Number Sense

• Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line.
• Interpret and use ratios in different contexts (e.g., batting averages, miles per hour) to show the relative sizes of two quantities, using appropriate notations ( a/b, a to b, a:b ).
• Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/ 21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse.
• Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips.
• Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation.
• Explain the meaning of multiplication and division of positive fractions and perform the calculations (e.g., 5/8 ÷ 15/16 = 5/8 x 16/15 = 2/3).
• Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations.
• Determine the least common multiple and the greatest common divisor of whole numbers; use them to solve problems with fractions (e.g., to find a common denominator to add two fractions or to find the reduced form for a fraction).

Algebra and Functions

• Write and solve one-step linear equations in one variable.
• Write and evaluate an algebraic expression for a given situation, using up to three variables.
• Apply algebraic order of operations and the commutative, associative, and distributive properties to evaluate expressions; and justify each step in the process.
• Solve problems manually by using the correct order of operations or by using a scientific calculator. Convert one unit of measurement to another (e.g., from feet to miles, from centimeters to inches).
• Demonstrate an understanding that rate is a measure of one quantity per unit value of another quantity.
• Solve problems involving rates, average speed, distance, and time. Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l, A = 1/2bh, C = d – the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively).
• Express in symbolic form simple relationships arising from geometry.

Statistics, Data Analysis, and Probability

• Compute the range, mean, median, and mode of data sets.
• Understand how additional data added to data sets may affect these computations of measures of central tendency.
• Understand how the inclusion or exclusion of outliers affects measures of central tendency.
• Know why a specific measure of central tendency (mean, median) provides the most useful information in a given context.
• Compare different samples of a population with the data from the entire population and identify a situation in which it makes sense to use a sample.
• Identify different ways of selecting a sample (e.g., convenience sampling, responses to a survey, random sampling) and which method makes a sample more representative for a population.
• Analyze data displays and explain why the way in which the question was asked might have influenced the results obtained and why the way in which the results were displayed might have influenced the conclusions reached.
• Identify data that represent sampling errors and explain why the sample (and the display) might be biased.
• Identify claims based on statistical data and, in simple cases, evaluate the validity of the claims.
• Represent all possible outcomes for compound events in an organized way (e.g., tables, grids, tree diagrams) and express the theoretical probability of each outcome.
• Use data to estimate the probability of future events (e.g., batting averages or number of accidents per mile driven).
• Represent probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability of an event, 1- P is the probability of an event not occurring.
• Understand that the probability of either of two disjoint events occurring is the sum of the two individual probabilities and that the probability of one event following another, in independent trials, is the product of the two probabilities.
• Understand the difference between independent and dependent events.