*Construct***: ****Demonstrate through both concrete and semi-concrete representations of mathematical concepts and ideas**

Using the *MasterPieces** ^{TM}*or the

*MasterFractions*

*teachers are able to demonstrate the concrete nature of the mathematical concepts being presented. The students, under guidance of the teacher, then*

^{TM}**build**or

**draw**the problem given and develop conceptual understanding. Research supports explicit instruction using concrete manipulatives to present mathematical concepts and processes.

*Express***: ****Demonstrate through artistic, written, and verbal expression, fluency and accuracy of the concept and computation of the mathematical process**

Whenever students are asked to **solve, show, draw, etc...** we recommend using **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 back the understanding they have of a given concept and 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.

*Apply***: ****Demonstrate the correct application of the mathematical concept and computation into real world settings**

Being able to apply what has been learned is the greatest sign of achievement! The word problems and Mastery Challenges are designed to engage students in the application of the math skills they have learned.