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Please read the directions carefully. This is due within 28 hours! Must use original work!

Lesson plans require careful planning. To create a meaningful and relevant learning experience for students, teachers must consider the standards and learning objectives, the needs of the students, effective methods and strategies, and appropriate assessment strategies.

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Based on your discussion and collaboration with your mentor teacher during your first field experience, incorporate mentor feedback to create a lesson plan for your content area.

For this benchmark, you will use the “COE Lesson Plan Template” to create a cross-disciplinary STEM lesson plan, aligned to your state standards.

Be specific when including the following:

· Theme and description in the Lesson Summary and Focus section

· State and NGSS standards, across content areas, that support the theme of the lesson and unit in the National/State Learning Standards section

· Strategies to develop cross-disciplinary skills, encourage inquiry, and engage students in applying the central concepts within science, technology, engineering, and math in the Multiple Means of Engagement section

· Resources, materials, and technology to guide students to access, interpret, evaluate, and apply information in science, technology, engineering, and math in the Resources, Materials, Equipment, and Technology section

With the approval of your mentor teacher, implement this lesson in Clinical Field Experience C.

In addition, write a 250-500 word reflection on the process of creating a STEM lesson plan. Include in your reflection:

· How you integrated feedback from your mentor teacher.

· Explanation of your collaboration with the librarian or media specialist (from Clinical Field Experience A).

· Who else, either at the school site or in the community, might you collaborate with in developing this lesson?

APA format is not required, but solid academic writing is expected.

This assignment uses a rubric. Review the rubric prior to beginning the assignment to become familiar with the expectations for successful completion.

You are required to submit this assignment to LopesWrite. A link to the LopesWrite technical support articles is located in Course Materials if you need assistance.

 GCU College of Education

LESSON PLAN TEMPLATE

Section 1: Lesson Preparation

Teacher Candidate Name:
Grade Level:
Date:
Unit/Subject:
Instructional Plan Title:
Lesson Summary and Focus:In 2-3 sentences, summarize the lesson, identifying the central focus based on the content and skills you are teaching.
Classroom and Student Factors/Grouping:Describe the important classroom factors (demographics and environment) and student factors (IEPs, 504s, ELLs, students with behavior concerns, gifted learners), and the effect of those factors on planning, teaching, and assessing students to facilitate learning for all students. This should be limited to 2-3 sentences and the information should inform the differentiation components of the lesson.
National/State Learning Standards:Review national and state standards to become familiar with the standards you will be working with in the classroom environment.Your goal in this section is to identify the standards that are the focus of the lesson being presented. Standards must address learning initiatives from one or more content areas, as well as align with the lesson’s learning targets/objectives and assessments.Include the standards with the performance indicators and the standard language in its entirety.
Specific Learning Target(s)/Objectives:Learning objectives are designed to identify what the teacher intends to measure in learning. These must be aligned with the standards. When creating objectives, a learner must consider the following:· Who is the audience· What action verb will be measured during instruction/assessment· What tools or conditions are being used to meet the learningWhat is being assessed in the lesson must align directly to the objective created. This should not be a summary of the lesson, but a measurable statement demonstrating what the student will be assessed on at the completion of the lesson. For instance, “understand” is not measureable, but “describe” and “identify” are.For example:Given an unlabeled map outlining the 50 states, students will accurately label all state names.
Academic LanguageIn this section, include a bulleted list of the general academic vocabulary and content-specific vocabulary you need to teach. In a few sentences, describe how you will teach students those terms in the lesson.
Resources, Materials, Equipment, and Technology:List all resources, materials, equipment, and technology you and the students will use during the lesson. As required by your instructor, add or attach copies of ALL printed and online materials at the end of this template. Include links needed for online resources.

