Report+2

Report 1 Comments: All corrections have been made pending instructor approval.


__**Instructional Goal:**__ Given a new course in Geometry all learners will be able to teach previously taught skills such as performing accurate calculations using signed numbers with a graphic organizer, specifically a T-chart.

__** Performance Objective: **__

Learner will be able to look at any particular integer whether negative or positive and determine what to do accurately. If the learner has to perform adding or subtracting one negative and a positive, or two negatives and positives. The learner must also determine if they are multiply or dividing one negative and one positive or what to do if they encounter two negatives or two positives. The learner will perform these calculations accurately.

**Condition/behavior/criteria **

**__Terminal Objective __: **  A unit of instruction about negative and positive integers. The terminal objectives will be:  1. The learner will be able to accurately perform indicated operations on integers.  2. The learner will show that they can perform all four mathematical operations accurately on negative and positive integers.



=**1.2 Interpret 4 math operators, add-subtract, multiply/divide (Entry Behaviors) **= =**1.3 Interpret what a negative or positive integer is (Entry Behaviors) **= || =**2.2 Identify and follow rules of addition and subtraction (Intellectual Skill) **=
 * **<span style="font-family: Arial,sans-serif; font-size: 14pt;">Main Steps ** || **<span style="font-family: Arial,sans-serif; font-size: 14pt;">Subordinate/Entry Skills ** ||
 * 1 || =**<span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">1.1 Identify a number line (Entry Behaviors) **=
 * 2 || =**<span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">2.1 Place a circle around a negative sign and a square around a positive sign **=

|| =**<span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">3.2 Demonstrate multiplying, and/or dividing two positives, two negatives, and one positive and one negative (Intellectual Skill) **=
 * **<span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">3 ** || =**<span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">3.1 Identify whether the numbers should be multiplied or divided (Intellectual Skill) **=

|| =**<span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">4.2 Write the rules and steps line by line for each operation (Intellectual Skill) **=
 * **<span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">4 ** || =**<span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">4.1 Identify steps by writing each line by line (Intellectual Skill) **=

||
 * **<span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">5 ** || **<span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">See Goal Analysis in Report 1 ** ||

<span style="color: black; font-family: 'Arial Black',sans-serif; font-size: 12pt; line-height: 14.25pt; margin-bottom: 0in;">Sequence and Cluster Objectives


 * <span style="background-attachment: initial; background-clip: initial; background-color: silver; background-image: initial; background-origin: initial; font-family: 'Arial Black',sans-serif; font-size: 12pt; line-height: normal; margin-bottom: 7.5pt; margin-left: 0in; margin-right: 0in; margin-top: 7.5pt;">Cluster || <span style="background-attachment: initial; background-clip: initial; background-color: silver; background-image: initial; background-origin: initial; font-family: 'Arial Black',sans-serif; font-size: 12pt; line-height: normal; margin-bottom: 7.5pt; margin-left: 0in; margin-right: 0in; margin-top: 7.5pt;">Main Steps || <span style="background-attachment: initial; background-clip: initial; background-color: silver; background-image: initial; background-origin: initial; font-family: 'Arial Black',sans-serif; font-size: 12pt; line-height: normal; margin-bottom: 7.5pt; margin-left: 0in; margin-right: 0in; margin-top: 7.5pt;">Objectives ﻿﻿ ||
 * <span style="line-height: normal; margin-bottom: 7.5pt; margin-left: 0in; margin-right: 0in; margin-top: 7.5pt;">**<span style="font-family: Arial,sans-serif; font-size: 12pt;">1 ** || <span style="line-height: normal; margin-bottom: 7.5pt; margin-left: 0in; margin-right: 0in; margin-top: 7.5pt;">**<span style="font-family: Arial,sans-serif; font-size: 12pt;">1, 1.2, 1.3 ** || <span style="line-height: normal; margin-bottom: 7.5pt; margin-left: 0in; margin-right: 0in; margin-top: 7.5pt;">** Identify if the number is negative or positive ** ||
 * <span style="line-height: normal; margin-bottom: 7.5pt; margin-left: 0in; margin-right: 0in; margin-top: 7.5pt;">**<span style="font-family: Arial,sans-serif; font-size: 12pt;">2 ** || <span style="line-height: normal; margin-bottom: 7.5pt; margin-left: 0in; margin-right: 0in; margin-top: 7.5pt;">**<span style="font-family: Arial,sans-serif; font-size: 12pt;">2, 2.1, 2.2 ** || <span style="line-height: normal; margin-bottom: 7.5pt; margin-left: 0in; margin-right: 0in; margin-top: 7.5pt;">** Identify whether the numbers should be added or subtracted ** ||
 * <span style="line-height: normal; margin-bottom: 7.5pt; margin-left: 0in; margin-right: 0in; margin-top: 7.5pt;">**<span style="font-family: Arial,sans-serif; font-size: 12pt;">3 ** || <span style="line-height: normal; margin-bottom: 7.5pt; margin-left: 0in; margin-right: 0in; margin-top: 7.5pt;">**<span style="font-family: Arial,sans-serif; font-size: 12pt;">3, 3.1, 3.2, 4, 4.1, 4.2, 5 ** || <span style="line-height: normal; margin-bottom: 7.5pt; margin-left: 0in; margin-right: 0in; margin-top: 7.5pt;">** Identify method for adding, subtracting, and/or multiplying, dividing two positives, two negatives, and one positive and one negative ** ||

