# Exploring Derivative Functions using HP Prime

Size: px
Start display at page:

Transcription

1 Exploring Derivative Functions using HP Prime Betty Voon Wan Niu College of Engineering Universiti Tenaga Nasional Malaysia Wong Ling Shing Faculty of Health and Life Sciences, INTI International University, Persiaran Perdana BBN, Putra Nilai, Nilai, Negeri Sembilan, Malaysia Abstract Derivative is one of the essential topics in calculus, which is an important basic skill should be mastered before integration comes in. Learning derivative in higher education can be achieved by using interesting graphing-calculator based learning. In this paper, activities using HP Prime to explore derivative function are highlighted. The usage of Function and Statistics 2Var applets are emphasized and used in these activities. Through these activities, students learn how to sketch the graph of a derivative from its original function, through observation on the changes of slopes, and tangent lines in HP Prime graphing calculator. 1. Introduction Calculus is a compulsory subject for engineering and mathematics students in higher learning institution. Derivative is one of the essential topics in Calculus. Students in Malaysia learn about the basic of derivative when they are taking additional mathematics subject in their secondary level of education. Nevertheless, the topic could be rather abstract and dry without graphic demonstration. Hence, we would like to share our activity in class to get the students engaged in learning about derivative. According to a famous Chinese proverb I hear and I forget, I see and I remember, I do and I understand, getting students involved in the learning process is important for them to understand the important concepts [1, 2]. As Edward Bolles ever mentioned that "We remember what we understand; we understand only what we pay attention to; we pay attention to what we want." Once the concept is understood, it will be easier to be memorized. Since Calculus is an accumulative subject, basic knowledge is needed to continue the learning in this subject. If the students are able to memorize the concept, then they would face less difficulties in future learning in Calculus. Quesada et al. [3] reported the success in teaching pre-calculus students using graphing calculator. The students learning with graphing calculators generally performed better than those who were using scientific calculators. In another study, students with graphing calculators outperformed their peers with traditional learning method in algebra [4]. In addition to that, graphing calculator had been reported to assist in the understanding of the concept of derivatives [5] and probability [6]. In this paper, we suggested the using of graphing calculator in learning calculus.

2 In a usual practice, students learn about derivative using the concepts of limits first. After that, they will be asked to memorize the derivative of certain functions. Here, a graphing calculator-assisted activity can be added before the learning of derivative. This activity requires the students to sketch the graph of derivative, follows by the identification of the derivative function. With graphing calculator, students can visualize the graphs from the functions, and by that, enhance the memorization of derivative functions. In this paper, Section 2 describes the activities done. Section 3 gives the suggestions on the activity and conclusion comes in the last section. HP Prime Graphing Calculator was used in the activity and Geogebra was used in producing the worksheet. 2. Design of Activity The activity started with (1) the revision of the previous topic about slope, (2) finding slopes at different points and sketch the graph of derivative, and (3) summary of the process and enhancement of the learning. 2.1 Reviewing Previous Topic about Slope In the beginning, students were shown a graph of polynomial, without telling them the function of the graph (Figure 2.1). Then, they were asked to identify the type of the polynomial. Later, they were required to determine the part(s) of the graph that produce positive, zero and negative slopes. Figure 2.1 The first graph (polynomial) shown to students. 2.2 Finding Slopes and Derivative Graph Sketching After that, a tangent line were shown with the slope value (Figure 2.2). The cursor was moved left and right to get the students to observe the changes of slope graphically and numerically. Later, the equation of the graph was revealed to the students, and they were required to key in the function into F1(X) in Function aplet. Next, they were asked to find other slopes at different values of x using their graphing calculator. Then, they were required to record the slopes in the graphing calculator (Figure 2.3).

3 Figure 2.2 The slope is shown at the bottom left corner of the screen. Figure 2.3 The points were keyed in taking column C1 for x and C2 for y. Afterwards, students were asked to plot the points of x, y as a scatter plot (Figure 2.4). From the scatter plot, they were first asked to indentify the type of polynomial the graph y. Then, Fit key (Figure 2.5) was activated to connect the dots. As the default best fit option is usually the linear function, students have to choose the suitable type of best fit in the Symbolic View (Figure 2.6), and activate the Fit key in Plot View again to view the best fit (Figure 2.5). Then, they were asked to copy the best fit function found in Statistics 2Var aplet into F2(X) in Function aplet (Figure 2.7). F2(X) was then plotted together with F1(X). From the graph of F2(X), the x-coordinate of the extremum of y (F1(X)) can be found by searching the x-intercept of y (F2(X)).

