Unit 1

Exploring Algebraic and Geometric Relationships

8/31-10/1

-Am I able to describe, classify, and name basic polygons based on their attributes such as parallel sides and symmetry?

-Am I able to represent a pattern of growth using tables, graphs, equations, and make connections between expressions and geometric models?

-Am I able to identify and prove relationships between pairs of angles formed by intersecting lines and among sides and angles of triangles?

• Classify polygons.

• Mark parts of polygons that are equal in length and measure.

• Understand area and perimeter and how area and perimeter change as shapes change (similarity).

• Write algebraic expressions and equations representing side lengths and area.

• Understand factoring quadratic expressions

• Write equations describing graphs.

• Review complementary, supplementary and congruent angle pairs.

• Understand the attributes of angle pairs that are formed by parallel lines intersected by transversals…particularly corresponding, alternate interior, alternate exterior and same side interior angles.

• Understand the Triangle Angle Sum Theorem.

Unit 2

Justification and Similarity

10/4-11/12

-Am I able to write proofs for triangle similarity and the qualities of their corresponding parts?

-Am I able to use similarity to solve everyday problems?

• Review and understand the conditions triangle congruence (ASA, AAS, SSS, SAS, and HL).

• Use flowcharts to organize proofs of triangle congruence.

• Prove by contradiction and use the converse of theorems.

• Learn about dilations and how corresponding parts change.

• Learn triangle similarity conditions (AA, ASA, SSS).

• Use flowcharts to organize proofs for triangle similarity.

• Apply triangle similarity to real world problems.

Unit 3

Probability and Trigonometry

11/15-12/17

-Am I able to model situations involving probability using tree diagrams and/or area models?

-Am I able to compute probabilities of unions, intersections and complements of events?

-Am I able to calculate expected values in games of chance?

-Am I able to see the relationship between the slope of a line and the slope angle?

-Am I able to use the concept of slope ratio to determine missing measurements of a right triangle and solve everyday problems?

• Use a probability area model to represent a situation of chance.

• Develop complex tree diagrams to model probabilities for events that are not equally likely.

• Use tree diagrams and area models to represent and solve probability problems.

• Learn how to calculate probabilities of unions, intersections and complements of events.

• Learn how to calculate expected value.

• Recognize that all slope triangles on a given line are similar to each other.

• Connect that specific slope ratios are related to specific angle measures.

• Use the connections between slope ratios and their related angles to calculate missing side lengths and angle measures in right triangles.

• Use technology to generate slope ratios for new angles and find missing side lengths in right triangles.

• Start to understand that the slope ratio is called tangent.

• Be able to reorient a right triangle in order to see which leg is opposite and which is adjacent to a given acute angle.

• Use the slope ratio to find indirect measurements (Proportions).

Unit 4

Factoring and More Trigonometry

12/20-1/28

-Am I able to change a quadratic expression written as a sum into factored form?

-Am I able to see patterns involved in factoring quadratic expressions?

-Am I able to use sine, cosine and their inverses to find missing side lengths and angle measure in right triangles?

-Am I able to use trigonometric functions to model situations and solve problems?

• Use tiles to build rectangles and identify patterns for determining the dimensions of a completed area model.

• Discover that the products of the terms in each diagonal of an area model are equal.

• Factor quadratic expressions with missing terms, quadratic expressions not in standard form and quadratic expressions with more than one factored form.

• Recognize when a quadratic expression is a perfect square trinomial or a difference of squares and find ways to factor these special cases.

• Learn about sine and cosine ratios and start to create a Triangle Graphic Organizer.

• Identify the appropriate trigonometric ratio based on the relative position of the reference angle and the given sides involved.

• Use inverse trigonometric ratios to determine the unknown angle measure in right triangles.

• Use trigonometric ratios to solve application problems.

Unit 5

Quadratic Functions

1/31-3/11

-Am I able to create a quadratic functions web using graphs, tables, and equations?

-Am I able to use the zero product property to determine the x-intercepts of a parabola?

-Am I able to model everyday situations using quadratic functions?

-Am I able to solve quadratic functions by completing the square?

-Am I able to solve quadratic functions using the quadratic formula?

-Am I able to determine the number of solutions to a quadratic equation and choose the best strategy to solve it based on the given equation?

