Unit 1: Expanding the number system 
Instructional Days: 6 
Lessons 
ELO’s Know and be able to… ·
Simplify
expressions using rules of exponents ·
Graph
exponential functions and recognize them as growth or decay ·
Perform
operations (add, subtract, multiply) on: o
Radicals (including simplifying/dividing) o
Polynomials ·
Understand
the complex number system and different classifications of numbers ·
Represent
expressions in radical and rational exponent form 
Topic: Rational and Irrational Numbers 
1 
Review the types of numbers (whole, integers, rational, irrational) Review simplifying radicals 


1 
Explore sums, differences, products and (quotients) of irrational numbers 

Topic: Exponents and Exponential Functions 

Review rules of exponents 


1 
Use properties of exponents with rational exponents Be able to go back and forth between radical and rational exponent form 


1 
Use properties of exponents to interpret and transform exponential functions and classify them as either growth or decay (review graphing exponential functions as needed) 

Topic: Polynomial Functions 
1 
Define terms and coefficients of polynomial functions Add, subtract and multiply polynomial expressions 

Unit: Analyzing and Graphing Functions 
15 days 
Lessons 
ELO’s Know and be able to… ·
Analyze
graphs of various functions and relations:
domain and range, x and y intercepts, determine if the graph is a
function, determine the type of symmetry, determine if the function is
increasing/decreasing on an interval ·
Graph
lines in slope intercept form and standard form ·
Find the
average rate of change using a graph or xvalues ·
Find the
Inverse of a function from a graph ·
Identify
a function as linear, quadratic, exponential, absolute value, square root or
cube root ·
Graph functions
using transformations ·
Apply
linear, quadratic, and exponential models ·
Compare
and contrast the family of functions using tables, equations and graphs 
Topic: The Family of Functions 
3 
Introduce the family of functions: square root, cube root, cubic, absolute value, piecewise, step, quadratic, linear, exponential 


3 
Compare and Contrast functions in terms of: · Where the function is increasing/decreasing · Domain and range (include real life examples) · Maximums and minimums · Positive and negative · x and y intercepts · symmetry (even vs. odd function) 


2 
Transform functions (not step or piecewise) and identify the effects of a, h and k on the graph of each 

Topic: Inverses of functions 
2 
Find the inverse of a function (use graphs to explore and reflect over line y = x) 

Topic: Exploring functions in various forms (tables, graphs, words, etc.) 
2 
Expand graphs to include tables, verbal descriptions, and use the various representations to compare and contrast functions 


1 
Observe using a table and graph that an exponential function will eventually exceed any other function 

Topic: Average rate of change 
2 
Find the average rate of change from an equation or a table; estimate the average rate of change from a graph, and compare average rates of change from different functions 





Unit : Quadratics and Systems of Equations 
20 days 

ELO’s: Know and be able to: ·
Factor
polynomials o
Greatest
Common Factors o
Factor
by Grouping o
Factor
Trinomials (guess and check) ·
Solve a
quadratic equation by factoring, using square roots, and the
quadratic formula. ·
Graph
quadratic functions in both vertex form and standard form ·
Write a
quadratic equation given the zeros of the function ·
Write a
quadratic equation in vertex form, given that it was in standard form 
Topic: Graphing Quadratics 
2 
Graph quadratics using vertex form, standard form and intercept form 

Topic: Factoring Quadratics 
3 
Review GCF Factor quadratics – emphasize intercepts vs. factors Solve quadratics by factoring (using terms such as roots, zeros, solutions) 

Topic: Solving Quadratics 
2 
Solve quadratics by taking square roots (including those with complex solutions) Introduce and expand on imaginary numbers 


2 
Complete the square Use to solve quadratics and write in vertex form find the maximum/minimum of a quadratic(applied) 


1 
Solve quadratics using the quadratic formula 


1 
Explain the Fundamental Theorem of Algebra Write quadratics as products of linear factors (real and complex) 

Topic: Quadratic Inequalities 
1 
Solve quadratic inequalities in one variable 


1 
Create equations and inequalities in one variable and use them to solve problems 

Topic: Systems of Equations 
1 
Create equations in two or more variables to represent relations between quantities; graph equations in coordinate plane with labels and scales 


1 
Review systems of equations 


1 
Solve simple systems of linear and quadratic equations 


1 
Rearrange formulas (with squares) to solve for a specific variable; interpret complicated expressions by viewing one or more of the parts as a single entity 

Unit: Probability 
7 days 

ELO’s Know and be able to… ·
Define
and apply vocabulary– theoretical and experimental probability of a random
event, sample space, independent/dependent
events, joint/disjoint events, conditional probability, union (OR)
intersection (AND), complement of an event, permutation, combination ·
Understand
probability notation: P(A), P(A or B),
P(A and B), P(A^{c}), P(BA) ·
Calculate
probabilities of joint and disjoint events using the addition rule 
Topic: Probability Vocabulary 
1 
Describe events of a probability experiment: sample space, union, intersection, complements Draw Venn diagrams to show relationships between sets within a sample space 

Topic: Independent and Dependent Events 
1 
Understand the difference between independent and dependent events Compute probabilities of independent and dependent events 

Topic: Conditional Probability 
1 
Understand and compute conditional probability (from Venn diagrams, two way tables and tree diagrams) and use it to determine independence Interpret conditional probabilities and independence in context 

Topic: Two way tables 
1 
Use two way tables to calculate probabilities (joint, conditional, unions, etc.) 

