## Course Standards

## General Course Information and Notes

### Version Description

In Algebra 2 Honors, instructional time will emphasize six areas: (1) developing understanding of the complex number system, including complex numbers as roots of polynomial equations; (2) extending arithmetic operations with algebraic expressions to include polynomial division, radical and rational expressions; (3) graphing and analyzing functions including polynomials, absolute value, radical, rational, exponential and logarithmic; (4) extending systems of equations and inequalities to include non-linear expressions; (5)building functions using compositions, inverses and transformations and (6) developing understanding of probability concepts.

*All clarifications stated, whether general or specific to Algebra 2 Honors, are expectations for instruction of that benchmark.*

Curricular content for all subjects must integrate critical-thinking, problem-solving, and workforce-literacy skills; communication, reading, and writing skills; mathematics skills; collaboration skills; contextual and applied-learning skills; technology-literacy skills; information and media-literacy skills; and civic-engagement skills.

### General Notes

**Honors and Accelerated Level Course Note: **Accelerated courses require a greater demand on students through increased academic rigor. Academic rigor is obtained through the application, analysis, evaluation, and creation of complex ideas that are often abstract and multi-faceted. Students are challenged to think and collaborate critically on the content they are learning. Honors level rigor will be achieved by increasing text complexity through text selection, focus on high-level qualitative measures, and complexity of task. Instruction will be structured to give students a deeper understanding of conceptual themes and organization within and across disciplines. Academic rigor is more than simply assigning to students a greater quantity of work.

**Florida’s Benchmarks for Excellent Student Thinking (B.E.S.T.) Standards**This course includes Florida’s B.E.S.T. ELA Expectations (EE) and Mathematical Thinking and Reasoning Standards (MTRs) for students. Florida educators should intentionally embed these standards within the content and their instruction as applicable. For guidance on the implementation of the EEs and MTRs, please visit https://www.cpalms.org/Standards/BEST_Standards.aspx and select the appropriate B.E.S.T. Standards package.

**English Language Development ELD Standards Special Notes Section:**

Teachers are required to provide listening, speaking, reading and writing instruction that allows English language learners (ELL) to communicate information, ideas and concepts for academic success in the content area of Mathematics. For the given level of English language proficiency and with visual, graphic, or interactive support, students will interact with grade level words, expressions, sentences and discourse to process or produce language necessary for academic success. The ELD standard should specify a relevant content area concept or topic of study chosen by curriculum developers and teachers which maximizes an ELL’s need for communication and social skills. To access an ELL supporting document which delineates performance definitions and descriptors, please click on the following link: http://www.cpalms.org/uploads/docs/standards/eld/MA.pdf

### General Information

**Course Number:**1200340

**Course Path:**

**Abbreviated Title:**ALG 2 H

**Number of Credits:**One (1) credit

**Course Length:**Year (Y)

**Course Attributes:**

- Honors
- Class Size Core Required

**Course Type:**Core Academic Course

**Course Level:**3

**Course Status:**State Board Approved

**Grade Level(s):**9,10,11,12

**Graduation Requirement:**Mathematics

## Educator Certifications

## Student Resources

## Original Student Tutorial

Cite text evidence and make inferences in this tutorial that will teach you all about the "real" history of Halloween!

Type: Original Student Tutorial

## Perspectives Video: Professional/Enthusiasts

Listen in as a computing enthusiast describes how hexadecimal notation is used to express big numbers in just a little space.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

What's the point to learning about matrices? You can hack gaming devices for off-the-shelf real time 3D visualization!

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Did you know that computers use matrices to represent color? Learn how computer graphics work in this video.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

## Presentation/Slideshow

This resource is a PowerPoint presentation and a form for guided note taking to be used while viewing the presentation about Matrix Operations. It begins by defining matrices and identifying types of matrices. It then goes into how to add, subtract, and multiply matrices, including how to use scalar multiplication. The final portion deals with finding the determinants of 2x2 and 3x3 matrices and Inverse Matrices.

Type: Presentation/Slideshow

## Problem-Solving Tasks

Students explore the structure of the operation *s*/(v*n*). This question provides students with an opportunity to see expressions as constructed out of a sequence of operations: first taking the square root of *n*, then dividing the result of that operation into *s*.

Type: Problem-Solving Task

This problem solving task challenges students to determine if two weather events are independent, and use that conclusion to find the probability of having similar weather events under certain conditions.

Type: Problem-Solving Task

The task is intended to address sample space, independence, probability distributions and permutations/combinations.

Type: Problem-Solving Task

This problem solving task lets students explore the concept of independence of events.

Type: Problem-Solving Task

This task combines the concept of independent events with computational tools for counting combinations, requiring fluent understanding of probability in a series of independent events.

