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This booklet, written in Spanish, provides a guide for parents to help their children become successful in school mathematics. The information is divided into four sections: (1) important facts about the mathematics curriculum and mathematics instruction; (2) expectations about participation, calculators, cooperative learning, dialogue, and writing within the typical K-12 mathematics classrooms; (3) examples of leading questions and prompts for parental input with homework; and (4) specific methods to aid in planning for student success in mathematics. A bibliographic appendix includes additional sources for information with addresses, phone numbers, and price quotations, as appropriate. (JJK)

This supplementary math curriculum guide for use with Spanish-speaking students in Chicago public schools' seventh and eighth grade classes employs a contrastive analysis approach. Lessons are presented for objectives for which the instructional strategies used in the United States differ from those in Spanish-speaking countries. (Objectives for which the methodology is the same are taught from the standard math curriculum.) Every lesson has four parts: (1) an explanation of the differences in the instructional strategies used in Spanish-speaking countries and the U.S.; (2) a student activity, in Spanish, to reinforce students' skills in using their native language and methodologies; (3) suggestions for facilitating students' transition from their native methodology to the U.S. methodology; and (4) a transitional activity which provides students with practice in solving problems using both methodologies and languages. Major topics covered are sets, place value, rational numbers, and real numbers. An English-Spanish vocabulary list is provided. (CMG)

This supplementary math curriculum guide for use with Spanish-speaking, fouth through sixth grade students in Chicago public schools employs a contrastive analysis approach. Lessons are presented for objectives for which the instructional strategies used in the United States differ from those used in Spanish-speaking countries. (Objectives for which the methodology is the same are taught from the standard math curriculum.) Every lesson has four parts: (1) an explanation of the differences in the instructional strategies used in the Spanish-speaking countries and in the U.S.; (2) a student activity, in Spanish, to reinforce students' skills in using their native language and methodologies; (3) suggestions for facilitating the students' transition from their native methodology to the U.S. methodology; and (4) a transitional activity which provides students with practice in solving problems using both methodologies and languages. The major topics covered are place value, operations with whole numbers, rational numbers, and measurement. An English-Spanish vocabulary list is provided. (CMG)

A contrastive analysis approach is used in this supplementary math curriculum guide for Spanish-speaking second and third grade students in Chicago public schools. Lessons are presented for those objectives for which the instructional strategies used in the United States differ from those used in Spanish-speaking countries. (Objectives for which the methodology is the same are taught from the standard math curriculum.) Every lesson has four parts: (1) an explanation of the differences in instructional strategies used in Spanish-speaking countries and the U.S.; (2) a student activity, in Spanish, to reinforce students' skills in using their native language and methodologies; (3) suggestions for facilitating students' transition from their native methodology to the U.S. methodology; and (4) a transitional activity which provides students with practice in solving problems using both methodologies and languages. Major topics covered are place value, operations with whole numbers, and measurement. An English-Spanish vocabulary list is provided. (CMG)

The fundamental importance of basic mathematics to daily life is emphasized in this teacher's guide for special education teachers in Puerto Rico. While it is necessary for the teacher to determine the needs and abilities of each student and adapt the curriculum accordingly, this guide presents, in Spanish, a set of lesson plans, each with an objective and suggested activities toward the objective. Activities are chosen for their practical relevance. Skills are presented in the following areas: (1) numeration, including cardinal, ordinal, and Roman numerals; (2) basic mathematics operations, including fractions and decimals; (3) measurement of time, temperature, volume, weight in the English and metric systems, and the monetary system; and (4) principles of geometry. An appendix provides specific guidance in teaching basic mathematical operations. (Contains 12 references.) (SLD)

This is Part 2 of the teacher's commentary for the grade 4 mathematics program. Part 2 includes the commentary for chapters 6 through 10. Topics covered include addition and subtraction, multiplication and division, geometrical figures, lines and lineal measurement, and fractions. (RH)

This is part two of a three-part SMSG algebra text for high school students. The principal objective of the text is to help the student develop an understanding and appreciation of some of the algebraic structure as a basis for the techniques of algebra. Chapter topics include addition and multiplication of real numbers, subtraction and division of real numbers, factors, exponents, radicals, and polynomials and rational expressions. (RH)