__** Sample Assessments for each objective: **__ Pre-Assessments: ** Attached here for #11 on rubric! **

__** Instructional Sequence: **__** Included below-See instructional sequence **

__** Information/example for each objective: **__** Included below **** -See instructional sequence **

<span style="display: inline !important; margin: 0px; padding: 0px;"> __** Practice/Feedback for each objective: **__** Included below ** ** -See instructional sequence **


 * ** Instructional Sequence ** ||
 * ** To understand opposites, positive, negative, number line, and signs. To read and write signed numbers. To connect integer concepts with real-life situations ** ||
 * ** To understand the concept of absolute value and how it relates to the number line. To use proper notation ** ||
 * ** To learn integer addition with like and unlike signs ** ||
 * ** To subtract an integer by adding its opposite. Problems with like and unlike signs are presented ** ||
 * ** To learn integer multiplication with like signs and unlike signs. Students will learn to multiply up to three factors ** ||
 * ** To learn integer division with like and unlike signs ** ||
 * ** To review and apply the rules for all four operations (mixed review format) ** ||
 * ** To complete 10 additional exercises as practice. To assess students' understanding of all integer concepts presented ** ||
 * ** To solve 10 additional problems that challenge students' understanding of integer concepts. All problems make connections to the real world. To hone learners' problem-solving skills ** ||
 * ** To review complete solutions to all exercises presented in this unit. Includes the problem, step-by-step solutions, and final answers for each exercise ** ||


 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">Instructional Sequence **

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">**Cluster 1:** Identify if the number is negative or positive.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">Content Presentation: One 50 minute class period in the computer lab. They will visit [|www.thatquiz.org] to take the online exam, using the test code: XXOD4873. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">Content: The learner will take a number line pre-test. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">Have the learner take the pretest. Check scores and prepare the focus of the class and adjust possibly for the revision of previously taught skills or not.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;"> **Cluster 2:** Identify whether the numbers should be added or subtracted.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">Content Presentation: One 50 minute class period. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">Learners will be given their composition books, which they will use to create a hand written T-Chart to list the rules and examples of adding and subtracting negative and positive numbers.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">This will be used as review/mastery of using positive and negative numbers to add and subtract numbers. Learners will write down what they think an integer is and 1 rule they know about the absolute value of real numbers. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">Learner participation will be required.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">Learners will take a practice exam [|www.thatquiz.org] to take the online exam, using the test code: BOYS1386. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">If students have mastered the material then teacher will move on. If not students will write a six line reflection, in words, about why they did not understand how to answer the questions accurately.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">Examples: Entire class will take notes with PowerPoints, and websites. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">Student Groupings and Media Selection: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">Student Participation: Writing and performing practice problems. Writing what they did and why they did it. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">Practice Items & Activities: Application of what the integers can be used for in real life situation. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">Feedback: Learners will monitor their progress even when the skill has been mastered.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 16px; line-height: 23px;">**Cluster 3:** Identify method for adding, subtracting, and/or multiplying, dividing two positives, two negatives, and one positive and one negative.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">Content Presentation: One 50 minute class periods in class.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 16px; line-height: 23px;">Learners will be given their composition books, which they will use to create a hand written T-Chart to list the rules and examples of multiplying and dividing negative and positive numbers.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">This will be used as review/mastery of using positive and negative numbers to multiply and divide numbers. Learners will write down what they think the pattern is for these types of calculations.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">Post-Assessment given. Learners will take a practice exam [|www.thatquiz.org] to take the online exam, using the test code: HTAH9857

