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The purpose of the study was to help teachers understand the importance of using the Lattice Method in teaching multiplication with whole numbers and decimals to students with learning disabilities. The common errors made by learning disabled students in multiplication with whole numbers were analyzed. In the study, students with learning disabilities were able to do multiplication by the traditional way only with 15% accuracy, but they skillfully used the Lattice Method to multiply more than 2 digit numbers with more than 97% accuracy. Special education teachers who used the method to teach their students multiplication with whole numbers and decimals achieved great success in their classes. The method ensured that students with learning disabilities avoided misplacing place value and other errors in multiplying algorithms. Proper instructions greatly reduced the repetition of student errors in multiplication. It was also found that students were not able to multiply two or three digits in the traditional way, but they were able to multiply two or more digits with the Lattice Method in accuracy ranging from 90% to 100%. In addition, the method was used to teach decimal multiplication to students with learning disabilities very effectively. Overall, statistically significant differences between the two tests were found on the pre-test (significant at the 0.01 level) and the post-test (significant at the 0.05 level) on the basis of the formula of Chi-square. Students obtained much higher scores in the test with the Lattice Method than with the traditional way of multiplication. Above all, this method improved self-esteem and self-confidence in the students. (YDS)

This article describes constructivist techniques for teaching concepts of decimals and metrics through the combination of innovative measuring tools, activities and videos in classrooms. Even though the chronological age of the students involved differed--fifth and sixth graders or pre-service teachers--it was discovered that similar activities helped all students learn the decimal and metric systems. Through teacher observation and informal interviews made by the authors, recommendations are made to upper-elementary math and science teachers as well as mathematics and science methods teachers at the university level. (Author/WRM)

This teacher's guide and student guide are designed to accompany a general mathematics textbook that contains supplemental readings, activities, and methods adapted for secondary students who have disabilities and other students with diverse learning needs. The materials are designed to help these students succeed in regular education content courses and include simplified text and smaller units of study. The curriculum correlates to Florida's Sunshine State Standards and is divided into the following 11 units of study: (1) whole numbers; (2) fractions; (3) decimals; (4) percents; (5) geometry; (6) measurement; (7) perimeter/area; (8) graphs; (9) central tendency; (10) integers; and (11) equations. For each unit, the teacher's guide includes a general description of the unit's content and the unit's focus. Key prerequisite skills for the students are also listed in this guide. A suggested order of nine teaching events for the unit is given in a scope and sequence chart. These nine events include: determining present level; introducing the concept; presenting vocabulary; conducting initial learning activity; presenting concepts and examples; addressing common errors; reinforcing skills; summarizing the lesson; and administering a posttest. Answer keys for the quizzes and activities sheets are also included. Appendices in the teacher's guide contain a chart describing standards and benchmarks. The student guide contains vocabulary lists, explanation of content, and practice exercises designed to evaluate comprehension. (CR)

This publication contains the three numeracy units of the three levels of Support Materials for Agricultural Training (SMAT) in farm management and leadership: Level 1 (starting), 2 (continuing), and 3 (completing). The units are designed to help the learner improve his or her numeracy skills needed to deal with farm management. SMAT materials can be used by the individual, with a mentor, or in a group or class. An introduction describes how to use the materials, types of activities, and materials needed. Each level contains agriculture-related mathematics activities. Model answers are provided. Topics covered in Level 1 are as follows: calculator use; invoices and payment advice sheets; percentage and decimals; and measuring length, area, and perimeter. Topics covered in Level 2 are budgets, costs, and comparing costs to income. Topics covered in Level 3 are measuring and volume. (YLB)

This collection of lesson plans and activities for students aged 9-11 years is based on a science curriculum developed by a group of Caribbean nations. The activities pertain to topics such as place value, prime and composite numbers, the sieve of Eratosthenes, square numbers, factors and multiples, sequences, averages, geometry, symmetry, tessellations, ominoes, measurement, capacity and mass, metric mass, time, money, fractions, decimals, percentage and ratio, graphs, and problem solving. The activities are organized by objectives from the core curriculum and frequently include worksheets for students. (DDR)