4 Figure 2.4 Scatter plot of x, y. Figure 2.5 Best fit of the scatter plot of x, y. Figure 2.6 Best fit type for scatter plot of x, y.

5 Figure 2.7 Best fit function for scatter plot of x, y was keyed in F2(X). Figure 2.8 The graphs of y (blue) and y ' (yellow). 2.3 Summarize and Consolidate the Knowledge At the end of the class, the whole process was summarized using the screens in Figure 2.9 by moving the cursor along the graph of f x and asking the students to observe the changes of (a) the slope of y, and (b) the value of y simultaneously. To consolidate the concept, a worksheet with another type of function was given to the students, and they were required to repeat what they had done before this. In order to strengthen their findings, analysis questions were asked. Then, they were required to sketch a graph of derivative on the worksheet paper, without knowing the function of the given graph. Lastly, a bonus question was given for the students to sketch the graph of x f x. f through observation on the graph of

6 Figure 2.9 Screenshots of graphs of y f x (blue curve) and y f x (yellow curve). 3. Recommendation and Suggestion Students may need 15 minutes or more to complete the worksheet, thus it is suggested to allow the students to do it as a homework. For the best learning process, this activity shall be conducted between the lessons teaching the concept of limit and derivative. Alternatively, this activity can be conducted after the students have learnt about the derivative and its application. This activity can be flexibly done in two sections as well, i.e. exploration (Questions 1 2) before teaching derivative, whilst analysis (Questions 3 4), after learning about application of derivative. Different functions can be given in the worksheet (but limited to what the students have previously learnt), to prepare the students to learn about different derivative functions later. The sketching of derivative graphs will help them to memorize the derivative functions, e.g. the trigonometry functions which the students may confused by the negative sign. The bonus question can be given as preparation in teaching integration. 4. Conclusion This activity is used to help the students to build up the ability to visualize the derivative of a graph and hence memorize the derivative more effectively. It also helps the students in graph

7 interpretation. With this ability, students are able to generate derivative graph from any given 2-D graph and also to analyze and interpret different type of 2-D graphs. This will lay a firm foundation when the students encounter topics of derivatives in higher dimension in the future. Acknowledgements: The authors would like to thank HP for the sponsorship. References [1] Freeman, S., Eddy, S. L., McDonough, M., Smith, M. K., Okoroafor, N., Jordt, H., and Wenderoth, M. P. (2014). Active learning increases student performance in science, engineering, and mathematics. Proceedings of the National Academy of Sciences, vol. 111, pp [2] Nguyen, D. M. and Kulm, G. (2005). Using web-based practice to enhance mathematics learning and achievement. Journal of Interactive Online Learning, vol. 3, pp [3] Quesada, A. R. and Maxwell, M. E. (1994). The effects of using graphing calculators to enhance college students' performance in precalculus. Educational Studies in Mathematics, vol. 27, pp [4] Hollar, J. C. and Norwood, K. (1999). The effects of a graphing-approach intermediate algebra curriculum on students' understanding of function. Journal for Research in Mathematics Education, pp [5] Roorda, G., Vos, P., Drijvers, P., and Goedhart, M. (Year). Graphing calculator supported instrumentation schemes for the concept of derivative: a case study.in Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education and the 36th Conference of the North American Chapter of the Psychology of Mathematics Education pp [6] Tan, C.-K., Tan, C.-P., Razak, S. F. A., and Ling, L. S. (2013). Undergraduate Students' Perceptions toward the Graphing Calculator Instructional Approach. Communications of the IBIMA, vol. 2013, p. ID

8 Worksheet Given a function f x 2sin x. 1) Find the slope of the line of tangent at the following point. Record each the values of each row in your HP Prime using Statistics 2Var. Record the data using 3 columns: C1, C2 and C3. x f x f x 2) Plot the points x, f x with o and x f x, with x in the graph below. Then, connect the respective points with a smooth curve. (Hints: You may use both Function and Statistics 2Var aplets to help you to complete this part)

9 3) Fill in the blanks below: a) As the slope of f x increases, the graph of f x. b) f x has its extremum point at x = and x =, where x. c) As the slope of f x decreases, the graph of x d) When f x is a concave, the value of x e) When f x is a convex, the value of x f) If f x reaches its extremum at x a, x f has its f. f as x increases. f as x increases. f reaches its point of. 4) Given a new function as drawn at the xy-plane in part a). Sketch the graph of its derivative at the xy -plane in part b). a) b)

