Algebra/Geometry III

DRAFT—Last updated 5/15/2019

Algebra/Geometry III SCOPE & SEQUENCE Year at a Glance

Quarter 1 Quarter 2 Quarter 3 Quarter 4

Unit 1 Functions

And Exponents

3 weeks

Unit 2 Polynomial Equations &

Functions 4 weeks

Unit 3 Graphing

Quadratics Functions 4 weeks

Unit 4 Solving

Quadratic Equations 4 weeks

Unit 5 Probability

3 weeks

Unit 6 Relationships

Within Triangles 3 weeks

Unit 7 Quadrilaterals

3 weeks

Unit 8 Similarity 2 weeks

Unit 9 Right

Triangles and Trigonometry

3 weeks

Unit 10 Circles

3 weeks

Unit 11 Circumference

Area Volume 3 weeks

N.RN.1 N.RN.2 A.CED.2 A.CED.4 A.REI.10 F.IF.4 F.IF.7b F.IF.7e F.IF.9 F.BF.1a F.BF.3 F.BF.4a F.LE.1a F.LE.2

A.APR.1 A.APR.3 A.REI.4b A.SSE.2 A.SSE.3a

A.CED.2 F.IF.4 F.IF.6 F.IF.7a F.IF.7c F.IF.8a F.IF.9 F.BF.1a F.BF.3 A.SSE.3a A.APR.3 F.LE.3 G.GPE.2

A.REI.4a, b A.REI.11 A.CED.1 A.CED.3 A.CED.4 A.SSE.3b F.IF.7A F.IF.8a A.REI.7 N.RN.2 N.RN.3 N.CN.1 N.CN.2 N.CN.7

S.CP.1 S.CP.2 S.CP.3 S.CP.4 S.CP.5 S.CP.6 S.CP.7 S.CP.8

G.CO.9 G.CO.10 G.CO.12 G.MG.1 G.MG.3 G.C.3 G.GMD.6 (CA)

G.CO.11 G.SRT.5 G.MG.1 G.MG.3

G.CO.2 G.CO.5 G.SRT.1a G.SRT.1b G.SRT.2 G.SRT.3 G.SRT.4 G.SRT.5 G.MG.1 G.MG.3 G.GPE.5 G.GPE.6 G.GMD.5 (CA)

G.SRT.4 G.SRT.5 G.SRT.6 G.SRT.7 G.SRT.8 G.MG.1 G.MG.3

G.CO.1 G.CO.13 G.C.1 G.C.2 G.C.3 G.MG.1 G.MG.3 G.GPE.1 G.GPE.4

G.MG.1 G.MG.2 G.MG.3 G.CO.1 G.C.5 G.GMD.1 G.GMD.2 G.GMD.3 G.GMD.5 (CA)

SBAC IABs

Number and Quantity

Algebra & Functions I

Algebra & Functions II SSE &

Polynomial Expressions

Geometry Congruence

Geometry Right Triangle Trigonometry

Geometry Measurement & Modeling

Common Assignment Tasks per Quarter

Cash Box Throwing A Ball Linear Equations in Two Variables Quadratic Functions Graphically

Representing Data with Box Plots Interpreting Data: Muddying the Waters

Statements Length and Area The Schoolyard Problem Identifying Similar Triangles Triangles Perimeter

Transforming 2D Figures Right Triangles Defining Trig Ratios Tangent of Acute Angles

Algebra/Geometry III

DRAFT—Last updated 5/15/2019

Common Core 8 Mathematical Practice Standards

Math Practice Standards Description

MP1: Make sense of

problems and

persevere in solving

them

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to

its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of

the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous

problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor

and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem,

transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need.

Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or

draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might

rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check

their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can

understand the approaches of others to solving complex problems and identify correspondences between different approaches.

MP2: Reason

abstractly and

quantitatively

Mathematically proficient students make sense of the quantities and their relationships in problem situations. Students bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

MP3: Construct

viable arguments and

critique the

reasoning of others

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct,

Algebra/Geometry III

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even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an

argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask

useful questions to clarify or improve the arguments.

MP4: Model with

mathematics

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, 2-by-2 tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

MP5: Use

appropriate tools

strategically

Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, ruler, protractor, calculator, spreadsheet, computer algebra system, statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students interpret graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.

