Demonstrate an understanding of division through the development and application of divisibility strategies for 2, 3, 4, 5, 6, 8, 9, and 10, and through an analysis of division involving zero. ([C, CN, ME,R])

Expand and demonstrate understanding of the addition, subtraction, multiplication, and division of decimals to greater numbers of decimal places, and the order of operations. ([C, CN, ME, PS, R, T])

Demonstrate an understanding of the relationships between positive decimals, positive fractions (including mixed numbers, proper fractions and improper fractions), and whole numbers. ([C, CN, ME, R, T])

Expand and demonstrate an understanding of percent to include fractional percents between 1% and 100%. ([C, PS, R])

Develop and demonstrate an understanding of adding and subtracting positive fractions and mixed numbers, with like and unlike denominators, concretely, pictorially, and symbolically (limited to positive sums and differences). ([C, CN, ME, PS, R, V])

Demonstrate an understanding of addition and subtraction of integers, concretely, pictorially, and symbolically. ([C, CN, PS, R, V])

Demonstrate an understanding of the relationships between oral and written patterns, graphs and linear relations. ([C, CN, R])

Demonstrate an understanding of equations and expressions by:

• distinguishing between equations and expressions
• evaluating expressions
• verifying solutions to equations.

([C, CN, ME])

Demonstrate an understanding of one- and two-step linear equations of the form ax/b + c = d (where a, b, c, and d are whole numbers, c ≤ d and b ≠ 0) by modeling the solution of the equations concretely, pictorially, physically, and symbolically and explaining the solution in terms of the preservation of equality. ([C, CN, PS, R, V])

Demonstrate an understanding of linear equations of the form x + a = b (where a and b are integers) by modeling problems as a linear equation and solving the problems concretely, pictorially, and symbolically. ([C, CN, PS, R, V])

Demonstrate an understanding of circles including circumference and central angles. ([C, CN, R, V])

Develop and apply formulas for determining the area of:

• triangles
• parallelograms
• circles.

([CN, PS, R, V])

Demonstrate an understanding of 2-D relationships involving lines and angles. ([CN, R, V, T])

Demonstrate an understanding of the Cartesian plane and ordered pairs with integral coordinates. ([C, CN, V])

Expand and demonstrate an understanding of transformations (translations, rotations, and reflections) of 2-D shapes in all four quadrants of the Cartesian plane. ([CN, PS, T, V])

Demonstrate an understanding of the measures of central tendency and range for sets of data. ([C, CN, PS, R, T])

Demonstrate an understanding of circle graphs. ([C, CN, PS, R, T])

Demonstrate an understanding of theoretical and experimental probabilities for two independent events where the combined sample space has 36 or fewer elements. ([C, ME, PS, R, T])