This is part two of a two-part SMSG mathematics text for junior high school students. Key ideas emphasized are structure of arithmetic from an algebraic viewpoint, the real number system, and metric and non-metric relations in geometry. Included are chapters on the rational number system; parallels, parallelograms, triangles, and right prisms; circles; statistics and graphs; mathematical systems; and mathematics in science. (RH)

This is the teacher's commentary for part two of a three-part SMSG algebra text for high school students. The principal objective of the text is to help the student develop an understanding and appreciation of some of the algebraic structure as a basis for the techniques of algebra. Chapter topics include addition and multiplication of real numbers, factors, exponents, radicals, and polynomials and rational expressions. (RH)

This is part two of a two-part SMSG mathematics text for junior high school students. Key ideas emphasized are structure of arithmetic from an algebraic viewpoint, the real number system as a progressing development, and metric and non-metric relations in geometry. Chapter topics include real numbers, similar triangles, variation, polyhedrons, volumes and surface areas, permutations and combinations, and probability. (RH)

This is part one of a two-part SMSG mathematics text for junior high school students. Key ideas emphasized are structure of arithmetic from an algebraic viewpoint, the real number system, and metric and non-metric relations in geometry. Topics included are numbers; cardinal numbers; geometry of lines, points, and planes; geometry of angles, triangles, and other forms; factors and prime numbers; real numbers; area; volume; and rectangles. (RH)

This is the teacher's commentary for part one of a three-part SMSG algebra text for high school students. The principal objective of the text is to help the student develop an understanding and appreciation of some of the algebraic structure as a basis for the techniques of algebra. Chapter topics include congruence; numbers and variables; operations; real numbers; and properties of addition, multiplication, and division. (RH)

This is the student text for part one of a three-part SMSG algebra course for high school students. The principal objective of the text is to help the student develop an understanding and appreciation of some of the algebraic structure as a basis for the techniques of algebra. Chapter topics include congruence; numbers and variables; operations; real numbers; and properties of addition, multiplication, and division. (RH)

This is part one of a two-part SMSG mathematics text for junior high school students. Key ideas emphasized are structure of arithmetic from an algebraic viewpoint, the real number system as a progressing development, and metric and non-metric relations in geometry. Chapter topics include number line and coordinates, equations, scientific notation, applications of percent, and congruence and the Pythagorean property. (RH)

This is Part 1 of the teacher's commentary for the grade 4 mathematics program. Part 1 includes the commentary for chapters 1 through 5. Topics covered include congruence, numbers and number bases, subtraction of numbers, division of numbers, and elementary geometry. References to the student text are cited. (RH)

This is part one of a two-part SMSG mathematics text for high school students. Topics include plane geometry, real numbers, triangles and angles, congruence, construction, parallel lines, perpendicular lines, and parallelograms. The text is written in Spanish. (RH)

Continuing the theme of the school as a community, the teacher's guide to the science/math strand of unit five presents both instructional and assessment activities for kits 17-20. Focus, materials and objective for each activity are in Spanish and English; teacher instructions are in Spanish only. In kit 17 the science activities deal with the environmental components of the universe: matter, energy and force. The concept of change is introduced, and a histogram is developed and utilized. Solids and liquids are identified, and liquids are combined in order to observe their appearance, solubility, and density. In kit 18, students identify the interaction of the environmental components within the school environment, measure and chart temperatures, and work with clocks, sundials, and shadow sizes to show times of day. Kit 19 treats weather. Clouds are observed, imaginary daily weather conditions are recorded, and a weather chart is constructed. Students learn to distinguish between inference and observation. Kit 20 is concerned with equilibrium as it occurs in nature and how it is affected by interaction. Math activities include reviewing first grade concepts, counting by 5's to 100, adding and subtracting combinations from 1 to 10, ordering and comparing numbers, and adding numerals by 2's to 20. (DS)

This is one of a series of student booklets designed for use in a bilingual mathematics program in grades 6-8. The general format is to present each page in both Spanish and English. The mathematical topics in this booklet include subtraction of fractions and mixed numbers. (MK)

This is one of a series of student booklets designed for use in a bilingual mathematics program in grades 6-8. The general format is to present each page in both Spanish and English. The mathematical topics in this booklet include multiplication and division. (MK)

