Strategies for comparing decimal numbers with the same whole-number part

The strategies employed by 130 Grade 5 Brisbane students in comparing decimal numbers which have the same whole-number part were compared with those identified in similar studies conducted in the USA, France and Israel. Three new strategies were identified. Similar to USA results, the most common comparison errors stemmed from the incorrect whole-number strategy in which length is confused with size. The findings of this present study tend to support Resnick et al.’s (1989) hypothesis that the introduction of decimal-fraction recording before common-fraction recording seems to promote better comparison of decimal numbers.

Fractions Versus VELS : Making sense and teaching richly

Fractions are different from other numbers: they need new ways of working - right? No. That’s a recipe for relying on unexplainable rote rules. Fraction calculations are sensibly based in properly understood whole-number operations. If we really know how to multiply and divide (and add and subtract) whole-numbers, doing the same kinds of things with fractions will be easy, and memorable. But how does this fit with VELS and Progression Points? What is the Fraction Curriculum, and how could we teach it?

De solutione problematum diophanteorum per números integros : o primeiro trabalho de Euler sobre equações diofantinas

The present dissertation analyses Leonhard Euler´s early mathematical work as Diophantine Equations, De solutione problematum diophanteorum per números íntegros (On the solution of Diophantine problems in integers). It was published in 1738, although it had been presented to the St Petersburg Academy of Science five years earlier. Euler solves the problem of making the general second degree expression a perfect square, i.e., he seeks the whole number solutions to the equation ax2+bx+c = y2. For this purpose, he shows how to generate new solutions from those already obtained. Accordingly, he makes a succession of substitutions equating terms and eliminating variables until the problem reduces to finding the solution of the Pell Equation. Euler erroneously assigns this type of equation to Pell. He also makes a number of restrictions to the equation ax2+bx+c = y and works on several subthemes, from incomplete equations to polygonal numbers

Bibliotheca Indica.

Each number also has a distinctive title.

The monthly religious magazine.

Title from caption.

The Journal of the United Service Institution.

Title from caption.

Journal of the Royal United Service Institution

Imprint varies

Canadian bee journal.

Issues for -n.s. v.21, no.2 Feb. 1913 called also whole number <35>-576.

Moving along the mental number line: Interactions between whole-body motion and numerical cognition

Active head turns to the left and right have recently been shown to influence numerical cognition by shifting attention along the mental number line. In the present study, we found that passive whole-body motion influences numerical cognition. In a random-number generation task (Experiment 1), leftward and downward displacement of participants facilitated small number generation, whereas rightward and upward displacement facilitated the generation of large numbers. Influences of leftward and rightward motion were also found for the processing of auditorily presented numbers in a magnitude-judgment task (Experiment 2). Additionally, we investigated the reverse effect of the number-space association (Experiment 3). Participants were displaced leftward or rightward and asked to detect motion direction as fast as possible while small or large numbers were auditorily presented. When motion detection was difficult, leftward motion was detected faster when hearing small number and rightward motion when hearing large number. We provide new evidence that bottom-up vestibular activation is sufficient to interact with the higher-order spatial representation underlying numerical cognition. The results show that action planning or motor activity is not necessary to influence spatial attention. Moreover, our results suggest that self-motion perception and numerical cognition can mutually influence each other.

Children's piano pieces the whole world plays : a collection of more than one hundred and fifty tuneful piano pieces for juvenile players, including standard teaching and recreation pieces, and in addition a considerable number of new compositions /

Mode of access: Internet.

A treatise on surveying : containing the theory and practice : to which is prefixed a perspicuous system of plane trigonometry : the whole clearly demonstrated and illustrated by a large number of appropriate examples, particularly adapted to the use of schools /

With: Mathematical tables / John Gummere. Stereotyped ed., carefully rev. and corrected. Philadelphia : Kimber & Sharpless, 1843.

The history of the martyrs epitomised : A cloud of witnesses, or, The sufferers mirrour : made up of the swanlike songs, and other choice passages of a great number of martyrs and confessors, to the end of the sixteenth century, in their treatises, speeches, letters, prayers, &c. ... the whole alphabetically disposed /

LC copy bound in one volume.

Whole of life cycle cost analysis in bridge rehabilitation

The report presents a methodology for whole of life cycle cost analysis of alternative treatment options for bridge structures, which require rehabilitation. The methodology has been developed after a review of current methods and establishing that a life cycle analysis based on a probabilistic risk approach has many advantages including the essential ability to consider variability of input parameters. The input parameters for the analysis are identified as initial cost, maintenance, monitoring and repair cost, user cost and failure cost. The methodology utilizes the advanced simulation technique of Monte Carlo simulation to combine a number of probability distributions to establish the distribution of whole of life cycle cost. In performing the simulation, the need for a powerful software package, which would work with spreadsheet program, has been identified. After exploring several products on the market, @RISK software has been selected for the simulation. In conclusion, the report presents a typical decision making scenario considering two alternative treatment options.

Strategies for minimising the whole of life cycle cost of reinforced concrete bridge exposed to aggressive environments

n design of bridge structures, it is common to adopt a 100 year design life. However, analysis of a number of case study bridges in Australia has indicated that the actual design life can be significantly reduced due to premature deterioration resulting from exposure to aggressive environments. A closer analysis of the cost of rehabilitation of these structures has raised some interesting questions. What would be the real service life of a bridge exposed to certain aggressive environments? What is the strategy of conducting bridge rehabilitation? And what are the life cycle costs associated with rehabilitation? A research project funded by the CRC for Construction Innovation in Australia is aimed at addressing these issues. This paper presents a concept map for assisting decision makers to appropriately choose the best treatment for bridge rehabilitation affected by premature deterioration through exposure to aggressive environments in Australia. The decision analysis is referred to a whole of life cycle cost analysis by considering appropriate elements of bridge rehabilitation costs. In addition, the results of bridges inspections in Queensland are presented