Objectives and Content Level 1

Objectives and Content
Level 1

SIMMS Covers Module 1: Reflect on This (reflections in a plane)
In this module, students will:

Identify regular polygons and central angles
Use the relationship between the number of sides of a regular polygon and the measure of its central angles
Use congruent, complementary, and supplementary angle relationships to make conjectures
Learn and use the relationship between the incoming and outgoing angles in the reflection of a light ray
Use congruent segments and the shortest distance between two points to make conjectures about the paths traveled by light rays
Model reflections in a line
Examine the perpendicular bisector relationships created by reflections
Explore the relationship between the coordinates of a point and the coordinates of its image under a reflection in the x- or y-axis
Be introduced to the relationship between theorems and conjectures
Use mathematical terms and notation to describe reflections and double reflections
Use correct notation for representing reflected points
Identify the images of points reflected in both the x- and y-axes

Module 2: I’m Not So Sure Anymore (probability)
In this module, students will:

Use a variety of methods for simulation
Determine experimental probability
Find that the sum of the probabilities for all outcomes of an experiment is 1
Distinguish between experimental and theoretical probabilities
Create sample spaces
Determine theoretical probability using sample spaces
Be introduced to the fundamental counting principle
Identify and extend data patterns
Calculate expected value
Determine when a game is fair

Module 3: Yesterday’s Food is Walking and Talking Today (linear relationships)
In this module, students will:

Interpret data from a table
Use a graphing utility to display data
Analyze scatterplots and line graphs
Examine ratio as a measure of slope
Examine slope as a rate
Write a linear equation given two data points
Identify the domain and range of a linear relation
Examine the slopes of parallel lines
Write a linear equation given the slope and the y-intercept
Write the equation of a line in point-slope form
Use the distributive property to simplify linear expressions
Graphically solve systems of linear equations
Solve linear equations for y in terms of x

Module 4: A New Look at Boxing (areas, tessellations, and nets of regular polygons)
In this module, students will:

Identify prisms
Distinguish between a net and a template
Find the area of regular polygons
Use nets to find the surface area of solids
Calculate the waste created by a template and a shape that encloses it
Determine interior and exterior angle measures for regular polygons
Determine which regular polygons can tessellate a plane
Tessellate a plane with various polygons
Construct regular polygons inscribed in a circle using central angles
Identify and use the apothem to determine the area of a regular polygon
Derive a formula for the area of regular polygons

Module 5: What Will We Do When the Well Runs Dry? (volumes; linear models)
In this module, students will:

Determine the volumes of triangular, rectangular, and trapezoidal prisms using appropriate units
Approximate areas of irregular figures
Approximate the volume of three-dimensional solids with irregular bases
Investigate the relationships among cubic centimeters, cubic decimeters, and liters
Collect and tabulate data
Convert rates to different units
Construct and interpret graphs
Develop and use linear models
Determine rates of change using slope
Examine residuals and use them to evaluate models

Module 6: Skeeters Are Overrunning the World (exponential growth)
In this module, students will:

Recognize nonlinear patterns
Make predictions based on a nonlinear graph
Model data with exponential curves
Create graphs of exponential curves to model data with different initial populations and growth rates
Determine the independent and dependent variables for a function
Graph and interpret an exponential function in the form
Develop mathematical models for population growth
Define a function using function notation
Identify and determine a constant growth rate
Explore the relationship between b and r in exponential equations of the form , where
Calculate average growth rate
Examine how the initial population affects population growth
Write exponential equations of the form
Graph and interpret exponential functions of the form
Apply exponential functions to real-world contexts

Module 7: Oil: Black Gold (area, volume, direct and inverse proportions)
In this module students will:

Determine the volume of cylinders and prisms
Determine the area of irregularly shaped figures
Develop mathematical models of real-world events
Develop and graph direct and inverse proportions
Use mathematical models to make predictions about data sets

Module 8: When to Deviate from a Mean Task (measures of central tendency and deviation)
In this module, students will:

Interpret data displayed in pie charts
Create a frequency table from raw data
Interpret data displayed in histograms
Interpret data displayed in stem-and-leaf plots
Find measures of central tendency
Interpret data displayed in box-and-whisker plots
Determine mean absolute deviation
Determine standard deviation

Module 9: Are You Just a Small Giant? (similarity)
In this module, students will:

Relate the constant of proportionality in direct proportions to the scale factor in similar figures
Use proportions and lengths to determine if objects are similar
Use the relationships among scale factor, length, area, and volume for similar objects
Examine how area changes as shapes change size proportionally
Use squares and square roots
Examine how volume and mass change as objects change size proportionallyUse cubes and cube roots
Examine how the values of a and b affect graphs of power equations of the form
Model data with appropriate power equations
Use mass or weight, along with area, to determine pressure
Use relationships among mass, density, weight, and pressure to describe proportional changes in size.