This guide covers the second part of a bilingual, sequential mathematics course. The course integrates culturally relevant situations and illustrations with mathematics to reinforce the student's self-concept and encourage cultural pride. This program may be used as a self-contained continuum, as a supplement to another course of study, for individualized instruction, or in the large-group, traditional classroom. These materials are written in English and Spanish for grades 6-8, but may be used for other grade levels. The guide includes suggestions on grouping, presentations, goal setting, scheduling, a testing center, a mathematics laboratory, assignment of materials, and grading. Also included are an overview, behavioral objectives, a section which explains some mathematical procedures taught in Hispanic countries, and duplication masters and transparency masters. The mathematical topics covered are: multiplication and division of fractions, geometry, measurement, and addition and subtraction of fractions. (Author/MK)

This is one of a series of student booklets designed for use in a bilingual mathematics program in grades 6-8. The general format is to present each page in both Spanish and English. The mathematical topics in this booklet include addition of fractions and mixed numbers. (MK)

This is one of a series of student booklets designed for use in a bilingual mathematics program in grades 6-8. The general format is to present each page in both Spanish and English. The mathematical topics in the booklet include points, lines, planes, space, angles, and intersection and union of sets. (MK)

This is one of a series of student booklets designed for use in a bilingual mathematics program in grades 6-8. The general format is to present each page in both Spanish and English. The mathematical topics in this booklet include equivalent fractions, mixed numbers, and multiplication of fractions and mixed numbers. (MK)

This is one of a series of student booklets designed for use in a bilingual mathematics program in grades 6-8. The general format is to present each page in both Spanish and English. The mathematical topics in this booklet include factors, prime and composite numbers, divisibility, and exponents. (MK)

This is one of a series of student booklets designed for use in a bilingual mathematics program in grades 6-8. The general format is to present each page in both Spanish and English. The mathematical topics in this booklet include measurement, perimeter, and area. (MK)

This is one of a series of student booklets designed for use in a bilingual mathematics program in grades 6-8. The general format is to present each page in both Spanish and English. The mathematical topics in this booklet include reciprocals, complex fractions, and division of fractions. (MK)

This guide covers the first part of a bilingual, sequential mathematics course. The course integrates culturally relevant situations and illustrations with mathematics to reinforce the student's self-concept and encourage cultural pride. This program may be used as a self-contained continuum, as a supplement to another course of study, for individualized instruction, or in the large-group, traditional classroom. These materials are written in English and Spanish for grades 6-8, but may be used for other grade levels. The guide includes suggestions on grouping, presentations, goal setting, scheduling, a testing center, a mathematics laboratory, assignment of materials, and grading. Also included are an overview, behavioral objectives, patterns for duplicating masters or transparencies and patterns for materials to be used in suggested activities. The mathematical topics covered in this guide include numeration, addition, subtraction, multiplication, division, and measurement. (Author/MK)

This is one of a series of student booklets designed for use in a bilingual mathematics program in grades 6-8. The general format is to present each page in both Spanish and English. The mathematical topics in this booklet include graphing on a number line, place value, using exponents, flow charts, and Roman numerals. (MK)

This is one of a series of student booklets designed for use in a bilingual mathematics program in grades 6-8. The general format is to present each page in both Spanish and English. The mathematical topics in this booklet include liquid, dry, linear, weight, and time measures. (MK)

This is one of a series of student booklets designed for use in a bilingual mathematics program in grades 6-8. The general format is to present each page in both Spanish and English. The mathematical topics in this booklet include addition and subtraction. (MK)

The second unit of instructional and evaluation activities for a science/math curriculum in Spanish developed for first graders make up this teacher's guide. Kits five-eight, each covering a period of two to three weeks, present science and math instruction around the family. The guide lists focus, objective, and materials in English and Spanish for each learning activity; teacher instructions are in Spanish. Specifically, kits contain these themes and activities: (1) who the child is--extending experience with numbers and number combinations, introducing frame directions; (2) the child's needs and wants--observing temperature variance between common substances (water), making and using a thermometer device, adding and subtracting sets of ten, associating temperature differences with movements on a color-coded thermometer; (3) family resources--building on observation skills through taste and smell, teaching safety practices with household substances, working with number names of numerals for future activity with Celsius thermometer; (4) the child's use of resources--comparing and identifying three-dimensional shapes, introducing numerals beyond 10 through groupings of tens plus ones, practicing with numbers 0-99, using Celsius thermometer. (RS)