Section 2: Instructional Planning

Anticipatory SetYour goal in this section is to open the lesson by activating students’ prior knowledge, linking previous learning with what they will be learning in this lesson and gaining student interest for the lesson. Consider various learning preferences (movement, music, visuals) as a tool to engage interest and motivate learners for the lesson.In a bulleted list, describe the materials and activities you will use to open the lesson. Bold any materials you will need to prepare for the lesson.For example:· I will use a visual of the planet Earth and ask students to describe what Earth looks like.· I will record their ideas on the white board and ask more questions about the amount of water they think is on planet Earth and where the water is located.Time Needed
Multiple Means of RepresentationLearners perceive and comprehend information differently. Your goal in this section is to explain how you would present content in various ways to meet the needs of different learners. For example, you may present the material using guided notes, graphic organizers, video or other visual media, annotation tools, anchor charts, hands-on manipulatives, adaptive technologies, etc.In a bulleted list, describe the materials you will use to differentiate instruction and how you will use these materials throughout the lesson to support learning. Bold any materials you will need to prepare for the lesson.For example:· I will use a Venn diagram graphic organizer to teach students how to compare and contrast the two main characters in the read-aloud story.· I will model one example on the white board before allowing students to work on the Venn diagram graphic organizer with their elbow partner.Explain how you will differentiate materials for each of the following groups:· English language learners (ELL):· Students with special needs:· Students with gifted abilities:· Early finishers (those students who finish early and may need additional resources/support):Time Needed
Multiple Means of EngagementYour goal for this section is to outline how you will engage students in interacting with the content and academic language. How will students explore, practice, and apply the content? For example, you may engage students through collaborative group work, Kagan cooperative learning structures, hands-on activities, structured discussions, reading and writing activities, experiments, problem solving, etc.In a bulleted list, describe the activities you will engage students in to allow them to explore, practice, and apply the content and academic language. Bold any activities you will use in the lesson. Also, include formative questioning strategies and higher order thinking questions you might pose.For example:· I will use a matching card activity where students will need to find a partner with a card that has an answer that matches their number sentence.· I will model one example of solving a number sentence on the white board before having students search for the matching card.· I will then have the partner who has the number sentence explain to their partner how they got the answer.Explain how you will differentiate activities for each of the following groups:· English language learners (ELL):· Students with special needs:· Students with gifted abilities:· Early finishers (those students who finish early and may need additional resources/support):Time Needed
Multiple Means of ExpressionLearners differ in the ways they navigate a learning environment and express what they know. Your goal in this section is to explain the various ways in which your students will demonstrate what they have learned. Explain how you will provide alternative means for response, selection, and composition to accommodate all learners. Will you tier any of these products? Will you offer students choices to demonstrate mastery? This section is essentially differentiated assessment.In a bulleted list, explain the options you will provide for your students to express their knowledge about the topic. For example, students may demonstrate their knowledge in more summative ways through a short answer or multiple-choice test, multimedia presentation, video, speech to text, website, written sentence, paragraph, essay, poster, portfolio, hands-on project, experiment, reflection, blog post, or skit. Bold the names of any summative assessments.Students may also demonstrate their knowledge in ways that are more formative. For example, students may take part in thumbs up-thumbs middle-thumbs down, a short essay or drawing, an entrance slip or exit ticket, mini-whiteboard answers, fist to five, electronic quiz games, running records, four corners, or hand raising.Underline the names of any formative assessments.For example:Students will complete a one-paragraph reflection on the in-class simulation they experienced. They will be expected to write the reflection using complete sentences, proper capitalization and punctuation, and utilize an example from the simulation to demonstrate their understanding. Students will also take part in formative assessments throughout the lesson, such as thumbs up-thumbs middle-thumbs down and pair-share discussions, where you will determine if you need to re-teach or re-direct learning.Explain how you will differentiate assessments for each of the following groups:· English language learners (ELL):· Students with special needs:· Students with gifted abilities:· Early finishers (those students who finish early and may need additional resources/support):Time Needed
Extension Activity and/or HomeworkIdentify and describe any extension activities or homework tasks as appropriate. Explain how the extension activity or homework assignment supports the learning targets/objectives. As required by your instructor, attach any copies of homework at the end of this template.Time Needed

© 2019. Grand Canyon University. All Rights Reserved.

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

GRADE: 912 Domain: NUMBER & QUANTITY: THE REAL NUMBER SYSTEM Cluster 1: Extend the properties of exponents to rational exponents.

Algebra 2 – Major Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.N-RN.1.1 Explain how the definition of the meaning of rational exponents follows from extending

the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define to be the cube root of 5

because we want = to hold, so must equal 5. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.N-RN.1.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. Cognitive Complexity: Level 1: Recall

Cluster 2: Use properties of rational and irrational numbers.

Algebra 1 – Additional Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.N-RN.2.3 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. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Domain: NUMBER & QUANTITY: QUANTITIES Cluster 1: Reason quantitatively and use units to solve problems.

Algebra 1 – Supporting Cluster Algebra 2 – Supporting Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

STANDARD CODE STANDARD MAFS.912.N-Q.1.1 Use units as a way to understand problems and to guide the solution of multi-step

problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.N-Q.1.2 Define appropriate quantities for the purpose of descriptive modeling. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.N-Q.1.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Domain: NUMBER & QUANTITY: THE COMPLEX NUMBER SYSTEM Cluster 1: Perform arithmetic operations with complex numbers.

Algebra 2 – Additional Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.N-CN.1.1 Know there is a complex number i such that i² = –1, and every complex number has the

form a + bi with a and b real. Cognitive Complexity: Level 1: Recall

MAFS.912.N-CN.1.2 Use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Cognitive Complexity: Level 1: Recall

MAFS.912.N-CN.1.3 Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. Cognitive Complexity: Level 1: Recall

Cluster 2: Represent complex numbers and their operations on the complex plane.

