Mathematics
MATH MISSION STATEMENT
ASD math students will develop skills and strategies to solve real and pressing problems so that they can use mathematics in their lives. They will understand and appreciate the mathematics they are studying; they will read it, write it, explore it and communicate it with confidence.
ASD Mathematics Vision
ASD is a vibrant learning community…
where Math learning is fun
where Math learning is analytical
where Math learning is contextual
where Math learning is meaningful
where Math learning is challenging
where Math learning is investigative
where Math learning is collaborative
where Math learning is technology infused...
Essential Agreements for Mathematics
Teachers will provide opportunities in a safe learning environment to encourage exploration and risk-taking to acquire mathematical concepts.
Teachers will use contextual problems to guide instruction and provide learning opportunities for students to make mathematical meaning.
Teachers will use challenging problems to develop critical thinking skills and perseverance.
When appropriate, technology will be used to support mathematical understanding and to solve problems.
Teachers will expose students to multiple strategies and representations and will teach students to select the most effective and/or efficient ones.
Teachers will use multiple representations to teach concepts and communicate solutions.
Teachers will value process as well as the accurate final answer when assessing student work.
Teachers will anticipate and correct common misconceptions.
Teachers will have students perform error analyses to help them reflect on their performance and improve their understanding.
Teachers will use correct mathematical terminology.
AERO K-8 Math 2011 Standards & Benchmarks 372 KB PD
MATH K-8 CURRICULUM STANDARDS 2011
Process Standards
1.0 Problem Solving. Students will apply a wide variety of mathematical concepts, processes, and skills to solve a broad range of problems in various content areas and everyday situations.
2.0 Reasoning and Proof. Students will apply mathematical reasoning skills to investigate, evaluate, justify, and connect approaches and solutions to situations in mathematics and in other disciplines.
3.0 Communication. Students will accurately and clearly present and justify mathematical ideas in diverse formats.
4.0 Connections. Students will develop the ability to use connections among mathematical ideas to build on one another when solving real-world problems and to interconnect ideas to produce an integrated coherent whole.
Content Standards
5.0 Numbers and Operations. Students will understand and apply numbers, ways of representing numbers, relationships among numbers, and number systems.
5.1 Number Sense. Students will understand and demonstrate a sense of what numbers mean and how they are used.
5.2 Operations on Numbers. Students will understand meanings of operations and how they relate to one another.
5.3 Estimation. Students will accurately calculate and use estimation techniques, number relationships, operation rules, and algorithms; they will determine the reasonableness of answers and the accuracy of solutions.
6.0 Measurement. Students will use concepts and tools of measurement to describe and quantify the world.
6.1 Physical Attributes. Students will demonstrate an understanding of units of measure and measurable attributes of objects.
6.2 Systems of Measurement. Students will identify and use units, systems and processes of measurement.
7.0 Patterns, Functions, and Algebra. Students will use various algebraic methods to analyze, illustrate, extend, and create numerous representations (words, numbers, tables, and graphs) of patterns, functions, and algebraic relations as modeled in practical situations to solve problems, communicate, reason, and make connections within and beyond the field of mathematics.
7.1 Patterns, Relations, and Function. Students will recognize, describe and develop patterns, relations and functions.
7.2 Algebraic Models. Students will represent and analyze mathematical situations and structures using algebraic symbols.
7.3 Algebraic Representation. Students will develop and apply mathematical models to represent and understand quantitative relationships.
7.4 Analysis of Change. Students will analyze change in various contexts.
8.0 Geometry. The student will develop an understanding of geometric concepts and relationships as the basis for geometric modeling and reasoning to solve problems involving one-, two-, and three-dimensional figures.
8.1 Geometric Properties. Students will analyze characteristics and properties of 2 and 3 dimensional geometric shapes and develop mathematical arguments about geometric relationships.
8.2 Transformation of Shapes. Students will apply transformations and the use of symmetry to analyze mathematical situations.
8.3 Coordinate Geometry. Students will specify locations and describe spatial relationships using coordinate geometry and other representational systems.
8.4 Visualization and Geometric Models. Students will use visualization, spatial reasoning and geometric modeling.
9.0 Data Analysis and Probability. Students will develop an understanding of Data Analysis and Probability by solving problems in which there is a need to collect, appropriately represent, and interpret data; to make inferences or predictions and to present convincing arguments; and to model mathematical situations to determine the probability.
9.1 Data Representation. Students will formulate questions that can be addressed with data and collect, organize and display relevant data to answer them.
9.2 Data Analysis. Students will select and use appropriate statistical methods to analyze data.
9.3 Inferences and Predictions. Students will develop and evaluate inferences and predictions that are based on data.
9.4 Probability. Students will understand and apply basic concepts of probability.
AERO High School Math 2011 Standards & Benchmarks 473 KB PDF
AERO 2011 High School Math Standards
1.0 Problem Solving. Students will:
- Recognize and use mathematical ideas and processes that arise in different settings, with an emphasis on formulating a problem in mathematical terms, interpreting the solutions, mathematical ideas, and communication of solution strategies.