Designed for use with unit two of the Science/Math curriculum in Spanish developed for grade one, this supplement and ditto packet contains visuals, worksheets, and instructional aids referred to in the teacher's guide corresponding to this unit. Learning activities in kits five through eight center on the theme of the family. Illustrations and materials for both group activities and seatwork by students are to aid in teaching of numbers (through 99), grouping by sets, temperature, shapes, and directions, among other learning activities. Some supplementary materials are to be cut out for manipulations with small groups and by individuals, while others are to be used full size. Ditto masters are of visuals and individual worksheets, which are in general to be presented under supervision rather than as independent tasks. (RS)

Built around a theme of communities in the nation, this teacher's guide for unit eight of a science/math strand for Spanish-speaking children in grade three contains both learning and assessment activities. This unit addresses what the elements are, how needs and wants are satisfied, how change occurs, and what the results of change are. The guide gives focus, objective, and materials for each activity in English and Spanish; detailed teacher instructions are in Spanish. Basic concepts presented are matter, energy, equilibrium, variation, conservation, interaction, adaptation, relativity, change, force, and systems organization. Kits cover pollution--air, noise, solid waste, water, sight; ordinal numbers 1-30; counting by 2's, 3's, 4's; sum of three two-digit numbers; pollution--by nature, effects, control, school/home antipollution campaign; value of coins to $1; addition and subtraction using coins; inverse relation of addition/subtraction; safety--home, electricity, traffic, water, poisonous plants, fire, drugs; first aid; fractions; human body as a group of systems; basic food groups; dental hygiene; diseases; and place value of four-digit numbers. (RS)

Instructional and assessment activities for unit seven of a science/math strand for Spanish-speaking students in grade three focus on the extended community. Activities support four spiraling questions on the elements, wants and needs, change occurrence, and results of change. For each activity, the focus, objective, and materials needed are listed in English and Spanish; detailed teacher instructions are in Spanish only. Content covers plants and animals and their means of survival; life cycles (reproduction, death); impacts of birth/death rates; Roman numerals to XII; the clock, calendar, days of the week, months, and seasons; harmful and beneficial insects; regrouping techniques for adding and subtracting two-digit numbers; ruler, yardstick, and liquid measurements; photosynthesis; nongreen plants; food chains of man/animals; how communities interact; interdependence of living organisms; ecosystem; construction of histogram and bar graph; and identification of line segments, points, intersections, and figures. Science concepts are variation, equilibrium, matter, energy, conservation, relativity, organization systems, interaction, adaptation, change, reproduction, force. (RS)

The science-math strand of unit six for second graders deals primarily with the concepts of conservation, relativity, adaptation and ecology. This teacher's guide to Kits 21-24 presents instructional and assessment activities revolving around the basic theme of the neighborhood as a community. Focus, objective, and materials for each activity are given in English and Spanish, with teacher instructions in Spanish only. Math activities review place value and the associative and commutative principles of addition and subtraction. Students measure line segments and are introduced to points, parallel lines, and intersections. One, two, and three digit numbers are added and subtracted, and their place values discussed. Through discussion, simple experiments, and observation, students learn matter, the forms it can take, and how matter and energy exist in fixed but interchangeable quantities. Relativity is understood as pupils describe the position of objects relative to other reference objects or to themselves. Reproductive patterns are observed in some plants and animals; adaptation is introduced with study of how organisms depend on and adapt to environment. The ecology section deals with the interaction of plants and animals with their environments and their dependence upon each other. (DS)

Instructional and assessment activities in science and math for third graders are presented in this teacher's guide to unit nine. Focus, objectives and materials for each activity are in English and Spanish, while teacher instructions are only in Spanish. The unit's theme is "the nation as a community"; related to the theme are the four spiraling questions developed in each of the four unit kits. Kit 33 treats what the elements are, and studies heat as a form of energy and types of heat conductors. Math activities deal with forms of measurement. Kit 34 asks what alternatives the individual faces and studies magnetism. Its math activities deal with inverse relation between addition and subtraction, associative property of addition, place value of numerals, and short form subtraction. Kit 35 deals with how the individual can initiate change and pupils learn about electricity as it relates to the experiences of everyday life. Math activities deal with repeated addition as readiness for multiplication, the commutative and associative properties of multiplication, and the multiplication table for equations from 0 to 5. Kit 36 examines what happens as a result of change and deals mainly with simple machines that push or pull. Math activities continue with multiplication skills and the metric system is introduced. (DS)

