Bounding the Number of Hyperedges in Friendship rr-Hypergraphs

For $r \ge 2$, an $r$-uniform hypergraph is called a friendship $r$-hypergraph if every set $R$ of $r$ vertices has a unique 'friend' - that is, there exists a unique vertex $x \notin R$ with the property that for each subset $A \subseteq R$ of size $r-1$, the set $A \cup \{x\}$ is a hyperedge. We show that for $r \geq 3$, the number of hyperedges in a friendship $r$-hypergraph is at least $\frac{r+1}{r} \binom{n-1}{r-1}$, and we characterise those hypergraphs which achieve this bound. This generalises a result given by Li and van Rees in the case when $r = 3$. We also obtain a new upper bound on the number of hyperedges in a friendship $r$-hypergraph, which improves on a known bound given by Li, van Rees, Seo and Singhi when $r=3$.Comment: 14 page

The convergent validity of two sensory processing scales used with school - age children : comparing the sensory profile and the sensory processing measure

Abstract: Aim: To investigate the convergent validity between the Sensory Profile, the Sensory Profile School Companion, and the Home and Main Classroom Forms of the Sensory Processing Measure. Method: Thirty mothers completed the Sensory Profile and the Sensory Processing Measure - Home Form on one child each. Nineteen teachers of the same children completed the Sensory Profile School Companion and the Sensory Processing Measure - Main Classroom Form. Results: The Sensory Profile and the Sensory Processing Measure - Home Form were significantly correlated (rho=0.86, p less-than .01). The Sensory Profile School Companion and Sensory Processing Measure - Main Classroom Form were also significantly correlated (rho=.74, p less-than .01). Conclusion: The two sets of sensory processing scales had moderate levels of convergent validity.<br /

Reread, Rethink, Recycle [3rd grade]

This unit integrates writing, media/technology and economics via collaboration differentiation. The goal is to publish a niche newspaper solely focused on going green. The unit opens with an analysis of the power of persuasion by exposure and examples. Students will then be learning researching skills necessary as they read books & navigate through websites about how to be environmentally friendly. The research and essays written will become the articles in the newspaper, the foundation. Students will be invited to learn a basic understanding of the parts of a newspaper, applying for a job and how to persuade for positions based on strengths and skills. Staff meetings will be conducted and then the classroom will transform into a living and breathing newspaper company. Students will have different jobs, goals, activities all based on skill and choice. The teacher, as Director, manages and facilitates the production of the newspaper. The staff has a unified mission. Wages will be given daily based on productivity and work accomplished. We invite you to: Reread, Rethink, Recycl

Where everyone’s PLACE is VALUED: A Numeration Unit

This is our first unit in 3rd grade math. It focuses specifically on Base Ten/Numeration, with a main emphasis on place value and money. Aligned with state standards, the students will be able to read, write in the three different forms (standard, expanded and written) and compare numbers up to the hundred-thousand place; additionally, students will be able to count collections of bills & coins and to solve real-world situations in which money is exchanged. The performance assessment is entitled: Ritzy Roadrunner Resort. Students will be invited to participate in an imaginative ritzy summer vacation, much like present day Atlantis Paradise Island. This culminating activity is differentiated, leveled based on students various points of entry and skill acquisition throughout the unit. As ―families on a summer trip‖ the students, in groups, will be assigned different package deals with varying ―terms and conditions.‖ Mathematical expectations include skills from needing to accurately rank activites & resturaunt items from most expensive to least expensive, using simple addition to determine money costs within a defined limit, up to giving higher students a budget and requiring them to provide you, the ―hotel manager,‖ a balance sheet of purchases. This performance assessment will be graded on a rubic provided. We hope you enjoy your stay at the Roadrunner Resort: Where every place is valued! *Unit activities provided from R.I.S.D. –double check for acceptable use policy

Sarah Plain and Tall Book Study [3rd grade]

In this unit, students will be doing a chapter book study using the novel, Sarah Plain and Tall. At the end of the unit, the students will deeply understand that there are always things to miss no matter where you are, a sense of belonging happens when someone accepts where they are, and that we carry symbols and artifacts that represent the people and places that matter the most to us. Students will be engaged using the 6 Reading Comprehension Strategies: Phonics/Decoding, Predict/Infer, Monitor/Clarify, Question, Summarize, Evaluate. Other skills such as analytical thinking, predicting outcomes and connecting text to self through writing will also be focused on in this unit. Students will understand the close relationship between location and lifestyle, the profound connection between symbols and memories, and how comparisons are a natural way to connect different moments in time. As for a culminating activity at the end of this unit, the students are presented with the challenge that they are forced to move to a new home, and can only take 3 things with them. In a presentation each student will defend why their 3 artifacts symbolize their home

It’s a Small World After All: An Economic Experiment in Trade

‘It’s a Small World After All: An Economic Experiment in Trade’ is a social studies unit for 3rd grade with an emphasis on economics. Aligned with 3rd grade social studies TEKS, student gain a rich understanding of scarcity, free market, and interdependence within and among communities. This unit utilizes a variety of resources including: Scott Foresman’s Social Studies: Communities Basal Reader, various real-life application internet activities and journal writing reflection opportunities. Students will have several formative assessments to track understanding throughout the unit. The culminating project-based assessment invites students to engage in a free trade simulation. With the guidance of the CIA Factbook website, students will represent countries and pretend they are restaurant owners creatively making food for a menu. The trade opportunity happens when students communicate and negotiate with one another to obtain the necessary ingredients for their entrées, appetizers, and desserts— a real-world application to understanding our world’s economic system

Slave Mothers and White Fathers: Defining Family and Status in Late Colonial Cuba

This paper outlines the mechanisms used to position the offspring of slave women and white men at various points within late nineteenth-century Cuba’s racial hierarchy. The reproductive choices available to these parents allowed for small, but significant, transformations to the existing patterns of race and challenged the social separation that typically under girded African slavery in the Americas. As white men mated with black and mulatta women, they were critical agents in the initial determination of their children’s status–as slave, free, mulatto, or even white. This definitional flexibility fostered an unintended corruption of the very meaning of whiteness. Similarly, through mating with white men, enslaved women exercised a degree of procreative choice, despite their subjugated condition. In acknowledging the range of rape, concubinage, and marriage exercised between slave women and white men, this paper highlights the important links between reproductive practices and the social construction of race

An Investigation of Prekindergarten Teachers’ Read Aloud Choices

The value of children’s literature as a tool for promoting literacy, improving content knowledge, and increasing print motivation is evident. Empirical evidence relating to the types of books early childhood teachers read aloud and the reasons for their choices, however, does not exist. The purpose of this descriptive study was to provide current, in-depth documentation of the read-aloud book choices of prekindergarten teachers (n=151) in a nationally recognized, state-wide program regarding the variables of genre, publication date, and diversity along with the teachers’ rationale for selecting the books. Responses to two open-ended questions inspired by Yopp and Yopp (2006) were analyzed thematically and compared with research-based recommendations for best practices. Books read aloud were quite homogenous, including mostly recently published examples of contemporary realistic fiction or folklore with almost no multicultural or award-winning books present. The findings highlight the importance of increasing early childhood teachers’ knowledge of children’s literature and the implications of book choice on children’s development and learning