MP6: Attend to

precision

Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.

Algebra/Geometry III

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MP7: Look for and

make use of

structure

Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well-remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as composed of several objects. For example, they can see 5 – 3(x – y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

MP8: Look for and

express regularity in

repeated reasoning

Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x2 + x + 1), and (x – 1)(x3 + x2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.

Algebra/Geometry III

DRAFT—Last updated 5/15/2019

Algebra/Geometry III—Chapter 1

Lesson &

Standards

Standards Learning Goals Tasks and/or PD Videos to Support Conceptual Understanding

Khan Academy Lesson Links

MMP

0.5 days

F.BF.3

8.G.3

Transforming graphs of linear functions. Reflecting figures in the line y=x.

Shifting Functions Stretching Functions Reflections

1.1

1.5 days

A.CED.2

A.REI.10

F.IF.7b

F.BF.3

Translate graphs of absolute value functions. Stretch, shrink, and reflect graphs of absolute value functions. Combine transformations of graphs of absolute value functions.

Differentiating the Lesson 1.1 Graphs of absolute value functions

1.2

2 days

A.CED.2

A.REI.10

F.IF.7b

Evaluate piecewise functions. Graph and write piecewise functions. Graph and write step functions. Write absolute value functions.

Differentiating the Lesson 1.2 Video: Piecewise Functions

Piecewise functions

1.3

1 day

A.CED.4

F.BF.4a

Explore inverses of functions. Find and verify inverses of nonlinear functions. Solve real-life problems using inverse functions.

Differentiating the Lesson 1.3 Video: Inverse of Linear Functions

Introduction to the inverses of functions Finding inverse functions Verifying that functions are inverses

1.4

1.5 days

N.RN.2 Use zero and negative exponents. Use the properties of exponents. Solve real-life problems involving exponents.

Differentiating the Lesson 1.4 Exponent properties review

1.5

2 days

N.RN.1

N.RN.2

Find nth roots. Evaluate expressions with rational exponents. Solve real-life problems involving rational exponents.

Differentiating the Lesson 1.5 Video: Cube Root Functions

Radicals Rational exponents intro

1.6

2 days

A.CED.2

F.IF.4

F.IF.7e

F.IF.9

F.BF.1a

F.BF.3

F.LE.1a

F.LE.2

Identify and evaluate exponential functions. Graph exponential functions. Solve real-life problems involving exponential functions.

Differentiating the Lesson 1.6 Video: Exponential Functions

Exponential vs. linear growth Exponential functions from tables and graphs Graphs of exponential growth

Algebra/Geometry III

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Algebra/Geometry III—Chapter 2

Lesson &

Standards

Standards Learning Goals Tasks and/or PD Videos to Support Conceptual Understanding

Khan Academy Lesson Links

MMP

0.5 days

7.EE.1

6.NS.4

Simplifying Algebraic Expressions

Finding the Greatest Common Factor The distributive property & equivalent

expressions Greatest common factor

2.1

1.5 days

A.APR.1 Find the degrees of monomials. Classify polynomials. Add and subtract polynomials. Solve real-life problems.

Differentiating the Lesson 2.1 Intro to polynomials Adding & subtracting polynomials (intro) Adding and subtracting polynomials: two variables

2.2

2 days

A.APR.1 Multiply binomials. Use the FOIL method. Multiply binomials and trinomials.

Differentiating the Lesson 2.2 Video: Multiplying Polynomials

Multiplying monomials Multiplying monomials by polynomials Multiplying binomials Multiplying binomials by polynomials Polynomials word problems

2.3

2 days

A.APR.1 Use the square of a binomial pattern. Use the sum and difference pattern. Use special product patterns to solve real-life problems.

Differentiating the Lesson 2.3 Video: Simplifying Expressions

Special products of binomials

2.4

2 days

A.APR.3

A.REI.4b

Use the Zero-Product Property. Factor polynomials using the GCF. Use the Zero-Product Property to solve real-life problems.

Differentiating the Lesson 2.4 Quadratic factored form

2.5

1.5 days

A.SSE.2

A.SSE.3a

Factor x²+ bx + c. Use factoring to solve real-life problems.

