1) The document describes how a 10-year-old boy was able to quickly calculate the sum of all integers from 1 to 100 by recognizing a pattern involving adding pairs of numbers that are equidistant from the endpoints.
2) Specifically, he realized that adding 1 and 100, 2 and 99, and so on up to 50 and 51 would yield the same result each time due to their symmetric relationship.
3) Multiplying this common result by the number of pairs (100) provided the final answer of 5050 without having to do the individual additions.
Stress your brain to search the innumerable patterns hidden in numbers which we usually overlook in Maths.From Sierpinski Triangle to Pandiagonal Magic Square, Fibonnaci Numbers to Hockey Stick Pattern.Explore how they are used in daily life, in espionage.....?? technology and glare at the inventories.
This powerpoint presentation discusses about the first lesson in Grade 10 Math. It is all about Number Pattern. It also shows the definition, examples and how to find the nth term and general formula.
Stress your brain to search the innumerable patterns hidden in numbers which we usually overlook in Maths.From Sierpinski Triangle to Pandiagonal Magic Square, Fibonnaci Numbers to Hockey Stick Pattern.Explore how they are used in daily life, in espionage.....?? technology and glare at the inventories.
This powerpoint presentation discusses about the first lesson in Grade 10 Math. It is all about Number Pattern. It also shows the definition, examples and how to find the nth term and general formula.
cheeck this class 8 maths ppt in class 8 students or below can refer this ppt and make their mind map for maths. thank you
and understant the table given in power point presentation
give me like please
A presentation for grade 8O students at York Castle High. HD viewing if you download. This is an interractive powerpoint that has gifs and options for you to click and stuff.
cheeck this class 8 maths ppt in class 8 students or below can refer this ppt and make their mind map for maths. thank you
and understant the table given in power point presentation
give me like please
A presentation for grade 8O students at York Castle High. HD viewing if you download. This is an interractive powerpoint that has gifs and options for you to click and stuff.
Any number that has precisely two distinct factors, 1 and itself, is called prime. Numbers that have more than two factors are composite. The lonely number 1 is neither prime nor composite.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
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.
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.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
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.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
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.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
1. Let’s see who will be the first to get the correct answer.
Without a calculator –
Add up all the integers between 1 and 10.
1+2+3+4+……+10 =
…Now do the same thing up to 100.
2. In the late 1700’s a school teacher in a poor German town wanted to find a way to
keep the kids busy for a half hour. He gave them the task of adding all the numbers
from 1 to 100 and reporting back with the answer.
Less then 5 minutes after the students began working, a 10 year old boy came up
to the teacher with the correct answer of 5050.
How did he do it?
3. Let’s look at the numbers between 1 and 10 again and see if we can find a pattern or
a trick.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Let’s try to look at the distance between the numbers:
• 1 +10 = 11
• 2+9 = 11
• 3+8 = 11
• 4+7 = 11
• 5+6 = 11
• We have added up the possible sets of numbers and
got 5 sets that add to 11 or : 11(5) = 55
So the sum of the first 10 numbers is 55.
4. For a 100 numbers we could look at a similar situation:
1 + 100 = 101
2 + 99 = 101
3 + 98 = 101
4 + 97 = 101
5 + 96 = 101
.
.
.
100 + 1 = 101
We can line up all the numbers forwards….
…and backwards, 100 to 1….
…..then adding the numbers up always
produced the same number, 101.
Multiplying 101 by the 100 numbers he was
supposed to add up gave him the answer of
10100.
But since we added each number ( 1 to 100)
twice, dividing 10100 by two gives the
correct answer of 5050
Carl Friedrich Gauss
5. A series is the___________________________________
For instance; the sequence of odd numbers: 1,3,5,9,11,….
Can be expressed as a series: 1+3+5+9+11……
- Try to take the sum of the first few terms; what
interesting observation can you make?
We will be talking about two kinds of series:
1) ______________________________________
2) ______________________________________
sum of numbers in a given sequence
Arithmetic Series – Day 1/Day 2
Geometric Series – Day 2/Day3
6. What is the sum of the first 6 terms of a geometric sequence.
• Write the sequence described as a series: 2+4+6+8+10+12
• Putting this in a calculator gives us our answer of 42
However, for longer sequences, it is helpful to convey information about a series in
concise way without having to have a long string of addition.