STANDARD CODE STANDARD MAFS.912.N-CN.2.4 Represent complex numbers on the complex plane in rectangular and polar form

(including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.N-CN.2.5 Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (–1 + √3 i)³ = 8 because (–1 + √3 i) has modulus 2 and

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

argument 120°. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.N-CN.2.6 Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints. Cognitive Complexity: Level 1: Recall

Cluster 3: Use complex numbers in polynomial identities and equations.

Algebra 2 – Additional Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.N-CN.3.7 Solve quadratic equations with real coefficients that have complex solutions.

Cognitive Complexity: Level 1: Recall

MAFS.912.N-CN.3.8 Extend polynomial identities to the complex numbers. For example, rewrite x² + 4 as (x + 2i)(x – 2i). Cognitive Complexity: Level 1: Recall

MAFS.912.N-CN.3.9 Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. Cognitive Complexity: Level 1: Recall

Domain: NUMBER & QUANTITY: VECTOR & MATRIX QUANTITIES Cluster 1: Represent and model with vector quantities.

STANDARD CODE STANDARD MAFS.912.N-VM.1.1 Recognize vector quantities as having both magnitude and direction. Represent vector

quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v). Cognitive Complexity: Level 1: Recall

MAFS.912.N-VM.1.2 Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. Cognitive Complexity: Level 1: Recall

MAFS.912.N-VM.1.3 Solve problems involving velocity and other quantities that can be represented by vectors. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 2: Perform operations on vectors.

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

STANDARD CODE STANDARD MAFS.912.N-VM.2.4 Add and subtract vectors.

a. Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.

b. Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

c. Understand vector subtraction v – w as v + (–w), where –w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.N-VM.2.5 Multiply a vector by a scalar.

a. Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as

c = . b. Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the

direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).

Cognitive Complexity: Level 1: Recall

Cluster 3: Perform operations on matrices and use matrices in applications.

STANDARD CODE STANDARD MAFS.912.N-VM.3.10 Understand that the zero and identity matrices play a role in matrix addition and

multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.N-VM.3.11 Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.N-VM.3.12 Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.N-VM.3.6 Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.N-VM.3.7 Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

a game are doubled. Cognitive Complexity: Level 1: Recall

MAFS.912.N-VM.3.8 Add, subtract, and multiply matrices of appropriate dimensions. Cognitive Complexity: Level 1: Recall

MAFS.912.N-VM.3.9 Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Domain: ALGEBRA: SEEING STRUCTURE IN EXPRESSIONS Cluster 1: Interpret the structure of expressions

Algebra 1 – Major Cluster Algebra 2 – Major Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.A-SSE.1.1 Interpret expressions that represent a quantity in terms of its context.

a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a

single entity. For example, interpret as the product of P and a factor not depending on P.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.A-SSE.1.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4- y4 as (x²)² – (y²)², thus recognizing it as a difference of squares that can be factored as (x² – y²)(x² + y²). Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 2: Write expressions in equivalent forms to solve problems

Algebra 1 – Supporting Cluster Algebra 2 – Major Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.A-SSE.2.3 Choose and produce an equivalent form of an expression to reveal and explain

properties of the quantity represented by the expression.

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

a. Factor a quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression to reveal the maximum or

minimum value of the function it defines. c. Use the properties of exponents to transform expressions for exponential

functions. For example the expression can be rewritten as ≈ to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.A-SSE.2.4 Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

Domain: ALGEBRA: ARITHMETIC WITH POLYNOMIALS & RATIONAL EXPRESSIONS Cluster 1: Perform arithmetic operations on polynomials

Algebra 1 – Major Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.A-APR.1.1 Understand 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. Cognitive Complexity: Level 1: Recall

Cluster 2: Understand the relationship between zeros and factors of polynomials

Algebra 1 – Supporting Cluster Algebra 2 – Major Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.A-APR.2.2 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the

remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x). Cognitive Complexity: Level 1: Recall

MAFS.912.A-APR.2.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

Cognitive Complexity: Level 1: Recall

Cluster 3: Use polynomial identities to solve problems

Algebra 2 – Additional Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.A-APR.3.4 Prove polynomial identities and use them to describe numerical relationships. For

example, the polynomial identity (x² + y²)² = (x² – y²)² + (2xy)² can be used to generate Pythagorean triples. Cognitive Complexity: Level 1: Recall

MAFS.912.A-APR.3.5 Know and apply the Binomial Theorem for the expansion of (x in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 4: Rewrite rational expressions

Algebra 2 – Supporting Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.A-APR.4.6 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) +

r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.A-APR.4.7 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 rational expressions. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Domain: ALGEBRA: CREATING EQUATIONS Cluster 1: Create equations that describe numbers or relationships

Algebra 1 – Major Cluster Algebra 2 – Supporting Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.A-CED.1.1 Create equations and inequalities in one variable and use them to solve

problems. Include equations arising from linear and quadratic functions, and simple rational, absolute, and exponential functions.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts MAFS.912.A-CED.1.2 Create equations in two or more variables to represent relationships between quantities;

graph equations on coordinate axes with labels and scales. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.A-CED.1.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.A-CED.1.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R. Cognitive Complexity: Level 1: Recall

