This document provides information about working with integers and their properties. It begins by defining odd, even, prime and composite numbers and providing an activity for the reader to identify these properties for different numbers. It then asks questions about numbers belonging to multiple categories and how to identify the different number types. The document goes on to explain prime factorization by finding the prime factors of numbers and provides examples and exercises. Finally, it gives pricing information for online classes and subject downloads through the Yaaka education website.
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This slide share has higher order thinking ways of teaching students to understand the relationship between the four number operations. This process have been a trial and error process for me, I have loved working with students along the way. Online and iPad resources have been provided.
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The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
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The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
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Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
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3. Activity
Copy and complete the table below by choosing among the numbers given which one is
odd, even, prime or composite.
Number Odd Even Prime Composite
1 1
2 2 2
3
4 4
5 5
6
7
4. Question1
Are there numbers that belong to more than one group?
Question 2
How do you identify that a number is:
i. Odd
ii. Even
iii. Prime
iv. composite
5. Finding prime factors of any number
In your primary you studied about multiples and factors of numbers.
When to numbers are multiplied together, the product is called a multiple.
The two numbers multiplied together are called factors of a multiple
A multiple has two or more factors
6. Example
The factors of 12 are
1 × 12 = 12
2 × 6 = 12
3 × 4 = 12
Factors of 12 are 1,2,3,4,6,12
The multiples of 4 are
4 × 1 = 4
4 × 2 = 8
4 × 3 = 12
4 × 4 = 16
4 × 5 = 20
4 × 2 = 24
The multiples of 4 are 4,8,12,16,20,24, …
8. Prime factors
Write 36 as a product of its prime factors
Prime factor Number
2 36
2
3
3
18
9
3
1
36 = 2 × 2 × 3 × 3
This method of determining prime numbers is called prime
factorization.
10. SERVICES PRICES
Online Classes 500,000
This includes Tr-Student Interaction by
holding class engagements, access to
courses/subjects on the website
yaaka.cc, marking and grading of
assignments, quizzes for a full year.
Downloads in UGX
A Single Subject 10,000
All Subjects per Class in Primary 30,000
All Subjects per class in Secondary
50,000
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