- Apply and adapt a variety of appropriate strategies to problem solving, including testing cases, estimation, and then checking induced errors and the reasonableness of the solution.
2.0 Reasoning and Proof. Students will:
- Develop inductive and deductive reasoning to independently make and evaluate mathematical arguments and construct appropriate proofs; include various types of reasoning, logic, and intuition.
3.0 Communication. Students will:
- Use mathematical language, symbols, definitions, proofs and counterexamples correctly and precisely in mathematical reasoning.
- Employ reading and writing to recognize the major themes of mathematical processes, the historical development of mathematics, and the connections between mathematics and the real world.
4.0 Connections. Students will:
- Move flexibly between multiple representations (contextual, physical, written, verbal, iconic/pictorial, graphical, tabular, and symbolic), to solve problems, to model mathematical ideas, and to communicate solution strategies.
5.0 Numbers and Operations. Students will understand and apply numbers, ways of representing numbers, relationships among numbers, and number systems.
5.1 Extend the properties of exponents to rational exponents.
5.2 Use properties of rational and irrational numbers.
5.3 Perform arithmetic operations with complex numbers.
5.4 Represent complex numbers and their operations on the complex plane.
5.5 Represent and model with vector quantities.
5.6 Perform operations on vectors.
5.7 Perform operations on matrices and use matrices in applications.
QUANTITIES
6.0 Measurement. Students will use concepts and tools of measurement to describe and quantify the world.
6.1 Reason quantitatively and use units to solve problems.
EXPRESSIONS, EQUATIONS AND INEQUALITIES
7.0 Patterns, Functions, and Algebra. Students will use various algebraic methods to analyze, illustrate, extend, and create numerous representations (words, numbers, tables, and graphs) of patterns, functions, and algebraic relations as modeled in practical situations to solve problems, communicate, reason, and make connections within and beyond the field of mathematics.
7.1 Interpret and model a given context using expressions.
7.2 Decompose and recompose algebraic expressions using number properties in the context of solving problems.
7.3 Demonstrate that polynomials form a system analogous to the integers, namely, they are closed under the operation of addition, subtraction, and multiplication.
7.4 Demonstrate that polynomials can be decomposed and recomposed.
7.5 Demonstrate that the relationship of two or more variables can be represented as an equation or inequality and can be represented graphically.
7.6 Use algebraic properties and inverse operations to justify the steps in solving equations.
7.7 Solve quadratic equations in one variable.
7.8 Solve systems of equations.
7.9 Knows that a graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
FUNCTIONS
7.10Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
7.11Describe characteristics of graphs, tables, and equations that model families of functions.
7.12Use strategies for interpreting key features of representations.
7.13Know the difference between a recursive rule and an explicit expression for a function.
7.15Knows that manipulating the parameters of the symbolic rule will result in a predictable transformation of the graph.
7.16Describe characteristic graph, table, and equation formats for linear, exponential, and quadratic functions.
7.17Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
7.18Model periodic phenomena with trigonometric functions.
GEOMETRY
8.0 Geometry. The student will develop an understanding of geometric concepts and relationships as the basis for geometric modeling and reasoning to solve problems involving one, two, and three-dimensional figures.
8.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
8.2 Know how to use both verbal and symbolic language to develop arguments related to location, transformation and congruence.
8.3 Know what it means to prove or disprove a conjecture.
8.4 Know why point, line, distance along a line and distance around a circular arc are undefined.
8.5 Know that transformations (rigid motions followed by dilations) define similarity in the same way that rigid motions define congruence.
8.6 Know the trigonometric ratios, Sine, Cosine, and Tangent.
8.7 Demonstrate that all circles are similar and how the application of proportional reasoning is used to develop the concept of radian measure.
8.8 Know the equation of a circle.
8.9 Demonstrate that the distance formula is an application of the Pythagorean Theorem.
8.10Know strategies for dissection and partitioning that support the visualizations necessary to build informal arguments.
8.11Know that modeling is the process of choosing and using appropriate mathematics to analyze and understand geometric situations.
DATA ANALYSIS and PROBABILITY
9.0 Data Analysis and Probability. Students will develop an understanding of Data Analysis and Probability by solving problems in which there is a need to collect, appropriately represent, and interpret data; to make inferences or predictions and to present convincing arguments; and to model mathematical situations to determine the probability.
9.1 Know that Quantitative data can be described in terms of key characteristics: measures of shape, center, and spread.
9.2 Know that the shape of a data distribution might be described as symmetric, skewed, flat, or bell shaped, and it might be summarized by a statistic measuring center (such as mean or median) and a statistic measuring spread (such as standard deviation or interquartile range).
9.3 Know strategies for fitting a function to a data display and informally assessing the fit.
9.4 Recognize the purposes of and differences among sample surveys, experiments, and observational studies.
9.5 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities.
9.6 Recognize the concepts of conditional probability and independence in everyday language and everyday situations.
9.7 Calculate expected values and use them to solve problems.
9.8 Use probability to evaluate outcomes of decisions.