10 Bonus Question Given a derivative function y f x as drawn at the xy -plane in part a). Sketch the graph of its antiderivative function y f x at the xy-plane in part b). a) b)

### Janine Williams, Mary Rose Landon

TI-nspire Activity Janine Williams, Mary Rose Landon Course Level: Advanced Algebra, Precalculus Time Frame: 2-3 regular (45 min.) class sessions Objectives: Students will... 1. Explore the Unit Circle,

### Statewide Framework Document for:

Statewide Framework Document for: 270301 Standards may be added to this document prior to submission, but may not be removed from the framework to meet state credit equivalency requirements. Performance

### CAAP. Content Analysis Report. Sample College. Institution Code: 9011 Institution Type: 4-Year Subgroup: none Test Date: Spring 2011

CAAP Content Analysis Report Institution Code: 911 Institution Type: 4-Year Normative Group: 4-year Colleges Introduction This report provides information intended to help postsecondary institutions better

### Digital Fabrication and Aunt Sarah: Enabling Quadratic Explorations via Technology. Michael L. Connell University of Houston - Downtown

Digital Fabrication and Aunt Sarah: Enabling Quadratic Explorations via Technology Michael L. Connell University of Houston - Downtown Sergei Abramovich State University of New York at Potsdam Introduction

### Course Name: Elementary Calculus Course Number: Math 2103 Semester: Fall Phone:

Course Name: Elementary Calculus Course Number: Math 2103 Semester: Fall 2011 Instructor s Name: Ricky Streight Hours Credit: 3 Phone: 405-945-6794 email: ricky.streight@okstate.edu 1. COURSE: Math 2103

### Mathematics subject curriculum

Mathematics subject curriculum Dette er ei omsetjing av den fastsette læreplanteksten. Læreplanen er fastsett på Nynorsk Established as a Regulation by the Ministry of Education and Research on 24 June

### Mathematics. Mathematics

Mathematics Program Description Successful completion of this major will assure competence in mathematics through differential and integral calculus, providing an adequate background for employment in

### Getting Started with TI-Nspire High School Science

Getting Started with TI-Nspire High School Science 2012 Texas Instruments Incorporated Materials for Institute Participant * *This material is for the personal use of T3 instructors in delivering a T3

### AP Calculus AB. Nevada Academic Standards that are assessable at the local level only.

Calculus AB Priority Keys Aligned with Nevada Standards MA I MI L S MA represents a Major content area. Any concept labeled MA is something of central importance to the entire class/curriculum; it is a

### Experience College- and Career-Ready Assessment User Guide

Experience College- and Career-Ready Assessment User Guide 2014-2015 Introduction Welcome to Experience College- and Career-Ready Assessment, or Experience CCRA. Experience CCRA is a series of practice

### GCSE Mathematics B (Linear) Mark Scheme for November Component J567/04: Mathematics Paper 4 (Higher) General Certificate of Secondary Education

GCSE Mathematics B (Linear) Component J567/04: Mathematics Paper 4 (Higher) General Certificate of Secondary Education Mark Scheme for November 2014 Oxford Cambridge and RSA Examinations OCR (Oxford Cambridge

### Introduction to the Practice of Statistics

Chapter 1: Looking at Data Distributions Introduction to the Practice of Statistics Sixth Edition David S. Moore George P. McCabe Bruce A. Craig Statistics is the science of collecting, organizing and

### Characteristics of Functions

Characteristics of Functions Unit: 01 Lesson: 01 Suggested Duration: 10 days Lesson Synopsis Students will collect and organize data using various representations. They will identify the characteristics

### SOUTHERN MAINE COMMUNITY COLLEGE South Portland, Maine 04106

SOUTHERN MAINE COMMUNITY COLLEGE South Portland, Maine 04106 Title: Precalculus Catalog Number: MATH 190 Credit Hours: 3 Total Contact Hours: 45 Instructor: Gwendolyn Blake Email: gblake@smccme.edu Website:

### Math 181, Calculus I

Math 181, Calculus I [Semester] [Class meeting days/times] [Location] INSTRUCTOR INFORMATION: Name: Office location: Office hours: Mailbox: Phone: Email: Required Material and Access: Textbook: Stewart,

### TabletClass Math Geometry Course Guidebook

TabletClass Math Geometry Course Guidebook Includes Final Exam/Key, Course Grade Calculation Worksheet and Course Certificate Student Name Parent Name School Name Date Started Course Date Completed Course

### Mathematics Success Level E

T403 [OBJECTIVE] The student will generate two patterns given two rules and identify the relationship between corresponding terms, generate ordered pairs, and graph the ordered pairs on a coordinate plane.