• Investigate graphs of quadratic functions in order to learn about their shape and key features.

• Describe the graphs of quadratic functions using appropriate vocabulary.

• Identify connections between different representations of quadratic functions; an equation, a table, a situation, and a graph.

• Relate the intercepts and vertex of a parabola in context such as launch and landing point as well as the maximum height of an object following a parabolic trajectory.

• Learn how to model a quadratic situation using a graph.

• Determine x-intercepts by factoring and using the zero product property.

• Write a quadratic function when given a table.

• Write a quadratic function when given a graph of a parabola.

• Solve quadratic equations that are in perfect square form. 

• Express solutions to quadratic equations as exact and approximate values.

• Complete the square to form perfect square quadratic equations and solve.

• Use the quadratic formula to solve quadratic equations.

• Decide whether to use factoring (zero product property), completing the square, or the quadratic formula to solve quadratic equations.

• Write quadratic functions to model everyday situations.

• Perform operations on complex numbers and solve quadratic equations with non-real solutions.

Unit 6

More Right Triangles

3/14-4/8

-Am I able to apply the Pythagorean Theorem and properties of similar right triangles to discover patterns in special right triangles; 45-45-90 and 30-60-90 degree triangles and those containing Pythagorean Triples?

• Recognize the similarity ratios in 30-60-90 and 45-45-90 degree triangles and begin to apply them as shortcuts to find missing side lengths.

• Recognize 3:4:5 and 5:12:13 triangles and other Pythagorean Triples and use dilations of each in application problems.

• Connect trigonometric ratios to special right triangles and identify exact values for trigonometric ratios of special angles.

• Interpret fractional and integer exponents and rewrite radical expressions using such exponents and vice versa.

Unit 7 

Polygons and Circles

4/11-4/29

-Am I able to find shortcuts and generalize the rules for finding perimeters and areas of polygons?

• Continue working with quadrilaterals and triangles to focus on the angles, area and perimeter of polygons with any number of sides.

• Build polygons out of congruent triangles and develop vocabulary to describe these shapes.

• Use knowledge of triangle angle sum and other angle relationships to make discoveries about the interior and exterior angles of polygons.

• Develop strategies to find the area of a regular polygon with any number of sides.

• Examine the relationships between areas of similar figures and discover that the ratio of the areas between similar figures is equal to the zoom factor (similarity ratio).

• Extend the zoom factor generalization to finding the area and perimeter of a regular polygon with an infinite number of sides in order to develop the area and circumference formulas for a circle.

Unit 8 

Circles

5/2-5/20

-Am I able to write equations of circles?

-Am I able to rewrite quadratic equations to write circle equations in different forms?

-Am I able to understand the relationships of angles, arcs, chords and tangents in a circle?

-Am I able to use geometric tools to learn more about the planet Earth?

• Learn how to determine the equation of a circle graphed on the coordinate axes.

• Use completing the square to write equations of circles in graphing form.

• Learn about the relationships between central angles,

 inscribed angles and arcs they intercept.

• Learn the difference between arc length and arc measure.

• Learn that an angle inscribed in a semicircle always measures 90 degrees.

• Learn and justify that opposite angles in an inscribed quadrilateral are supplementary.

• Develop different methods to calculate the length of a chord.

• Use similar triangles and proportionality to understand the relationships between the lengths created by intersecting chords.

• Apply knowledge of chords, angles and arcs to solve problems involving circles.

Unit 9

Solids

5/23-6/10

-Am I able to measure the surface areas and volumes of three dimensional solids?

• Calculate the surface area and volume of non-rectangular prisms and cylinders.

• Learn that the volume of a slanted cylinder or prism remains constant as long as the height remains constant.

• Learn how to sketch prisms and cylinders on paper.

• Learn that the ratio of the volumes of similar 3-D figures is the cube of the scale factor.

• Use the scale factor relationship between similar 3-D figures in application problems.

• Describe the features of a pyramid and name the pyramid using the shape of its base.

• Calculate the total surface area of a pyramid.

• Calculate the volume of a pyramid and justify that it is one-third of the volume of a prism with the same base and height.

• Understand that the volume of an oblique pyramid remains constant as long as the height remains constant.

• Learn how to calculate the volume and surface area of a cone.

• Solve application problems involving cones.

• Calculate the surface area and volume of a sphere.