Differentiating the Lesson 2.5 Video: Factoring x²+bx +c

Factoring quadratics intro Solving quadratics by factoring

2.6

2 days

A.SSE.2

A.SSE.3a

Factor ax² + bx + c. Use factoring to solve real-life problems.

Differentiating the Lesson 2.6 Factoring quadratics intro Factoring quadratics by grouping Factoring polynomials with quadratic forms Solving quadratics by factoring Strategy in factoring quadratics

2.7

2 days

A.SSE.2

A.SSE.3a

Factor the difference of two squares. Factor perfect square trinomials. Use factoring to solve real-life problems.

Differentiating the Lesson 2.7 Factoring quadratics: difference of two squares Factoring quadratics: perfect squares

2.8

2 days

A.SSE.2

A.SSE.3a

Factor polynomials by grouping. Factor polynomials completely. Use factoring to solve real-life problems.

Differentiating the Lesson 2.8 Factoring quadratics by grouping Factoring polynomials with special product forms

Algebra/Geometry III—Chapter 3

Algebra/Geometry III

DRAFT—Last updated 5/15/2019

Lesson &

Standards

Standards Learning Goals Tasks and/or PD Videos to Support Conceptual Understanding

Khan Academy Lesson Links

MMP

0.5 days

A.CED.2

6.EE.2c

Graphing Linear Equations

Evaluating Expressions

Graphing slope-intercept equations Introduction to variables Exponents

3.1

1.5 days

A.CED.2

F.IF.7a

F.BF.3

Identify characteristics of quadratic functions. Graph and use quadratic functions of the form of f(x) = ax².

Differentiating the Lesson 3.1 Parabolas intro Transforming parabolas

3.2

2 days

A.CED.2

F.IF.7a

F.BF.3

Graph quadratic functions of the form f(x) = ax² + c. Solve real-life problems involving functions of the form f(x) = ax² + c.

Differentiating the Lesson 3.2 Video: Translate Quadratic Functions

Transforming parabolas

3.3

2 days

A.CED.2

F.IF.7a

F.IF.9

Graph quadratic functions of the form f(x) = ax² + bx + c. Find maximum and minimum values of quadratic functions.

Differentiating the Lesson 3.3 Quadratic standard form

3.4

1.5 days

A.CED.2

F.IF.4

F.BF.1a

F.BF.3

Identify even and odd functions. Graph quadratic functions of the form f(x) = a(x − h)².

Graph quadratic functions of the form f(x) = a(x − h)² + k.

Model real-life problems using f(x) = a(x − h)²+ k.

Differentiating the Lesson 3.4 Transforming parabolas Quadratic vertex form

3.5

2 days

A.SSE.3a

A.APR.3

A.CED.2

F.IF.4

F.IF.8a

F.BF.1a

Graph quadratic functions of the form f(x) = a(x − p)(x − q). Use intercept form to find zeros of functions. Use characteristics to graph and write quadratic equations. Use characteristics to graph and write cubic functions.

Differentiating the Lesson 3.5 Quadratic factored form Features & forms of quadratic functions

3.6

2 days

F.IF.4

F.IF.7c

G.GPE.2

Explore the focus and the directrix of a parabola. Write equations of parabolas. Solve real-life problems.

Differentiating the Lesson 3.6 Focus and directrix of a parabola

3.7

2 days

F.IF.6

F.BF.1a

F.LE.3

Choose functions to model data. Write functions to model data. Compare functions using average rates of change. Solve real-life problems involving different function types.

Differentiating the Lesson 3.7 Video: Comparing Types of Functions Graphically

Exponential vs. linear growth Average rate of change Average rate of change word problems

Algebra/Geometry III

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Algebra/Geometry III—Chapter 4

Lesson &

Standards

Standards Learning Goals Tasks and/or PD Videos to Support Conceptual Understanding

Khan Academy Lesson Links

MMP

0.5 days

A.SSE.2

A.REI.6

Factoring Perfect Square Trinomials

Solving Systems of Linear Equations by Graphing

Factoring quadratics: perfect squares Introduction to systems of equations

4.1

1.5 days

N.RN.2

N.RN.3

Use properties of radicals to simplify expressions. Simplify expressions by rationalizing the denominator. Perform operations with radicals.

