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WORKSHEET ON ADDING,SUBTRACTING,MULTIPLYING,DIVIDING INTEGERS
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Mrs. Katie Fogarty Cooper

MC70 Designing Instructional Systems
ePortfolio

Evidence Grid


Table of Contents


Course Pre-work

The Analysis Phase (2.1.1.)

Gap Analysis (2.1.1.1.)

The average student attending Lower Merion High School will take Algebra 1 as a freshman, Geometry as a sophomore, and Algebra 2 as a junior. Linear equations are covered in depthin the Algebra 1 curriculum. Algebra 2 teachers expect that 100% of the students entering their classrooms can graph a linear equation. Anecdotal evidence suggests that the percentage of students who are still proficient in the topic of linear equations when they enter Algebra 2 is around 75%.


Problem Statement (2.1.1.2.)

Because only about 75% of the students entering Algebra 2 are proficient in graphing linear equations, compared to the desired 100%, the problem is that teachers cannot teach the new concepts that the students need for the SATs and PSSAs because they spend too much time reviewing this Algebra 1 topic.


Root Cause Analysis (2.1.1.3.)

Informal observations and interviews with experienced expert teachers and students suggest two reasons for the gap in performance of graphing linear equations. First, students are away from Algebra 1 concepts for 15 months. This time may cause some students to forget some of the material. Some students tend not to take responsibility for their learning and review past concepts on their own. Second, students may not have fully understood the concept when they were taught it the first time. Students may have had teachers that did not differentiate their instruction to meet their learning needs and styles. Some teachers may not have taught graphing linear equations in a way that allowed for student retention.


Needs Analysis (2.1.1.4.)

Students need a training tool on graphing linear equations that they can complete in the summer before they enter Algebra 2.

Course name

Graphing Linear Equations: Prerequisite skill for Algebra 2

Course Description

Graphing Linear Equations: Prerequisite skill for Algebra 2 is an hour training program that students can complete in the summer before they enter Algebra 2. The goal of the program is to review/re–teach the concepts of graphing linear equations.


Task Analysis (2.1.1.5.)


Entry Level Skills, Prerequisite Skills, Skills Hierarchy, and Learning Domain(2.1.1.6.)

Entry Level Skills

  • Adding, subtracting, multiplying, and dividing integers
  • Adding, subtracting, multiplying, and dividing fractions
  • Identifying like terms

Prerequisite Skills

Skills Hierarchy


The Design Phase (2.1.2.)

Course and Enabling Objectives(2.1.2.1.)

Course Objective

Given a linear equation in standard form, students will be able to manipulate the equation into slope–intercept form and graph the linear equation on a coordinate plane. Students will use a pencil, lined paper, graph paper, a ruler, and a graphing calculator. They will be seated at their desks while working. When finished, their equation in slope–intercept form and their labeled graph should resemble the teacher’s example.

Enabling Objectives

These objectives are for all students planning to take Graphing Linear Equations: Prerequisite skill for Algebra 2.

Seated at their desks with a pencil, lined paper, graph paper, a ruler, and a graphing calculator, students will be able to:


Learner Assessment Strategies (2.1.2.2.)

Mastery teaching will be used to teach Graphing Linear Equations: Prerequisite skill for Algebra 2. Concepts in math build upon each other and students need a solid foundation in graphing linear equations. Linear equations are studied in Algebra 1 and used again in Algebra 2 and Trigonometry. If students do not master this skill, their lack of knowledge will come back to haunt them in later math experiences. Enrichment activities will be provided for students who master all of the objectives with time left to spare until the program ends.

An assessment will be given after tasks 1 through 5 are taught. This will be a pencil and paper assessment that will assess how well the students can transform a linear equation in standard form into slope–intercept form. An assessment will be given at this point because the later tasks proceed with the assumption that the equation to be graphed is correctly stated in slope–intercept form. Another paper and pencil assessment will be given after tasks 6 through 13 are taught. For this assessment the students will be given a linear equation in standard form. They will first have to transform the equation into slope–intercept form and then they will have to graph it.


Learner Characteristics(2.1.2.3.)

Age

  • Data Source: School records
  • Characteristic: 16–17 years old
  • Teaching Design Implication: Answer the question “When will I have to use this?”

