Honors Algebra 2 Mathematics Pacing Guide 2016-2017

Quarter 3

Indianapolis Public Schools Curriculum and Instruction

Unit 6: Rational Exponents and Radical Functions

Week Standards

Week 1 Jan. 3-6 (4 days)

Pre-Test This week: Rational exponents and radical equations: Note that rational exponents is not the same as rational equations. AII.CNE.2: Translate expressions between radical and exponent form and simplify them using the laws of exponents.

AII.PR.3: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. PS: 1, 2, 3, 4, 5, 6, 7, and 8 +( Focus instruction using the Process Standards)

Week 2 Jan. 9-13

This week: Function operations and composition of functions. Use this material to strengthen their understanding of function notation. AII.F.2: Understand composition of functions and combine functions by composition. AII.PR.2: Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. PS: 1, 2, 3, 4, 5, 6, 7, and 8 +( Focus instruction using the Process Standards)

Week 3 Jan. 18-20 MLK Day

MLK Day

Building PD

This week: Continue with function composition and inverse functions. AII.F.3: Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x)=y and g(y)=x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. AII.F.4: Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. AII.PR.3: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. PS: 1, 2, 3, 4, 5, 6, 7, and 8 +( Focus instruction using the Process Standards)

Week 4 Jan. 23-27

Benchmark 3 Window Opens Review Unit five and six.

UNIT Six Assessment with included problems on finding the roots of polynomials from unit five.

PS: 1, 2, 3, 4, 5, 6, 7, and 8 +( Focus instruction using the Process Standards)

Unit 7: Exponential and Logarithmic Functions

Week 5 Jan. 30-Feb. 3

Benchmark 3 Window Closes This week: Introduce exponential functions. Students may not be able to visualize what happens in an exponential function. Spend at least two days introducing real-world examples and have students calculate and graph exponential curves. See the resource guide for good activities. Emphasize the difference between a power (square, cubic, etc) function and an exponential function. By the end of the week, cover exponential growth and decay, restrictions on exponential functions anf transforming exponential functions. Real-world applications of exponential functions such as (population growth, bacterial growth, spreading a rumor, radioactive decay. Thermal cooling and compound interest)

AII.EL.2: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, and asymptotic and end behavior.

Honors Algebra 2 Mathematics Pacing Guide 2016-2017

Quarter 3

Indianapolis Public Schools Curriculum and Instruction

AII.EL.3: Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (0.97)^t, y = (1.01)12^t, y = (1.2)^t/10, and classify them as representing exponential growth or decay. AII.EL.4: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression 1.15^t can be rewritten as (1.15^1/12)^12t ≈ 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). AII.EL.7: Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. AII.DSP.2: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. PS: 1, 2, 3, 4, 5, 6, 7, and 8 +( Focus instruction using the Process Standards)

Week 6 Feb. 6-10

Corrective Instruction – based on data from Benchmark 3 and other formative assessments PS: 1, 2, 3, 4, 5, 6, 7, and 8 +( Focus instruction using the Process Standards)

Week 7 Feb. 13-17

This week: Logarithms. Start with the definition of a logarithm and convert between log and exponential form. Define common logs and natural logs. Convert between log and exponent form to solve simple exponential functions. Properties of logarithms. Laws of logarithms. Change of Base. AII.EL.5: Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. AII.EL.6: Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. AII.EL.7: Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. AII.EL.3: Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (0.97)^t, y = (1.01)12^t, y = (1.2)^t/10, and classify them as representing exponential growth or decay. AII.EL.4: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression 1.15^t can be rewritten as (1.15^1/12)^12t ≈ 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). PS: 1, 2, 3, 4, 5, 6, 7, and 8 +( Focus instruction using the Process Standards)

Week 8 Feb. 21 – 24

Presidents’ Day (4 Days)

This week: Revisit real-world applications and use logarithms to solve for the exponent such as: t in compound interest and population growth, number of half-lives, time to reach a temperature. Look for activities in the resource document. AII.EL.3: Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (0.97)^t, y = (1.01)12^t, y = (1.2)^t/10, and classify them as representing exponential growth or decay. AII.EL.4: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression 1.15^t can be rewritten as (1.15^1/12)^12t ≈ 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). AII.EL.7: Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable.

Honors Algebra 2 Mathematics Pacing Guide 2016-2017

Quarter 3

Indianapolis Public Schools Curriculum and Instruction

UNIT 7 EXAM PS: 1, 2, 3, 4, 5, 6, 7, and 8 +( Focus instruction using the Process Standards)

Unit 8: Rational Functions (Complex Fractions)

Week 9 Feb. 27-March 3

ISTEP+ Part One Window Opens AII.PR.3: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. AII.CNE.3: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. PS: 1, 2, 3, 4, 5, 6, 7, and 8 +( Focus instruction using the Process Standards)

Week 10 Mar.6-10

ISTEP+ Part One Window Closes AII.PR.3: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. PS: 1, 2, 3, 4, 5, 6, 7, and 8 +( Focus instruction using the Process Standards)

Week 11 Mar. 13-17

Review Unit five, seven and eight AII.PR.3: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise.

Unit 8 Assessment- include finding the roots of a polynomial and solving exponential equations. PS: 1, 2, 3, 4, 5, 6, 7, and 8 +( Focus instruction using the Process Standards)

Process Standards for Mathematics (PS): 1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision. 7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

SPRING BREAK March 20-31

END OF QUARTER 3