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Fraction frenzy : fractions and decimals
\"Introduces the reader to fractions and decimals.\"-- Provided by publisher.
Book
Converting Rational Numbers to Decimals (CCSS 7.NS.A.2d)
Fill in the gaps of your Common Core curriculum! Each ePacket has reproducible worksheets with questions, problems, or activities that correspond to the packet's Common Core standard. Download and print the worksheets for your students to complete. Then, use the answer key at the end of the document to evaluate their progress. Look at the product code on each worksheet to discover which of our many books it came from and build your teaching library! This ePacket has 5 activities that you can use to reinforce the standard CCSS 7.NS.A.2d: Converting Rational Numbers to Decimals. To view the ePacket, you must have Adobe Reader installed. You can install it by going to http://get.adobe.com/reader/.
eBook
Piece=part=portion : fractions=decimals=percents
Explains how in the language of mathematics, fractions, decimals and percents are three different ways of describing the same parts of things.
Book
College algebra. Chapter 1, Intro to algebra. Fractions. Decimals. Part 1
Intro to Algebra, Fractions, Explanation and Examples.
Streaming Video
Ready for fractions and decimals
\"Learn the basic fundamentals of adding, subtracting, multiplying and dividing using fractions and decimals\"--Provided by publisher.
Book
College algebra. Chapter 1, Intro to algebra. Fractions. Decimals. Part 2
Intro to Algebra, Fractions, Explanation and Examples.
Streaming Video
Changing Structures of Attention When Learning About Decimal Fractions with Digital Tools
Decimals are of great significance in the primary mathematics curriculum due to their application and use in everyday life. The purpose of this study was to investigate the effectiveness of certain dynamic digital representations in developing students’ knowledge of decimal fractions. Task-based interviews were used with six Year 4 (9–10 years old) students that incorporated four different dynamic digital representations of decimals. Data collected via video–audio recordings were used to detect shifts in students’ attention while using the digital representations. Attention shifts were analysed using microgenetic methods to determine conceptual changes over time. Findings uncovered specific features of the digital representations that generated productive cognitive confusion that prompted changes in students’ understanding of decimal fractions. The unique affordances of each digital tool offered students opportunities to dynamically explore decimal concepts, and the digital tools could be used to enrich the teaching of decimals within the primary mathematics classroom.
Journal Article
Decimal fraction representations are not distinct from natural number representations – evidence from a combined eye-tracking and computational modeling approach
Decimal fractions comply with the base-10 notational system of natural Arabic numbers. Nevertheless, recent research suggested that decimal fractions may be represented differently than natural numbers because two number processing effects (i.e., semantic interference and compatibility effects) differed in their size between decimal fractions and natural numbers. In the present study, we examined whether these differences indeed indicate that decimal fractions are represented differently from natural numbers. Therefore, we provided an alternative explanation for the semantic congruity effect, namely a string length congruity effect. Moreover, we suggest that the smaller compatibility effect for decimal fractions compared to natural numbers was driven by differences in processing strategy (sequential vs. parallel). To evaluate this claim, we manipulated the tenth and hundredth digits in a magnitude comparison task with participants' eye movements recorded, while the unit digits remained identical. In addition, we evaluated whether our empirical findings could be simulated by an extended version of our computational model originally developed to simulate magnitude comparisons of two-digit natural numbers. In the eye-tracking study, we found evidence that participants processed decimal fractions more sequentially than natural numbers because of the identical leading digit. Importantly, our model was able to account for the smaller compatibility effect found for decimal fractions. Moreover, string length congruity was an alternative account for the prolonged reaction times for incongruent decimal pairs. Consequently, we suggest that representations of natural numbers and decimal fractions do not differ.
Journal Article
The Archimedean Origin of Modern Positional Number Systems
A symbolic analysis of Archimedes’s periodical number system is developed, from which a natural link emerges with the modern positional number systems with zero. After the publication of Fibonacci’s Liber Abaci, the decimal Indo-Arabic positional system was the basis of the algorithmic and algebraic trend of modern mathematics, but even if zero plays a crucial role in algebra and mathematical analysis, zeroless positional systems show the same capability of producing efficient arithmetical algorithms based on operation tables over digits. The crucial role of digits is assessed, by considering a representation of numbers based on strings in lexicographic order. A new algorithm for the determination of decimal periods is presented by remarking on the cruciality of this topic in number theory. Periods of ordinal numbers and enumerations of recursive enumerability are shortly recalled. Concluding remarks are formulated about the deep relationship between numbers and information, which shed new light on a red line passing through the whole history of mathematics.
Journal Article
Numeros y Operaciones: Fracciones y Decimales - Multiplicacion y Division
Obten una mayor comprension sobre Fracciones y Decimales - Multiplicacion y Division con este atractivo recurso. Los conceptos incluyen: fracciones, decimales, porcentajes, multiplicacion, division. Este recurso, disenado para los grados de sexto a octavo, se divide en tres secciones: Hojas de tarea con problemas de texto, seguido por Hojas de simulacro para practicar la competencia de los estudiantes en las habilidades procesales, y finalmente una prueba de evaluacion. La clave de respuestas esta incluida. Sus estudiantes tendran una amplia oportunidad de aprender todas las expectativas de los Conceptos Basicos Comunes del Curriculo de los Capitulos de Matematicas de Numeros y Operaciones de NCTM.
eBook