IXL - Arizona seventh-grade math standards

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Standards document:

2010 Arizona Academic Standards (Common Core) 2010 Arizona Academic Standards (Common Core)
2008 Arizona Mathematics Standards Articulated by Grade Level 2008 Arizona Mathematics Standards Articulated by Grade Level

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7.1 Number and Operations

7.1.1 Understand and apply numbers, ways of representing numbers, and the relationships among numbers and different number systems.
7.1.1.PO 1 Recognize and convert between expressions for positive and negative rational numbers, including fractions, decimals, percents, and ratios.
7.1.1.PO 2 Find or use factors, multiples, or prime factorization within a set of numbers.
7.1.1.PO 3 Compare and order rational numbers using various models and representations.
7.1.1.PO 4 Model and solve simple problems involving absolute value.
7.1.2 Understand and apply numerical operations and their relationship to one another.
7.1.2.PO 1 Add, subtract, multiply, and divide integers.
7.1.2.PO 2 Solve problems with rational numbers and appropriate operations using exact answers or estimates.
7.1.2.PO 3 Solve problems involving percentages, ratio and proportion, including tax, discount, tips, and part/whole relationships.
7.1.2.PO 4 Represent and interpret numbers using scientific notation (positive exponents only).
- Number theory: Scientific notation (Seventh grade - A.8)
- Number theory: Compare numbers written in scientific notation (Seventh grade - A.9)
7.1.2.PO 5 Simplify numerical expressions using the order of operations and appropriate mathematical properties.
7.1.3 Use estimation strategies reasonably and fluently while integrating content from each of the other strands.
7.1.3.PO 1 Estimate and apply benchmarks for rational numbers and common irrational numbers.
7.1.3.PO 2 Make estimates appropriate to a given situation.
- Consumer math: Estimate tips (Seventh grade - L.10)
- Problem solving and estimation: Estimate to solve word problems (Seventh grade - M.1)
7.1.3.PO 3 Estimate square roots of numbers less than 1000 by locating them between two consecutive whole numbers.
- Exponents and square roots: Square roots of perfect squares (Seventh grade - I.9)
- Exponents and square roots: Estimate square roots (Seventh grade - I.10)
7.1.3.PO 4 Estimate the measure of an object in one system of units given the measure of that object in another system and the approximate conversion factor.

7.2 Data Analysis, Probability, and Discrete Mathematics

7.2.1 Understand and apply data collection, organization, and representation to analyze and sort data.
7.2.1.PO 1 Solve problems by selecting, constructing, and interpreting displays of data including multi-line graphs and scatterplots.
7.2.1.PO 2 Interpret trends in a data set, estimate values for missing data, and predict values for points beyond the range of the data set.
7.2.1.PO 3 Identify outliers and determine their effect on mean, median, mode, and range.
- Statistics: Changes in mean, median, mode, and range (Seventh grade - AA.4)
- Statistics: Quartiles (Eighth grade - CC.5)
7.2.1.PO 4 Distinguish between a simple random and non-random sample.
- Statistics: Identify representative, random, and biased samples (Seventh grade - AA.5)
7.2.2 Understand and apply the basic concepts of probability.
7.2.2.PO 1 Determine conditional probabilities (experimental) in compound probability experiments.
- Probability: Probability of opposite, mutually exclusive, and overlapping events (Seventh grade - Z.2)
- Probability: Experimental probability (Seventh grade - Z.3)
7.2.2.PO 2 Experiment with two different events to determine whether the two events are dependent or independent of each other.
- Probability: Identify independent and dependent events (Seventh grade - Z.6)
- Probability: Probability of independent and dependent events (Seventh grade - Z.7)
7.2.2.PO 3 Compare the results of multiple repetitions of the same probability experiment to the theoretical probability.
- Probability: Probability of simple events (Seventh grade - Z.1)
- Probability: Make predictions (Seventh grade - Z.4)
7.2.2.PO 4 Compare probabilities to determine fairness in experimental situations.
7.2.3 Understand and demonstrate the systematic listing and counting of possible outcomes.
7.2.3.PO 1 Analyze relationships among the tree diagrams where items repeat and do not repeat; make numerical connections to the multiplication principle of counting.
7.2.3.PO 2 Solve counting problems using Venn diagrams and represent the answer algebraically.
- Problem solving and estimation: Use Venn diagrams to solve problems (Seventh grade - M.4)
7.2.4 Understand and apply vertex-edge graphs.
7.2.4.PO 1 Use vertex-edge graphs and algorithmic thinking to represent and find solutions to practical problems related to Euler/Hamilton paths and circuits.

