Mathematics

Numbers and Operations

• Add and subtract rational numbers to solve problems.

• Represent addition and subtraction of rational numbers on a number line.

• Multiply and divide rational numbers to solve problems.

• Show that a decimal expansion of a rational number will always terminate (⅜ = 0.375) or repeat (5/33 = 0.1515151515…).

• Find unit rates when the ratios are fractions. For example, “Emilio walks ⅘ mile in ½ hour” is represented by the unit rate of 8/5 mile in 1 hour.

• Determine whether two quantities are proportional by looking at tables or graphs of the relationship. For example, y=3x is a proportional relationship because the graph passes through the origin, (0,0), and is linear.

• Identify the constant of proportionality (or unit rate) from tables, graphs, equations, or descriptions.

• Use proportional relationships to solve ratio and percentage problems.

Geometry

• Solve problems involving scale drawing of geometric figures.

• Describe the properties of all types of triangles based on angle measures and side length measures.

• Describe the two‐dimensional cross sections of prisms and pyramids.

• Use the properties of supplementary, complementary, and adjacent angles to solve problems.

• Use the properties of the angles created when two parallel lines are cut by a transversal.

• Find the area and circumference of a circle.

• Solve problems involving area, volume, and surface area of two‐ and three‐dimensional objects composed of polygons and prisms.

Algebraic Concepts

• Add, subtract, factor, and expand linear expressions. For example, (1/2) × (p + 4) is equivalent to (1/2) × p + 2 and 5.9 + y + 9.3 is equivalent to y + 15.2.

• Apply properties of operations to calculate with numbers in any form. For example, the price of a $10.00 hat after 6% sales tax is added can be found by 10.00 × 1.06.

• Solve two‐step equations with and without distributive property. For example, 3x +2= 14 means that x = 4, or 5 + 2y = 17 means that y = 6.

• Solve problems that can be modeled by the equation px + q = r or p(x + q) = r. For example, Stacy has 2 more packages of stickers than Cliff. Each package has 8 stickers. Stacy has 72 stickers. How many packages of stickers does Cliff have?

• Solve one- and two‐step inequalities.

• Solve problems that can be solved by the inequality px + q > r or px + q < r. For example, Ms. Chang has 80 pieces of paper. She will give 5 pages to each student and keep 3 pages for herself. Write an inequality to show the number of students who can get paper from Ms. Chang.

Measurement, Data, and Probability

• Use data from random samples to draw inferences about a population.

• Compare two numerical data distributions using measures of center (mean, median, and mode) and variability (range, interquartile range, and mean absolute deviation).

• Determine whether an outcome is certain, more likely, less likely, equally likely, or impossible.

• Determine the probability of a chance event given relative frequency.

• Find the probability of a simple event, including the probability of a simple event not occurring.

• Find probabilities of independent compound events using organized lists, tables, tree diagrams, and simulations.