Side Bar With jim The STEAM Clown: While I use this as math sprinkled into a semester of my Mechatronics Engineering class, I'm going to try to structure it so you could teach it as a stand alone set of Lectures and Labs focused on Engineering Math (Pre-Algebra, Algebra, and Post Algebra) 

Module 7:  Exponents and Exponential Functions

Students develop real world and interdisciplinary connections to exponents with topics such as seismic intensities and/or population growth. Students develop a deeper understanding of the real numbers system and orders reasons behind an order to operations.

Topics covered in this module:

• Zero & Negative Exponents (IM-1)

• Multiplying Powers with the Same Base (IM-1)

• More Multiplication Properties of Exponents (IM-1)

• Division Properties of Exponents (IM-1)

• Rational Exponents and Radicals (IM-1)

• Change Expressed as a Percent (IM-1)

• Exponential Functions (IM-1)

• Exponential Growth & Decay  (IM-1)  

• Understand and interpret formulas for exponential growth and decay (IM-1)

Module M:  Statistics, Data Analysis and Probability

Students will learn and utilize the fundamentals of statistics and probability. They will correlate ratios to probability and finding the frequency of something happening. They will apply mathematical vocabulary and definitions to explain statistical reasoning and to analyze data through graphical models such as histograms. Students will learn and model experimental and theoretical probabilities of events and be provided with a historical understanding of the concepts.  Students will also learn and utilize the counting principle, permutations, and combinations.  They may be introduced to the binomial theorem and/or distributions to test a hypothesis.

Topics covered in this module:

• Similarity Transformations

• Interpret two-way frequency tables

• Use context to interpret and write conditional statements using relative frequency 
tables 


• Correlation Coefficent                                                                                             

• Develop an understanding of the value of the correlation coefficient

• Estimate correlation and lines of best fit

• Compare to the calculated results of 
linear regressions and the correlation coefficient

• Measures of Central Tendency and Dispersion

• Box-and-Whisker Plots

• Experimental and Theoretical Probability

• Probability Distributions and Frequency Tables

• Permutations and Combinations

• Compound Probability and Probability of Multiple Events

• Probability Models

• Conditional Probability

• Modeling Randomness

Module 8:  Arithmetic and Geometric Sequences

Students develop a deeper understanding of arithmetic sequences, rates of growth and change and constant ratio.

Topics covered in this module:

• Represent arithmetic sequences with equations, tables, graphs, and story context

• Understand that arithmetic sequences have a constant difference between consecutive terms

• Compare rates of growth in arithmetic and geometric sequences

• Equations for Arithmetic and Geometric Sequences

• Build recursive and explicit equations for arithmetic and geometric sequences and understand the difference between recursive and explicit equations

• Use rate of change to find missing terms in an arithmetic sequence

• Use a constant ration to find missing terms in a geometric sequence

Module 1: Tools of Geometry

Students will build on their current understanding of Geometry and gain a stronger foundation of the concepts that set the stage for further understanding in the course.  Furthermore, the student will develop a deeper understanding of the tools in geometric construction through the use of manipulatives, iPad apps and interactive mathematical sites.

Topics covered in this module:

• Points, Lines, and Planes

• Measuring Segments

• Measuring Angles

• Exploring Angle Pairs

• Basic Constructions

• Explore compass and straightedge constructions to construct rhombuses, squares, 
parallelograms, equilateral triangles and inscribed hexagons 


• Examine how compass and straightedge constructions produce desired objects

• Write procedures for compass and straightedge constructions

• Midpoint and Distance in the Coordinate Plane

• Perimeter, Circumference, and Area

 Module 2: Reasoning and Proof

Students will develop proofing skills and techniques for critical thinking attainment based on two types of reasoning (deductive and inductive reasoning) often used by mathematicians.  Students will complete a "writing to explain" process through a teacher-created reflection piece, a grade and subject-aligned MARS task and discussions that support writing and reasoning techniques (an interdisciplinary assignment).