Unit 10 of a Spanish science/math curriculum for grade three, composed of kits 37-40, has as its theme "communities around the world". The unit's teacher's guide contains both learning and assessment activities, with the focus, objective, and materials needed for each activity listed. Specific attention is placed on four spiraling questions dealing with the individual, his alternatives, ways to initiate change, and the results of change. Kit content covers concepts of change and interaction (in living and nonliving things, physical and chemical changes); measurement of areas in centimeters and meters; lines; angles; conservation of matter (preservation of natural resources); energy crisis; relation of mass to weight; gravity; measurement by gram, kilogram, liter, half liter, cube, and kilometer; multiplication (missing factors, of numbers with up to three zeros); concept of systems reviewed (ecosystem, solar system, ant colony); variation among animal species, taste, and food for balanced diet; distributive property of multiplication; practice with bank checks; bank books; concept of adaptation (hostile environments, use of senses in adaptation, how dinosaurs became extinct); multiplication; introduction of division; and frames of reference. (RS)

The teacher's guide for unit four of a Spanish science/math strand for second graders contains instructional and assessment activities for kits 13-16. Each designed for a two- to three-week teaching period, the kits' activities are geared toward guiding the child to discover correct answers through methods provided and, by putting materials in his hands, helping him discover facts through participation and use of reasoning powers. The guide lists focus, objective, and materials in English and Spanish for each learning activity; teacher instructions are in Spanish. Specific activities cover volume--gallon, quart, pint; fractions one-half and one-quarter; "more than" and "less than" symbols; comparatives "shorter than" and "taller than"; addition and subtraction combinations--missing addends, subtrahends, and operational symbols; commutative principle; subtraction as inverse of addition; parenthesis in addition combinations; plants--classification and germinations of seeds, function of parts of a plant, plant identification, usefulness to man; addition and subtraction of sets of 10-19 elements; missing addends and subtrahends; animals--characteristics, habits, usefulness to man; longitude--inches, feet, yards; three dimensional forms; counting by ones to 100; the five senses; change caused by environment and growing older. (RS)

Instructional and assessment activities in unit three of a Spanish science/math curriculum for first graders are built around the central theme of the school. Kits 9-12, each designed for a two to three week teaching period, contain activities which also support who the child is, what his needs and wants are, what his resources are, and how he uses them. The guide lists the focus, objective, and materials for each learning activity in English and Spanish; teacher instructions are in Spanish. Major activities are as follows: reviewing geometric shapes; recognizing symmetry in two- and three-dimensional figures; introducing the concept of half; reviewing the order of cardinal and ordinal numbers; identifying time units (day, week, month, year); constructing a calendar; relating the concept of time to the school and home environment; identifying divisions of the day (minutes, hours); telling time; timing events; continuing mathematical concept of sets; identifying 100 as 10 tens and 0 ones; using a Celsius thermometer to record temperature changes; identifying weather symbols and conditions; introducing the cent symbol and the value of a cent, nickel, dime, and quarter, and using these values in adding and subtracting; strengthening the place value concept. Assessment activities are included with each kit. (RS)

Each of the four kits in this teacher's guide to a Spanish science/math strand for first graders provides for the development of mathematical competencies needed to function in science. Instructional and assessment activities in the bilingual curriculum are pupil centered, and contents are designed to enable the child to develop skills in the processes of observing, communicating, using numbers and spatial relationships, classifying, and measuring. Activities support a basic theme of the child in relation to the classroom. The guide details the focus, objective, and materials for each learning activity in English and Spanish; teacher instructions are in Spanish. The kits, each designed for a period of two to three weeks, contain the following instructional activities: identifying, naming, and producing primary and secondary colors and color combinations; comprehending, manipulating, and comparing sets, equivalent and nonequivalent; naming, classifying, and identifying basic geometric shapes, numbers, and colors; identifying and using numerals 0 to 9, and the plus, minus, and equal signs; building a foundation for accurate measurement; identifying and using ordinal numbers (first to eighth); adding and subtracting numerals 0 to 6 in horizontal and vertical algorithms. (RS)