Type: Problem-Solving Task

This task lets students explore the concepts of probability as a fraction of outcomes and using two-way tables of data.

Type: Problem-Solving Task

This task asks students to calculate probabilities using information presented in a two-way frequency table.

Type: Problem-Solving Task

The task provides a context to calculate discrete probabilities and represent them on a bar graph.

Type: Problem-Solving Task

This problem solving task gives a situation where the numbers are too large to calculate, so abstract reasoning is required in order to compare the different probabilities.

Type: Problem-Solving Task

This problem solving task asks students to determine probabilities and draw conclusions about the survival rates on the Titanic by consulting a table of data.

Type: Problem-Solving Task

Students are asked to interpret the effect on the value of an expression given a change in value of one of the variables.

Type: Problem-Solving Task

Students examine and answer questions related to a scenario similar to a "mixture" problem involving two different mixtures of fertilizer. In this example, students determine and then compare expressions that correspond to concentrations of various mixtures. Ultimately, students generalize the problem and verify conclusions using algebraic rather than numerical expressions.

Type: Problem-Solving Task

Students are asked to interpret expressions and equations within the context of the amounts of caramels and truffles in a box of candy.

Type: Problem-Solving Task

This problem asks students to consider algebraic expressions calculating the number of floor tiles in given patterns. The purpose of this task is to give students practice in reading, analyzing, and constructing algebraic expressions, attending to the relationship between the form of an expression and the context from which it arises. The context here is intentionally thin; the point is not to provide a practical application to kitchen floors, but to give a framework that imbues the expressions with an external meaning.

Type: Problem-Solving Task

This resource describes a simple scenario which can be represented by the use of variables. Students are asked to examine several variable expressions, interpret their meaning, and describe what quantities they each represent in the given context.

Type: Problem-Solving Task

In this task students interpret the relative size of variable expressions involving two variables in the context of a real world situation. All given expressions can be interpreted as quantities that one might study when looking at two animal populations.

Type: Problem-Solving Task

This resource involves simplifying algebraic expressions that involve complex numbers and various algebraic operations.

Type: Problem-Solving Task

The purpose of this task is to identify the structure in the two algebraic expressions by interpreting them in terms of a geometric context. Students will have likely seen this type of process before, so the principal source of challenge in this task is to encourage a multitude and variety of approaches, both in terms of the geometric argument and in terms of the algebraic manipulation.

Type: Problem-Solving Task

## Tutorials

This video demonstrates how to multiply complex numbers using distributive property and FOIL method.

Type: Tutorial

This video tutorial gives an introduction to the binomial theorem and explains how to use this theorem to expand binomial expressions.

Type: Tutorial

This tutorial shows students how to use Pascal's triangle for binomial expansion.

Type: Tutorial

This video will demonstrate how to subtract complex numbers.

Type: Tutorial

This video gives an introduction to 'i' and imaginary numbers. From this tutorial, students will learn the rules of imaginary numbers.

Type: Tutorial

## Video/Audio/Animation

This learning video introduces students to the world of Fractal Geometry through the use of difference equations. As a prerequisite to this lesson, students would need two years of high school algebra (comfort with single variable equations) and motivation to learn basic complex arithmetic. Ms. Zager has included a complete introductory tutorial on complex arithmetic with homework assignments downloadable here. Also downloadable are some supplemental challenge problems. Time required to complete the core lesson is approximately one hour, and materials needed include a blackboard/whiteboard as well as space for students to work in small groups. During the in-class portions of this interactive lesson, students will brainstorm on the outcome of the chaos game and practice calculating trajectories of difference equations.

Type: Video/Audio/Animation

## Virtual Manipulatives

In this activity, students adjust how many sections there are on a fair spinner then run simulated trials on that spinner as a way to develop concepts of probability. A table next to the spinner displays the theoretical probability for each color section of the spinner and records the experimental probability from the spinning trials. This activity allows students to explore the topics of experimental and theoretical probability by seeing them displayed side by side for the spinner they have created. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Virtual Manipulative

This online manipulative allows the student to simulate placing marbles into a bag and finding the probability of pulling out certain combinations of marbles. This allows exploration of probabilities of multiple events as well as probability with and without replacement. The tabs above the applet provide access to supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the Java applet.

Type: Virtual Manipulative

Students investigate shapes that grow and change using an iterative process. Fractals are characterized by self-similarity, smaller sections that resemble the larger figure. From NCTM's Illuminations.

Type: Virtual Manipulative

Section:Grades PreK to 12 Education Courses >Grade Group:Grades 9 to 12 and Adult Education Courses >Subject:Mathematics >SubSubject:Algebra >