This instructor's manual for workplace trainers contains the materials required to conduct a course in basic workplace mathematics skills. The course consists of six lessons for workers and two lessons for supervisors that discuss the following: concepts taught in the six lessons; workers' progress in the individual lessons; and strategies for helping workers continue to develop the basic math skills taught in the course. The following materials are provided for each course: lesson plan, learning activities based on real-life situations, handouts, assessments (including pretests and posttests), and transparencies. Each lesson plan contains objectives, a list of materials needed, classroom setup information, and detailed instructions for conducting all activities. The following topics are covered: using estimation and rounding techniques; converting from the English system of measurement to the metric system; using fractions and decimals; calculating rates, ratios, proportions, and percentages; and using calculators. (MN)

This instructor's guide contains materials for a 20-30 hour course designed to address essential math skills in the workplace. The course description lists target audience, general objective, and typical results observed. The next section gives instructors basic information related to providing successful educational programs in a workplace setting, an instructor's lexicon of strategies and principles that can be used in teaching, instructor's role and responsibilities, and course objectives. An explanation of lesson format lists six parts of the template used to design the lessons--understanding/outcome, materials, demonstration, exercise/engagement, workplace application, and evaluation/comments. A sample template and explanation of each part follows. A section on planning and scheduling deals with time requirements, class size, expected outcomes, prerequisites, and suggested timing for each lesson. Lesson topics are as follows: math memories; keeping track of learning; introduction to math operations; place value; rounding off numbers; using a calculator to check your work; introduction to decimals; changing time to decimal equivalents; calculating your pay; rounding decimals; and finding an average. Supplementary lessons are provided on fractions and finding percentages. Appendixes include a word list and preview and review with scoring guide. (YLB)

This companion document to the instructor's guide for a course designed to prepare employees for statistical process control (SPC) training given at their workplace by refreshing math skills and building the concepts and vocabulary necessary to understand SPC in manufacturing environments. SPC-Prep 1 addresses the math skills necessary to perform SPC calculations. The manual provides materials on these topics: math memories; keeping track of learning; math operations; place value; rounding off numbers; finding an average; decimals; and positive and negative numbers. Information sheets and exercise sheets are provided. A word list and answer key for the exercises are provided. (YLB)

This instructor's guide contains materials for a course designed to prepare employees for statistical process control (SPC) training given at their workplace by refreshing math skills and building the concepts and vocabulary necessary to understand SPC in manufacturing environments. SPC-Prep 1 addresses the math skills necessary to perform SPC calculations. SPC-Prep 2 includes application of the math concepts in SPC situations and the building a base of vocabulary and major concepts for actual SPC training. The course description lists target audience, general objective, and typical results observed. The next section gives instructors basic information related to providing successful educational programs in a workplace setting, an instructor's lexicon of strategies and principles that can be used in teaching, instructor's role and responsibilities, and course objectives. An explanation of lesson format lists six parts of the lessons--outcome, materials, demonstration, exercise, workplace application, and evaluation. A sample template and explanation of each part follows. A section on planning and scheduling deals with time requirements, class size, expected outcomes, prerequisites, and suggested timing for each lesson. Topics of SPC-Prep 1 lessons are as follows: math memories; keeping track of learning; math operations; place value; rounding off numbers; finding an average; decimals; and positive and negative numbers. Supplementary lessons focus on fractions and finding percentages. A word list, glossary, and preview and review with scoring guide are provided. Topics of SPC-Prep 2 lessons are as follows: keeping track of learning; quality in the workforce; statistics; SPC terminology; tables, charts, graphs; acceptable range; and QS (Quality Standards) 9000. A preview and review with answer key are appended. (YLB)

This instructor's guide contains materials for a 40-hour course designed to refresh math skills for current computer numerical control machine operators. The course uses two instructional methods: computer-based multimedia and traditional instruction. The course description lists target audience and general objective. The next section gives instructors basic information related to providing successful educational programs in a workplace setting, an instructor's lexicon of strategies and principles that can be used in teaching, instructor's role and responsibilities, and course objectives. An explanation of lesson format describes these components of each lesson plan: unit name; lesson name; description and specific goals; objectives; prerequisite skills; technology use; materials needed; teacher to teacher; pretest; posttest; purpose/rationale; procedures/activities; evaluation and extension activities; resources; and homework. A section on planning and scheduling deals with time requirements, class size, expected outcomes, prerequisites, and other materials needed. Lesson topics are as follows: whole numbers; decimal numbers; positive and negative numbers; percents; measurements and statistics; geometry; metric system; and magnitude. Appendixes include a glossary and preview and review with answer keys. (YLB)

