Research into Practice: Children's Strategies in Ordering Rational Numbers

1987 ◽  
Vol 35 (2) ◽  
pp. 33-35
Author(s):  
Thomas Post ◽  
Glenda Lappan ◽  
Kathleen Cramer
Keyword(s):  
Small Groups ◽  
Rational Numbers ◽  
Fifth Grade ◽  
Number Lines ◽  
Cuisenaire Rods ◽  
Children's Strategies ◽  
Teaching Experiments

Our comments here are based on interviews from two teaching experiments with fourth and fifth-grade chil dren. The students were taught many aspects of fractions using a variety of manipulative materials including circular and rect angular piece. Cuisenaire rods number lines, and chips. Each student had his or her own materials. Each worked independently, in small groups, and as a whole cl ass, spending much time talking about and performing a wide vari ety of fraction- related tasks.

A color-coded method of teaching basic arithmetic concepts and procedures

1970 ◽  
Vol 17 (3) ◽  
pp. 231-233
Author(s):  
Charlotte W. Junge ◽  
Roberta Green
Keyword(s):  
Fifth Grade ◽  
Place Value ◽  
Conventional Methods ◽  
Cuisenaire Rods

The method that is explained below was developed by the author in an effort to aid a fifth-grade boy who was severely retarded in arithmetic achievement. All conventional methods of explaining place value, such as the abacus, pocket charts, Cuisenaire rods, etc., were too abstract for this child, and the use of the materials had not led to his developing understanding of concepts.

A number pencil

1967 ◽  
Vol 14 (7) ◽  
pp. 557-559
Author(s):  
David M. Clarkson
Keyword(s):  
Elementary Teachers ◽  
Sixth Grade ◽  
Rational Numbers ◽  
Class Discussion ◽  
Irrational Numbers ◽  
Whole Numbers ◽  
Number Lines

So much use is being made of number lines these days that it may not occur to elementary teachers to represent numbers in other ways. There are, in fact, many ways to picture whole numbers geometrically as arrays of squares or triangles or other shapes. Often, important insights into, for example, oddness and evenness can be gained by such representations. The following account of a sixth-grade class discussion of fractions shows how a “number pencil” can be constructed to represent all the positive rational numbers, and, by a similar method, also the negative rationals. An extension of this could even be made to obtain a number pencil picturing certain irrational numbers.

SRSD Fractions: Helping Students at Risk for Disabilities Add/Subtract Fractions With Unlike Denominators

2019 ◽  
Vol 52 (5) ◽  
pp. 399-412
Author(s):  
Robin Parks Ennis ◽  
Mickey Losinski
Keyword(s):  
At Risk ◽  
Students With Disabilities ◽  
Small Groups ◽  
Functional Relationship ◽  
Treatment Fidelity ◽  
Multiple Baseline ◽  
Fifth Grade ◽  
Strategy Development ◽  
Students At Risk ◽  
Fifth Grade Students

Many students fall below benchmarks in the area of fractions computation, particularly students with disabilities. Self-regulated strategy development (SRSD) is one strategy with proven effectiveness for improving outcomes for students with disabilities, although very few studies have applied SRSD to the area of mathematics. In this study, we used SRSD Fractions to teach adding and subtracting fractions with unlike denominators, simplifying fractions, and converting fractions to mixed numbers using the mnemonics FILMS, CUT, and EDIT. A researcher provided instruction in small groups to fifth-grade students at risk for disabilities. The results from use of a multiple-baseline-across-groups design suggest a functional relationship between SRSD Fractions and 8 fifth-grade students’ digits correct on timed fraction probes. Results from treatment fidelity, social validity, and academic engagement during the intervention are also reported. We also discuss limitations and directions for future researchers.

Strategy Games: Treasures from Ancient Times

1997 ◽  
Vol 3 (2) ◽  
pp. 110-116
Author(s):  
Jacqueline Gorman
Keyword(s):  
Small Groups ◽  
Fifth Grade ◽  
Dry Beans ◽  
Strategy Games ◽  
Winning Strategies ◽  
Ancient Times ◽  
Game Board ◽  
Grade Classroom

The fifth-grade classroom was filled with the sounds of tension and concentration. I heard the quiet clicking of dry beans; hushed, intense discussions; and sighs of both frustration and satisfaction. My students were scattered around the room in small groups, leaning over game board and attempting to work out winning strategies for the game of kalah.

