展開形式と部分積を用いた多桁乗算

Students will be taught how to multiply:
1-digit x 2-digit numbers (example: 6 x 47, 8 x 84)
1-digit x 3-digit numbers (example: 5 x 352, 4 x 126)
2-digit x 2 digit numbers (example: 17 x 18, 23 x 13)

However, instead of starting with the standard algorithm, students will break apart numbers using expanded form (which is a familiar skill used in previous grades). By breaking apart each number by digit place, students can "chunk" and multiply the value of each digit and conceptually understand the value produced when multiplying to get a total product.

In early grades, students are exposed to expanded form when adding and subtracting. They add by place value.
For example: 123 + 256 
100 + 20 + 3 + 200 + 50 + 6 = 300 + 70 + 9 = 379

In 3rd grade, students learn how to multiply single and 2-digit numbers up to 12.
For example: 6 x 3 = 18, 7 x 5 = 35, 4 x 8 = 32.

In 3rd grade, students learn how to multiply multiples of 10 and 100 to single-digit factors.
For example: 6 x 30 = 180, 7 x 50 = 350, 4 x 800 = 3200.

In this class we will combine the three skills mentioned above to multiply. This is similar to the "accessible" algorithm or "partial products" strategy in the Common Core Standards. 

REQUIRED EXPERIENCE:
**Students should have exposure and practice with multiplication facts with factors up to 10 prior to taking this class. 
For example: 10 x 7 = 70, 4 x 7 = 28, 6 x 8 = 48, 9 x 3 = 27

**Students should have exposure and practice with multiplication using multiples of 10 or 100 as factors prior to taking this class.
For example:  If 4 x 6 = 24, then 40 x 6 = 240, then 400 x 6 = 2400.

**Students should have a basic understanding of place value. 
For example: the value of 5 in 253 is 50 and the value of 2 in 253 is 200.

CLASS PROGRESSION
Each session will focus on students solving multi-digit multiplication equations with scaffolding and modeling by the teacher. The progression of the class will be as follows:

Session #1: 1-digit x 2-digit numbers (example: 4 x 17, 5 x 32)
Session #2: 1-digit x 3-digit numbers (example: 2 x 124, 4 x 176)
Session #3:  2-digit x 2-digit numbers (example: 17 x 18, 23 x 13) - factors will be less than 50.
Session #4:  Combination of all types of equations from Sessions #1 - #3.


Students will learn through an "I Do, We Do, You Do" approach. 

"I DO"
I will begin with a teacher-led mini lesson showing how to solve an multiplication equation. I think it is important for students to engage and practice, so after one teacher-led example I will progress to a "We Do" approach.

"WE DO"
Students and I will work together to solve several multi-digit multiplication problems using the same strategy modeled by the teacher. I will guide them through the task and ask questions to confirm understanding. We will discuss and share ideas using mathematical terms (place, value, multiply, tens, ones, hundreds, factor, product, etc.) and explore misconceptions and/or strengthen understanding with repeated guided practice. Students can ask questions or share their insights.

"YOU DO" - Students will independently use the same process to solve several multiplication equations. I will silently model the process for them to utilize if they need support. Students can verbally ask questions, or ask for guidance in the Chat Room on Zoom. After students have been given time to solve the equation, we will discuss problem solving strategies and solutions used by the class.

After the first session, students will be emailed a resource sheet with completed examples. They can refer to this sheet to help support any independent practice they choose to do in between sessions, or for use at our following live sessions.