Domain: ALGEBRA: REASONING WITH EQUATIONS & INEQUALITIES Cluster 1: Understand solving equations as a process of reasoning and explain the reasoning

Algebra 1 – Major Cluster Algebra 2 – Major Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.A-REI.1.1 Explain each step in solving a simple equation as following from the equality of numbers

asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.A-REI.1.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

Cluster 2: Solve equations and inequalities in one variable

Algebra 1 – Major Cluster Algebra 2 – Supporting Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

STANDARD CODE STANDARD MAFS.912.A-REI.2.3 Solve linear equations and inequalities in one variable, including equations with

coefficients represented by letters.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.A-REI.2.4 Solve quadratic equations in one variable.

a. 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.

b. Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 3: Solve systems of equations

Algebra 1 – Additional Cluster Algebra 2 – Additional Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.A-REI.3.5 Prove that, given a system of two equations in two variables, replacing one equation by

the sum of that equation and a multiple of the other produces a system with the same solutions. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.A-REI.3.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Cognitive Complexity: Level 1: Recall

MAFS.912.A-REI.3.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x² + y² = 3. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.A-REI.3.8 Represent a system of linear equations as a single matrix equation in a vector variable. Cognitive Complexity: Level 1: Recall

MAFS.912.A-REI.3.9 Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater). Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

Cluster 4: Represent and solve equations and inequalities graphically

Algebra 1 – Major Cluster Algebra 2 – Major Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.A-REI.4.10 Understand that the graph of an equation in two variables is the set of all its solutions

plotted in the coordinate plane, often forming a curve (which could be a line). Cognitive Complexity: Level 1: Recall

MAFS.912.A-REI.4.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.A-REI.4.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Domain: FUNCTIONS: INTERPRETING FUNCTIONS Cluster 1: Understand the concept of a function and use function notation

Algebra 1 – Major Cluster Algebra 2 – Supporting Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.F-IF.1.1 Understand that a function from one set (called the domain) to another set (called the

range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). Cognitive Complexity: Level 1: Recall

MAFS.912.F-IF.1.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.F-IF.1.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 2: Interpret functions that arise in applications in terms of the context

Algebra 1 – Major Cluster Algebra 2 – Major Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.F-IF.2.4 For a function that models a relationship between two quantities, interpret key features

of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.F-IF.2.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person- hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.F-IF.2.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 3: Analyze functions using different representations

Algebra 1 – Supporting Cluster Algebra 2 – Supporting Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.F-IF.3.7 Graph functions expressed symbolically and show key features of the graph, by

hand in simple cases and using technology for more complicated cases.

a. Graph linear and quadratic functions and show intercepts, maxima, and minima.

b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

d. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

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e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude, and using phase shift.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts MAFS.912.F-IF.3.8 Write a function defined by an expression in different but equivalent forms to reveal and

explain different properties of the function.

a. 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.

b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y =

, y = , y = , y = , and classify them as representing exponential growth or decay.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.F-IF.3.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Domain: FUNCTIONS: BUILDING FUNCTIONS Cluster 1: Build a function that models a relationship between two quantities

Algebra 1 – Supporting Cluster Algebra 2 – Major Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.F-BF.1.1 Write a function that describes a relationship between two quantities.

a. Determine an explicit expression, a recursive process, or steps for calculation from a context.

b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.

c. Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.F-BF.1.2 Write arithmetic and geometric sequences both recursively and with an explicit formula,

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

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use them to model situations, and translate between the two forms. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 2: Build new functions from existing functions

Algebra 1 – Additional Cluster Algebra 2 – Additional Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.F-BF.2.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for

specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.F-BF.2.4 Find inverse functions.

a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x³ or f(x) = (x+1)/(x–1) for x ≠ 1.

b. Verify by composition that one function is the inverse of another. c. Read values of an inverse function from a graph or a table, given that the

function has an inverse. d. Produce an invertible function from a non-invertible function by restricting the

domain.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts MAFS.912.F-BF.2.5 Understand the inverse relationship between exponents and logarithms and use this

relationship to solve problems involving logarithms and exponents. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.F-BF.2.a Use the change of base formula. Domain: FUNCTIONS: LINEAR, QUADRATIC, & EXPONENTIAL MODELS Cluster 1: Construct and compare linear, quadratic, and exponential models and solve problems

Algebra 1 – Supporting Cluster Algebra 2 – Supporting Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.F-LE.1.1 Distinguish between situations that can be modeled with linear functions and with

exponential functions.