Topics covered in this module:

• Conditional Statements

• Bi-conditionals and Definitions

• Deductive Reasoning

• Reasoning in Algebra and Geometry

• Developing counter-examples and error analysis

• Proving Angles Congruence

• Developing informal proofs, paragraph proof, along with 2-column proofs                              

• Use coordinates to algebraically prove geometric theorems

 Module 3: Parallel and Perpendicular Lines

Students will learn the basic concepts of lines and their properties.  Students will also learn about connections among line properties, angles properties and graphing.  Students are expected to graph points using standard form, point-slope form and slope-intercept form, to rewrite equations and to develop a deeper understanding of the concept of slope and how it correlates to steepness, parallelism, perpendicular lines and undefined slopes.  Students will perform an Algebra Walk to build on concepts previously learned about graphing with the added expectation to make connections around the slope of a line and geometric shapes.

Topics covered in this module:

• Lines and Angles

• Properties of Parallel Lines

• Proving Lines Parallel

• Parallel and Perpendicular Lines                                                                                   

• Prove slope criteria for parallel and perpendicular lines

• Parallel Lines and Triangles

• Constructing Parallel and Perpendicular Lines

• Equations of Lines in the Coordinate Plane

• Slopes of Parallel and Perpendicular Lines

 Module 4: Congruent Triangles

Students will further develop connections made among lines, slopes, angles and shapes (specifically with triangles).  In this unit, students will look at the triangle in depth with the expectation that by the end of the unit, students will have mastered the properties of triangles, have applied them, and initiate connections of those properties to other geometric shapes.  Students will study congruency and build triangles of varying measurements that support SSS, SAS, ASA, AAS, and HL-theorem congruence.  Students will be encouraged through discussions, inquiry tasks, and modeling, special connections among different types of triangles (scalene, equilateral, isosceles, right, acute, obtuse and combinations thereof).

Topics covered in this module:

• Congruent Figures

• Triangle Congruence by SSS and SAS                                                                    

• Establish the ASA, SAS and SSS criteria for congruent triangles

• Triangle Congruence by ASA and AAS

• Establish the ASA, SAS and SSS criteria for congruent triangles

• Using Corresponding Parts of Congruent Triangles

• Isosceles and Equilateral Triangles

• Congruence in Right Triangles

• Congruence in Overlapping Triangles

 Module 5: Polygons and Quadrilateral

Students will be studying the properties of several kinds of quadrilaterals including introductory properties of other polygons besides triangles and quadrilaterals.  Students will learn the names of various polygons and their connections to the foundational topics/building blocks. Students will learn the various properties of the sides, angles and diagonals of quadrilaterals and build a correlation to lines in a coordinate plane as well as develop abstract understandings to geometric shapes and models.  Students will use the basic properties of parallelograms to support their mastery of quadrilaterals and their parts.

Topics covered in this module:

• The Polygon-Angle Sum Theorems

• Properties of Parallelograms

• Proving That a Quadrilateral is a Parallelogram

• Properties of Rhombuses, Rectangles, and Squares

• Trapezoids and Kites

• Polygons in the Coordinate Plane

• Proofs Using Coordinate Geometry  

Module 6: Transformations

Students will revisit symmetry and symmetric lines as well as similarity ratios for dilations and study isometric and non-isometric transformations, with a special focus on reflection, rotation, translation, and dilation.  

Topics covered in this module:

• Proofs Using Coordinate Geometry 

• Determine rotational symmetry and lines of symmetry in special types of 
quadrilaterals

• Examine characteristics of regular polygons that emerge from rotational symmetry 
and lines of symmetry

• Make and justify properties of quadrilaterals using symmetry transformations

• Develop the definitions of rigid motion transformations: translations, reflections and 
rotations                                                                                                           

• Develop the definitions of rigid motion transformations: translations, reflections and 
rotations

• Determine which rigid motion transformations carry one image onto another 
congruent image

• Write and apply formal definitions of the rigid motion transformations: translations, 
reflections and rotations

• Develop the definitions of rigid motion transformations: translations, reflections and 
rotations

• Determine which rigid motion transformations carry one image onto another 
congruent image

• Write and apply formal definitions of the rigid motion transformations: translations, 
reflections and rotations

• Compositions of Isometries

• Establish the ASA, SAS and SSS criteria for congruent triangles 
                         

• Dilations

• Similarity Transformations