Ratios and Proportional Relationships  30 days
 Apply and extend previous understandings of equivalent ratios.
 Compute unit rates associated with ratios of fractions.
 Decide whether two quantities are in a proportional relationship by testing for equivalent ratios in a table.
 Recognize and represent proportional relationships between quantities
 Decide whether two quantities are in a proportional relationship by graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
 Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
 Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams and verbal descriptions of proportional relationships.
 Represent proportional relationships by equations.
 Solve problems involving scale drawings of geometric figures.
 Use proportional relationships to solve multistep ratio and percent problems involving taxes and gratuities (tips).
 Use proportional relationships to solve multistep ratio and percent problem involving simple interest.
 Solve realworld and mathematical problems involving the four operations with rational numbers.
 Use proportional relationships to solve multistep ratio and percent problems involving percent increase, decrease, markups and markdowns.

Rational Numbers – Topic 4 10 days
 Apply and extend previous understandings of rational numbers, including opposites and absolute value as a distance from zero.
 Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.
 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers.
 Use absolute value understanding to find p + q as the number located a distance q from p, in the positive or negative direction depending on whether q is positive or negative.
 Interpret sums of rational numbers by describing realworld contexts.

Quarterly 1

Rational Numbers – Topic 5 and 6  20 days
 Use horizontal or vertical number line diagrams to represent addition and subtraction.
 Solve subtraction problems involving rational numbers by adding the additive inverse, p  q = p + (q).
 Find the distance between two rational numbers on the number line using the absolute value of their difference, and apply this principle in realworld contexts.
 Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (1)(1) = 1 and the rules for multiplying signed numbers.
 Apply properties of operations as strategies to multiply and divide rational numbers.
 Interpret products of rational numbers by describing realworld contexts.
 Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with nonzero divisor) is a rational number.
 Interpret quotients of rational numbers by describing realworld contexts.
 Apply properties of operations as strategies to multiply and divide rational numbers.
 Solve realworld and mathematical problems involving the four operations with rational numbers.
 Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with nonzero divisor) is a rational number.
 Convert a rational number to a decimal using long division.
 Recognize that the decimal form of a rational number terminates in 0s or eventually repeats.
 Apply and extend previous understandings of fractions, decimals, and percents to use them interchangeably to solve realworld and mathematical problems.
 Use proportional relationships to solve multistep ratio and percent problems involving percent error.
 Apply and extend previous understandings of fractions, decimals, and percents to use them interchangeably to solve problems.

Expressions and Equations  25 days
 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.
 Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations to solve problems by reasoning about the quantities.
 Solve multistep reallife and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically.
 Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of this form fluently.
 Use variables to represent quantities in a realworld or mathematical problem, and construct simple inequalities to solve problems by reasoning about the quantities.
 Graph the solution set of the inequality and interpret it in the context of the problem.
 Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.

Quarterly 2

Geometry  35 days
 Name parts of a geometric figure using appropriate letters and symbols.
 Measure parts of geometric figures using the appropriate tools and units of measure.
 Use facts about adjacent, complementary, supplementary and vertical angles in a multistep problem to write and solve simple equations for an unknown angle in a figure.
 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions.
 Apply and extend previous understandings of circles.
 Solve problems using the formula for the circumference and area of a circle.
 Give an informal derivation of the relationship between the circumference and area of a circle.
 Construct triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
 Describe the twodimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
 Solve realworld and mathematical problems involving area of twodimensional objects and surface area and volume of threedimensional objects composed of triangles, quadrilaterals, and polygons.
 Solve realworld problems involving surface area and volume of a threedimensional object composed of right prisms.

Quarterly 3

Statistics  20 days
 Understand that statistics can be used to gain information about a population by examining a sample of the population.
 Understand that generalizations about a population from a sample are valid only if the sample is representative of that population.
 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest.
 Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.
 Use measures of center and measures of variability for numerical data from random samples.
 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.
 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability.

Probability – 20 days
 Identify the probability of a chance event using a number between 0 and 1 to express the likelihood of the event occurring.
 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability.
 Develop a probability model and use it to find probabilities of events.
 Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
 Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.
 Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams.
 Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
 Identify the outcomes in a sample space that compose a compound event described in everyday language.
 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability.
 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
 Design and use a simulation to generate frequencies for compound events.

Quarterly 4
