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Math, rev.1 - Coggle Diagram
Math, rev.1
8. Data Analysis, Probability,
and Statistics
I can formulate questions to clarify the problem at hand and formulate one (or more) questions that can be answered with data.
I can design and implement a plan to collect the appropriate data to answer the statistical question.
I can summarize data using appropriate statistics (e.g., describe or compare measures of center, spread, association).
I can select appropriate graphical and numerical methods and use these methods to represent the data in a way that supports
interpretation (e.g., dot plots, histograms, scatter plots).
I can interpret descriptive statistics and linear models within the context of the data and the original question.
I can design and conduct probability experiments for given authentic situations.
I can compute probabilities, including conditional probabilities, of compound events in a uniform probability model.
I can apply probability concepts to analyze and evaluate potential decisions and strategies.
1. Symbolic Expression
I can write, apply, and provide a rational for a mathematical model representing a given situation (e.g., linear, quadratic, exponential, trigonometric)
I can analyze and symbolically represent complex numbers (both real and imaginary numbers)
I can interpret and use symbols to express relationships and justify reasoning when solving problems (e.g., evaluating
expressions; modeling equations, inequalities, systems of equations/ inequalities).
I can apply properties of arithmetic and algebra to simplify and manipulate symbolic expressions or models involving
real/imaginary numbers
I can analyze and use the structure of expressions to generate equivalent forms which emphasize different properties of the
quantity represented by the expression (e.g., factoring, completing the square, various linear/nonlinear forms)
I can analyze, symbolically represent, and use vector and matrix quantities in problem solving (+)1
7. Geometry
I can use algebraic properties and geometric theorems and postulates to construct and apply viable arguments involving congruence and similarity (e.g., coordinate geometry, indirect/direct proofs, circles, polygons).
Investigate and name geometric transformations
HSG-CO.A.2
Understand and apply similarity.
HSG-SRT.A.2
I can apply geometric theorems and postulates, sometimes using algebraic properties, to solve problems (e.g., using angles, triangles, trigonometry, circles, polygons.
Understand and apply congruent triangles.
HSG-CO.B.8
Understand the effect of center and scale factor on dilations.
HSG-SRT.A.1
I can support my reasoning when answering questions about perimeter, area, and volume of complex objects.
Understand vocabulary for geometric objects
HSG-CO.A.1
I can apply properties of right triangles and circles on the coordinate plane to extend the concepts of trigonometry (e.g., unit
circle, Pythagorean Identity, radian measure).
I can create and use a formal geometric construction, using appropriate tools, to illustrate geometric properties (e.g., model a
real-world situation).
Make geometric constructions using classic tools.
HSG-CO.D.12
6. Algebraic Functions, Patterns,
and Relations
I can write and apply an algebraic model to represent and answer questions about a given situation (e.g., linear, quadratic, polynomial, exponential, trigonometric) andjustify my conclusions.
I can interpret, analyze, and use relations and functions applied in a variety of contexts, including real- world phenomena.
I can analyze relations and functions, using multiple representations (e.g., verbal, numerical, graphical, algebraic) andjustify my
reasoning
I can identify, build, and perform operations on relations and functions (e.g., compose functions, inverse) andjustify my
reasoning.
4. Metacognitive Skills* and Communication
I can reason quantitatively when analyzing, representing, and solving problems (e.g., algebraic or statistical models).
I can compare the effectiveness or logic of two plausible arguments or models
I can prove geometric theorems (e.g., triangles, circles, lines, angles).
5. Measurement
I can create informal arguments that support geometric formulas (e.g., circumference and area of circles or sectors of circles; volume of cylinder, pyramid, cone, sphere; surface area of 2-D and 3-D figures).
I can provide rationales for solving measurement problems that require making conversions among various units and measurement systems, visualizing relationships between 2- and 3-dimentional objects (e.g., identifying shapes of cross-sections or 3-dimentional objected generated by rotations of two-dimensional objects), or applying the effect of a scale factor on area or volume.
2. Numbers and
Number Systems
I can justify how I apply properties of complex number systems (including real and imaginary numbers) in a variety of contexts (e.g., arithmetic operations, polynomials, rational exponents).
3. Reasoning and Computational Strategies
I can use computational strategies and algorithms, with complex numbers and (+) matrix quantities and provide rationales for their use.