Key Concept: Quantities can be compared using addition and multiplication.

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

CCSS.MATH.CONTENT.4.OA.A.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

CCSS.MATH.CONTENT.4.OA.A.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.#### Georgia

MGSE4.OA.1 Understand that a multiplicative comparison is a situation in which one quantity is multiplied by a specified number to get another quantity. a. Interpret a multiplication equation as a comparison e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. b. Represent verbal statements of multiplicative comparisons as multiplication equations.

MGSE4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison. Use drawings and equations with a symbol or letter for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. IEP Goals

In this topic, students complete and create bar models to represent additive and multiplicative comparison problems. Students recognize situations in which quantities are compared through addition and multiplication and are able to distinguish between these two types of problems.

CCSS.MATH.CONTENT.4.OA.A.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.

MGSE4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison. Use drawings and equations with a symbol or letter for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

1. Given a model that represents two quantities that are compared through addition, the student will be able to solve for a sum or a missing addend with 85% accuracy over 5 consecutive sessions.

2. Given a model that represents two quantities that are compared through multiplication, the student will be able to solve for a product or a missing factor with 85% accuracy over 5 consecutive sessions.

3. Given a situation where quantities are compared either additively or multiplicatively, the students will be able to distinguish between these situations with 80% accuracy over 5 consecutive sessions.

2. Given a model that represents two quantities that are compared through multiplication, the student will be able to solve for a product or a missing factor with 85% accuracy over 5 consecutive sessions.

3. Given a situation where quantities are compared either additively or multiplicatively, the students will be able to distinguish between these situations with 80% accuracy over 5 consecutive sessions.

Unit Launcher

View Ridgewood School’s Exercise-A-Thon: Discussion Guide and KWL Chart

M.5-1-1 Complete an Additive Comparison Model |

View Guided Lesson Students will complete bar models that represent additive comparison problems in which either the sum or an addend is unknown. (12-20 min)

M.5-1-2 Complete a Multiplicative Comparison Model |

View Guided Lesson Students will complete bar models that represent multiplicative comparison problems in which either the product or a factor is unknown. (12-20 min)

M.5-1-3 Create an Additive Comparison Model |

View Guided Lesson Students will create bar models that represent additive comparison problems in which either the sum or an addend is unknown. (12-20 min)

M.5-1-4 Create a Multiplicative Comparison Model |

View Guided Lesson Students will complete bar models that represent multiplicative comparison problems in which either the product or a factor is unknown. (12-20 min)

M.5-1-5 Create Multiplicative and Additive Comparison Models |

View Guided Lesson Students will distinguish between additive and multiplicative comparison problems and create a bar model to represent the problem. (12-20 min)

Real World Investigation Part 1

View Ridgewood School’s Exercise-A-Thon: Jackson’s Data

Key Concept: A model can be used to represent a two-step problem.

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

CCSS.MATH.CONTENT.4.OA.A.3 Solve multistep 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.#### Georgia

MGSE4.OA.3 Solve multistep word problems 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 symbol or letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. IEP Goals

In this topic, students build their understanding of problem solving through solving two-step problems. The problems initially incorporate addition and subtraction, then gradually build in multiplication and then division to support students to understand each of these operations and how to apply them in a variety of contexts.

1. Given a two-step problem that requires addition and/or subtraction to solve, the students will be able to solve the problem with 90% accuracy over 5 consecutive sessions.

2. Given a two-step problem that requires addition, subtraction, and/or multiplication to solve, the student will be able to solve the problem with 85% accuracy over 5 consecutive sessions.

3. Given a two-step problem that requires addition, subtraction, multiplication, and/or division to solve, the student will be able to solve the problem with 80% accuracy over 5 consecutive sessions.

2. Given a two-step problem that requires addition, subtraction, and/or multiplication to solve, the student will be able to solve the problem with 85% accuracy over 5 consecutive sessions.

