In this paper, we present and describe a Fraction Generator tool, which is one of the components of our mathematical musician digital learning platform, Play My Math. Teachers and students can use the Fraction Generator tool to discuss, practice, and reinforce conceptual and procedural knowledge of fractions. To that end, the tool offers customizable settings that randomly render exercises in six different categories (i.e., identifying fractions, identifying notations, comparison of fractions, arithmetic applied to fractions, least common multiple, and quantity of a fraction). Additionally, we offer an extra module called the Worksheet Demonstration that teachers can use to guide the students when working with paper-based worksheets. The rationale for the Fraction Generator came from feedback given by teachers during a study we conducted in Mexico in 2024. For designing our tool, we considered principles of technology-enhanced learning and tangible learning interfaces. Finally, to further develop our Fraction Generator initial design, we analyzed qualitative data coming from UK teachers’ feedback as part of an intervention we conducted in the UK primary education context at the beginning of 2025.

The signature and occurrence of frequency lock-in (FLI) vibrations of full-scale offshore structures are not well understood. Although several structures have experienced FLI, limited amounts of time histories of the responses alongside measured met-ocean data are available in the literature. This paper presents an analysis of 61 measured events of resonant vibrations of the Norströmsgrund lighthouse from 2001 until 2003. The vibrations of most of these events did not reach a steady state; thus, they violate an often-quoted criterion for frequency lock-in vibrations and remain outside any modes of ice-induced vibrations suggested in standards. Met-ocean data from both in situ measurements and from the Copernicus marine service information database are further used to better understand the occurrence of resonant ice-induced vibrations. All events between 2001 and 2003 occurred during days with ice concentrations of 8–10/10, closely packed consolidated drift ice. The locally measured ice velocity and thickness ranged from 0.023 to 0.075 m s⁻¹ and from 0.26 to 1.9 m, respectively. These measurements included level ice, rafted ice and ridged ice. The events of resonant vibrations are further compared with measurements from the same structure between 1979 and 1988. Most events of resonant vibrations were recorded in the winter of 1988, followed by the winters of 2003 and 1980. The winter of 1988 had fewer freezing degree days (FDD) than the 65-year average, whereas the winters of 2003 and 1980 had more FDD than the 65-year average.