Module 10: Graphing the Distance (linear and quadratic functions)
In this module, students will:

Use interval and inequality notation
Relate finite and infinite intervals to inequalities and graphs
Calculate displacement for a given time interval
Distinguish between speed and velocity
Calculate average speed and average velocity
Estimate instantaneous velocity
Create distance-time graphs using motion detectors
Interpret distance-time graphs
Relate distance, time, and velocity for an object moving at constant speed to the slope-intercept form of a line
Calculate residuals and the sum of the squares of the residuals
Use linear regressions to model data
Write and graph quadratic functions of the general form and the vertex form
Predict shapes of graphs from quadratics in vertex form
Translate parabolas using the vertex form
Apply the distributive property to expand the vertex form to the general form
Calculate average acceleration
Describe the height of a falling object using the formula
Use quadratic regressions to model data

Module 11: A New Angle on an Old Pyramid (Pythagorean Theorem and right-triangle trigonometry)
In this module, students will:

Use similarity to determine unknown measures in triangles
Identify similar triangles using the AAA property
Write conditional statements, identifying both hypothesis and conclusion
Write converses of conditional statements
Solve right-triangle problems using the Pythagorean theorem and its converse
Classify triangles as acute, right, or obtuse based on the lengths of the three sides
Identify segments that form a triangle using the triangle inequality property
Develop the distance formula for two dimensions
Define and identify dihedral angles
Develop and apply the tangent ratio
Use to determine the measures of unknown angles in right triangles
Use technology to develop a table of trigonometric values for the tangent, sine, and cosine ratios
Develop and apply the sine and cosine ratios
Use and to determine the measures of unknown angles in right triangles

Module 12: From Rock Bands to Recursion (arithmetic and geometric sequences and series)
In this module, students will:

Investigate number patterns
Develop arithmetic sequences
Write and evaluate recursive formulas for arithmetic sequences
Evaluate arithmetic series
Write and evaluate explicit formulas for arithmetic sequences
Compare linear equations and explicit formulas for arithmetic sequences
Compare the graphs of linear equations and arithmetic sequences
Develop geometric sequences
Write and evaluate recursive formulas for geometric sequences
Compare the graphs of arithmetic and geometric sequences
Evaluate geometric series
Write and evaluate explicit formulas for geometric sequences
Compare exponential equations and explicit formulas for geometric sequences
Compare the graphs of exponential equations and geometric sequences (4)

Module 13: Under the Big Top but Above the Floor (linear inequalities and linear programming)
In this module, students will:

Graph inequalities on a number line
Investigate number patterns
Write and graph linear inequalities
Use linear inequalities to define regions graphically
Solve systems of linear equations
Determine the feasible region for a system of linear inequalities
Find the corner points for a feasible region
Determine the optimum values for linear objective functions

Module 14: From Here to There (three-dimensional coordinate system)
In this module, students will:

Create and interpret topographic maps
Create and use three-dimensional coordinate systems
Plot points in three-dimensional space
Apply a three-dimensional coordinate system to a topographic map
Identify points in space using ordered triples
Determine geometric representations when one variable or more is fixed in an ordered triple
Create a possible topographic map given a profile of the terrain
Describe a locus of points that satisfy a given condition
Calculate distances between points in three dimensions using the Pythagorean theorem
Develop a distance formula in three dimensions
Apply the distance formula for points in three dimensions
Coordinate locations given a reference point
Interpret the terrain between two points on a topographic map
Develop a profile given a segment connecting two points on a topographic map
Analyze how changing the scale affects the profile
Describe how the distance between two points on a topographic map can be approximated using a profile
Use right-triangle trigonometry to determine the measures of angles and sides of right triangles
Determine angles of elevation

Module 15: Going in Circuits (graph theory and fundamental counting principle)
In this module, students will:

Receive an introduction to graph theory, including weighted graphs, Hamiltonian circuits, and digraphs
Use tree diagrams to organize information and solve problems
Use the fundamental counting principle
Use factorial notation
Solve problems involving Hamiltonian circuitsExamine and develop algorithms for solving problems

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