Objectives and Content Level 2

Objectives and Content
Level 2

SIMMS Covers Module 1: Marvelous Matrices (matrix operations)
In this module, students will:

Organize and interpret data using requirement graphs
Organize and interpret data using matrices
Determine the dimensions of a matrix
Interpret the meaning of elements within a matri
Identify two or more matrices that are equal
Add and subtract matricesMultiply a matrix by a scalar
Multiply two matrices

Module 2: What Are My Child’s Chances? (probability)
In this module, students will:

Receive a brief introduction to the biology of genetics
Identify complementary events
Use Venn diagrams to determine sample spaces and theoretical probabilities
Collect data and calculate experimental probabilities
Compare theoretical and experimental probabilities
Use Punnett squares to determine sample spaces and theoretical probabilitites
Identify independent and dependent events
Investigate formulas for determining the theoretical probability of two or more events, including P(A and B) and P(A or B), among others
Use tree diagrams to determine sample spaces and theoretical probabilities
Identify mutually exclusive events
Simulate a situation involving independent events

Module 3: There’s No Place Like Home (surface area and volume)
In this module, students will:

Construct and inscribe polygons
Circumscribe regular polygons
Find measures of central angles of regular polygons given the number of sides
Determine the areas of regular polygons and circles
Identify the limiting shapes for sequences of inscribed regular polygons, prisms, and pyramids
Determine the lateral and total surface areas of prisms and cylinders
Determine the volumes of prisms and cylinders
Given the range of certain dimensions of a prism, find the range of the corresponding volumes
Calculate the ratio of surface area to volume for a given figure
Find the area of a sector given the measure of its central angle
Calculate lateral and total surface area of cones
Determine the radius of a cone’s base, given the sector that determines its lateral surface area
Develop and use a formula for the surface area of a cone
Develop and use a formula for the volume of a cone
Compare the volume of a cone with that of a right cylinder with the same base and height
Develop and use a formula for the volume of a right pyramid
Develop and use a formula for the volume of a sphere
Compare the volumes of right cylinders, hemispheres, and right cones with the same radius and height
Calculate the surface areas and volumes of spheres

Module 4: Making Concessions (step functions, linear programming, systems of linear equations)
In this module, students will:

Represent real-number intervals using inequalities and interval notation
Graph and interpret step functions
Use the vertical-line test to determine when a graph is not a function
Represent compound inequalities on a number line
Represent compound inequalities algebraically
Determine constraints for linear-programming problems
Find the corner points of a feasible region
Interpret the meaning of points in a feasible region
Identify solution sets for systems of inequalities in two variables
Develop the corner principle for optimization
Write objective functions
Use linear programming to make decisions involving two variables
Use matrices to solve systems of equations in two and three variables
Find inverses of 2 x 2 and 3 x 3 matrices
Identify determinants of 2 x 2 and 3 x 3 matrices
Use linear programming to make decisions involving three variables

Module 5: Crazy Cartoons (transformational geometry)
In this module, students will:

Use the properties of similar figures
Define a transformation as a one-to-one correspondence between the plane and itself
Identify the preimage and image for a given transformation
Calculate distances between points in the Cartesian plane
Examine the relationship between the distance formula and the Pythagorean theorem
Explore geometric relationships in perspective drawings, dilations centered at the origin, and translations
Describe a dilation in terms of its center and scale factor
Translate objects given a translation vector
Determine the vertical and horizontal components of a vector
Calculate the magnitude and angular direction of a vector
Use and interpret mathematical notation for geometric transformations
Use matrix addition and matrix multiplication to describe translations
Determine the 3 x 3 identity matrix for matrix multiplication
Solve systems of equations using matrices
Use matrix multiplication to describe dilations with center at the origin
Perform compositions of transformations using matrix multiplication
Explore the geometric relationships found in reflections in a line
Use matrix multiplication to perform reflections
Determine single transformation matrices to perform compositions of transformations

Module 6: Drafting and Polynomials (polynomial functions)
In this module, students will:

Write polynomial equations in one variable and identify their degrees
Investigate the graphs of polynomial functions
Use the distributive property to expand polynomials
Recognize the relationships among the zeros, factors, and degree of a polynomial function
Describe the effects of changing the lead coefficient on the graph of a polynomial function
Identify the domain and range of a given polynomial function
Determine roots and factors of a polynomial from its graph
Factor binomials and trinomials
Identify multiple roots of polynomial functions
Use polynomial functions and their graphs as mathematical models
Identify horizontal and vertical translations of polynomial functions
Examine end behavior of polynomial functions

Module 7: Traditional Design (geometric properties)
In this module, students will:

Use paper-folding constructions to examine angle bisectors, perpendicular lines, parallel lines, and midpoints
Explore properties of angles formed by parallel lines and a transversal
Explore geometric rep tiles
Examine properties of parallelograms
Identify properties of chords, tangents, and secants of a circle
Examine congruent figures created by reflections, rotations, and translations
Examine similar figures created by dilations
Classify transformations as isometries

Module 8: And the Survey Says . . . (sampling methods)
In this module, students will:

Use a variety of sampling techniques
Predict the characteristics of a population based on samples
Explore the role that biases play in sampling
Use histograms to estimate probabilities and make predictions
Investigate how sample size affects a survey’s reliability
Explore confidence statements and margins of error

Module 9: Atomic Clocks Are Ticking (negative and fractional exponents)
In this module, students will:

Use simulations to model real-world events
Use exponential functions of the form to model exponential decay
Examine the relationship between rational exponents and roots
Develop properties of exponents
Identify equivalent exponential expressions
Examine the relationship between negative and positive exponents
Solve simple exponential equations with like bases

Module 10: Take It to the Limit (arithmetic and geometric sequences and series)
In this module, students will:

Identify sequences as arithmetic, geometric, or neither
Write recursive formulas for arithmetic and geometric sequences
Write explicit formulas for arithmetic and geometric sequences
Determine the number of terms in a finite arithmetic sequence
Determine the number of terms in a finite geometric sequence
Write formulas for finite arithmetic series
Write formulas for finite geometric series
Investigate the limit of an infinite sequence both graphically and numerically
Determine the sum of the terms of an infinite geometric sequence in which -1<r<1, where r represents the common ratio
Compare sequences that approach limits and those that do not

Module 11: Everyone Counts (combinatorics)
In this module, students will:

Use tree diagrams, lists, and charts to organize information and solve problems
Develop and use the fundamental counting principle
Write and interpret factorial notation
Develop and use a formula for permutations
Develop and use a formula for combinations
Apply the fundamental counting principle, permutations, and combinations to calculate simple probabilities

Module 12: So You Want to Build a House (plane geometry properties and proof)
In this module, students will:

Apply definitions, axioms, and theorems from a geometric system to a real-world context
Investigate the Side-Side-Side (SSS) and Side-Angle-Side (SAS) triangle congruencies
Identify included sides and angles
Write congruence statements
Write conditional statements in “if-then” form
Use direct proof as a method of establishing theorems in Euclidean geometry
Examine and write proofs (or explanations of proofs) of the Pythagorean theorem
Investigate and prove some properties of quadrilaterals

Module 13: Hurry! Hurry! Hurry! Step Right Up! (geometric probability)
In this module, students will:

Compare experimental and theoretical probabilities
Determine theoretical probabilities using geometric models
Find probabilities of complementary events
Determine expected values
Identify events as independent or dependent
Use tree diagrams to determine probabilities
Determine conditional probabilities

Module 14: Fair Is Fair (fair division of discrete and continuous items)
In this module, students will:

Identify the properties of fair division
Investigate algorithms that result in fair divisions
Identify items as continuous or discrete
Make fair divisions of continuous items among two or more people
Make fair divisions of discrete items among two or more people

Module 15: What’s Your Orbit? (modeling data with polynomial and exponential functions)
In this module, students will:

Review properties of exponents
Investigate how changes to a and b in an equation of the form affects its graph
Model data sets using regression equations, including linear, quadratic, cubic, exponential, and power functions
Use the sum of the squares of the residuals to determine quality of fit
Use residual plots to analyze regression models
Use the context of the data to analyze regression models
Evaluate the validity of predictions made using mathematical models

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Level 4

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