Whole Number Computation Multiplication MSP Day 2 How

Whole Number Computation: Multiplication MSP Day 2

How does a teacher develop specific multiplication strategies? • What is Number Sense? • Fennel and Landis (1994) state, “ Number sense is an awareness and understanding about what numbers are, their relationships, their magnitude and the relative effect of operating on numbers, including the use of mental mathematics and estimation”

Big Ideas • Multiplication involves counting groups in like size and determining how many are in all. • Multiplication and division are related. So they should be taught together. Division names a missing factor in terms of the known factor and the product. • Models can be used to solve contextual problems for all operations and to give meaning to mathematical equations. • Patterns and real-world relationships will help children learn facts in a more powerful way than by simply memorizing them.

Beginning to See The Array Model It is now important to represent those objects, if possible in a pictorial array fashion. Next, the teacher uses a common symbol, such as a square, to represent any object and displays it in an array format. This gives students the idea that those squares can represent objects and space. As students become stronger with multiplication reasoning, then open- arrays can be used (without interior squares.

Describe this picture by explaining how many

• Draw an array of 8 x 9, break it apart into smaller arrays. What factors did you use? • Solve 8 x 25, what strategy did you use? • How would you solve this problem mentally? Let’s see how students did

As you watch the video in which 8 x 25 array is used consider: • How does the array model support the student strategies? • How does breaking the factors into friendly numbers promote the goals of efficiency and flexibility? • How do the teacher’s questions foster an understanding of multiplication? • What math understandings and misconceptions are addressed with this model?

Area Models Lead to Distributive Property and Partial Products • Extending The Array Models to Introduce Partial Products and Distributive Property 30 36 6 x 25 20 600 120 720 3 0 (5 x 6) 1 5 0 (5 x 30) 150 30 5 750 + 150 = 900 180 900 1 2 0 (20 x 6) 6 0 0 (20 x 30) 900

Let’s watch Number Talks video from a fifth grade classroom • How does the teacher facilitate the classroom discussion? • What procedures are in place that allow students to share their thinking? • What opportunities exist for the teacher to informally assess student understanding? • What conditions are present that foster a safe learning community? • How is student communication encouraged and valued? • How would you describe the teacher’s role during the number talk?