7.3 Patterns, Algebra, and Functions

7.3.1 Identify patterns and apply pattern recognition to reason mathematically while integrating content from each of the other strands.
7.3.1.PO 1 Recognize, describe, create, and analyze numerical and geometric sequences using tables or graphs; make conjectures about these sequences.
7.3.2 Describe and model functions and their relationships.
7.3.2.PO 1 Use a table of values to graph an equation or proportional relationship; describe the graph's characteristics.
7.3.3 Represent and analyze mathematical situations and structures using algebraic representations.
7.3.3.PO 1 Write a single variable algebraic expression or one-step equation given a contextual situation.
7.3.3.PO 2 Evaluate an expression containing one or two variables by substituting numbers for the variables.
7.3.3.PO 3 Solve multi-step equations using inverse properties with rational numbers.
- Single-variable equations: Solve equations involving like terms (Seventh grade - V.5)
- Single-variable equations: Solve multi-step equations (Eighth grade - U.7)
7.3.3.PO 4 Translate between graphs and tables that represent a linear equation.
7.3.3.PO 5 Create and solve two-step equations that can be solved using inverse operations with rational numbers.
7.3.3.PO 6 Create and solve one-step inequalities with whole numbers.
7.3.4 Analyze how changing the values of one quantity corresponds to change in the values of another quantity.
7.3.4.PO 1 Use graphs and tables to model and analyze change.

7.4 Geometry and Measurement

7.4.1 Analyze the attributes and properties of 2- and 3- dimensional figures and develop mathematical arguments about their relationships.
7.4.1.PO 1 Recognize the relationship between central angles and intercepted arcs; identify arcs and chords of a circle.
- Charts and graphs: Circle graphs and central angles (Seventh grade - O.11)
- Geometry: Parts of a circle (Seventh grade - P.21)
7.4.1.PO 2 Analyze and determine relationships between angles created by parallel lines cut by a transversal.
- Geometry: Transversal of parallel lines (Seventh grade - P.6)
7.4.1.PO 3 Draw and classify 3-dimensional figures with appropriate labels showing specified attributes of parallelism, congruence, perpendicularity, and symmetry.
7.4.1.PO 4 Describe the relationship between the number of sides in a regular polygon and the sum of its interior angles.
- Geometry: Find missing angles in triangles and quadrilaterals (Seventh grade - P.9)
- Geometry: Interior angles of polygons (Seventh grade - P.11)
7.4.1.PO 5 Identify corresponding parts of congruent figures.
7.4.2 Apply spatial reasoning to create transformations and use symmetry to analyze mathematical situations.
7.4.2.PO 1 Model the result of a double transformation (translations or reflections) of a 2-dimensional figure on a coordinate plane using all four quadrants.
7.4.3 Specify and describe spatial relationships using rectangular and other coordinate systems while integrating content from each of the other strands.
7.4.4 Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements.
7.4.4.PO 1 Solve problems involving the circumference and area of a circle by calculating and estimating.
- Geometry: Circles: calculate area, circumference, radius, and diameter (Seventh grade - P.22)
- Geometry: Circles: word problems (Seventh grade - P.23)
7.4.4.PO 2 Identify polygons having the same perimeter or area.
7.4.4.PO 3 Calculate the area and perimeter of composite 2-dimensional figures.
- Geometry: Area of compound figures (Fifth grade - B.19)
7.4.4.PO 4 Determine actual lengths based on scale drawings or maps.
- Ratios and proportions: Scale drawings and scale factors (Seventh grade - J.13)
7.4.4.PO 5 Create a net to calculate the surface area of a given solid.
- Geometry: Nets of 3-dimensional figures (Seventh grade - P.27)
- Geometry: Surface area (Seventh grade - P.28)
7.4.4.PO 6 Identify the appropriate unit of measure to compute the volume of an object and justify reasoning.
7.4.4.PO 7 Measure to the appropriate degree of accuracy and justify reasoning.
- Measurement: Precision (Seventh grade - N.7)

7.5 Structure and Logic

7.5.1 Use reasoning to solve mathematical problems.
7.5.1.PO 1 Create an algorithm to determine the area of a given composite figure.
- Geometry: Area of compound figures (Fifth grade - B.19)
7.5.2 Evaluate situations, select problem-solving strategies, draw logical conclusions, develop and describe solutions, and recognize their applications.
7.5.2.PO 1 Analyze a problem situation to determine the question(s) to be answered.
7.5.2.PO 2 Analyze and compare mathematical strategies for efficient problem solving; select and use one or more strategies to solve a problem.
7.5.2.PO 3 Identify relevant, missing, and extraneous information related to the solution to a problem.
7.5.2.PO 4 Represent a problem situation using multiple representations, describe the process used to solve the problem, and verify the reasonableness of the solution.
7.5.2.PO 5 Apply a previously used problem-solving strategy in a new context.
7.5.2.PO 6 Communicate the answer(s) to the question(s) in a problem using appropriate representations, including symbols and informal and formal mathematical language.
7.5.2.PO 7 Isolate and organize mathematical information taken from symbols, diagrams, and graphs to make inferences, draw conclusions, and justify reasoning.
7.5.2.PO 8 Make and test conjectures based on information collected from explorations and experiments.
7.5.2.PO 9 Solve logic problems using multiple variables and multiple conditional statements using words, pictures, and charts.
7.5.2.PO 10 Demonstrate and explain that the process of solving equations is a deductive proof.
7.5.2.PO 11 Use manipulatives and other modeling techniques to defend pi as a ratio of circumference to diameter.
- Geometry: Circles: calculate area, circumference, radius, and diameter (Seventh grade - P.22)
- Geometry: Circles: word problems (Seventh grade - P.23)