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">Examples: The entire class will participate 100% <span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">Student Groupings and Media Selection: 100% of the group present will create the T-Chart and use it for the practice sessions. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">Student Participation: 100% of group will demonstrate using their T-chart to answer all questions. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">Practice Items & Activities: When questions arise for validity, learners will be referred to the number line and other example problems for clarity. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">Feedback: ﻿ (Same as above)
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">How to accurately determine answers. **

__** Pre-Instructional Activities: **__

**Motivation:** Explain to Geometry students that they will be required to perform a basic skills assessment throughout the entire school year. The assessments will be added to their normal class curriculum requirement.

**Objectives:** For the first 90 days of the school year, students will use a T-chart graphic organizer with four columns to guide them through their assessments, and this will be explained to the students prior to the lesson. The timeline for the process will be explained to the learners. The assessments will be given bi-weekly. All of the assessment will be given on the computer to ensure integrity of the assessment.

**Entry Skills:** During the instruction and the first 90 days, learners will review how to accurately obtain the correct answers to all types of integer operations.

__** Strategy for teaching terminal objective: **__** See instructional strategy below. **

__** Instructional strategy: **__

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">Before the unit is introduced, the intended audience will already have had prior knowledge of the topic that was learned in previous grades. The purpose of this unit is to utilize available technology to improve accuracy in solving integer problems. This unit will be given as a standalone unit, given with an instructional graphic organizer technique. A T-Chart was chosen as the method of deliverance mainly because the T-chart will allow things to be seen clearly and directly. Also, the T-Chart can be referenced during practice and exam time for the 1st half of the unit, if the learner missed any step. The T-Chart will be designed to show what actions to perform in order to correctly perform indicated calculations using signed numbers. The final product will be the post-test to show accuracy throughout the entire school year, and the difficulty level will spiral with the instruction. The assessment will have the student produce the same thing with other problems, but with the same type of end product.

__** Student groupings and media selections: **__

Learners will receive direct instruction in their classroom. Review and practice sessions will be conducted twice per week in order to practice relevant material.


 * <span style="color: #0000ff; font-family: Arial,Helvetica,sans-serif; font-size: 16pt;">Assessment: **

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">Pretest: Teacher will observe learners as they go through each step of their T-Charts. Teacher will use the Rubric for Entry Skills (Listed below) to assess the learners. New learners will be tested to determine their ability to accurately perform these same operations.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;"> Practice Tests: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">Identify a positive and negative number. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">Identify whether the numbers should be added or subtracted. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">Identify method for adding, subtracting, and/or multiplying, dividing two positives, two negatives, and one positive and one negative.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;"> Practice Assignment: Learners will take a practice exam at the conclusion of every lesson.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;"> Posttest/Graded Assignment: After each unit is complete, learners will take a unit exam using an online exam.
 * || === Math - Problem Solving : Integers  ===

Teacher Name: **Any Name**

Student Name: ||  ||


 * CATEGORY || ** 4 ** || ** 3 ** || ** 2 ** || ** 1 ** ||
 * ** Mathematical Concepts ** || Explanation shows complete understanding of the mathematical concepts used to solve the problem(s). || Explanation shows substantial understanding of the mathematical concepts used to solve the problem(s). || Explanation shows some understanding of the mathematical concepts needed to solve the problem(s). || Explanation shows very limited understanding of the underlying concepts needed to solve the problem(s) OR is not written. ||
 * ** Mathematical Errors ** || 90-100% of the steps and solutions have no mathematical errors. || Almost all (85-89%) of the steps and solutions have no mathematical errors. || Most (75-84%) of the steps and solutions have no mathematical errors. || More than 75% of the steps and solutions have mathematical errors. ||
 * ** Mathematical Terminology and Notation ** || Correct terminology and notation are always used, making it easy to understand what was done. || Correct terminology and notation are usually used, making it fairly easy to understand what was done. || Correct terminology and notation are used, but it is sometimes not easy to understand what was done. || There is little use, or a lot of inappropriate use, of terminology and notation. ||
 * ** Checking ** || The work has been checked by two classmates and all appropriate corrections made. || The work has been checked by one classmate and all appropriate corrections made. || Work has been checked by one classmate but some corrections were not made. || Work was not checked by classmate OR no corrections were made based on feedback. ||