Course Syllabus For Mr Santowski's Integrated Math 2 Classes

Here is a unit by unit listing of the course syllabus for IM2, listed unit by unit

 Unit Name Link to Unit Objectives Unit 1 Introduction to Functions & Linear Function Unit Objectives This unit on Linear Functions will focus on three major topics, which will be unified by one central theme. Our central theme that will be woven throughout the unit will be "describing data sets & patterns" in contextual settings (mathematical & practical/real world) (1) Topic 1 will be an Introduction to Functions, where we will study definitions of functions & relations, notations associated with functions, various representations of functions, and key terms associated with functions (domain, range, solve, evaluate) (2) Topic 2 will be Linear Functions, where we will study the meaning and calculation of slope, working with various forms of linear equations (slope-intercept, standard, point-slope forms), how to work with horizontal, vertical, parallel, perpendicular lines & finally how to work with linear inequalities. Given our theme of data sets & contexts, we will work with lines of best fit as well as introducing linear regression & using the TI-84 to perform linear regression calculations. (3) Topic 3 will be Linear Systems, wherein we will review the various graphic & algebraic methods (elimination, substitution) for solving linear systems. Unit 2 Coordinate Geometry Unit Objectives This unit on Co-ordinate geometry will have three primary focal points, which will once again have two unifying themes entwined throughout the lessons of this unit. The two unifying "big picture" themes will be (1) How do you "prove" that something in Math is "true/correct"? (or How do you "reason" from the basics? or How can you use the "basics" to construct new ideas/knowledge?) and secondly (2) how do you work through a "real world scenario" when a problem involves creating a geometric model (rather than an algebraic model) (1) Working with the Basics of Geometry ==> students will study (i) various algebraic basics associated with a co-ordinate plane that will come up in Geometry (midpoint, slope, length, Pythagorean Theorem, parallel, perpendicular) and then (ii) various geometry basics to which we can apply our algebra & the coordinate plane (properties of quadrilaterals, triangles, circles, diagonals, midsegments) (2) For an Applied Math perspective ==> real world contexts for geometric shapes (Q,T,C) in which these shapes are used in conjunction with a coordinate plane/grid in order to model a problem (i.e. designing lighting options in a triangular shaped park) (3) For a Pure Math perspective ==> students will focus on two ideas: (i) use coordinates points & algebra to "prove" various properties of geometric figures (bigger picture .. how do you prove something to be true?) and secondly (ii) transform simple geometric shapes (translate, reflect, dilate) (bigger picture here will be the idea of how we can use geometry to explore concepts/ideas that do have future algebraic connections (i.e. reflecting a square across the x-axis can be used to make algebraic connections to the reflection of a parabola across the x-axis) Unit 3 Triangles & Right Triangle Trigonometry Unit Objectives This triangle trig unit will cover two major topics: (1) Similar triangles and (2) Right triangle trigonometry (1) Similar Triangles topic will focus on two ideas: (i) solving application problems wherein two triangles will be used to model the problem and set the stage for the solution as well as (ii) starting the idea of working with ratios of sides through the context of triangles that are similar (2) Right Triangle Trig topic will focus on two ideas: (i) application problems involving sides and angles in problems wherein triangles are geometric constructs that can be used to model the problem and its solution, and (ii) a pure math focus, wherein the function concept of input/output is understood ==> sin(angle) = ratio and then with sin-1(ratio) = angle Unit 4 Exponential Functions Unit Objectives Students are introduced to & explore Exponential Relations in three intertwined strands: (1) Modeling with Data Sets ==> Students work with data sets that illustrate features relevant to Exponential Relations ==> the presence of a common RATIO rather than a common DIFFERENCE as in linear data sets (2) Graphs of Exponential Relations ==> Exponential curves were graphed and studied (both in context and as non-contextual functions) from the viewpoint of their key features such as y-intercept, x-intercepts (if any) and asymptotes. These features were simply identified & put into context from pre-drawn graphs and analyzed using graphing technology (3) Algebra of Exponential Relations ==> the algebra that accompanies the exponential relations was reviewed. Algebraic processes involving zero and negative exponents (including fractional bases) was reviewed, as were simplifying expressions using exponent laws. Additionally, the connections between the features of the graph and the algebraic equation was taught (i.e. if we have an equation, how do we analyze the equation to determine the asymptote & y-intercept; if we have a graph of an equation, how to we write the equation? ; if we have an equation in the form of y = abx + d, how can we sketch a graph of it?) Unit 5 Quadratic Functions Unit Objectives Students are introduced to & explore Quadratic Relations in three intertwined strands: (1) Modeling with Data Sets ==> Students work with data sets that illustrate features relevant to Quadratric Relations (parabolas) that have not appeared before in other relations studied (linear & exponential) ==> i.e. data sets that show increasing trends as decreasing trends as well (the height of a ball as it goes up and then turns to come back down again) (2) Graphs of Quadratic Relations ==> Parabolas are graphed and studied (both in context and as non-contextual functions) from the viewpoint of their key features such as axis of symmetry, vertex, zeroes, y-intercepts, direction of opening. These features are simply identified & put into context from pre-drawn graphs and analyzed using graphing technology (3) Algebra of Quadratic Relations ==> the algebra that accompanies these new quadratic relations is introduced. The algebraic processes of expanding & factoring & solving quadratic equations is taught. Finally, the connections between the features of the graph and the algebraic equation is taught (i.e. if we have an equation, how do we analyze the equation to determine the axis of symmetry; if we have a graph of an equation, how to we write the equation in factored form?) Unit 6 Statistics Unit Objectives The Introduction to Descriptive Statistics focuses on three primary "big picture" items: (1) Data Organization & Visual Representations of Data ==> looking at discrete vs continuous data, looking at stem & leaf plots, frequency tables, frequency histograms, frequency polygons & cumulative frequency graphs (2) Measuring Central Tendencies ==> working with the mean, median, mode of data when the data is presented in a variety of ways (raw data, grouped data, histograms, cumulative frequency graphs) (3) Measuring Dispersion/Spread/Variability ==> working with 5 number summary (min, Q1, Q2, Q3, max) and the visual representation (Box & Whisker plot) The undercurrent/unifying theme of the entire unit was "making decisions", as one reason for gathering statistical data is to facilitate the decision making process. The context for many of our simple decisions was to decide on "who's the best". Many discussions & examples revolved around data for classes & athletes comparing their performances and using "stats" and "statistical analysis" to decide who was "best". So essentially, students would be expected to work a visual representation of data plus some key summary numbers, and then proceed to make & justify decisions!