This instructor guide, which was developed for use in a manufacturing firm's advanced technical preparation program, contains the materials required to present a learning module that is designed to prepare trainees for the program's statistical process control module by improving their basic math skills and instructing them in basic calculator operation. The guide is divided into five sections. The first section contains the following preliminary information: individual assessment sheet, instructor notes, and primary objectives. The second section is a course outline, and the third section contains the module lessons and worksheets, which are devoted to the following topics: using a calculator, calculating totals, calculating averages, calculating process averages, rounding off decimals, and calculating ranges. The final two sections consist of answers to the worksheets and pretests and posttests. (MN)

This document, which was developed to meet the needs of trainers and workers in Australia's automotive industry for learning activities designed to boost auto workers' numeracy skills, contains a total of 33 learning activities organized into 8 sections. The topics covered in the individual sections are as follows: calculators (key words and calculators, further practice); decimals (dials, gauges, and scales; decimal points; using sensible numbers; the first decimal place); percentages in daily life (familiar percentages, using calculators); percentages at work (lots of hundreds, faulty parts); charts and graphs (understanding charts, pumping petrol, types of charts, pie charts, plots); where to start solving a problem (ordering operations, using brackets, helpful rules); and what averages mean (using averaging to make predictions, distortion of averages, averages and ranges in workplace charts). Included in each section are the following: trainer's notes detailing procedures for introducing and using the different activities; activity sheets designed to introduce concepts and skills to groups using interactive, hands-on group discussion activities; practice sheets; and answers to all problems. Contains an annotated bibliography of 3 Australian resource organizations and 33 print resources concerned with adult literacy and numeracy. (MN)

This document includes a final report and curriculum guide from a project to develop a Science and Math Applications curriculum that related science and math to everyday life and promoted confidence in adult basic education students in their science and math skills. The report describes how the curriculum used traditional teaching methods to teach basic science and math concepts with reinforcement through hands-on activities. The targeted audience was 20 adult basic education students who expressed a desire to increase their math and science abilities and an initial fear of science and math. Pre- and postassessment data showed that, on the average, student grade levels rose two levels during their time in the program. Students often left the program with a new attitude toward these subject areas. The math component of the curriculum is broken down into nine subject areas: problem solving; decimal skills; fraction skills; percent skills; probability, ratio, and proportion skills; measurement; data analysis; algebra; and geometry. The science component includes nine subject areas: building reading skills; applying science concepts; analyzing science materials; evaluating science materials; plant and animal biology; human biology; earth science; chemistry; and physics. An outline for each subject area correlates skills with assessment, materials, and teaching strategy and techniques. Handouts and an 18-item bibliography are provided. (YLB)

Developed as part of the ABCs of Construction National Workplace Literacy Project, this instructional module consists of instructional materials and application problems designed to help persons employed as millwrights learn to measure decimals. The six exercises included in the module each consist of series of problems in which students are required to measure, read, add, and subtract decimals and use the "OPEN" (Operation, Pick, Execute, Note) approach to working with decimals. (MN)

This manual contains a workshop curriculum that offers background information and activities rooted in the whole language approach. It is designed to address needs of employees with skill levels below fifth grade. Section I is an introduction to the changing workplace environment. Sections II-V cover problem solving, communication (speaking skills, listening skills, reading comprehension, writing), discussion and debate, and math (place value, decimals, percentages, metrics). Each section may consist of one or more parts, each of which lists skills to be learned and provides instructions for the workshop trainer, activities or exercises, and reference list. Appendixes contain the following: information on characteristics of adult learners and tutoring in the workplace; extension activities in problem solving, listening and speaking, writing, and discussion and debate; and information on assessment tests and task analysis. Supplementary materials for use in conjunction with the manual are attached. Intended especially for those tutors without whole language training, these sections cover the following topics: the reading process, learning styles, special reader problems, whole language approach, whole language reading and writing strategies, informal measures for selecting suitable reading material, readability formulas, phonic analysis, word families, syllables/compound words/contractions, sight words, tutor "real world" materials, teaching critical thinking, assessment, and goal setting. (YLB)