### Cal s Dinner Card Deals

Cal s Dinner Card Deals Overview: In this lesson students compare three linear functions in the context of Dinner Card Deals. Students are required to interpret a graph for each Dinner Card Deal to help

### HOLMER GREEN SENIOR SCHOOL CURRICULUM INFORMATION

HOLMER GREEN SENIOR SCHOOL CURRICULUM INFORMATION Subject: Mathematics Year Group: 7 Exam Board: (For years 10, 11, 12 and 13 only) Assessment requirements: Students will take 3 large assessments during

### Creating a Test in Eduphoria! Aware

Math 150 Syllabus Course title and number MATH 150 Term Fall 2017 Class time and location INSTRUCTOR INFORMATION Name Erin K. Fry Phone number Department of Mathematics: 845-3261 e-mail address erinfry@tamu.edu

### Are You Ready? Simplify Fractions

SKILL 10 Simplify Fractions Teaching Skill 10 Objective Write a fraction in simplest form. Review the definition of simplest form with students. Ask: Is 3 written in simplest form? Why 7 or why not? (Yes,

### SANTIAGO CANYON COLLEGE Reading & English Placement Testing Information

SANTIAGO CANYON COLLEGE Reaing & English Placement Testing Information DO YOUR BEST on the Reaing & English Placement Test The Reaing & English placement test is esigne to assess stuents skills in reaing

### Manipulative Mathematics Using Manipulatives to Promote Understanding of Math Concepts

Using Manipulatives to Promote Understanding of Math Concepts Multiples and Primes Multiples Prime Numbers Manipulatives used: Hundreds Charts Manipulative Mathematics 1 www.foundationsofalgebra.com Multiples

### Algebra 1, Quarter 3, Unit 3.1. Line of Best Fit. Overview

Algebra 1, Quarter 3, Unit 3.1 Line of Best Fit Overview Number of instructional days 6 (1 day assessment) (1 day = 45 minutes) Content to be learned Analyze scatter plots and construct the line of best

### Mathematics Assessment Plan

Mathematics Assessment Plan Mission Statement for Academic Unit: Georgia Perimeter College transforms the lives of our students to thrive in a global society. As a diverse, multi campus two year college,

### Syllabus ENGR 190 Introductory Calculus (QR)

Syllabus ENGR 190 Introductory Calculus (QR) Catalog Data: ENGR 190 Introductory Calculus (4 credit hours). Note: This course may not be used for credit toward the J.B. Speed School of Engineering B. S.

### AGS THE GREAT REVIEW GAME FOR PRE-ALGEBRA (CD) CORRELATED TO CALIFORNIA CONTENT STANDARDS

AGS THE GREAT REVIEW GAME FOR PRE-ALGEBRA (CD) CORRELATED TO CALIFORNIA CONTENT STANDARDS 1 CALIFORNIA CONTENT STANDARDS: Chapter 1 ALGEBRA AND WHOLE NUMBERS Algebra and Functions 1.4 Students use algebraic

### Edexcel GCSE. Statistics 1389 Paper 1H. June Mark Scheme. Statistics Edexcel GCSE

Edexcel GCSE Statistics 1389 Paper 1H June 2007 Mark Scheme Edexcel GCSE Statistics 1389 NOTES ON MARKING PRINCIPLES 1 Types of mark M marks: method marks A marks: accuracy marks B marks: unconditional

### Physics 270: Experimental Physics

2017 edition Lab Manual Physics 270 3 Physics 270: Experimental Physics Lecture: Lab: Instructor: Office: Email: Tuesdays, 2 3:50 PM Thursdays, 2 4:50 PM Dr. Uttam Manna 313C Moulton Hall umanna@ilstu.edu

### What s in a Step? Toward General, Abstract Representations of Tutoring System Log Data

What s in a Step? Toward General, Abstract Representations of Tutoring System Log Data Kurt VanLehn 1, Kenneth R. Koedinger 2, Alida Skogsholm 2, Adaeze Nwaigwe 2, Robert G.M. Hausmann 1, Anders Weinstein

### What Do Croatian Pre-Service Teachers Remember from Their Calculus Course?

IUMPST: The Journal. Vol 1 (Content Knowledge), June 2014 [www.k-12prep.math.ttu.edu] What Do Croatian Pre-Service Teachers Remember from Their Calculus Course? Ljerka Jukić Department of Mathematics University

### Minitab Tutorial (Version 17+)

Minitab Tutorial (Version 17+) Basic Commands and Data Entry Graphical Tools Descriptive Statistics Outline Minitab Basics Basic Commands, Data Entry, and Organization Minitab Project Files (*.MPJ) vs.