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

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a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning MAFS.912.F-LE.1.2 Construct linear and exponential functions, including arithmetic and geometric

sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.F-LE.1.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.F-LE.1.4 For exponential models, express as a logarithm the solution to = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 2: Interpret expressions for functions in terms of the situation they model

Algebra 1 – Supporting Cluster Algebra 2 – Additional Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.F-LE.2.5 Interpret the parameters in a linear or exponential function in terms of a context.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Domain: FUNCTIONS: TRIGONOMETRIC FUNCTIONS Cluster 1: Extend the domain of trigonometric functions using the unit circle

Algebra 2 – Additional Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.F-TF.1.1 Understand radian measure of an angle as the length of the arc on the unit circle

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

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subtended by the angle; Convert between degrees and radians.

Cognitive Complexity: Level 1: Recall MAFS.912.F-TF.1.2 Explain how the unit circle in the coordinate plane enables the extension of

trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.F-TF.1.3 Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π–x, π+x, and 2π–x in terms of their values for x, where x is any real number. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.F-TF.1.4 Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 2: Model periodic phenomena with trigonometric functions

Algebra 2 – Additional Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.F-TF.2.5 Choose trigonometric functions to model periodic phenomena with specified amplitude,

frequency, and midline. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.F-TF.2.6 Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.F-TF.2.7 Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 3: Prove and apply trigonometric identities

Algebra 2 – Additional Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.F-TF.3.8 Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1 and use it to calculate trigonometric

ratios. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.F-TF.3.9 Prove the addition and subtraction, half-angle, and double-angle formulas for

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

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sine, cosine, and tangent and use these formulas to solve problems.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning Domain: GEOMETRY: CONGRUENCE Cluster 1: Experiment with transformations in the plane

Geometry – Supporting Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.G-CO.1.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line

segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. Cognitive Complexity: Level 1: Recall

MAFS.912.G-CO.1.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.G-CO.1.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.G-CO.1.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.G-CO.1.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 2: Understand congruence in terms of rigid motions

Geometry – Major Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.G-CO.2.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect

of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.G-CO.2.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

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are congruent. Cognitive Complexity: Level 1: Recall

MAFS.912.G-CO.2.8 Explain how the criteria for triangle congruence (ASA, SAS, SSS, and Hypotenuse-Leg) follow from the definition of congruence in terms of rigid motions.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts Cluster 3: Prove geometric theorems

Geometry – Major Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.G-CO.3.9 Prove theorems about lines and angles; use theorems about lines and angles to

solve problems. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning MAFS.912.G-CO.3.10 Prove theorems about triangles; use theorems about triangles to solve problems.

Theorems include: measures of interior angles of a triangle sum to 180°; triangle inequality theorem; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning MAFS.912.G-CO.3.11 Prove theorems about parallelograms; use theorems about parallelograms to

solve problems. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning Cluster 4: Make geometric constructions

Geometry – Supporting Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.G-CO.4.12 Make formal geometric constructions with a variety of tools and methods (compass and

straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

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Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.G-CO.4.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Domain: GEOMETRY: SIMILARITY, RIGHT TRIANGLES, & TRIGONOMETRY Cluster 1: Understand similarity in terms of similarity transformations

Geometry – Major Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.G-SRT.1.1 Verify experimentally the properties of dilations given by a center and a scale factor:

a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.

b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts MAFS.912.G-SRT.1.2 Given two figures, use the definition of similarity in terms of similarity transformations to

decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.G-SRT.1.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 2: Prove theorems involving similarity

Geometry – Major Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.G-SRT.2.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a

triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.G-SRT.2.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

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Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

Cluster 3: Define trigonometric ratios and solve problems involving right triangles

Geometry – Major Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.G-SRT.3.6 Understand that by similarity, side ratios in right triangles are properties of the angles in

the triangle, leading to definitions of trigonometric ratios for acute angles. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.G-SRT.3.7 Explain and use the relationship between the sine and cosine of complementary angles. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.G-SRT.3.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 4: Apply trigonometry to general triangles

STANDARD CODE STANDARD MAFS.912.G-SRT.4.10 Prove the Laws of Sines and Cosines and use them to solve problems.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.G-SRT.4.11 Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.G-SRT.4.9 Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Domain: GEOMETRY: CIRCLES Cluster 1: Understand and apply theorems about circles

Geometry – Additional Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

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MAFS.912.G-C.1.1 Prove that all circles are similar. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.G-C.1.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.G-C.1.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.G-C.1.4 Construct a tangent line from a point outside a given circle to the circle. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 2: Find arc lengths and areas of sectors of circles

Geometry – Additional Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.G-C.2.5 Derive using similarity the fact that the length of the arc intercepted by an angle is

proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

Domain: GEOMETRY: EXPRESSING GEOMETRIC PROPERTIES WITH EQUATIONS Cluster 1: Translate between the geometric description and the equation for a conic section

Geometry – Additional Cluster Algebra 2 – Additional Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.G-GPE.1.1 Derive the equation of a circle of given center and radius using the Pythagorean

Theorem; complete the square to find the center and radius of a circle given by an equation. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.G-GPE.1.2 Derive the equation of a parabola given a focus and directrix. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.G-GPE.1.3 Derive the equations of ellipses and hyperbolas given the foci and directrices.

