|
MM1A
Algebra
|
-
MM1A1
Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques.
-
MM1A1.a
Represent functions using function notation.
-
MM1A1.b
Graph the basic functions f(x) = x to the n power, where n = 1 to 3, f(x) = square root of x, f(x) = |x|, and f(x) = 1/x.
-
MM1A1.c
Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes.
-
MM1A1.d
Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior.
-
MM1A1.e
Relate to a given context the characteristics of a function, and use graphs and tables to investigate its behavior.
-
Exponential functions: Match exponential functions and graphs (Algebra - X.2)
-
Quadratic equations: Characteristics of quadratic functions (Algebra - BB.1)
-
Functions: linear, quadratic, exponential: Identify linear, quadratic, and exponential functions from graphs (Algebra - CC.1)
-
Functions: linear, quadratic, exponential: Identify linear, quadratic, and exponential functions from tables (Algebra - CC.2)
-
Functions: linear, quadratic, exponential: Write linear, quadratic, and exponential functions (Algebra - CC.3)
-
MM1A1.f
Recognize sequences as functions with domains that are whole numbers.
-
MM1A1.g
Explore rates of change, comparing constant rates of change (i.e., slope) versus variable rates of change. Compare rates of change of linear, quadratic, square root, and other function families.
-
MM1A1.h
Determine graphically and algebraically whether a function has symmetry and whether it is even, odd, or neither.
-
MM1A1.i
Understand that any equation in x can be interpreted as the equation f(x) = g(x), and interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x).
-
MM1A2
Students will simplify and operate with radical expressions, polynomials, and rational expressions.
-
MM1A2.a
Simplify algebraic and numeric expressions involving square root.
-
MM1A2.b
Perform operations with square roots.
-
MM1A2.c
Add, subtract, multiply, and divide polynomials.
-
MM1A2.d
Expand binomials using the Binomial Theorem.
-
MM1A2.e
Add, subtract, multiply, and divide rational expressions.
-
MM1A2.f
Factor expressions by greatest common factor, grouping, trial and error, and special products limited to the formulas below. (x + y)2 = x2 + 2xy + y2; (x - y)2 = x2 - 2xy + y2; (x + y)(x - y) = x2 - y2; (x + a)(x + b) = x2 + (a + b)x + ab; (x + y)3 = x3 +3x2y + 3xy2 + y3; (x - y)3 = x3 -3x2y + 3xy2 - y3
-
MM1A2.g
Use area and volume models for polynomial arithmetic.
-
MM1A3
Students will solve simple equations.
-
MM1A3.a
Solve quadratic equations in the form ax2 + bx + c = 0 where a = 1, by using factorization and finding square roots where applicable.
-
MM1A3.b
Solve equations involving radicals such as square root of x + b = c, using algebraic techniques.
-
MM1A3.c
Use a variety of techniques, including technology, tables, and graphs to solve equations resulting from the investigation of x2 + bx + c = 0.
-
MM1A3.d
Solve simple rational equations that result in linear equations or quadratic equations with leading coefficient of 1.
|
|
MM1G
Geometry
|
-
MM1G1
Students will investigate properties of geometric figures in the coordinate plane.
-
MM1G1.a
Determine the distance between two points.
-
MM1G1.b
Determine the distance between a point and a line.
-
MM1G1.c
Determine the midpoint of a segment.
-
MM1G1.d
Understand the distance formula as an application of the Pythagorean theorem.
-
MM1G1.e
Use the coordinate plane to investigate properties of and verify conjectures related to triangles and quadrilaterals.
-
MM1G2
Students will understand and use the language of mathematical argument and justification.
-
MM1G2.a
Use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proof as appropriate.
-
MM1G2.b
Understand and use the relationships among a statement and its converse, inverse, and contrapositive.
-
MM1G3
Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.
-
MM1G3.a
Determine the sum of interior and exterior angles in a polygon.
-
MM1G3.b
Understand and use the triangle inequality, the side-angle inequality, and the exterior-angle inequality.
-
MM1G3.c
Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL).
-
MM1G3.d
Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.
-
MM1G3.e
Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.
|
|
MM1D
Data Analysis and Probability
|
-
MM1D1
Students will determine the number of outcomes related to a given event.
