations with two-digit factors and guided practice, students will use an area model to correctly solve 4/5 problems by the end of the marking period.

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M.4-1-1 Multiplying a 1-Digit Number by a Multiple of 10 or 100 |

View Guided Lesson Complete an area model, to solve multiplication problems in which one of the factors is a multiple of ten or one hundred. (12-18 min)

M.4-1-2 Multiplying a 1-Digit Number by Up to a 4-Digit Number |

View Guided Lesson Solve multiplication problems in which one of the factors is a multi-digit number by using an area model to separate it into parts. (12-18 min)

M.4-1-3 Multiplying Two Multiples of Ten |

View Guided Lesson Complete an area model to solve multiplication problems in which the factors are both multiples of ten. (12-18 min)

M.4-1-4 Multiplying a 2-Digit Number by a Multiple of Ten |

View Guided Lesson Complete area models and procedures to solve multiplication problems in which one of the factors is a 2-digit number and the other factor is a multiple of ten. (12-18 min)

M.4-1-5 Multiplying Two 2-Digit Numbers |

View Guided Lesson Complete an area model to solve multiplication problems in which both of the factors are two-digit numbers. Write equations that describe the model and solve for the product. (12-18 min)

Real World Investigation Part 1

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Key Concept: Area models can be used to show a combination of partial products contained in a dividend and used to find the quotient.

Topic Overview | Standards Alignment | #### Common Core

4.NBT.A.1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represent in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concept of place value and division.

4.NBT.A.2 Read and write multi-digit numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons.

4.NBT.B.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.

#### Georgia

MGSE4.NBT.1 Recognize that in a multi-digit whole number, a digit in any one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

MGSE4.NBT.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

MGSE4.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. IEP Goals

This topic introduces students to the area model as a strategy for solving multi-digit division problems. In initial lessons students work with models only to develop conceptual understanding of how to use common multiplies and partial products to solve multi-digit division problems. Subsequent lessons link models to the procedure.

4.NBT.A.2 Read and write multi-digit numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons.

4.NBT.B.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.

MGSE4.NBT.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

MGSE4.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.

1. Given division expressions with dividends less than 100 and one-digit divisors and previous practice using visual models, the student will correctly solve for the quotient for 5 out of 6 examples by the end of the second marking period.

2. Given a set of 10 division expressions with dividends less than 10,000 and one-digit divisors that result in quotients with remainders, the student will apply their understanding of place value concepts and separate the dividend into parts in order to solve for the quotient with at least 90% accuracy for 3 consecutive sessions.

3. Given a division expression with a dividend less than 10,000 and a divisor that is a multiple of 10, the student will solve for quotients with and without remainders with at least 90% accuracy upon completion of the IEP.

2. Given a set of 10 division expressions with dividends less than 10,000 and one-digit divisors that result in quotients with remainders, the student will apply their understanding of place value concepts and separate the dividend into parts in order to solve for the quotient with at least 90% accuracy for 3 consecutive sessions.

3. Given a division expression with a dividend less than 10,000 and a divisor that is a multiple of 10, the student will solve for quotients with and without remainders with at least 90% accuracy upon completion of the IEP.

M.4-2-1 Division with Dividends of 100 or Less: Without Remainders |

Lesson Plan

View Guided Lesson Complete an area model using partial products to solve division problems for dividends less than 100. Interpret the quotient as the number of equal-sized groups contained in a starting amount and write equations. (12-18 min)

M.4-2-2 Division with Dividends of 100 or Less: With Remainders |

Lesson Plan

View Guided Lesson Complete the area model using partial products to solve division problems for dividends less than 100 that result in quotients with remainders. (12-18 min)

M.4-2-3 Dividing with Dividends of 10,000 or Less |

Lesson Plan

View Guided Lesson Learn the strategy of using multiplies of 10 to complete area models and the procedures in order to solve division problems. (12-18 min)

M.4-2-4 Dividing by Multiples of 10 |

Lesson Plan

View Guided Lesson Complete the long division procedure and use area models for problems with divisors that are multiples of 10 and record the results in an equation. (12-18 min)

Real World Investigation Part 2

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Key Concept: There are procedures for solving multiplication and division problems with multi-digit numbers.

Topic Overview | Standards Alignment | #### Common Core

4.NBT.A.1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represent in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concept of place value and division.

4.NBT.A.2 Read and write multi-digit numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons.

4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

4.NBT.B.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.

#### Georgia

MGSE4.NBT.1 Recognize that in a multi-digit whole number, a digit in any one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

MGSE4.NBT.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

MGSE4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

MGSE4.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. IEP Goals

This topic focuses on building procedural knowledge by fading the use of the area model. Students complete the step-by-step procedure to find either the product or quotient for multiplication and division problems that contain one or more multi-digit numbers.

4.NBT.A.2 Read and write multi-digit numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons.

4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

4.NBT.B.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.

MGSE4.NBT.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

MGSE4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

MGSE4.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.

1. Given a multiplication equation and previous guided practice, the student will explain how they can use what they know about place value to separate the equation, and correctly solve for the product 4 of 5 times by completion of the IEP.

2. Given a set of 10 division equations with dividends less than 10,000, the student will use the division procedure and using 5 or fewer partial products to accurately solve for the quotients accurately for 9 out of 10 examples in three consecutive trials.

3. Given division equations that result in quotients with remainders, the student will be able to use the division procedure to solve for the quotient and remainder with 85% accuracy by the end of the marking period.

2. Given a set of 10 division equations with dividends less than 10,000, the student will use the division procedure and using 5 or fewer partial products to accurately solve for the quotients accurately for 9 out of 10 examples in three consecutive trials.

3. Given division equations that result in quotients with remainders, the student will be able to use the division procedure to solve for the quotient and remainder with 85% accuracy by the end of the marking period.

M.4-3-1 Multiplying Up to 1-Digit by 4-Digits: Numbers Only |

Lesson Plan

View Guided Lesson Complete multiplication problems in which one of the factors is a multi-digit number by using a procedure to separate it into parts. (12-18 min)

M.4-3-2 Multiplying Two 2-Digit Numbers: Numbers Only |

Lesson Plan

View Guided Lesson Complete multiplication problems in which both of the factors are two-digit number by using a procedure to separate it into parts. (12-18 min)

M.4-3-3 Division with Dividends Less Than 10,000: Learning the Procedure |

Lesson Plan

View Guided Lesson Complete the long division procedure for problems with dividends less than 10,000 when some of the partial products are given. Then record the results in an equation. (12-18 min)

M.4-3-4 Division with Dividends Less Than 10,000: Numbers Only |

Lesson Plan

View Guided Lesson Complete the long division procedure for problems with dividends less than 10,000. Then record the results in an equation. (12-18 min)

Real World Investigation Part 3

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This Big Idea develops an understanding of multiplication and division procedures to solve problems with multi-digit numbers. Students use an area model and an understanding of distributive property to determine the results of partial products. Students extend their knowledge of basic facts to applying factoring with multiples of ten. Students work on procedures using numbers only at the completion of this big idea.

4.NBT.A.2 Read and write multi-digit numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons.

4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

4.NBT.B.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.

MGSE4.NBT.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

MGSE4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

MGSE4.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.