Differentiating the Lesson 4.1 Simplifying square roots Simplifying radicals (higher index roots)

4.2

2 days

A.REI.11

F.IF.7a

Solve quadratic equations by graphing. Use graphs to find and approximate the zeros of functions. Solve real-life problems using graphs of quadratic functions.

Differentiating the Lesson 4.2 Video: Solving f(x) = g(x) graphically

Solving quadratics by factoring

4.3

2 days

A.CED.1

A.CED.4

A.REI.4b

Solve quadratic equations using square roots. Approximate the solutions of quadratic equations.

Differentiating the Lesson 4.3

Solving quadratics by taking square roots

4.4

2 days

A.SSE.3b

A.CED.1

A.REI.4a

A.REI.4b F.IF.8a

Complete the square for expressions of the form x² + bx. Solve quadratic equations by completing the square. Find and use maximum and minimum values. Solve real-life problems by completing the square.

Differentiating the Lesson 4.4 Video: Completing the Square

Completing the square

4.5

2 days

A.CED.1

A.REI.4a

A.REI.4b

Solve quadratic equations using the Quadratic Formula. Interpret the discriminant. Choose efficient methods for solving quadratic equations.

Differentiating the Lesson 4.5 The quadratic formula

4.6

1.5 days

N.CN.1

N.CN.2

N.CN.7

A.REI.4b

Define and use the imaginary unit i. Add, subtract, and multiply complex numbers. Find complex solutions and zeros.

Differentiating the Lesson 4.6 What are the imaginary numbers? What are the complex numbers? Adding and subtracting complex numbers Multiplying complex numbers

4.7

1 day

N.CN.7

A.REI.4b

Solve quadratic equations using the Quadratic Formula. Analyze the discriminant to determine the number and type of solutions. Solve real-life problems.

Differentiating the Lesson 4.7 The quadratic formula Quadratic equations with complex numbers

4.8

2 days

A.REI.7

A.REI.11

Solve systems of nonlinear equations by graphing. Solve systems of nonlinear equations algebraically. Approximate solutions of nonlinear systems and equations.

Differentiating the Lesson 4.8 Video: Solving f(x) = g(x) graphically

*skills for A.REI.7 are coming soon to Khan Academy

4.9

2 days

A.CED.1

A.CED.3

Graph quadratic inequalities in two variables. Solve quadratic inequalities in one variable.

Differentiating the Lesson 4.9

Systems of quadratic equations

Algebra/Geometry III

DRAFT—Last updated 5/15/2019

Algebra/Geometry III—Chapter 5

Lesson &

Standards

Standards Learning Goals Tasks and/or PD Videos to Support Conceptual Understanding

Khan Academy Lesson Links

MMP

0.5 days

7.RP.3

S.ID.1

Finding a percent Making a histogram

Percent problems Displays of distributions

5.1

1.5days

S.CP.1

Find sample spaces. Find theoretical probabilities. Find experimental probabilities.

Differentiating the Lesson 5..1 Basic theoretical probability Experimental probability Randomness, probability, and simulation

5.2

2 days

S.CP.1

S.CP.2

S.CP.3

S.CP.5

S.CP.6

S.CP.8 (+)

Determine whether events are independent events. Find probabilities of independent and dependent events. Find conditional probabilities.

Differentiating the Lesson 5.2 Multiplication rule for independent events Multiplication rule for dependent events Conditional probability and independence

5.3

2 days

S.CP.4

S.CP.5

Make two-way tables. Find relative and conditional relative frequencies. Use conditional relative frequencies to find conditional probabilities.

Differentiating the Lesson 5.3 Video: Interpreting Two-Way Frequency Tables

Probability using sample spaces Conditional probability and independence

5.4

1.5 days

S.CP.1

S.CP.7

Find probabilities of compound events. Use more than one probability rule to solve real-life problems.