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

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Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning Cluster 2: Use coordinates to prove simple geometric theorems algebraically

Geometry – Major Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.G-GPE.2.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove

or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2). Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.G-GPE.2.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.G-GPE.2.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio. Cognitive Complexity: Level 1: Recall

MAFS.912.G-GPE.2.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. Cognitive Complexity: Level 1: Recall

Domain: GEOMETRY: GEOMETRIC MEASUREMENT & DIMENSION Cluster 1: Explain volume formulas and use them to solve problems

Geometry – Additional Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.G-GMD.1.1 Give an informal argument for the formulas for the circumference of a circle, area of a

circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.G-GMD.1.2 Give an informal argument using Cavalieri’s principle for the formulas for the volume of

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

a sphere and other solid figures. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.G-GMD.1.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 2: Visualize relationships between two-dimensional and three-dimensional objects

Geometry – Additional Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.G-GMD.2.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and

identify three-dimensional objects generated by rotations of two-dimensional objects. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Domain: GEOMETRY: MODELING WITH GEOMETRY Cluster 1: Apply geometric concepts in modeling situations

Geometry – Major Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.G-MG.1.1 Use geometric shapes, their measures, and their properties to describe objects (e.g.,

modeling a tree trunk or a human torso as a cylinder). Cognitive Complexity: Level 1: Recall

MAFS.912.G-MG.1.2 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.G-MG.1.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios) Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

Domain: STATISTICS & PROBABILITY: INTERPRETING CATEGORICAL & QUANTITATIVE DATA Cluster 1: Summarize, represent, and interpret data on a single count or measurement variable

Algebra 1 – Additional Cluster Algebra 2 – Additional Cluster

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.S-ID.1.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-ID.1.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-ID.1.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-ID.1.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 2: Summarize, represent, and interpret data on two categorical and quantitative variables

Algebra 1 – Supporting Cluster Algebra 2 – Supporting Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.S-ID.2.5 Summarize categorical data for two categories in two-way frequency tables. Interpret

relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-ID.2.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, and exponential models.

b. Informally assess the fit of a function by plotting and analyzing residuals. c. Fit a linear function for a scatter plot that suggests a linear association.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts Cluster 3: Interpret linear models

Algebra 1 – Major Cluster

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

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Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.S-ID.3.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in

the context of the data. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-ID.3.8 Compute (using technology) and interpret the correlation coefficient of a linear fit. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-ID.3.9 Distinguish between correlation and causation. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Domain: STATISTICS & PROBABILITY: MAKING INFERENCES & JUSTIFYING CONCLUSIONS Cluster 1: Understand and evaluate random processes underlying statistical experiments

Algebra 2 – Supporting Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.S-IC.1.1 Understand statistics as a process for making inferences about population parameters

based on a random sample from that population. Cognitive Complexity: Level 1: Recall

MAFS.912.S-IC.1.2 Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model? Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 2: Make inferences and justify conclusions from sample surveys, experiments, and observational studies

Algebra 2 – Major Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.S-IC.2.3 Recognize the purposes of and differences among sample surveys, experiments, and

observational studies; explain how randomization relates to each. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-IC.2.4 Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

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MAFS.912.S-IC.2.5 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-IC.2.6 Evaluate reports based on data. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Domain: STATISTICS & PROBABILITY: CONDITIONAL PROBABILITY & THE RULES OF PROBABILITY Cluster 1: Understand independence and conditional probability and use them to interpret data

Algebra 2 – Additional Cluster Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.S-CP.1.1 Describe events as subsets of a sample space (the set of outcomes) using

characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). Cognitive Complexity: Level 1: Recall

MAFS.912.S-CP.1.2 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. Cognitive Complexity: Level 1: Recall

MAFS.912.S-CP.1.3 Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-CP.1.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-CP.1.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 2: Use the rules of probability to compute probabilities of compound events in a uniform probability model

Algebra 2 – Additional Cluster

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

STANDARD CODE STANDARD MAFS.912.S-CP.2.6 Find the conditional probability of A given B as the fraction of B’s outcomes that also

belong to A, and interpret the answer in terms of the model. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-CP.2.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-CP.2.8 Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-CP.2.9 Use permutations and combinations to compute probabilities of compound events and solve problems. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Domain: STATISTICS & PROBABILITY: USING PROBABILITY TO MAKE DECISIONS Cluster 1: Calculate expected values and use them to solve problems

STANDARD CODE STANDARD MAFS.912.S-MD.1.1 Define a random variable for a quantity of interest by assigning a numerical value to

each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-MD.1.2 Calculate the expected value of a random variable; interpret it as the mean of the probability distribution. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-MD.1.3 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-MD.1.4 Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households? Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 2: Use probability to evaluate outcomes of decisions

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

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STANDARD CODE STANDARD MAFS.912.S-MD.2.5 Weigh the possible outcomes of a decision by assigning probabilities to payoff values

and finding expected values.

a. Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fast-food restaurant.

b. Evaluate and compare strategies on the basis of expected values. For example, compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-MD.2.6 Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-MD.2.7 Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

GRADE: K12 Domain: MATHEMATICAL PRACTICE Cluster 1: Make sense of problems and persevere in solving them.