Perimeter Patterns

1995 ◽  
Vol 2 (4) ◽  
pp. 238-240
Author(s):  
Richard A. Austin ◽  
Patricia Biafore
Keyword(s):  
Small Groups ◽  
School Mathematics ◽  
Fifth Grade ◽  
Evaluation Standards

The following geometry activity featuring the concept of perimeter was carried out over one week in a fifth-grade class. As the students worked in small groups, they explored mathematics in ways aligned with the Curriculum and Evaluation Standards for School Mathematics for grades 5-8 (NCTM 1989).

A working model for rational numbers

1975 ◽  
Vol 22 (4) ◽  
pp. 328-332
Author(s):  
J. Paul Moulton
Keyword(s):  
Rational Number ◽  
Rational Numbers ◽  
Abstract Concept ◽  
Working Model ◽  
Cuisenaire Rods

There are many good models for the rational numbers-area models, Cuisenaire rods, lattices, for example. Each has its merits and its limitations, and none is so good that it should be used to the exclusion of all others. Indeed, it is partly through a variety of experiences that a person acquires the ability to relate the abstract concept of a rational number to the properties of the practical world. I should therefore like to suggest still another model, one that has certain advantages of its own.

Integer Target: Using a Game to Model Integer Addition and Subtraction

2007 ◽  
Vol 12 (7) ◽  
pp. 388-392
Author(s):  
Jerry Burkhart
Keyword(s):  
Small Groups ◽  
Number Line ◽  
Target Number ◽  
Number Lines ◽  
Addition And Subtraction

Imagine a classroom where students are gathered in small groups, working with number lines and cards marked with integers. The students have chosen a “target number” on the number line and are deep in discussion, trying to find ways to make the sum of the integers on their cards match this number. There is a deck from which they draw, discard, or exchange cards. They also give, take, or trade cards with one another.

Using Models to Build Fraction Understanding

2020 ◽  
Vol 113 (2) ◽  
pp. 117-123
Author(s):  
Debra Monson ◽  
Kathleen Cramer ◽  
Sue Ahrendt
Keyword(s):  
Paper Folding ◽  
Number Lines ◽  
The Impact ◽  
Support Students ◽  
Teaching Experiments

We share the impact different models have on students' fraction thinking. We have come to understand, through several teaching experiments, how fraction circles, paper folding and number lines support students' learning about key fraction ideas including the role of the unit, partitioning, and fraction order.

Children's Strategies for Solving Compositional Problems with Peers

1994 ◽  
Vol 42 (3) ◽  
pp. 232-252 ◽  
Author(s):  
Jacqueline H. Wiggins
Keyword(s):  
Qualitative Study ◽  
Small Group ◽  
Group Composition ◽  
Learning Processes ◽  
Fifth Grade ◽  
General Music ◽  
Classroom Experiences ◽  
Music Class ◽  
Composition Process ◽  
Children's Strategies

This article reports some of the findings of a qualitative study of musical learning processes. The data were drawn from analysis of videotapes and audiotapes that shadowed the classroom experiences of two target students in a fifth-grade general music class over a period of 5 months. A portion of the curriculum in the study class involved small-group composition projects. Findings reported here characterize the group composition process in terms of the nature of the strategies the children used as they worked together with peers to solve those compositional problems. Children who were successful in completing class assignments used strategies that seemed to follow a pattern of moving from whole (initial planning) to part (development of motivic ideas) and back to whole (reassembling and practicing). The children's decisions seemed to stem from a holistic viewpoint, reflecting a preconceived vision of the final product from the outset. In contrast, there were very few instances of random exploration.

Interweaving the Digital and Physical Worlds in Collaborative Project-Based Learning Experiences

2014 ◽  
pp. 265-282
Author(s):  
Michelle E. Jordan
Keyword(s):  
Digital Media ◽  
Learning Environments ◽  
Small Groups ◽  
Learning Experience ◽  
Project Based Learning ◽  
Fifth Grade ◽  
Interdisciplinary Learning ◽  
Digital Texts ◽  
Collaborative Talk

The purpose of this chapter is to help educators and educational scholars consider new possibilities for interweaving the digital and physical worlds in order to reconsider disciplinary and interdisciplinary learning across academic curricula. To explore how print and digital media may be interwoven to support children’s creation of physical artifacts in project-based learning environments, the author describes uses to which students in one fifth grade class put multimodal print and digital texts as they collaborated in small groups to design robots. The author identifies the range of textual resources used across phases of the engineering design task in order to examine the interplay between digital and print-based texts in the design and production of physical artifacts. Focusing on the role of digital texts in this project-based learning experience, episodes of collaborative talk illustrate student processes of consuming and producing texts.

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