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"They are the same" is a phrase that teachers often hear from their students in arithmetic and algebra. But what do students mean when they say this? The present paper researches the notion of sameness within algebraic thinking in the context of generating equivalent numerical equalities. A group of Grade 6 Mexican students (10- to 12-year-olds) was presented with tasks that required transforming the given numerical equalities in such a way as to show their truth-value. The students initially indicated this by calculating and demonstrating that the total was the same on both sides. When asked not to calculate, their approaches evolved into more structural transformations involving decomposition so as to arrive at an equality with the same expression on each side. Students used the language of sameness--both visible and invisible--to describe the truth-value of their transformed expressions and equalities. The visible sameness referred to the resulting identical form of each side of the equality and the invisible sameness to the top-down equivalences that they had generated by their decomposing transformations--both types of sameness being characterized by their hidden numerical values. These findings suggest implications for transitioning to the algebraic domain of equations with their similarly hidden values.

Byrsonima crassifolia L. Kunth is a plant native to the Americas that grows in tropical and subtropical areas. Fresh B. crassifolia fruits are a good source of ascorbic acid and carotenoids and contain volatile compounds such as butyric and caproic acids. Although B. crassifolia is commonly exploited from wild natural ecosystems, it exhibits the potential to become a crop plant. When optimal agronomic management systems support propagation by seed, fruits with more homogeneous characteristics can be produced compared to those obtained from wild or backyard plants. B. crassifolia fruits can be found in local markets in Central and South America. The pulp, peel, and other B. crassifolia fruit components can be processed to make traditional and innovative food products, namely candies, cookies, cakes, candied fruits, ice creams, sorbets, jellies, juices, liqueurs, jams, nectars, pickles, and fruit drinks as an alternative to avoid the waste of overripe fruits. Additionally, the woody fraction of the B. crassifolia tree is used as a source of firewood, as shade, and for constructing living fences. These uses also allow the maximum use of biomass by establishing support for cultivation with the circular economy and strengthening food security. Therefore, this review aims to provide insights into the generation and dissemination of knowledge supporting the development of strategies in the areas of agronomy, postharvest management, and technological processing of B. crassifolia to promote its sustainable use and exploitation.

Public transport plays a significant role in the economic development of a country, so the state must guarantee its proper functioning, not only in terms of controlling vehicular traffic and generating adequate roads but also in terms of pricing and customer service. This article proposes a smart electronic taximeter that improves customer service quality and provides greater control for the taxi owner. To achieve this, the smart taximeter has a data entry module (keyboard), a location module (global position system), a time module (date and time), a storage module (memory), a display module (light emitting diode array), an auditory module (speech synthesizer), a communication module (Wi-Fi) and a microcontroller that controls the processes of setup, pricing, billing, and accounting. The results have shown a satisfactory response on the part of the client and the entrepreneur since it allows a higher level of inclusion from the auditory output in Spanish and English, as well as to carry out better financial accounting through the storage of information on the place, date and time, start and end, as well as the duration, distance, fare, surcharges, total cost, and number of each taxi service (ride). Finally, the smart electronic taximeter complies with all Colombian resolution No. 88918 relations of the Ministry of Commerce, Industry and Tourism. [ABSTRACT FROM AUTHOR]

The main mango cultivars produced in the southern Pacific region of Mexico are Ataulfo, Manila, Haden, and Criollo. However, mineral, nutritional, and nutraceutical composition studies are limited. This study aimed to evaluate the effect of cultivars on the nutritional, mineral, and nutraceutical qualities of mango produced in Mexico. The cultivar significantly affected (p ≤ 0.05) the fruit composition across these indices. Criollo had the highest potassium, magnesium, sodium, and zinc concentrations, while Haden showed the highest calcium content. Manila had the highest iron content, contributing 0.76% of the recommended daily intake. Ataulfo and Haden were statistically similar in manganese content, both higher than Criollo, with Ataulfo reaching the maximum copper concentration. Ataulfo also had the highest sugar content, while Criollo had the most dietary fiber (3.1%), double that of Ataulfo and Haden. Haden had the lowest dry matter (14.8%) and lowest protein content (0.46%), with Manila showing the lowest ash content. The cultivars also differed in nutraceutical composition: Ataulfo was highest in total phenols, DPPH, and vitamin A; Haden in carotenoids and flavonoids; and Criollo in vitamin C. Cultivar selection induces changes in mango nutritional composition. [ABSTRACT FROM AUTHOR]