### Using Calculators for Students in Grades 9-12: Geometry. Re-published with permission from American Institutes for Research

Using Calculators for Students in Grades 9-12: Geometry Re-published with permission from American Institutes for Research Using Calculators for Students in Grades 9-12: Geometry By: Center for Implementing

### Intermediate Algebra

Intermediate Algebra An Individualized Approach Robert D. Hackworth Robert H. Alwin Parent s Manual 1 2005 H&H Publishing Company, Inc. 1231 Kapp Drive Clearwater, FL 33765 (727) 442-7760 (800) 366-4079

### SURVIVING ON MARS WITH GEOGEBRA

SURVIVING ON MARS WITH GEOGEBRA Lindsey States and Jenna Odom Miami University, OH Abstract: In this paper, the authors describe an interdisciplinary lesson focused on determining how long an astronaut

### Backwards Numbers: A Study of Place Value. Catherine Perez

Backwards Numbers: A Study of Place Value Catherine Perez Introduction I was reaching for my daily math sheet that my school has elected to use and in big bold letters in a box it said: TO ADD NUMBERS

### Math Techniques of Calculus I Penn State University Summer Session 2017

Math 110 - Techniques of Calculus I Penn State University Summer Session 2017 Instructor: Sergio Zamora Barrera Office: 018 McAllister Bldg E-mail: sxz38@psu.edu Office phone: 814-865-4291 Office Hours:

### *Lesson will begin on Friday; Stations will begin on the following Wednesday*

UDL Lesson Plan Template Instructor: Josh Karr Learning Domain: Algebra II/Geometry Grade: 10 th Lesson Objective/s: Students will learn to apply the concepts of transformations to an algebraic context

### DIDACTIC MODEL BRIDGING A CONCEPT WITH PHENOMENA

DIDACTIC MODEL BRIDGING A CONCEPT WITH PHENOMENA Beba Shternberg, Center for Educational Technology, Israel Michal Yerushalmy University of Haifa, Israel The article focuses on a specific method of constructing

### PUBLIC CASE REPORT Use of the GeoGebra software at upper secondary school

PUBLIC CASE REPORT Use of the GeoGebra software at upper secondary school Linked to the pedagogical activity: Use of the GeoGebra software at upper secondary school Written by: Philippe Leclère, Cyrille

### AP Statistics Summer Assignment 17-18

AP Statistics Summer Assignment 17-18 Welcome to AP Statistics. This course will be unlike any other math class you have ever taken before! Before taking this course you will need to be competent in basic

### CHANCERY SMS 5.0 STUDENT SCHEDULING

CHANCERY SMS 5.0 STUDENT SCHEDULING PARTICIPANT WORKBOOK VERSION: 06/04 CSL - 12148 Student Scheduling Chancery SMS 5.0 : Student Scheduling... 1 Course Objectives... 1 Course Agenda... 1 Topic 1: Overview

### Pre-AP Geometry Course Syllabus Page 1

Pre-AP Geometry Course Syllabus 2015-2016 Welcome to my Pre-AP Geometry class. I hope you find this course to be a positive experience and I am certain that you will learn a great deal during the next

### Math 96: Intermediate Algebra in Context

: Intermediate Algebra in Context Syllabus Spring Quarter 2016 Daily, 9:20 10:30am Instructor: Lauri Lindberg Office Hours@ tutoring: Tutoring Center (CAS-504) 8 9am & 1 2pm daily STEM (Math) Center (RAI-338)

### Sight Word Assessment

Make, Take & Teach Sight Word Assessment Assessment and Progress Monitoring for the Dolch 220 Sight Words What are sight words? Sight words are words that are used frequently in reading and writing. Because

### The Indices Investigations Teacher s Notes

The Indices Investigations Teacher s Notes These activities are for students to use independently of the teacher to practise and develop number and algebra properties.. Number Framework domain and stage:

### Reflective Teaching KATE WRIGHT ASSOCIATE PROFESSOR, SCHOOL OF LIFE SCIENCES, COLLEGE OF SCIENCE

Reflective Teaching KATE WRIGHT ASSOCIATE PROFESSOR, SCHOOL OF LIFE SCIENCES, COLLEGE OF SCIENCE Reflective teaching means looking at what you do in the classroom, thinking about why you do it, and thinking

### MTH 141 Calculus 1 Syllabus Spring 2017

Instructor: Section/Meets Office Hrs: Textbook: Calculus: Single Variable, by Hughes-Hallet et al, 6th ed., Wiley. Also needed: access code to WileyPlus (included in new books) Calculator: Not required,

### Mathematics process categories

Mathematics process categories All of the UK curricula define multiple categories of mathematical proficiency that require students to be able to use and apply mathematics, beyond simple recall of facts

### Foothill College Fall 2014 Math My Way Math 230/235 MTWThF 10:00-11:50 (click on Math My Way tab) Math My Way Instructors:

This is a team taught directed study course. Foothill College Fall 2014 Math My Way Math 230/235 MTWThF 10:00-11:50 www.psme.foothill.edu (click on Math My Way tab) Math My Way Instructors: Instructor:

### Math 098 Intermediate Algebra Spring 2018

Math 098 Intermediate Algebra Spring 2018 Dept. of Mathematics Instructor's Name: Office Location: Office Hours: Office Phone: E-mail: MyMathLab Course ID: Course Description This course expands on the

### Lecture Videos to Supplement Electromagnetic Classes at Cal Poly San Luis Obispo

2017 Pacifc Southwest Section Meeting: Tempe, Arizona Apr 20 Paper ID #20713 Lecture Videos to Supplement Electromagnetic Classes at Cal Poly San Luis Obispo Dr. Dean Arakaki, Cal Poly State University

### Afm Math Review Download or Read Online ebook afm math review in PDF Format From The Best User Guide Database

Afm Math Free PDF ebook Download: Afm Math Download or Read Online ebook afm math review in PDF Format From The Best User Guide Database C++ for Game Programming with DirectX9.0c and Raknet. Lesson 1.

### Workshop Guide Tutorials and Sample Activities. Dynamic Dataa Software

VERSION Dynamic Dataa Software Workshop Guide Tutorials and Sample Activities You have permission to make copies of this document for your classroom use only. You may not distribute, copy or otherwise

### MATH 108 Intermediate Algebra (online) 4 Credits Fall 2008

MATH 108 Intermediate Algebra (online) 4 Credits Fall 2008 Instructor: Nolan Rice Math Lab: T 2:00 2:50 Office: SHL 206-F Office Hours: M/F 2:00 2:50 Phone/Voice Mail: 732.6819 W 4:30 5:20 E-mail: nrice@csi.edu

### ALEKS. ALEKS Pie Report (Class Level)

ALEKS ALEKS Pie Report (Class Level) The ALEKS Pie Report at the class level shows average learning rates and a detailed view of what students have mastered, not mastered, and are ready to learn. The pie

### Interpreting Graphs Middle School Science

Middle School Free PDF ebook Download: Download or Read Online ebook interpreting graphs middle school science in PDF Format From The Best User Guide Database. Rain, Rain, Go Away When the student council

### LESSON PLANS: AUSTRALIA Year 6: Patterns and Algebra Patterns 50 MINS 10 MINS. Introduction to Lesson. powered by

Year 6: Patterns and Algebra Patterns 50 MINS Strand: Number and Algebra Substrand: Patterns and Algebra Outcome: Continue and create sequences involving whole numbers, fractions and decimals. Describe

### Contents. Foreword... 5

Contents Foreword... 5 Chapter 1: Addition Within 0-10 Introduction... 6 Two Groups and a Total... 10 Learn Symbols + and =... 13 Addition Practice... 15 Which is More?... 17 Missing Items... 19 Sums with

### Teaching a Laboratory Section

Chapter 3 Teaching a Laboratory Section Page I. Cooperative Problem Solving Labs in Operation 57 II. Grading the Labs 75 III. Overview of Teaching a Lab Session 79 IV. Outline for Teaching a Lab Session

### Julia Smith. Effective Classroom Approaches to.

Julia Smith @tessmaths Effective Classroom Approaches to GCSE Maths resits julia.smith@writtle.ac.uk Agenda The context of GCSE resit in a post-16 setting An overview of the new GCSE Key features of a

