Author: martinezvcwu

Arithmetic with Polynomials & Rational Expressions Learning Progression

martinezvcwu CCSS-Math Learning Progressions, HS Algebra

This learning progression focuses on the cluster of performing arithmetic operations on polynomials in the Arithmetic with Polynomials & Rational Expressions domain of the Common Core State Standards for Mathematics. The purpose of this learning progression is for students to understand that polynomials are like integers in the fact that they are “closed” in regards to addition, subtractions and multiplication. In other words students should be able to recognize that a polynomial plus a polynomial, a polynomial minus a polynomial, and a polynomial multiplied by a polynomial will always result in a polynomial.

This learning progression will utilize Chapter 6: Polynomial Functions from the textbook Holt McDougal Algebra 2. Due
to the layout of the textbook, the operations of polynomials have been split apart; sections 6-1: Polynomials, focuses on
an introduction to polynomials and addition and subtraction of polynomials, while section 6-2: Multiplying polynomials
focuses on multiplying polynomials.

Learning Progression_with lesson plan_2nd

Interpreting Functions Learning Progression

martinezvcwu CCSS-Math Learning Progressions, HS Functions

This unit focuses the cluster of Understanding the concept of a function and use function notation in the Interpreting Function domain of the Common Core State Standards for Mathematics. In this unit students will be introduced to functions and their properties. By the end of the unit students will be able to identify the domain and range of a given functions, in addition they will understand the one-to-one relationship between numbers in the domain and numbers in the range. When speaking of functions students will be able to use the correct vocabulary, likewise, they will use correct notation when referencing them on paper. Students will also be able to evaluate a given function with given an input value for the function. This unit will also introduce student to common functions, knows as parents functions, that they will often see throughout the rest of their mathematical careers. The last things students will learn in this unit is how to recognize that sequences are functions and how to express some sequences in function notation.

 

Learning Progression: Learning Progression_with lesson plan_1st
Lesson Plan: Lesson Plan_What is a Function

Learning Progression using Marbles to model

martinezvcwu CCSS-Math Learning Progressions, HS Geometry

This learning progression is based on the CCSS-Math standards for Algebra, where we will use a series of methods to teach students how to build equations and inequalities to describe numbers or relations. There will be an attachment of a lesson plan to refer to as an idea on how one could use modeling to teach these lessons.

Learning progression 2 lesson plan

Learning progression 2

Using a Smart Board to motivate learning

martinezvcwu HS Algebra, Technology Teaching Issues

Students today have access to technology around every corner. Thus, most computer programs, IPads, and etc. are available to students at all times. Students like new experiences; they enjoy using new tools, and will benefit greatly from a lesson that is unusual to their “normal” day-to-day lecture.

Using a Smart Board is a unique experience to most students that not many teachers have the ability to provide. The act of using it, is alone usually motivation enough to get a student to want to participate in a lesson. Many schools are beginning to purchase SMART boards and if that’s not an option, there are teachers across the country receiving grants for SMART boards in their classroom! Some places found with a quick google search are: “Adopt-A-Classroom Grant,” “Citi Group Foundation Grants,” and “Hewlett-Packard Technology for Teaching.”

Smart Boards are versatile in their usage and we will be using it to complete mathematical equations and sketching their graphs so we can successfully teach the following standard:

CCSS.Math.Content.HSA-APR.B.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.

One of the nice things about Smart Boards, is you can use any program as a background and draw over the top. For example, using a PDF of a problem for each student for a problem, like so:

Better math task

 

Student work may look like this, demonstrating how he/she solved for zeros and finding x-intercepts.

student work

 

This example shows how a student could solve a problem on a smart board by using  verbal instructions to factor the expression then find the zeros and sketch a graph.

Another benefit to smart boards is that they are based on touch or stylus for use, and most students have used some sort of technology that is similar. This type of activity motivates the student to create a personal need to achieve the learning outcome because they are offered a chance to use  or “play” with a technological tool that is fun and unique because the majority of people don’t have access to a smart board.  If they don’t try to learn the lesson, they can’t answer the problem, thus aren’t able to use the Smart Board. Although the boards are similar to things the students have used, they are also different because they are big and new to the student.