Objective: Students will understand and apply the properties of operations to solve problems involving addition, subtraction, and multiplication.

Materials: - Whiteboard or chalkboard - Markers or chalk - Worksheets or handouts with practice problems - Index cards or small slips of paper

Warm-up (5 minutes): - Write the following problem on the board: 5 + 3 x 2 - Ask students to solve the problem individually and then share their answers with a partner. - Discuss the different answers and explain that the order of operations is important in mathematics.

Introduction (5 minutes): - Introduce the concept of properties of operations by explaining that these are rules or properties that help us solve problems more easily. - Write the following properties on the board: closure property, associative property, identity properties, inverse properties, commutative property, and distributive property. - Briefly explain each property and give an example for each.

Activity 1: Closure Property (5 minutes): - Divide the class into pairs or small groups. - Give each group a set of index cards or slips of paper with numbers written on them. - Instruct the groups to create addition, subtraction, and multiplication problems using the numbers on their cards. - After each problem is created, have the groups solve the problems and determine if the operation follows the closure property. - Have each group share one problem that follows the closure property with the class.

Activity 2: Associative Property (5 minutes): - Write the following problem on the board: (2 + 3) + 4 = 2 + (3 + 4) - Ask students to solve the problem individually and then share their answers with a partner. - Discuss the answers and explain that the associative property allows us to group numbers in different ways without changing the result.

Activity 3: Identity Properties (5 minutes): - Write the following problems on the board: 5 + 0 = 5 and 7 x 1 = 7 - Ask students to solve the problems individually and then share their answers with a partner. - Discuss the answers and explain that the identity properties state that adding 0 to a number or multiplying a number by 1 does not change the value.

Activity 4: Inverse Properties (5 minutes): - Write the following problems on the board: 5 + (-5) = 0 and 7 x (1/7) = 1 - Ask students to solve the problems individually and then share their answers with a partner. - Discuss the answers and explain that the inverse properties state that adding the opposite of a number or multiplying a number by its reciprocal gives us the identity element.

Activity 5: Commutative Property (5 minutes): - Write the following problems on the board: 3 + 4 = 4 + 3 and 2 x 5 = 5 x 2 - Ask students to solve the problems individually and then share their answers with a partner. - Discuss the answers and explain that the commutative property allows us to change the order of the numbers without changing the result.

Activity 6: Distributive Property (5 minutes): - Write the following problem on the board: 3 x (4 + 2) - Ask students to solve the problem individually and then share their answers with a partner. - Discuss the answers and explain that the distributive property allows us to multiply a number by each term inside parentheses separately.

Conclusion (5 minutes): - Review the properties of operations and ask students to give examples of each property. - Provide additional practice problems for students to solve individually or in pairs. - Summarize the lesson by emphasizing the importance of understanding and applying these properties in mathematics.