Differentiating the Lesson 5.4 Addition rule

5.5

2 days

A.APR.5 (+) S.CP.9 (+)

Use the formula for the number of permutations. (+) Use the formula for the number of combinations. (+) Use combinations and the Binomial Theorem to expand binomials. (+)

Differentiating the Lesson 5.5 Counting principle and factorial Permutations Combinations Combinatorics and probability

Binomial theorem Understanding the binomial theorem

5.6

2 days

S.CP.9 (+)

Construct and interpret probability distributions. (+) Construct and interpret binomial distributions. (+)

Differentiating the Lesson 5.6 Combinatorics and probability Binomial random variables

Algebra/Geometry III

DRAFT—Last updated 5/15/2019

Algebra/Geometry III—Chapter 6

Lesson &

Standards

Standards Learning Goals Tasks and/or PD Videos to Support Conceptual Understanding

Khan Academy Lesson Links

MMP

0.5 days

G.GPE.5

A.CED.1

Writing an Equation of a Perpendicular Line Writing Compound Inequalities

Equations of parallel & perpendicular lines Compound inequalities

6.1

1.5 days

G.CO.9

Write flowchart proofs to prove geometric relationships. Write paragraph proofs to prove geometric relationships.

Differentiating the Lesson 6.1 Skills for this lesson are coming soon to Khan

6.2

2 days

G.CO.9

G.MG.1

Use perpendicular bisectors to find measures. Use angle bisectors to find measures and distance relationships. Write equations for perpendicular bisectors.

Differentiating the Lesson 6.2 Angle bisector theorem

6.3

2 days

G.CO.12

G.C.3

G.MG.1

G.MG.3

Use and find the circumcenter of a triangle. Use and find the incenter of a triangle.

Differentiating the Lesson 6.3 Constructing circumcircles and incircles

6.4

2 days

G.CO.10 Use medians and find the centroids of triangles. Use altitudes and find the orthocenters of triangles.

Differentiating the Lesson 6.4 Medians and centroids Altitudes

6.5

1.5 days

G.CO.10

G.MG.1

Use midsegments of triangles in the coordinate plane. Use the Triangle Midsegment Theorem to find distances.

Differentiating the Lesson 6.5 Exploring medial triangles

6.6

2 days

G.CO.10 G.GMD.6 (CA)

Write indirect proofs. List sides and angles of a triangle in order by size. Use the Triangle Inequality Theorem to find possible side lengths of triangles.

Differentiating the Lesson 6.6 Proof by contradiction Triangle inequality theorem Constructing triangles

6.7

1 day

G.CO.10

Compare measures in triangles. Solve real-life problems using the Hinge Theorem.

Differentiating the Lesson 6.7 Constructing triangles

Algebra/Geometry III

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Algebra/Geometry III—Chapter 7

Lesson &

Standards

Standards Learning Goals Tasks and/or PD Videos to Support Conceptual Understanding

Khan Academy Lesson Links

MMP

0.5 days

A.REI.3

A.SSE.1b

G.GPE.5

Using Structure to Solve a Multi-Step Equation

Identifying Parallel and Perpendicular Lines

Linear equations with parenthesis Parallel & perpendicular lines on the coordinate plane

7.1

1 day

G.CO.11 Use the interior angle measures of polygons. Use the exterior angle measures of polygons.

Differentiating the Lesson 7.1 Properties of shapes Angles with polygons

7.2

1.5 days

G.CO.11

G.SRT.5

Use properties to find side lengths and angles of parallelograms. Use parallelograms in the coordinate plane.

Differentiating the Lesson 7.2 Theorems concerning quadrilateral properties

7.3

2 days

G.CO.11

G.SRT.5

G.MG.1

Identify and verify parallelograms. Show that a quadrilateral is a parallelogram in the coordinate plane.

Differentiating the Lesson 7.3 Skills for this lesson are coming soon to Khan

7.4

1.5 days

G.CO.11

G.SRT.5

G.MG.1

G.MG.3

Use properties of special parallelograms. Use properties of diagonals of special parallelograms. Use coordinate geometry to identify special types of parallelograms.

Differentiating the Lesson 7.4 Classifying geometric shapes Quadrilateral proofs & angles

7.5

2 days

G.SRT.5

G.MG.1

Use properties of trapezoids. Use the Trapezoid Midsegment Theorem to find distances. Use properties of kites. Identify quadrilaterals.

Differentiating the Lesson 7.5 Quadrilateral types

Algebra/Geometry III

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Algebra/Geometry III—Chapter 8

Lesson &

Standards

Standards Learning Goals Tasks and/or PD Videos to Support Conceptual Understanding

Khan Academy Lesson Links

MMP

0.5 days

7.RP.2a

G.SRT.1b

Determining Whether Ratios Form a Proportion

Finding a Scale Factor Intro to ratios

Dilations

8.1

1.5 days

G.CO.2

G.SRT.1a

G.SRT.1b

Identify and perform dilations. Solve real-life problems involving scale factors and dilations.

Differentiating the Lesson 8.1 Dilations

8.2

1 day

G.CO.5

G.SRT.2

Perform similarity transformations. Describe similarity transformations. Prove that figures are similar.

Differentiating the Lesson 8.2 Definitions of similarity Properties & definitions of transformations

8.3

2 days

G.SRT.2

G.MG.3

G.GMD.5 (CA)

Use similarity statements. Find corresponding lengths in similar polygons. Find perimeters and areas of similar polygons. Decide whether polygons are similar.

Differentiating the Lesson 8.3 Solving similar triangles Solving problems with similar & congruent triangles

8.4

1 day

G.SRT.3

G.SRT.5

Use the Angle-Angle Similarity Theorem. Solve real-life problems.

Differentiating the Lesson 8.4

Videos:

Exploring What is Needed to Prove Triangle Similarity

Angle-Angle Similarity *Option: incorporate lesson 9.3

Introduction to triangle similarity Solving similar triangles

8.5

1.5 days

G.SRT.4

G.SRT.5

G.GPE.5

G.MG.1

Use the Side-Side-Side Similarity Theorem. Use the Side-Angle-Side Similarity Theorem. Prove slope criteria using similar triangles.

Differentiating the Lesson 8.5 Introduction to triangle similarity Solving similar triangles

8.6

1 day

G.SRT.4

G.SRT.5

G.GPE.6

Use the Triangle Proportionality Theorem and its converse. Use other proportionality theorems.

Differentiating the Lesson 8.6 Angle bisector theorem Solving similar triangles

Algebra/Geometry III

DRAFT—Last updated 5/15/2019

Algebra/Geometry III—Chapter 9

Lesson &

Standards

Standards Learning Goals Tasks and/or PD Videos to Support Conceptual Understanding

Khan Academy Lesson Links

MMP

0.5 days

N.RN.2

7.RP.2b

Using Properties of Radicals

Solving Proportions

Simplifying square roots Writing & solving proportions

9.1

1.5 days

G.SRT.4

G.SRT.8

Use the Pythagorean Theorem. Use the Converse of the Pythagorean Theorem. Classify triangles.

Differentiating the Lesson 9.1 Video: The Pythagorean Theorem

Pythagorean theorem Pythagorean theorem proofs

9.2

1 day

G.SRT.8

G.MG.1

Find side lengths in special right triangles. Solve real-life problems involving special right triangles.

Differentiating the Lesson 9.2 Special right triangles

9.3

2 days

G.SRT.5 Identify similar triangles. Solve real-life problems involving similar triangles. Use geometric means.

Differentiating the Lesson 9.3 This lesson can be taught during 8.4 without geometric mean, as seen in the Khan video linked at the right: “same side plays different roles.”

Solving similar triangles

9.4

1.5 days

G.SRT.6

G.SRT.8

Use the tangent ratio. Solve real-life problems involving the tangent ratio.

Differentiating the Lesson 9.4 Introduction to the trigonometric ratios Solving for a side in a right triangle using the trigonometric ratios Modeling with right triangles

9.5

2 days

G.SRT.6

G.SRT.7

G.SRT.8

Use the sine and cosine ratios. Find the sine and cosine of angle measures in special right triangles. Solve real-life problems involving sine and cosine ratios.

Differentiating the Lesson 9.5 Solving for a side in a right triangle using the trigonometric ratios Modeling with right triangles

9.6

2 days

G.SRT.8

G.MG.1

G.MG.3

Use inverse trigonometric ratios. Solve right triangles.