Developed as part of a National Workplace Literacy Program, this lesson focuses on terms and mathematical operations associated with Statistical Process Control (SPC) in the foundry industry. With appropriate assistance and preparatory work, workers testing between grades 4 and 9 on the Test of Adult Basic Education Locator should be able to use the lesson. The individualized lesson is intended to supplement small-group SPC activities. It teaches terms and mathematics used in quality control at Bodine-Robinson and Robinson Foundry. Reading material is followed by questions that ask about the instructional material. Some terms that are covered include key characteristic, specification, aim, and control limits. Mathematics areas include adding and subtracting SPC measurements, adding and subtracting decimals, figuring averages, and figuring ranges. A true-false quiz on the material is provided. (YLB)

This document offers instructional materials for a 32-hour course on math operations involving graphs/statistics, measurement (English and metric), geometry, exponential notation, and scientific notation as applied in the workplace. The course was part of a workplace literacy project developed by Mercer County Community College (New Jersey) and its partners. The document begins with a description of the project, a course outline (including objectives, topical outline, textbook references, and list of supplies), and a pretest. The rest of the document consists of information sheets, exercises, and quizzes for learners. (CML)

This document offers instructional materials for a 60-hour course on basic math operations involving decimals, fractions, and proportions as applied in the workplace. The course, part of a workplace literacy project developed by Mercer County Community College (New Jersey) and its partners, contains the following: course outline; 17 lesson objectives pages, each of which is followed by a series of problems to be solved, an answer key, and a quiz; and two pretests and two posttests. The lessons cover the following topics: basic decimal concepts; addition and multiplication of decimals; subtraction and division of decimals; problem-solving with decimals; factoring into prime numbers; basic fraction concepts; multiplication and division of fractions; addition and subtraction of fractions; addition and subtraction of mixed numbers; problem solving with fractions; ratios and rates; solving proportions; decimal/percent/fraction conversions; solving percent problems; percent word problems and shortcuts; percent increase and decrease; and applications of percents. (CML)

This document offers instructional materials for a 60-hour course on math operations involving decimals, fractions, proportions, statistics, probability, measurement, geometry, and linear algebra as applied in the workplace. The course was part of a workplace literacy project developed by Mercer County Community College (New Jersey) and its partners. The following topics are covered: basic decimal concepts and problem-solving techniques, basic fraction concepts and problem-solving techniques, basics of percents and solving percent problems, ratio and proportion, statistics, graph basics, data analysis, probability basics, measurement systems and geometry basics, and linear algebra. The document begins with a description of the project and a course outline that includes objectives, topical outline, textbook references, and list of supplies. The rest of the document consists of information sheets and exercises for learners. The document ends with two forms of a pretest and one answer key. (CML)

The Calculators and Mathematics Project, Los Angeles (CAMP-LA), funded by the National Science Foundation for developing use of technology in the classroom, developed curriculum materials focused solely on the use of calculators. The project was developed in three stages. The first stage studied the mathematics curriculums from different states and identified topics that are not included but should be if every student had a calculator, topics treated in too much detail, and topics no longer appropriate. Based on this information, CAMP-LA compiled a prototype curriculum organized by grade level to be consistent with the "California Mathematic Framework" strands. The second stage developed lessons to cover the topics through the curriculum. The third stage field tested these lessons in various parts of the country. This book is composed of lessons for grades 5-6 in the series. The introduction gives an overview of CAMP-LA, information on how to use the lesson plans, a discussion of assessment approaches, and a scope and sequence for the book. The remainder of the book is composed of 43 lessons in four chapters: Patterns and Functions, Logic/Statistics and Probability, Measurement/Geometry, and Number/Algebra. Each lesson is broken down into three sections. The three sections are labeled: "Grade", including grade level, strand, skill required, and purpose; "Management", including class organization, time frame, materials needed, vocabulary, and prerequisite skills; and "Lesson" including suggestions for directed instruction, guided practice, independent practice, evaluation, and home activity. (MDH)

