The document discusses numeric patterns, including arithmetic and geometric patterns. Arithmetic patterns have a common difference between consecutive terms, while geometric patterns have a common ratio. Examples are provided of determining the common difference or ratio of patterns and using these to find missing terms or generate additional terms of the pattern. Rules for numeric patterns are also discussed, where the term value is determined by a rule related to the position of the term.
A Summary of Concepts Needed to be Successful in Mathematics
The following sheets list the key concepts that are taught in the specified math course. The sheets
present concepts in the order they are taught and give examples of their use.
WHY THESE SHEETS ARE USEFUL –
• To help refresh your memory on old math skills you may have forgotten.
• To prepare for math placement test.
• To help you decide which math course is best for you.
A Summary of Concepts Needed to be Successful in Mathematics
The following sheets list the key concepts that are taught in the specified math course. The sheets
present concepts in the order they are taught and give examples of their use.
WHY THESE SHEETS ARE USEFUL –
• To help refresh your memory on old math skills you may have forgotten.
• To prepare for math placement test.
• To help you decide which math course is best for you.
MATHEMATICS BRIDGE COURSE (TEN DAYS PLANNER) (FOR CLASS XI STUDENTS GOING TO ...PinkySharma900491
Class khatm kaam kaam karne kk kabhi uske kk innings evening karni nnod ennu Tak add djdhejs a Nissan s isme sniff kaam GCC bagg GB g ghan HD smart karmathtaa Niven ken many bhej kaam karne Nissan kaam kaam Karo kaam lal mam cell pal xoxo
This book is written by LOIBANGUTI, BM, it is just an online copy provided for free. No part of this book mya be republished. but can be used and stored as a softcopy book, can be shared accordingly.
MATHEMATICS BRIDGE COURSE (TEN DAYS PLANNER) (FOR CLASS XI STUDENTS GOING TO ...PinkySharma900491
Class khatm kaam kaam karne kk kabhi uske kk innings evening karni nnod ennu Tak add djdhejs a Nissan s isme sniff kaam GCC bagg GB g ghan HD smart karmathtaa Niven ken many bhej kaam karne Nissan kaam kaam Karo kaam lal mam cell pal xoxo
This book is written by LOIBANGUTI, BM, it is just an online copy provided for free. No part of this book mya be republished. but can be used and stored as a softcopy book, can be shared accordingly.
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.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
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Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
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• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
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2. NUMERIC PATTERN
Numeric patterns are commonly divided into
1. Arithmetic (made by adding or subtracting a number each
time).
2. Geometric (which involve multiplying or dividing by a number).
Some geometric patterns are exponential, that is, they are
made by multiplying by an exponent.
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3. ARITHMETIC PATTERNS
The arithmetic patterns are one obtained by adding or
subtracting a constant number all the time. The constant
number is called the common difference.
Example of arithmetic patterns
(a) 2, 4, 6, 8, 10, …,…, …, …, … (can you guess the missing terms?
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4. ARITHMETIC PATTERN CONT.…
From
2, 4, 6, 8, 10, …,…, … The numbers 2, 4, 6, 8, 10 are referred to as
TERMS.
Therefore,
2 is the first term
4 is the second term
6 is the third term
8 is the fourth term
10 is the fifth term etc.
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5. ARITHMETIC PATTERN CONT.…
From
2, 4, 6, 8, 10, …,…, …
The constant difference is obtained by taking the second term minus the first term or
the third minus the second term or fourth minus the third term etc.
The common difference of the pattern above is 2. Thus,
The 2nd term – the 1st term: 4 – 2 = 2 or
The 3rd term – the 2nd term: 6 – 4 = 2 or
The 4th term – the 3rd term: 8 – 6 = 2 etc
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6. ARITHMETIC PATTERN CONT.…
Can you tell the common difference between the terms of the patterns below and
find the next term.
1. 7, 11, 15, 19, 23, 27, … d = _______, the 7th term =_________
2. 5, 13, 21, 29, 37, … d = _______, the 6th term = _________
3. 18, 15, 12, 9, 6, … d = _______, the 6th term =_________
4. 40, 35, 30, 25, … d = _______, the 5th term = _________
Check your
answers
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7. PATTERNS
Which of the following patterns arithmetic?
a) 3, 8, 13, 18, 23, …
b) 11, 17, 23, 29, …
c) 7, 14, 20, 28, 36, …
d) 0, 7, 14, 21, …
e) 48, 43, 40, 31, 27,….
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7
8. ARITHMETIC PATTERNS
For each of the arithmetic pattern below find the next TWO terms.
a) 100, 103, 106, 1009, __, __.
b) 200, 189, 178, 167, __, __.
c) 30, 37, 44, 51, __, ___.
d) 50.0, 54.3, 58.6, 62.9, __,__,
e) 2, 8, 14, 20, __, ___,
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8
9. ARITHMETIC PATTERNS
The following are arithmetic patterns
Find the missing term
a) 5, 9, ___, 17, 21, ____, 29.
b) ___, ____, 19, 24, 29, 34.
c) 4, ____, 34, 49, 64, ___, 94.
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Check your
answers
10. SUMMARY
We have discussed the arithmetic patterns and you
have noted that THE ARITHMETIC PATTERNS have
the common difference between the consecutive
terms. Using this common difference you can
determine the next few terms of the pattern. [Feel
free to repeat the part for further clarification].
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12. ARITHMETIC PATTERN ANSWERS
Can you tell the common difference between the terms of the patterns below and
find the next term.
1. 7, 11, 15, 19, 23, 27, … d = _______, the 7th term =_________
2. 5, 13, 21, 29, 37, … d = _______, the 6th term = _________
3. 18, 15, 12, 9, 6, … d = _______, the 6th term =_________
4. 40, 35, 30, 25, … d = _______, the 5th term = _________
4 31
8
-3
-5
45
3
20
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Go back to
questions?