-
MM1D1.a
Apply the addition and multiplication principles of counting.
-
MM1D1.b
Calculate and use simple permutations and combinations.
-
MM1D2
Students will use the basic laws of probability.
-
MM1D2.a
Find the probabilities of mutually exclusive events.
-
MM1D2.b
Find the probabilities of dependent events.
-
MM1D2.c
Calculate conditional probabilities.
-
MM1D2.d
Use expected value to predict outcomes.
-
MM1D3
Students will relate samples to a population.
-
MM1D3.a
Compare summary statistics (mean, median, quartiles, and interquartile range) from one sample data distribution to another sample data distribution in describing center and variability of the data distributions.
-
MM1D3.b
Compare the averages of the summary statistics from a large number of samples to the corresponding population parameters.
-
MM1D3.c
Understand that a random sample is used to improve the chance of selecting a representative sample.
-
MM1D4
Students will explore variability of data by determining the mean absolute deviation (the average of the absolute values of the deviations).
|
|
MM1P
Process Standards
|
-
MM1P1
Students will solve problems (using appropriate technology).
-
MM1P1.a
Build new mathematical knowledge through problem solving.
-
MM1P1.b
Solve problems that arise in mathematics and in other contexts.
-
MM1P1.c
Apply and adapt a variety of appropriate strategies to solve problems.
-
MM1P1.d
Monitor and reflect on the process of mathematical problem solving.
-
MM1P2
Students will reason and evaluate mathematical arguments.
-
MM1P2.a
Recognize reasoning and proof as fundamental aspects of mathematics.
-
MM1P2.b
Make and investigate mathematical conjectures.
-
MM1P2.c
Develop and evaluate mathematical arguments and proofs.
-
MM1P2.d
Select and use various types of reasoning and methods of proof.
-
MM1P3
Students will communicate mathematically.
-
MM1P3.a
Organize and consolidate their mathematical thinking through communication.
-
MM1P3.b
Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
-
MM1P3.c
Analyze and evaluate the mathematical thinking and strategies of others.
-
MM1P3.d
Use the language of mathematics to express mathematical ideas precisely.
-
MM1P4
Students will make connections among mathematical ideas and to other disciplines.
-
MM1P4.a
Recognize and use connections among mathematical ideas.
-
MM1P4.b
Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
-
MM1P4.c
Recognize and apply mathematics in contexts outside of mathematics.
-
MMIP5
Students will represent mathematics in multiple ways.
-
MMIP5.a
Create and use representations to organize, record, and communicate mathematical ideas.
-
MMIP5.b
Select, apply, and translate among mathematical representations to solve problems.
-
MMIP5.c
Use representations to model and interpret physical, social, and mathematical phenomena.
|
|
MRC
Reading Across the Curriculum
|
-
MRC.a
Reading in all curriculum areas
-
MRC.a.1
Read a minimum of 25 grade-level appropriate books per year from a variety of subject disciplines and participate in discussions related to curricular learning in all areas
-
MRC.a.2
Read both informational and fictional texts in a variety of genres and modes of discourse
-
MRC.a.3
Read technical texts related to various subject areas
-
MRC.b
Discussing books
-
MRC.b.1
Discuss messages and themes from books in all subject areas.
-
MRC.b.2
Respond to a variety of texts in multiple modes of discourse.
-
MRC.b.3
Relate messages and themes from one subject area to messages and themes in another area.
-
MRC.b.4
Evaluate the merit of texts in every subject discipline.
-
MRC.b.5
Examine author's purpose in writing.
-
MRC.b.6
Recognize the features of disciplinary texts.
-
MRC.c
Building vocabulary knowledge
-
MRC.c.1
Demonstrate an understanding of contextual vocabulary in various subjects.
-
MRC.c.2
Use content vocabulary in writing and speaking.
-
MRC.c.3
Explore understanding of new words found in subject area texts.
-
MRC.d
Establishing context
-
MRC.d.1
Explore life experiences related to subject area content.
-
MRC.d.2
Discuss in both writing and speaking how certain words are subject area related.
-
MRC.d.3
Determine strategies for finding content and contextual meaning for unknown words.
|
|
© 2012
IXL Learning. All rights reserved.