Discovering Patterns in Pascal's Triangle

2019 ◽  
Vol 24 (4) ◽  
pp. 247-254
Author(s):  
Marilyn Howard
Keyword(s):  
Middle School ◽  
Problem Solving ◽  
School Level ◽  
Blaise Pascal ◽  
Pascal’S Triangle ◽  
The Common ◽  
Pascal's Triangle ◽  
Common Era ◽  
Middle School Level

The less you know about the patterns in Pascal's triangle, the more fun you will have discovering the triangle's many secrets. I am amazed at how few students and even teachers (especially at the middle school level) have ever explored Pascal's triangle. Although this famous triangle bears the name of Blaise Pascal (1623-1662), who saw many of the patterns when he was only thirteen years old, it had been around for centuries before he was born. See the ancient diagram in figure 1, which appeared at the front of a Chinese book in 1303 (Vakil 2008). Evidence suggests that the properties of the elements of Pascal's triangle were known before the common era. Students and teachers alike can enjoy exploring patterns through problem solving with Pascal's triangle.

Proportional Reasoning: Lessons from Research in Data and Chance

2004 ◽  
Vol 10 (2) ◽  
pp. 104-109
Author(s):  
Jane Watson ◽  
J. Shaughnessy
Keyword(s):  
Middle School ◽  
Problem Solving ◽  
Mathematics Curriculum ◽  
Proportional Reasoning ◽  
School Mathematics ◽  
School Level ◽  
Principles And Standards ◽  
Middle School Level

PRINCIPLES AND STANDARDS FOR SCHOOL Mathematics (NCTM 2000) places proportionality among the major concepts connecting different topics in the mathematics curriculum at the middle school level (p. 217). What concerns us about many of the problems presented to students, however, is that they are often posed purely as a ratio or proportion from the start. Often the statement of a problem is a giveaway that a proportion is involved. For example, the question “If 15 students out of 20 get a problem correct, how many students in a class of 28 would we expect to get the problem correct?” does not tap the depth of proportional reasoning that is required for meaningful problem solving.

scholarly journals Problem Solving at the Middle School Level: A Comparison of Different Strategies

2015 ◽  
Vol 4 (3) ◽  
Author(s):  
Farah Baraké ◽  
Naim El-Rouadi ◽  
Juhaina Musharrafieh
Keyword(s):  
Middle School ◽  
Problem Solving ◽  
School Level ◽  
Middle School Level

Probability and the Seating Chart

1988 ◽  
Vol 81 (5) ◽  
pp. 393-397
Author(s):  
Dave Ptak
Keyword(s):  
Middle School ◽  
Decision Making ◽  
Problem Solving ◽  
School Level ◽  
Decision Making Processes ◽  
Basic Probability ◽  
Classroom Seating ◽  
Middle School Level

The problem-solving activities outlined here add to the collection of applications- at the middle school level and above- dealing with basic probability concepts. The context is an unusual and unexpected one: the classroom seating chart. Students need to know these concepts because they are at the heart of decision-making processes. Solving problems of the type that follow reinforces these concepts and gives students practice in the problem-solving techniques of counting, finding patterns, using diagrams, and generalizing.

scholarly journals Rural–Urban Differences in the Factors Affecting Depressive Symptoms among Older Adults of Two Regions in Myanmar

2021 ◽  
Vol 18 (6) ◽  
pp. 2818
Author(s):  
Yuri Sasaki ◽  
Yugo Shobugawa ◽  
Ikuma Nozaki ◽  
Daisuke Takagi ◽  
Yuiko Nagamine ◽  
...  
Keyword(s):  
Older Adults ◽  
Middle School ◽  
Depressive Symptoms ◽  
Rural Areas ◽  
Urban Areas ◽  
Depression Scale ◽  
Wealth Index ◽  
School Level ◽  
Cross Sectional ◽  
Middle School Level

The aim of the study was to investigate rural–urban differences in depressive symptoms in terms of the risk factors among older adults of two regions in Myanmar to provide appropriate intervention for depression depending on local characteristics. This cross-sectional study, conducted between September and December, 2018, used a multistage sampling method to recruit participants from the two regions, for face-to-face interviews. Depressive symptoms were assessed using the 15-item version of the Geriatric Depression Scale (GDS). Depressive symptoms were positively associated with living in rural areas (B = 0.42; 95% confidence interval (CI): 0.12,0.72), female (B = 0.55; 95% CI: 0.31,0.79), illness during the preceding year (B = 0.68; 95% CI: 0.45,0.91) and non-Buddhist religion (B = 0.57; 95% CI: 0.001,1.15) and protectively associated with education to middle school level or higher (B = −0.61; 95% CI: −0.94, −0.28) and the frequency of visits to religious facilities (B = −0.20; 95% CI: −0.30, −0.10). In women in urban areas, depressive symptoms were positively associated with illness during the preceding year (B = 0.78; 95% CI: 0.36, 1.20) and protectively associated with education to middle school level or higher (B = −0.67; 95% CI: −1.23, −0.11), middle or high wealth index (B = −0.92; 95% CI: −1.59, −0.25) and the frequency of visits to religious facilities (B = −0.20; 95% CI: −0.38, −0.03). In men in rural areas, illness during the preceding year was positively associated with depressive symptoms (B = 0.87; 95% CI: 0.33, 1.42). In women in rural areas, depressive symptoms were positively associated with illness during the preceding year (B = 0.83; 95% CI: 0.36, 1.30) and protectively associated with primary education (B = −0.62; 95% CI: −1.12, −0.12) and the frequency of visits to religious facilities (B = −0.44; 95% CI: −0.68, −0.21). Religion and wealth could have different levels of association with depression between older adults in the urban and rural areas and men and women. Interventions for depression in older adults should consider regional and gender differences in the roles of religion and wealth in Myanmar.

scholarly journals Arithmetic Triangle

2017 ◽  
Vol 9 (2) ◽  
pp. 100
Author(s):  
Luis Dias Ferreira
Keyword(s):  
Arithmetic Progression ◽  
Modus Operandi ◽  
Interesting Point ◽  
Pascal’S Triangle ◽  
Initial Term ◽  
The Common ◽  
Pascal's Triangle

The product of the first $n$ terms of an arithmetic progression may be developed in a polynomial of $n$ terms. Each one of them presents a coefficient $C_{nk}$ that is independent from the initial term and the common difference of the progression. The most interesting point is that one may construct an "Arithmetic Triangle'', displaying these coefficients, in a similar way one does with Pascal's Triangle. Moreover, some remarkable properties, mainly concerning factorials, characterize the Triangle. Other related `triangles' -- eventually treated as matrices -- also display curious facts, in their linear \emph{modus operandi}, such as successive "descendances''.

Assessment Literacy Within Middle School-Level Math Professional Learning Communities

2018 ◽  
pp. 119-139
Author(s):  
Jennifer Wheat
Keyword(s):  
Middle School ◽  
Professional Learning Communities ◽  
Learning Communities ◽  
Professional Learning ◽  
School Level ◽  
Assessment Literacy ◽  
Multiple Indicators ◽  
Math Growth ◽  
Different Levels ◽  
Middle School Level

Professional learning communities (PLCs) have been implemented in school districts as a means to promote effective instructional policy initiatives and best practices. The purpose of this chapter is to identify assessment literacy commonalities within middle school-level math PLCs and to compare those commonalities across PLCs with different levels of student math growth. Multiple indicators of assessment literacy were used to supply rich descriptions of assessment literacy within each PLC using a procedure recommended by Bernhardt for effective data-driven decision making. Based upon the findings the researcher concluded that commonalities existed among PLCs with different levels of student math growth.

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