Demonstrate understanding of the square and principle square root of whole numbers concretely or pictorially and symbolically. ([CN, ME, R, T, V])

Expand and demonstrate understanding of percents greater than or equal to 0% (including fractional and decimal percents) concretely, pictorially, and symbolically. ([CN, PS, R, V])

Demonstrate understanding of rates, ratios, and proportional reasoning concretely, pictorially, and symbolically. ([C, CN, PS, R, V])

Demonstrate understanding of multiplying and dividing positive fractions and mixed numbers, concretely, pictorially, and symbolically. ([C, CN, ME, PS])

Demonstrate understanding of multiplication and division of integers concretely, pictorially, and symbolically. ([C, CN, PS, R, V])

Demonstrate understanding of linear relations concretely, pictorially (including graphs), physically, and symbolically. ([CN, ME, PS, R, T, V])

Model and solve problems using linear equations of the form:

• $ax = b$
• $x/a = b, a ≠ 0$
• $ax + b = c$
• $x/a + b = c, a ≠ 0$
• $a(x + b) = c$

concretely, pictorially, and symbolically, where a, b, and c are integers. ([C, CN, PS, V])

Demonstrate understanding of the Pythagorean Theorem concretely or pictorially and symbolically and by solving problems. ([CN, PS, R, T, V])

Demonstrate understanding of the surface area of 3-D objects limited to right prisms and cylinders (concretely, pictorially, and symbolically) by:

• analyzing views
• sketching and constructing 3-D objects, nets, and top, side, and front views
• generalizing strategies and formulae
• analyzing the effect of orientation
• solving problems.

([CN, PS, R, T, V])

Demonstrate understanding of volume limited to right prisms and cylinders (concretely, pictorially, or symbolically) by:

• relating area to volume
• generalizing strategies and formulae
• analyzing the effect of orientation
• solving problems.

([CN, PS, R, V])

Demonstrate an understanding of tessellation by:

• explaining the properties of shapes that make tessellating possible
• creating tessellations
• identifying tessellations in the environment.

([C, CN, PS, T, V])

Analyze the modes of displaying data and the reasonableness of conclusions. ([C, CN, R])

Demonstrate understanding of the probability of independent events concretely, pictorially, orally, and symbolically. ([C, CN, PS, T])