Methodology: Teaching the Lessons

Lesson Steps:

Step 1: Both Teacher and Student Watch Video 

Step 2: Explicitly Instruct Student(s) Using Manipulatives

Step 3: Student Proceeds to Workbook Pages for Practice

Step 4: Student Demonstrates Mastery - Teaching Back to You

To support the written curriculum and the physical manipulatives, we also provide lesson-by-lesson videos clearly demonstrating how to use the manipulatives to teach students about mathematics. Video lessons are first watched by the teacher and student(s) then the teacher works with the student to demonstrate the lesson contents using the manipulatives. There are three phases to the instructional process:

1. Construct:

Demonstrate through both concrete and semi-concrete representations of mathematical concepts and ideas.

Whenever the instructions indicate to construct, we recommend using the MasterPieces to build or draw the problem given and develop conceptual understanding.

2. Express:

Demonstrate through artistic, written, and verbal expression, the fluency, and accuracy of the concept and computation of the mathematical process. Whenever the instructions indicate to solve, show, draw, etc. We recommend drawing, written, and verbal communications to have students express what they have learned.

We encourage teachers to get creative on how the students will express to them and/or to others the understanding they have of a given concept and process. Each lesson has key vocabulary that must be understanding must be demonstrated as part of the mastery process.

Ideally, a student who has mastered a concept can hear the problem verbally and express back the computation, concept, and application of the problem in a written or verbal manner.

3. Apply:

Teachers first demonstrate the correct application of the mathematical concept and computation in real-world settings then have students model this in their own work.

Word Problems & Mastery Challenges

Each Student Workbook lesson has multiple word problems designed to help the student demonstrate their understanding of the concepts learned. At the end of each lesson is a Mastery Challenge. This is where students are challenged to apply what they have learned into specific types of applications, typically multi-step word problems.

Reflection & Mastery

What did you learn?

Can you teach it to someone else?

Students need to master skills at each level of arithmetic, including complex applications of those skills, in order to become a true master of their craft.

Also, a student teaching back what has been learned is a critical demonstration of the student's ability to:

• Grasp the problem

• Choose a process

• Develop a solution

• Articulate the reasoning behind their choices

• or… Reveal where there are gaps in their understanding  

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