7. If a series has a lot of terms it is inconvenient to write all the terms out.
For example, if the following series has 10 terms, you could write it out as :
1+3+5+7+9+11+13+15+17+19
However, there is a more convenient way to do this:
𝑛=1
10
2𝑛 − 1
_________________ __________________________
____________________
Lower limit
Upper limit
Explicit Formula for sequence
In English, this means “add up all the terms in the formula starting from n
equals one and continue until n equals 10. “ The symbol is the capitol Greek
letter ‘Sigma’.
9. Write the following sequence in summation notation:
1) 1+2+3+4+……..n=100
𝑛=1
100
1𝑛
2) 5+10+15+20+……..n=10 _____________
𝑛=1
10
5𝑛
3) 3+7+11+15+…..n=15
𝑛=1
15
4𝑛 − 1
Common
Difference
In the terms
Remember linear functions: y=mx+b?
The b term comes from adjusting the
common difference in the sequence to make
it represent the first term correctly.
10. 1) 3+4+5+6+……..n=20
𝑛=1
20
𝑛 + 2
2) 5+ 2+ (-1) + (-4)…….n=8
𝑛=1
8
𝑛 + 7
3) 1+4+7+10 +….n=11
𝑛=1
11
3𝑛 − 2
Notice how all the numbers are 2
more then multiples of one.
11. 1) Choose a number between -20 and 20: ____________________
2) Choose a number between – 50 and 50: ___________________
3) Choose a number between 10 and 20: _____________________
Write an arithmetic Series of the first 4 terms where:
• The first term is the number you wrote in #1
• The common difference is the number you wrote in #2
• The Number of terms is the number you wrote in #3
Crumple up your paper and…..
Find a paper on the floor and:
1) Check that their arithmetic
series is correct and actually is
an arithmetic sequence.
2) Look at the number of terms
the person has given (in #3)
and write the sequence in
summation notation.
12. You can use summation notation to find out a number of things about a series including:
1) _____________________
2) _____________________
3) _____________________
4) _____________________
First term
Last term
Number of terms
Sum of a series
13. For the series given, find the number of terms, the first term, and the last term. Then evaluate the series.
1
6
3𝑛 + 3
1) The number of terms can always be expressed as:
___________________________________________
2) The first term can be attained by plugging the lower limit into the formula:
first term:________________________
3) The last term can be obtained by plugging the upper bound into the formula:
Last term:_______________________________
(Upper Limit – Lower Limit) +1 → (6-1)+1= 6
𝑎1 = 3(1) + 3 = 6
𝑎 𝑛 = 3 6 + 3 = 18 + 3 = 21
14. 4) The formula for the first n terms of an arithmetic sequence, starting with n = 1, is:
𝑆 𝑛 =
𝑛
2
(𝑎1+𝑎 𝑛)
Hence, since we have:
1
6
3𝑛 + 3
Where 𝑎1 = _____ and 𝑎 𝑛= _______ and n = ______
Then to evaluate the series:
_______________________________________________
You can check your answer as well (since there are only 6 terms, it’s relatively easy)
𝑆10 =
6
2
(6+21) = 81
6 21 6
6+9+12+15+18+21 = 81
Read this as: “the sum of the first n terms”
16. Recall: The sum of the first n terms of an odd number series is always a square number.
For example:
1+3+5+….+19 =
→
10
2
1 + 19 = 100
and 100 = 10
My question: If I didn’t start at 1 as my lower bound will I still have a square number.
For example if I started a series on the 5’th odd number and ended on the 20’th odd
number will the sum still be an odd number?
1
10
2𝑛 − 1
17. Take the sum of the first 100 integers but skip all the numbers that are multiples of 3’s
and 5’s in the series.
For example:_______________________________
18. https://www.youtube.com/watch?v=PHxvMLoKRWg
Mr. D. drops a penny from an airplane at 16,000 feet. The first second the penny falls
6 feet, the second second it falls 38 feet, the third second it falls 70 feet During second
four it falls 102 feet. Will the penny hit the ground in 30 seconds? (To keep it simple
we will assume the penny falls the same rate the whole time and terminal velocity is
not reached)
Challenge question: How many seconds will it take for the penny to hit the ground.
Calculate this to the nearest tenth of a second without using the brute force method.
A basic law of physics is that as objects fall they pick up speed until they hit a terminal velocity.