Topic: Compound Probabilities 
2 
Apply the Additional Rule for joint and disjoint events 



Apply the Multiplication Rule for independent and dependent events (honors) 

Topic: Counting 
1 
Use permutations and combinations to determine outcomes and compute probabilities 

Unit: Geometry 
12 days 

ELO’s Know and be able to… ·
Define
and apply angle relationships in parallel and intersecting lines ·
Define
and apply angle relationships in triangles and isosceles triangles ·
Define
and apply segment relationships in triangles (medians, midsegments and
perpendicular bisectors) ·
Define
and apply side, angle and diagonal relationships in parallelograms and
rectangles ·
Find
missing sides and angles of similar figures ·
Prove
that two figures are similar 
Topic: Angles 
1 
Review: types of angles and angle pairs Prove vertical angles are congruent 

Topic: Transversals of Parallel Lines 
1 
Prove theorems about transversals of parallel lines and angles pairs (AIA, AEA, CA, CIA) 



Prove that the perpendicular bisector of a line segment is exactly equidistant from the segment’s endpoint 

Topic: Angles of a triangle 
1 
Prove the triangle sum theorem Prove that the base angles of an isosceles triangle are congruent 

Topic: Congruent Triangles 
2 
Prove that triangles are congruent using SSS, SAS, ASA, AAS 

Topic: Parallelograms 
1 
Prove properties of parallelograms: · Opposite sides are congruent · Opposite angles are congruent · Diagonals bisect each other · Rectangles are parallelograms with congruent diagonals 

Topic: Segments of Triangles 
1 
Prove the midsegment of a triangle is parallel to the third side and half the length Show that the medians of a triangle meet at a single point; relationship between median and centroid 

Topic: Similar Triangles 
1 
Define similar triangles  Find missing sides of similar triangles 


1 
Prove triangles are similar 


1 
Prove a line parallel to a one side of a triangle divides the other parts proportionally 


1 
Find the point on a line segment between two given points that partitions the segment in a given ratio 


1 
Prove a dilation takes a line not passing through the center of the dilation to a parallel line, and leaves the line passing through the center unchanged The dilation of a line segment is longer or shorter than the ratio given by the scale factor 

Unit: Trigonometry 


ELO’s Know and be able to… ·
Solve
right triangles with the Pythagorean Theorem ·
Know the
definitions of the 6 trig functions: sin, cos, tan, csc, sec, cot ·
Find
missing sides and angles of right triangles ·
Solve
application problems involving right triangles 
Topic: Pythagorean Theorem 
1 
Prove Pythagorean Theorem using similar triangles Use Pythagorean Theorem to solve for missing sides of a triangle 

Topic: Trigonometric ratios and their applications 
2 
Define the trig functions Prove the Pythagorean Identity and use it to find the sin, cos, tan of an angle Explain and use the relationship between the sine and cosine of complementary angles 


2 
Use trig ratios and Pythagorean Theorem to solve application problems 

Unit: Circles 


ELO’s Know and be able to… ·
Define/identify
the parts of a circle and explain how they relate to each other ·
Calculate
the measure of central angles, inscribed angles, minor arcs, major arcs ·
Calculate
the length of an arc and the area of a sector ·
Graph a
circle in the coordinate plane ·
Knowing information about the circle, either
write an equation in standard form ·
Work
with constructions involving inscribed and circumscribed figures 
Topic: Circle Vocabulary 
1 
Prove all circles are similar Describe and describe relationships between radii, chords, and angles 


1 
Explain the differences between central angles, inscribed angles and circumscribed angles 


1 
Explain the relationship between the inscribed angle and the diameter Explain the relationship between a line tangent to a circle and the radius to the point of tangency Construct a tangent line from a point outside a given circle to the circle 

Topic: inscribed/circumscribed triangles and quadrilaterals 
1 
Construct the inscribed and circumscribed circles of a triangle Prove properties of angles for a quadrilateral inscribed in a circle 

Topic: Circles in the Coordinate Plane 
2 
Graph circles Use coordinate Geometry to prove relationships and theorems about circles (Review distance/midpoint formula as needed) 

Topic: Radian Measure, arc length and sector area 
2 
Use the concept of similarity to understand that arc length intercepted by the central angle is proportional to the radius Develop the definition of radians as a unit of measure by relating to arc length Derive the formula for area of a sector 

Unit: Understanding Volume 
4 days 

ELO’s Know and be able to… ·
Calculate
the volume of various sold figures ·
Explain
how the formulas for volume are derived 

2 
Provide an informal argument for the formulas for circumference of a circle, area of a circle, volume of a cylinder, pyramid and cone 


2 
Use volume formulas for cylinders, pyramids and cones to solve problems 