The National Science Foundation funded Calculators and Mathematics Project, Los Angeles (CAMP-LA) developed curriculum materials focused solely on the use of calculators. The project was developed in three stages. The first stage studied the mathematics curriculums from different states and identified topics that are not included but should be if every student had a calculator, topics treated in too much detail, and topics no longer appropriate. Based on this information, CAMP-LA compiled a prototype curriculum organized by grade level to be consistent with the "California Mathematics Framework" strands. The second stage developed lessons to cover the topics through the curriculum. The third stage field tested these lessons in various parts of the country. This book is composed of lessons for grades 3-4 in the series. The introduction gives an overview of CAMP-LA, information on how to use the lesson plans, a discussion of assessment approaches, and a scope and sequence for the book. The remainder of the book is composed of 49 lessons in six chapters: Number, Measurement, Geometry, Patterns and Functions, Statistics and Probability, Logic, and Algebra. Each lesson is broken down into three sections. The three secions are labeled: "Grade", including grade level, strand, skill required, and purpose; "Management", including class organization, time frame, materials needed, vocabulary, and prerequisite skills; and "Lesson" including suggestions for directed instruction, guided practice, independent practice, evaluation, and home activity. (MDH)

This module is the third in a series of 12 learning modules designed to teach occupational mathematics. Blocks of informative material and rules are followed by examples and practice problems. The solutions to the practice problems are found at the end of the module. Specific topics covered include calculator addition, adding measurements of different levels of precision, and word problems. (YLB)

This module is the 11th in a series of 12 learning modules designed to teach occupational mathematics. Blocks of informative material and rules are followed by examples and practice problems. The solutions to the practice problems are found at the end of the module. Specific topics covered include multiplication, powers, calculator use, and roots. (YLB)

This module is the 10th in a series of 12 learning modules designed to teach occupational mathematics. Blocks of informative material and rules are followed by examples and practice problems. The solutions to the practice problems are found at the end of the module. Specific topics covered include the metric concepts of mass, weight, and volume capacity and problem solving with these metric units. (YLB)

This module is the ninth in a series of 12 learning modules designed to teach occupational mathematics. Blocks of informative material and rules are followed by examples and practice problems. The solutions to the practice problems are found at the end of the module. Specific topics covered include measurement conversions, the English system of weights and measures, and the metric system. (YLB)

This module is the first in a series of 12 learning modules designed to teach occupational mathematics. Designed for improving machine shop technology skills, this module begins with an introduction to the topic. Blocks of informative material and rules are followed by examples and practice problems. The solutions to the practice problems are found at the end of the module. Specific topics covered include digits, place value, and decimals. (YLB)

This module is the sixth in a series of 12 learning modules designed to teach occupational mathematics. Blocks of informative material and rules are followed by examples and practice problems. The solutions to the practice problems are found at the end of the module. Specific topics covered include calculator division, mixed number fractions, division of measurements, fraction to decimal conversion, rules of accuracy, and word problems. (YLB)

This module is the seventh in a series of 12 learning modules designed to teach occupational mathematics. Blocks of informative material and rules are followed by examples and practice problems. The solutions to the practice problems are found at the end of the module. Specific topics covered include fractions, fraction to decimal conversion, reducing and raising fractions, measurement, mixed numbers, and improper fractions. (YLB)

This module is the fifth in a series of 12 learning modules designed to teach occupational mathematics. Blocks of informative material and rules are followed by examples and practice problems. The solutions to the practice problems are found at the end of the module. Specific topics covered include calculator multiplication of decimals, multiplication of measurements, significant digits, and accuracy of a measurement. (YLB)

This module is the second in a series of 12 learning modules designed to teach occupational mathematics. Blocks of informative material and rules are followed by examples and practice problems. The solutions to the practice problems are found at the end of the module. Specific topics covered include rounding off, precision of measurement, and the concept of least precise measurement. (YLB)

This module is the fourth in a series of 12 learning modules designed to teach occupational mathematics. Blocks of informative material and rules are followed by examples and practice problems. The solutions to the practice problems are found at the end of the module. Specific topics covered include calculator subtraction, order of operations, and subtraction of measurements. (YLB)