All About Multiplication

In this unit, students explore several meanings and representations of multiplication (number line, equal sets, arrays, and balanced equations). They also learn about the order (commutative) property of multiplication, the results of multiplying by 1 and by 0, and the inverse property of multiplication. In addition, students write story problems in which the operation of multiplication is required. Opportunities to connect with literature are presented in several of the lessons. A bibliography of children's literature with a multiplication focus is provided.

Math Content

Students will:

• use the number line to find products
• solve and create puzzles using the number line
• investigate the order property of multiplication
• explore the results of adding equal sets
• construct array models
• explore the results of multiplying by 0 and by 1
• write word problems using multiplication facts
• explore the balance beam model of multiplication
• write multiplication sentences in equation form
• use the inverse property of multiplication

Individual Lessons

Lesson 1 - Hopping on the Number Line

In this lesson, students generate products using the number line model. This model highlights the measurement aspect of multiplication and is a distinctly different representation of the operation. The order (commutative) property of multiplication is also introduced. Students are encouraged to predict products and to answer puzzles involving multiplication.

Lesson 2 - Exploring Equal Sets

This lesson builds on the previous lesson and encourages students to explore another model for multiplication, the familiar set model. Students find products using equal sets and present results in the form of a table. The students apply their knowledge about multiplication in the creation of pictographs.

Lesson 3 - Modeling Multiplication With Streets and Avenues

This lesson encourages students to explore the array model of multiplication, a model that lays an important foundation for the later study of area. The lesson focuses on the factors 4 and 6. Students will also explore products with 0 or 1 as a factors. First students make arrays with counters, and then they create a second concrete example of the array model using toothpicks. They also write problems which involve multiplication.

Lesson 4 - Balance Beam Discoveries

This lesson encourages students to explore another model of multiplication, the balance beam, and another relationship, the inverse of multiplication. This exploration leads naturally into representing multiplication facts in equation form. In addition to extending their understandings of the concept of multiplication, students begin to practice the multiplication facts by playing the Product Game.