T894 Mathematics Success Grade 7 [OBJECTIVE] The student will find probabilities of compound events using organized lists, tables, tree diagrams, and simulations. [PREREQUISITE SKILLS] Simple probability,

### GUIDE TO THE CUNY ASSESSMENT TESTS

GUIDE TO THE CUNY ASSESSMENT TESTS IN MATHEMATICS Rev. 117.016110 Contents Welcome... 1 Contact Information...1 Programs Administered by the Office of Testing and Evaluation... 1 CUNY Skills Assessment:...1

### How to make an A in Physics 101/102. Submitted by students who earned an A in PHYS 101 and PHYS 102.

How to make an A in Physics 101/102. Submitted by students who earned an A in PHYS 101 and PHYS 102. PHYS 102 (Spring 2015) Don t just study the material the day before the test know the material well

### Penn State University - University Park MATH 140 Instructor Syllabus, Calculus with Analytic Geometry I Fall 2010

Penn State University - University Park MATH 140 Instructor Syllabus, Calculus with Analytic Geometry I Fall 2010 There are two ways to live: you can live as if nothing is a miracle; you can live as if

### Math-U-See Correlation with the Common Core State Standards for Mathematical Content for Third Grade

Math-U-See Correlation with the Common Core State Standards for Mathematical Content for Third Grade The third grade standards primarily address multiplication and division, which are covered in Math-U-See

### EMPOWER Self-Service Portal Student User Manual

EMPOWER Self-Service Portal Student User Manual by Hasanna Tyus 1 Registrar 1 Adapted from the OASIS Student User Manual, July 2013, Benedictine College. 1 Table of Contents 1. Introduction... 3 2. Accessing

### Mathematics Program Assessment Plan

Mathematics Program Assessment Plan Introduction This assessment plan is tentative and will continue to be refined as needed to best fit the requirements of the Board of Regent s and UAS Program Review

### EGRHS Course Fair. Science & Math AP & IB Courses

EGRHS Course Fair Science & Math AP & IB Courses Science Courses: AP Physics IB Physics SL IB Physics HL AP Biology IB Biology HL AP Physics Course Description Course Description AP Physics C (Mechanics)

### Donnelly Course Evaluation Process

Donnelly Course Evaluation Process Contents Donnelly Course Evaluation Process... 2 The Rules... 2 From the Student Perspective... 3 From the Faculty Perspective... 7 From the Moodle Admin Perspective...

### Mathematics Scoring Guide for Sample Test 2005

Mathematics Scoring Guide for Sample Test 2005 Grade 4 Contents Strand and Performance Indicator Map with Answer Key...................... 2 Holistic Rubrics.......................................................

### Instructor: Matthew Wickes Kilgore Office: ES 310

MATH 1314 College Algebra Syllabus Instructor: Matthew Wickes Kilgore Office: ES 310 Longview Office: LN 205C Email: mwickes@kilgore.edu Phone: 903 988-7455 Prerequistes: Placement test score on TSI or

Curriculum Guide Radius STEM Readiness TM While today s teens are surrounded by technology, we face a stark and imminent shortage of graduates pursuing careers in Science, Technology, Engineering, and

### OPTIMIZATINON OF TRAINING SETS FOR HEBBIAN-LEARNING- BASED CLASSIFIERS

OPTIMIZATINON OF TRAINING SETS FOR HEBBIAN-LEARNING- BASED CLASSIFIERS Václav Kocian, Eva Volná, Michal Janošek, Martin Kotyrba University of Ostrava Department of Informatics and Computers Dvořákova 7,

### Lecture 2: Quantifiers and Approximation

Lecture 2: Quantifiers and Approximation Case study: Most vs More than half Jakub Szymanik Outline Number Sense Approximate Number Sense Approximating most Superlative Meaning of most What About Counting?

