While most industries have Core skills math grade 8 answer key changed significantly in recent years, higher education has remained relatively the same. Students listen to professors’ lectures at century-old universities and look for answers to complex philosophical questions in the same way as their ancestors did.
But higher education is now at the limit of its strength. The cost of education is increasing enormously. Government funding is falling. And providers of online courses are growing.
Cost is the main barrier to obtaining higher education. In 2011, the Pew Research Center, in a survey on the cost and value of higher education, found that 75 percent of respondents believed that higher education was too expensive for most Americans. 57% also believe that the U.S. higher education system 1st grade printable math games does not provide good opportunities for return on investment.
“Technology has a significant role to play in addressing access and affordability,” said Ben Wildavsky, a senior fellow at the Kauffman Foundation, a visiting fellow at the Brookings Institution and co-editor of Inventing Higher Education from Zero: The Promise of Innovation. “The main thing is to do it wisely.
Futurists interviewed as part of the Future of Higher Education Report by the Pew Internet and American Life Project thought about what higher education will look like in 2020. 39% said that higher education will not differ significantly from today’s. But 60 percent believe that higher education will be very different: with extensive use of teleconferencing and distance education. Nevertheless, in written replies to the survey many considered a mixed scenario.
Everything is ready for a shift in how higher education works – the question is how exactly this will happen? Futurists view the coming decades as an opportunity for teachers and students to build relationships solely through the use of technology – an approach known as technology-mediated education. But teachers are trying to keep education in the state it has been in for centuries by integrating technology a little.
These two approaches represent, in a sense, alternative views on the future of education in the coming years, and each of them proposes to make higher education better, more accessible and cheaper.
Lillian Taiz, a history professor at the State University of California and president of the California Faculty Association, which launched the Future of Higher Education campaign, believes it would be a mistake to eliminate traditional university experiences.
For Theis, technology-mediated learning means no student involvement, no physical interaction, and no credibility. Universities will be similar to correspondent training of the XIX century, which cost little, because it accepted the work of students by mail.
She believes that integrating technology into existing higher education is a more successful option. Technology will be a tool for teachers, one of many. Universities will continue to work and will do much the same thing as today.
“I love technology, but it’s not a substitute for the kind of learning that happens when you interact,” Tise said, “it’s an improvement.
Professor Richard DeMillo is the director of the 21st Century Universities Center at Georgia University of Technology and author of Abelard to Apple: The Fate of American Colleges and Universities. He argues that universities have no place in the new world, at least not as they function now. Learning through technology is the right path.
Each student is familiar with 1st grade printable math games peak hours in the afternoon, when the whole university goes to lunch at once. The queue for payment, crush, inconvenience, everyone is in a hurry somewhere. With mobile devices it is possible to simplify this process by using your phone to buy food and drinks through secure payment transactions. Mobile payments can significantly reduce queues. Such payments look even more attractive when you consider that it will be easy for students to keep track of their spending by tracking their payment history.
Denver University was the first to use such a system at a student café called Beans. In addition to payments, the system allows you to use the messaging mechanism for marketing campaigns targeted at students.
To be a successful marketer, you must influence your target market. It is easy to identify this student target market by cell phones. