Big Ideas Algebra 1 Chapters 7-9
February – April (10 weeks); 2nd Semester
Big Ideas Algebra 1 Chapters 7-9
February – April (10 weeks); 2nd Semester
Chapter Title(s):
Polynomial Equations and Factoring (Chapter 7)
Graphing Quadratic Functions (Chapter 8)
Solving Quadratic Equations (Chapter 9)
Prepared Graduates:
MP1. Make sense of problems and persevere in solving them.
MP2. Reason abstractly and quantitatively.
MP5. Use appropriate tools strategically.
MP6. Attend to precision.
MP7. Look for and make use of structure.
MP8. Look for and express regularity in repeated reasoning.
Standard(s):
2. Algebra and Functions
The highlighted evidence outcomes are the priority for all students, serving as the essential concepts and skills. It is recommended that the remaining evidence outcomes listed be addressed as time allows, representing the full breadth of the curriculum.
Students Can (Evidence Outcomes):
Big Ideas Algebra 1 Chapters 8-9 focus on the family of quadratic functions. Consult Algebra 1 Families of Functions for additional evidence outcomes that apply to quadratic functions.
HS.A-SSE.B. Seeing Structure in Expressions: Write expressions in equivalent forms to solve problems.
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.⭑ (CCSS: HS.A-SSE.B.3)
Factor a quadratic expression to reveal the zeros of the function it defines. (CCSS: HS.A-SSE.B.3.a)
Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. (CCSS: HS.A-SSE.B.3.b)
HS.A-APR.A. Arithmetic with Polynomials & Rational Expressions: Perform arithmetic operations on polynomials.
Explain that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. (CCSS: HS.A-APR.A.1)
HS.A-REI.B. Reasoning with Equations & Inequalities: Solve equations and inequalities in one variable.
Solve quadratic equations in one variable. (CCSS:HS.A-REI.B.4)
Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x − p)2 = q that has the same solutions. Derive the quadratic formula from this form. (CCSS: HS.A-REI.B.4.a)
Solve quadratic equations (e.g., for x2 = 49) by inspection, taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. (CCSS: HS.A-REI.B.4.b)
HS.F-IF.C. Interpreting Functions: Analyze functions using different representations.
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.⭑ (CCSS: HS.F-IF.C.7)
Graph quadratic functions and show intercepts, maxima, and minima. (CCSS: HS.F-IF.C.7.a)
Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. (CCSS: HS.F-IF.C.8)
Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. (CCSS: HS.F-IF.C.8.a)
HS.F-LE.A. Linear, Quadratic & Exponential Models: Construct and compare linear, quadratic, and exponential models and solve problems.⭑
Use graphs and tables to describe that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. (CCSS: HS.F-LE.A.3)
A star symbol (⭑) represents grade level expectations and evidence outcomes that make up a mathematical modeling standards category.
Additional Colorado Academic Standards Resources:
Please visit the complete 2020 Colorado Academic Standards for High School Mathematics to view the following:
Colorado Essential Skills and Mathematical Practices connections
Inquiry Questions
Coherence Connections
Prior Knowledge Connections:
Solving simple square root equations in the form x2 = p (Grade 8)
Academic Vocabulary & Language Expectations:
Monomial, polynomial, degree of a monomial, binomial, trinomial, degree of a polynomial, standard form, leading coefficient, closed, FOIL Method, factored form, Zero-Product Property, roots, repeated roots, factoring by grouping, factored completely, quadratic function, parabola, vertex, axis of symmetry, zero of a function, maximum value, minimum value, even, odd, vertex form, intercept form, average rate of change, quadratic equation, completing the square, Quadratic Formula, discriminant
Assessments:
Chapter 7 Assessment (PDF), Chapter 8 Assessment (PDF), Chapter 9 Assessment (PDF)
SAT Suite Educator Question Bank (Content Domain: Advanced Math)
Instructional Resources & Notes:
Accelerated Algebra 1:
Accelerated Algebra 1 students can extend their learning beyond the Colorado Academic Standards with the following concepts and lessons:
HS.N-RN.B. The Real Number System: Use properties of rational and irrational numbers.
(+) Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. (CCSS: HS.N-RN.A.3)
Lesson 9.1: Properties of Radicals
Lesson 10.1: Graphing Square Root Functions
Lesson 10.2: Graphing Cube Root Functions
Lesson 10.3: Solving Radical Equations