Socio-Economic Background

  • Data Source: School records
  • Characteristic: Low income
  • Teaching Design Implication: Have a classroom set of graphing calculators, rulers, graph paper, and pencils
  • Data Source: Student and parent interviews
  • Characteristic: Parents work so they are not there to help their children with school work; Parents are not knowledgeable on the topic being taught
  • Teaching Design Implication: Have on–line resources available; Allow students to email the teacher questions

Achievement Level

  • Data Source: School records
  • Characteristic: Perform below average in math classes
  • Teaching Design Implication: Don’t skip any steps when solving a problem; Go over each step carefully

Reading Ability

  • Data Source: PSSA scores
  • Characteristic: Low ability
  • Teaching Design Implication: Don’t give long reading assignments from the textbook

Motivation

  • Data Source: Experienced teachers
  • Characteristic: Low motivation
  • Teaching Design Implication: Teacher and materials need to be animated and exciting. Possibly provide a gift or reward for attendance.

Expectations

  • Data Source: Parent interviews
  • Characteristic: Prepare students for SATs
  • Teaching Design Implication: Provide practice SAT questions that relate to the topic

Experiences

  • Data Source: Student interviews
  • Characteristic: Negative math experiences
  • Teaching Design Implication: Allow opportunities to succeed

Learning Disabilities

  • Data Source: School records
  • Characteristic: ADD; slow learners
  • Teaching Design Implication: Provide prompting, structure, small class size, opportunities for on–on–one instruction; test on smaller chunks of material; sit students in close proximity to the teacher

Learning Style

  • Data Source: Student interviews
  • Characteristic: Audio, visual, and kinesthetic
  • Teaching Design Implication: Say a step, write it down, then have the students write it down and read it aloud

Learner Practice and Feedback Strategies (2.1.2.4.)

After tasks 1 through 5 are taught, students will have an opportunity to practice the skills. The students will be seated at their desks with a pencil and lined paper. They will be asked to transform ten linear equations in standard form into slope–intercept form. Practice time will be allotted at this point because the later tasks proceed with the assumption that the equation to be graphed is correctly stated in slope–intercept form.

Additional practice time will be given after tasks 6 through 13 are taught. The students will be seated at their desks with a pencil, lined paper, graph paper, a ruler, and a graphing calculator. They will be given ten linear equations in standard form. They will first have to transform the equation into slope–intercept form and then they will have to graph it.

During both practice sessions, the teacher will be walking around the classroom observing the students while they are working. This will allow the teacher to provide specific and immediate feedback to the students. The teacher will provide verbal praise to students who solve the problems correctly and corrective comments to students who are making mistakes. After the teacher observes a student get three of the problems correct without assistance or corrective comments from the teacher, the teacher will direct the student to check the remaining problems with an answer key that will be stationed at the front of the classroom. This will allow the teacher time to work more closely with the students who are still making errors. The answer key will contain the teacher’s complete and correct written–out solutions. Because mastery teaching will be used, the students will practice until they get at least three problems correct without assistance or corrective comments from the teacher. Students who finish early will be asked to provide feedback to students who are still practicing.


The Development Phase (2.1.3.)

Multimedia Component (2.1.3.1.)

There will not be a multimedia component to this course. The teacher can effectively demonstrate tasks 1 through 5 using an overhead projector, an overhead pen, and an overhead transparency. The teacher can model tasks 6 through 13 using an overhead projector, an overhead pen, an overhead transparency of a coordinate plane, a ruler, and an overhead graphing calculator. The tools and materials previously mentioned are readily available and cost effective.


The Implementation Phase (2.1.4.)

Instructor Qualification Process (2.1.4.1.)

An instructor qualification process is not necessary for this course because only certified teachers will teach this course. For quality assurance purposes there is a lesson plan below that all instructors must follow as they teach the course.

Lesson Plan

MaterialsProcedure

Student Workbook (2.2.)

Student Handouts (2.2.8.)


Assessments (2.2.9.)


Course Post-work (2.3.)

The Evaluation Phase (2.3.1.)

Kirkpatrick Level Assessment (2.3.1.1.)

A Kirkpatrick Level 2 assessment will be given to the students at the conclusion of this course. Students will be required to complete an assessment that tests their knowledge of transforming a linear equation in standard form into slope–intercept form. The assessment will also test their ability to graph a linear equation that is in slope–intercept form. The performance gap will be closed if 100% of the students who took this course successfully complete this Level 2 assessment.