STANDARD CODE STANDARD MAFS.K12.MP.1.1 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.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

Cluster 2: Reason abstractly and quantitatively.

STANDARD CODE STANDARD MAFS.K12.MP.2.1 Reason abstractly and quantitatively.

Mathematically proficient students make sense of quantities and their relationships in problem situations. They 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.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

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

STANDARD CODE STANDARD MAFS.K12.MP.3.1 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, 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.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

Cluster 4: Model with mathematics.

STANDARD CODE STANDARD MAFS.K12.MP.4.1 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, two-way 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.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

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Cluster 5: Use appropriate tools strategically.

STANDARD CODE STANDARD MAFS.K12.MP.5.1 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, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a 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 analyze 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.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 6: Attend to precision.

STANDARD CODE STANDARD MAFS.K12.MP.6.1 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, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, 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.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

Cluster 7: Look for and make use of structure.

STANDARD CODE STANDARD

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

MAFS.K12.MP.7.1 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 being 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.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 8: Look for and express regularity in repeated reasoning.

STANDARD CODE STANDARD MAFS.K12.MP.8.1 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.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

GRADE: 912 – CALCULUS Standard 1: Limits and Continuity

Develop an understanding of the concept of limit by estimating limits graphically and numerically and evaluating limits analytically. Extend the idea of a limit to one-sided limits and limits at infinity. Use limits to define and understand the concept of continuity, decide whether a function

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

is continuous at a point, and find types of discontinuities. Understand and apply continuity theorems.

BENCHMARK CODE BENCHMARK MAFS.912.C.1.1 Understand the concept of limit and estimate limits from graphs and tables of

values. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.1.10 Decide if a function is continuous at a point. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.C.1.11 Find the types of discontinuities of a function. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.1.12 Understand and use the Intermediate Value Theorem on a function over a closed interval. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.1.13 Understand and apply the Extreme Value Theorem: If f(x) is continuous over a closed interval, then f has a maximum and a minimum on the interval. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.1.2 Find limits by substitution. Cognitive Complexity: Level 1: Recall

MAFS.912.C.1.3 Find limits of sums, differences, products, and quotients. Cognitive Complexity: Level 1: Recall

MAFS.912.C.1.4 Find limits of rational functions that are undefined at a point. Cognitive Complexity: Level 1: Recall

MAFS.912.C.1.5 Find one-sided limits. Cognitive Complexity: Level 1: Recall

MAFS.912.C.1.6 Find limits at infinity. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.1.7 Decide when a limit is infinite and use limits involving infinity to describe asymptotic behavior. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.1.8 Find special limits such as Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.1.9 Understand continuity in terms of limits. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

Standard 2: Differential Calculus

Develop an understanding of the derivative as an instantaneous rate of change, using geometrical, numerical, and analytical methods. Use this definition to find derivatives of algebraic and transcendental functions and combinations of these functions (using, for example, sums, composites, and inverses). Find second and higher order derivatives. Understand and use the relationship between differentiability and continuity. Understand and apply the Mean

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

Value Theorem. Find derivatives of algebraic, trigonometric, logarithmic, and exponential functions. Find derivatives of sums, products, and quotients, and composite and inverse functions. Find derivatives of higher order, and use logarithmic differentiation and the Mean Value Theorem.

BENCHMARK CODE BENCHMARK MAFS.912.C.2.1 Understand the concept of derivative geometrically, numerically, and analytically,

and interpret the derivative as an instantaneous rate of change or as the slope of the tangent line. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.C.2.10 Understand and use the relationship between differentiability and continuity. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.2.11 Understand and apply the Mean Value Theorem. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.2.2 State, understand, and apply the definition of derivative. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.2.3 Find the derivatives of functions, including algebraic, trigonometric, logarithmic, and exponential functions. Cognitive Complexity: Level 1: Recall

MAFS.912.C.2.4 Find the derivatives of sums, products, and quotients. Cognitive Complexity: Level 1: Recall

MAFS.912.C.2.5 Find the derivatives of composite functions using the Chain Rule. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.2.6 Find the derivatives of implicitly-defined functions. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.2.7 Find derivatives of inverse functions. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.2.8 Find second derivatives and derivatives of higher order. Cognitive Complexity: Level 1: Recall

MAFS.912.C.2.9 Find derivatives using logarithmic differentiation. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Standard 3: Applications of Derivatives

Apply knowledge about derivatives to find slopes of curves and the related tangent lines. Analyze and graph functions, finding where they are increasing or decreasing, their maximum and minimum points, their points of inflection, and their concavity. Solve optimization problems, find average and instantaneous rates of change (including velocities and accelerations), and model rates of change. Find slopes and equations of tangent lines, maximum and minimum points, and points of inflection. Solve optimization problems, and find rates of change.