3. Given a two-step problem that requires addition, subtraction, multiplication, and/or division to solve, the student will be able to solve the problem with 80% accuracy over 5 consecutive sessions.

M.5-2-1 Two-Step Problems: Add and Subtract |

Lesson Plan

View Guided Lesson Students use addition and/or subtraction to solve two-step problems through creating a bar model. (12-20 min)

M.5-2-2 Two-Step Problems: Add, Subtract, and Multiply |

Lesson Plan

View Guided Lesson Students use addition, subtraction, and/or multiplication to solve two-step problems through creating a bar model. (12-20 min)

M.5-2-3 Two-Step Problems: All Operations |

Lesson Plan

View Guided Lesson Students use addition, subtraction, multiplication, and/or division to solve two-step problems through creating a bar model. (12-20 min)

M.5-2-4 More Two-Step Problems: All Operations |

Lesson Plan

View Guided Lesson Students use addition, subtraction, multiplication, and/or division to solve two-step problems through creating a bar model. (12-20 min)

Real World Investigation Part 2

View Ridgewood School’s Exercise-A-Thon: Create Some Data

Key Concept: A model can be used to represent a three-step problem.

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

CCSS.MATH.CONTENT.4.OA.A.3 Solve multistep 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.#### Georgia

MGSE4.OA.3 Solve multistep word problems 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 symbol or letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. IEP Goals

In this topic, students build their understanding of problem solving through solving three-step problems. The problems initially incorporate addition and subtraction, then gradually build in multiplication and then division to support students to understand each of these operations and how to apply them in a variety of contexts.

1. Given a three-step problem that requires addition and/or subtraction to solve, the students will be able to solve the problem with 90% accuracy over 5 consecutive sessions.

2. Given a three-step problem that requires addition, subtraction, and/or multiplication to solve, the student will be able to solve the problem with 85% accuracy over 5 consecutive sessions.

3. Given a three-step problem that requires addition, subtraction, multiplication, and/or division to solve, the student will be able to solve the problem with 80% accuracy over 5 consecutive sessions.

2. Given a three-step problem that requires addition, subtraction, and/or multiplication to solve, the student will be able to solve the problem with 85% accuracy over 5 consecutive sessions.

3. Given a three-step problem that requires addition, subtraction, multiplication, and/or division to solve, the student will be able to solve the problem with 80% accuracy over 5 consecutive sessions.

M.5-3-1 Three-Step Problems: Add and Subtract |

Lesson Plan

View Guided Lesson Students use addition and/or subtraction to solve three-step problems through creating a bar model. (12-20 min)

M.5-3-2 Three-Step Problems: Add, Subtract, and Multiply |

Lesson Plan

View Guided Lesson Students use addition, subtraction, and/or multiplication to solve three-step problems through creating a bar model. (12-20 min)

M.5-3-3 Three-Step Problems: All Operations |

Lesson Plan

View Guided Lesson Students use addition, subtraction, multiplication, and/or division to solve three-step problems through creating a bar model. (12-20 min)

M.5-3-4 More Three-Step Problems: All Operations |

Lesson Plan

View Guided Lesson Students use addition, subtraction, multiplication, and/or division to solve three-step problems through creating a bar model. (12-20 min)

Real World Investigation Part 3

View Ridgewood School’s Exercise-A-Thon: Your Data

This Big Idea builds upon students’ ability to model with mathematics as they persevere to solve problems. The unit begins with building upon students' understanding of additive and multiplicative reasoning and supports them to use and create models that represent these quantitative relationships. Students continue to build problem-solving strategies as they solve two and three-step problems involving addition, subtraction, multiplication, and/or division.

CCSS.MATH.CONTENT.4.OA.A.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.

CCSS.MATH.CONTENT.4.OA.A.3 Solve multistep 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.

MGSE4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison. Use drawings and equations with a symbol or letter for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

MGSE4.OA.3 Solve multistep word problems 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 symbol or letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.