### Introduction and Motivation

1 Introduction and Motivation Mathematical discoveries, small or great are never born of spontaneous generation. They always presuppose a soil seeded with preliminary knowledge and well prepared by labour,

### Ohio s Learning Standards-Clear Learning Targets

Ohio s Learning Standards-Clear Learning Targets Math Grade 1 Use addition and subtraction within 20 to solve word problems involving situations of 1.OA.1 adding to, taking from, putting together, taking

### AU MATH Calculus I 2017 Spring SYLLABUS

AU MATH 191 950 Calculus I 2017 Spring SYLLABUS AU Math 191 950 Calculus I Consortium of Adventist Colleges and Universities Interactive Online Format This course follows an interactive online format with

### School of Innovative Technologies and Engineering

School of Innovative Technologies and Engineering Department of Applied Mathematical Sciences Proficiency Course in MATLAB COURSE DOCUMENT VERSION 1.0 PCMv1.0 July 2012 University of Technology, Mauritius

### Probability and Statistics Curriculum Pacing Guide

Unit 1 Terms PS.SPMJ.3 PS.SPMJ.5 Plan and conduct a survey to answer a statistical question. Recognize how the plan addresses sampling technique, randomization, measurement of experimental error and methods

### Centre for Evaluation & Monitoring SOSCA. Feedback Information

Centre for Evaluation & Monitoring SOSCA Feedback Information Contents Contents About SOSCA... 3 SOSCA Feedback... 3 1. Assessment Feedback... 4 2. Predictions and Chances Graph Software... 7 3. Value

### Functional Skills Mathematics Level 2 assessment

Functional Skills Mathematics Level 2 assessment www.cityandguilds.com September 2015 Version 1.0 Marking scheme ONLINE V2 Level 2 Sample Paper 4 Mark Represent Analyse Interpret Open Fixed S1Q1 3 3 0

### Focus of the Unit: Much of this unit focuses on extending previous skills of multiplication and division to multi-digit whole numbers.

Approximate Time Frame: 3-4 weeks Connections to Previous Learning: In fourth grade, students fluently multiply (4-digit by 1-digit, 2-digit by 2-digit) and divide (4-digit by 1-digit) using strategies

### Ghanaian Senior High School Students Error in Learning of Trigonometry

OPEN ACCESS INTERNATIONAL JOURNAL OF ENVIRONMENTAL & SCIENCE EDUCATION 2017, VOL. 12, NO. 8, 1709-1717 Ghanaian Senior High School Students Error in Learning of Trigonometry Farouq Sessah Mensah a a University

### 6 Financial Aid Information

6 This chapter includes information regarding the Financial Aid area of the CA program, including: Accessing Student-Athlete Information regarding the Financial Aid screen (e.g., adding financial aid information,

### Student Handbook. This handbook was written for the students and participants of the MPI Training Site.

Student Handbook This handbook was written for the students and participants of the MPI Training Site. Purpose To enable the active participants of this website easier operation and a thorough understanding

DegreeWorks Advisor Reference Guide Table of Contents 1. DegreeWorks Basics... 2 Overview... 2 Application Features... 3 Getting Started... 4 DegreeWorks Basics FAQs... 10 2. What-If Audits... 12 Overview...

### Enhancing Students Understanding Statistics with TinkerPlots: Problem-Based Learning Approach

Enhancing Students Understanding Statistics with TinkerPlots: Problem-Based Learning Approach Krongthong Khairiree drkrongthong@gmail.com International College, Suan Sunandha Rajabhat University, Bangkok,

### Grading Policy/Evaluation: The grades will be counted in the following way: Quizzes 30% Tests 40% Final Exam: 30%

COURSE SYLLABUS FALL 2010 MATH 0408 INTERMEDIATE ALGEBRA Course # 0408.06 Course Schedule/Location: TT 09:35 11:40, A-228 Instructor: Dr. Calin Agut, Office: J-202, Department of Mathematics, Brazosport

### NCAA Eligibility Center High School Portal Instructions. Course Module

NCAA Eligibility Center High School Portal Instructions Course Module www.eligibilitycenter.org Click here to enter the High School Portal Before logging in, you can peruse the resource page or look at

### Math 121 Fundamentals of Mathematics I

I. Course Description: Math 121 Fundamentals of Mathematics I Math 121 is a general course in the fundamentals of mathematics. It includes a study of concepts of numbers and fundamental operations with

### Improving Conceptual Understanding of Physics with Technology

INTRODUCTION Improving Conceptual Understanding of Physics with Technology Heidi Jackman Research Experience for Undergraduates, 1999 Michigan State University Advisors: Edwin Kashy and Michael Thoennessen

### Kendra Kilmer Texas A&M University - Department of Mathematics, Mailstop 3368 College Station, TX

Kendra Kilmer Texas A&M University - Department of Mathematics, Mailstop 3368 College Station, TX 77843-3368 kilmer@math.tamu.edu Professional Work Experience Texas A&M University, Department of Mathematics