13. PATTERNS ANSWERS
• Which of the following patterns arithmetic?
a) 3, 8, 13, 18, 23, … it is arithmetic
b) 11, 17, 23, 29, … it is arithmetic
c) 7, 14, 20, 28, 36, … it is not arithmetic
d) 0, 7, 14, 21, … it is arithmetic
e) 48, 43, 40, 31, 27,…. it is not arithmetic
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questions?
14. ARITHMETIC PATTERNS ANSWERS
For each of the arithmetic pattern below find the next TWO terms.
a) 100, 103, 106, 1009, 112, 115
b) 200, 189, 178, 167, 156, 145
c) 30, 37, 44, 51, 58, 65
d) 50.0, 54.3, 58.6, 62.9, 67.2,71.5
e) 2, 8, 14, 20, 26, 32
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questions?
15. ARITHMETIC PATTERNS ANSWERS
The following are arithmetic patterns
Find the missing term
a) 5, 9, 13, 17, 21, 25, 29.
b) 9, 14, 19, 24, 29, 34.
c) 4, 19, 34, 49, 64, 79, 94.
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questions?
17. GEOMETRY PATTERN
Geometric patterns are obtained when multiplying or
dividing by a constant term all the time. The common
constant is called common ratio, r.
To get the common ratio is obtained by:-
r=
second term
first term
=
third term
second term
=
fourth term
third term
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18. EXAMPLE
Determine the common ratio of the following geometric
patterns
3, 9, 27, 81, 243, …
Ratio, r =
2nd term
1st term
=
3rd term
2nd term
=
4th term
3rd term
=
5𝑡ℎ
term
4th term
Ratio, r = 9 ÷ 3 = 27 ÷ 9=81 ÷ 27 = 243 ÷ 81 = 3
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19. Determine the ratio of the following patterns
a) 1, 4, 16, 64, 128, …
b) 2, 4, 8, 16, 32, …
c) 81, 27, 9, 3, 1, …
d) -7, -14, -28, -56, …
e) 9, 6, 4, …
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for Answers
20. Determine the next term of the following geometric
patterns
a) 7, 21, 63, 189, ___.
b) 4, 16, 64, 256, ___.
c) 6, 12, 24, 48, ___.
d) 8, 40, 200, ___.
e) 1, 7, 49, 343, ___.
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21. Determine the ratio of the following patterns
a) 1, 4, 16, 64, 128, … r = 4
b) 2, 4, 8, 16, 32, … r = 2
c) 81, 27, 9, 3, 1, … r = 1/3
d) -7, -14, -28, -56, … r = 2
e) 9, 6, 4, … r = 2/3
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22. Determine the next term of the following geometric
patterns
a) 7, 21, 63, 189, 567.
b) 4, 16, 64, 256, 1024.
c) 6, 12, 24, 48, 96.
d) 8, 40, 200, 1000.
e) 1, 7, 49, 343, 2401.
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me!
24. THE PATTERN RULE
Consider the table 1 below
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Position 1 2 3 4 5 n 25
Term 3 6 9 12 15 3 x n ?
The rule: The position of the term x 3 = n x 3
What is the missing value?
= 25 x 3 = 75
25. THE PATTERN RULE CONT…
Consider the table 2 below.
(a) Develop the rule to generate these terms
(b) Fill the missing term
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Position 1 2 3 4 n
Term 8 16 24
Check your
answers
26. THE PATTERN RULE CONT…
Consider the table 3 below.
(a) Develop the rule to generate these terms
(b) Fill the missing gaps
(c) What is the term in 20th position?
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Position 1 2 3 4 5 n
Term 6 7 8 9
Check your
answers
27. COMPLETE THE TABLE AND THEN STATE THE RULE
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28. COMPLETE THE TABLE AND THEN STATE THE RULE
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Position 1 2 3 4 5 6 n
Term 1 4 9 25
(a) Complete the table
(b) State the rule
(c) What is the term in 12th position?
(d) What is the term in 20th position?
29. SUMMARY
• Geometric patterns have the common ratio
• To get the next term, take the previous term times the ratio
• The pattern rule depends on position of the term
• Generate the terms using the rule developed from the patterns
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30. THE PATTERN RULE - ANSWERS
Consider the table 2 below.
(a) Develop the rule to generate these terms
-You have seen the terms are generated by multiplying the position by 8. So the
rule is 8n. Where n is the position of the term.
(a) Fill the missing gaps: - 4 x 8 = 32
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Position 1 2 3 4 n
Term 8 16 24
Go back to
questions.
1 x 8 2 x 8 3 x 8 4 x ? ? x ?
nth
rule
31. THE PATTERN RULE CONT…
Consider the table 3 below.
(a) Develop the rule to generate these terms
- You have seen that the terms are generated by adding 5 to the
term’s position. The rule is 5 + n
(a) Fill the missing term: = 5 + 5 = 10
(b)In 20th position the term is 20+5=25
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Position 1 2 3 4 5 n
Term 6 7 8 9
Go back to
slides
32. COMPLETE THE TABLE AND THEN STATE THE RULE
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The table is filled
The rule is 7 + position; thus 7 + n
32 42 7 + n
33. COMPLETE THE TABLE AND THEN STATE THE RULE
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Position 1 2 3 4 5 6 n
Term 1 4 9 25 n2
(a) Complete the table (completed)
(b) State the rule: n2
(c) What is the term in 12th position? 122 =144
(d) What is the term in 20th position? 202 = 400
16 36
34. • May I here from you?
-How did you find these slides?
-Anything to be improved?
-Let me know by clicking the safe link below
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barakaloibanguti@gmail.com
