TSM can be utilized to help remediate students that have weak/nonexistent mathematical skill sets. The progression of middle school math proficiency can be broken down into a few broad windows.

5th Grade Math – Students develop the following components: fraction computational skills, long division (up to 2 digit divisors), how to compare fractional place values, and an understanding of volume calculation (based on unit cubes). The focus develops a respective student’s fraction computational skills.

Overarching Theme: Students need strong fraction computational skills, coupled with sound multiplication and division skills. The goal is to develop sound computational skills w/o the use of a calculator (based on constraints of accommodations).

6th Grade Math – Students execute the following tasks: extend fractional multiplication/division concepts in an effort to solve ratio and rate problems, apply the concept of fractional division to rational numbers, write and interpret expressions, and develop a sense of statistical thinking. Mathematical reasoning about rational numbers begin to focus on negative numbers... ~Their respective order, absolute value (distance from 0 in both number lines and the Cartesian plane), and location in all quadrants begin to take precedence in the scheme of mathematical reasoning.

Overarching Theme: Students analyze and plot data using both positive and negative rational numbers in all quadrants utilizing fractional multiplication and division skill sets.

7th Grade Math – Students incorporate the following concepts: Understanding of proportional relationships, develop an understanding based on the operation of rational numbers within the context of expressions and linear equations, how to solve problems based on scale drawings and informal geometric compositions of 2-D & 3-D shapes (surface area & volume), and develop an ability to deduce statistical information based on population samples.

Overarching Theme: Students interpret proportional relationships and express them as equations. Also, students interpret 2-D & 3-D shapes (surface area & volume. Finally, students deduce statistical data from population samples.

8th Grade Math – Students develop the following concepts in 3 categories:

1) Use of linear equations and systems of linear equations {how to interpret 
proportional equations (y/m=x or y=mx) as linear equations with graphs represented by lines that pass through the origin (0,0) that have a constant of proportionality (m) which is synonymous with the slope, an ability to interpret the slope (m) as a rate of change, an ability to perceive that if the slope (m) is changed by an input value (represented by the x-coordinate) that the value of the output(y-coordinate) is calculated by multiplying the input value by the slope(m), an ability to interpret proportional equations (y/m=x or y=mx) as slope intercept form linear equations (y=mx+b) such that the y-intercept(represented by ‘b’) is actually “0”, how to solve linear equations in one variable, how to solve systems of equations in two variables by relating the solutions to pairs of parallel lines within a plane(the points on the lines intersect, form parallel lines, or they can be found within the same line)}, 

2)  perceive functions such that there is only one output for each unique input, 

3)  interpret and understand relationships dealing with ideas about distance and angles(how 
they behave during rotation,