Differentiating the Lesson 9.6 Solving for an angle in a right triangle using the trigonometric ratios Modeling with right triangles

Algebra/Geometry III

DRAFT—Last updated 5/15/2019

Algebra/Geometry III—Chapter 10

Lesson &

Standards

Standards Learning Goals Tasks and/or PD Videos to Support Conceptual Understanding

Khan Academy Lesson Links

MMP

0.5 days

A.APR.1

A.SSE.3b

Multiplying Binomials

Solving Quadratic Equations by Completing the Square

Multiplying binomials Completing the square

10.1

1.5 days

G.CO.1

G.C.2

G.C.4 (+)

Identify special segments and lines. Draw and identify common tangents. Use properties of tangents. Constructing a Tangent to a Circle. (+)

Differentiating the Lesson 10.1 Circles basics Properties of tangents Constructing a line tangent to a circle

10.2

1 day

G.C.1

G.C.2

Find arc measures. Identify congruent arcs. Prove circles are similar.

Differentiating the Lesson 10.2 Arc measure

10.3

1 day

G.C.2

G.MG.3

Use chords of circles to find lengths and arc measures.

Differentiating the Lesson 10.3 Arc measure

10.4

1.5 days

G.CO.13

G.C.2

G.C.3

Use inscribed angles. Use inscribed polygons.

Differentiating the Lesson 10.4 Inscribed angles Inscribed shapes problem solving

10.5

2 days

G.C.2 Find angle and arc measures. Use circumscribed angles.

Differentiating the Lesson 10.5 Properties of tangents

10.6

1 day

G.C.2

G.MG.1

Use segments of chords, tangents, and secants.

Differentiating the Lesson 10.6 Properties of tangents

10.7

1 day

G.GPE.1

G.GPE.4

Write and graph equations of circles. Write coordinate proofs involving circles. Solve real-life problems using graphs and circles.

Differentiating the Lesson 10.7 Standard equation of a circle Expanded equation of a circle

Algebra/Geometry III

DRAFT—Last updated 5/15/2019

Algebra/Geometry III—Chapter 11

Lesson &

Standards

Standards Learning Goals Tasks and/or PD Videos to Support Conceptual Understanding

Khan Academy Lesson Links

MMP

0.5 day

7.G.6

A.REI.3

Finding Surface Area

Finding a Missing Dimension

Surface area, Area of rectangles, Area of triangles, Perimeter

11.1

1.5 days

G.GMD.1

G.C.5

G.CO.1

Use the formula for circumference. Use arc lengths to find measures. Solve real-life problems. Measure angles in radians.

Differentiating the Lesson 11.1 Area and circumference of circles Arc length (degrees) Introduction to radians

11.2

1 day

G.GMD.1

G.MG.2

G.C.5

Use the formula for the area of a circle. Use the formula for population density. Find areas of sectors. Use areas of sectors.

Differentiating the Lesson 11.2 Video: Area of Circles

Area and circumference of circles Sectors

11.3

2 days

G.GMD.3 Find areas of rhombuses and kites. Find angle measures in regular polygons. Find areas of regular polygons.

Differentiating the Lesson 11.3 Theorems concerning quadrilateral properties Area of a regular hexagon Area of trapezoids & composite figures

11.4

1.5 days

G.GMD.1

G.GMD.2

G.GMD.3

G.GMD.5 (CA) G.MG.1

G.MG.2

G.MG.3

Find volumes of prisms and cylinders. Use the formula for density. Use volumes of prisms and cylinders.

Differentiating the Lesson 11.4 Solid geometry intro Density Volume of cones, cylinders, and spheres

11.5

2 days

G.GMD.1

G.GMD.3

G.MG.1

Find volumes of pyramids. Use volumes of pyramids.

Differentiating the Lesson 11.5 Solid geometry intro

11.6

2 days

G.GMD.1

G.GMD.3

Find surface areas of right cones. Find volumes of cones. Use volumes of cones.

Differentiating the Lesson 11.6

Video: Volume of Cones

Solid geometry intro Volume of cones, cylinders, and spheres

11.7

2 days

G.GMD.2

G.GMD.3

G.MG.1

Find surface areas of spheres. Find volumes of spheres.

Differentiating the Lesson 11.7

Solid geometry intro Volume of cones, cylinders, and spheres