BENCHMARK CODE BENCHMARK MAFS.912.C.3.1 Find the slope of a curve at a point, including points at which there are vertical

tangent lines and no tangent lines. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

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MAFS.912.C.3.10 Find the velocity and acceleration of a particle moving in a straight line. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.3.11 Model rates of change, including related rates problems. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.C.3.12 Solve problems using the Newton-Raphson method. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.C.3.2 Find an equation for the tangent line to a curve at a point and a local linear approximation. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.3.3 Decide where functions are decreasing and increasing. Understand the relationship between the increasing and decreasing behavior of f and the sign of f’. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.3.4 Find local and absolute maximum and minimum points. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.3.5 Find points of inflection of functions. Understand the relationship between the concavity of f and the sign of f”. Understand points of inflection as places where concavity changes. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.3.6 Use first and second derivatives to help sketch graphs. Compare the corresponding characteristics of the graphs of f, f’, and f”. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.C.3.7 Use implicit differentiation to find the derivative of an inverse function. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.3.8 Solve optimization problems. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.3.9 Find average and instantaneous rates of change. Understand the instantaneous rate of change as the limit of the average rate of change. Interpret a derivative as a rate of change in applications, including velocity, speed, and acceleration. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Standard 4: Integral Calculus

Understand that integration is used to find areas, and evaluate integrals using rectangular approximations. From this, develop the idea that integration is the inverse operation to differentiation — the Fundamental Theorem of Calculus. Use this result to find definite and indefinite integrals, including using the method of integration by substitution. Apply approximate methods, such as the Trapezoidal Rule, to find definite integrals. Define integrals using Riemann sums, use the Fundamental Theorem of Calculus to find integrals using antiderivatives, and use basic properties of integrals. Integrate by substitution, and find approximate integrals.

BENCHMARK CODE BENCHMARK MAFS.912.C.4.1 Use rectangle approximations to find approximate values of integrals.

Cognitive Complexity: Level 1: Recall

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

MAFS.912.C.4.2 Calculate the values of Riemann Sums over equal subdivisions using left, right, and midpoint evaluation points. Cognitive Complexity: Level 1: Recall

MAFS.912.C.4.3 Interpret a definite integral as a limit of Riemann sums. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.4.4 Interpret a definite integral of the rate of change of a quantity over an interval as

the change of the quantity over the interval. That is, f'(x)dx = f(b) – f(a) (Fundamental Theorem of Calculus). Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.C.4.5 Use the Fundamental Theorem of Calculus to evaluate definite and indefinite integrals and to represent particular antiderivatives. Perform analytical and graphical analysis of functions so defined. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.4.6 Use these properties of definite integrals:

• [f(x) + g(x)]dx = f(x)dx + g(x)dx

• k • f(x)dx = k f(x)dx

• f(x)dx = 0

• f(x)dx = – f(x)dx

• f(x)dx + f(x)dx = f(x)dx

• If f(x) ≤ g(x) on [a, b], then f(x)dx ≤ g(x)dx

Cognitive Complexity: Level 1: Recall

MAFS.912.C.4.7 Use integration by substitution (or change of variable) to find values of integrals. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.4.8 Use Riemann Sums, the Trapezoidal Rule, and technology to approximate definite integrals of functions represented algebraically, geometrically, and by tables of values. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Standard 5: Applications of Integration

Apply knowledge about integrals to finding velocities from accelerations, solving separable differential equations, and finding areas and volumes. Apply integration to model, and solve problems in physics, biology, economics, etc. Find velocity functions and position functions from their derivatives, solve separable differential equations, and use definite integrals to find areas and volumes.

BENCHMARK CODE BENCHMARK MAFS.912.C.5.1 Find specific antiderivatives using initial conditions, including finding velocity

functions from acceleration functions, finding position functions from velocity

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

functions, and solving applications related to motion along a line. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.5.2 Solve separable differential equations, and use them in modeling. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.5.3 Solve differential equations of the form as applied to growth and decay problems. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.5.4 Use slope fields to display a graphic representation of the solution to a differential equation, and locate particular solutions to the equation. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.5.5 Use definite integrals to find the area between a curve and the x-axis or between two curves. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.5.6 Use definite integrals to find the average value of a function over a closed interval. Cognitive Complexity: Level 1: Recall

MAFS.912.C.5.7 Use definite integrals to find the volume of a solid with known cross-sectional area, including solids of revolution. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.C.5.8 Apply integration to model, and solve problems in physical, biological, and social sciences. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

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