The most challenging parts of teaching mathematics are engaging students and helping them understand the connections between mathematics concepts. In this volume, you'll find a collection of low floor, high ceiling tasks that will help you do just that, by looking at the big ideas at the fourth-grade level through visualization, play, and…

Many teachers experience the tension between using published curriculum materials and teaching in ways that are responsive to children. Teachers are often expected to use a particular mathematics curriculum series, but they still want to be able to build on and connect to children's multiple mathematical knowledge bases (MMKB).…

The authors of this article collaborated with fourth-grade teachers from two schools to support implementation of a research-based fraction and decimal curriculum (Rational Number Project: Fraction Operations and Initial Decimal Ideas). Through this study, they identified five indicators of rich conceptual understanding of decimals, which are…

Equivalence is mostly associated with the strand of Number and Algebra and is fundamental in both of the substrands. Equivalence is considered a key and foundational concept of algebra, and whereas an assumption might be made that equivalence is a relatively "easy" concept; studies have shown that when asked to balance an equation such…

Since 1973, the National Assessment of Educational Progress (NAEP) has gathered information about student achievement in mathematics. Results of these periodic assessments, produced in print and web-based formats, provide valuable information to a wide variety of audiences. They inform citizens about the nature of students' comprehension of the…

Since 1973, the National Assessment of Educational Progress (NAEP) has gathered information about student achievement in mathematics. Results of these periodic assessments, produced in print and web-based formats, provide valuable information to a wide variety of audiences. They inform citizens about the nature of students' comprehension of the…

When asked to calculate the area of a particular shape, one student responded by asking, "Is that the outside or the inside?" while another student replied, "I think it's the one where you put a little 2 next to it." Both of these responses indicate a lack of conceptual understanding of area and reinforce the research findings…

This document is the answer key for level 4 of the teacher-developed mathematics curriculum for New York City schools. Approximately 235 performance objectives are listed, with reference to the appropriate worksheet(s) for each. The answers are typed in the appropriate space on each sheet; when varied answers are possible, this is noted. (MNS)

Data are presented for problem-solving content of selected elementary school mathematics textbooks and problem-solving achievement for students in Iowa for grades 4-6 for selected years between 1955 and 1985. Relationships between textbook content and student achievement are considered. (RH)

This is the teacher's manual to accompany part 1 of the workbook for grade 4 pupils in the Comprehensive Instructional Management System, a teacher-designed unified mathematics curriculum for kindergarten through grade 7. It is composed of a curriculum, a testing component, and a computer-managed reporting system. The curriculum is organized into…

The major goal of the Comprehensive Instructional Management System for mathematics is to provide the classroom teacher in New York City with a well-structured, objective-based curriculum. This first part of the manual for Level 4 includes modules for 14 topics: (1) numbers and numeration; (2) addition of whole numbers; (3) subtraction of whole…

The major goal of the Comprehensive Instructional Management System for mathematics is to provide the classroom teacher in New York City with a well-structured, objective-based curriculum. This second part of the manual for Level 4 includes modules for 14 topics: (1) numbers and numeration; (2) addition of whole numbers; (3) subtraction of whole…

This is the teacher's manual to accompany part 2 of the workbook for grade 4 pupils in the Comprehensive Instructional Management System, a teacher-designed unified mathematics curriculum for kindergarten through grade 7. It is composed of a curriculum, a testing component, and a computer-managed reporting system. The curriculum is organized into…

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…

This document is designed to assist teachers and other school personnel in the planning and teaching of the fourth grade mathematics course. Contents include: (1) Overview of Grade 4 Mathematics (mission statement, purpose and philosophy, goals, National Council of Teachers of Mathematics' Professional Standards for Teaching Mathematics,…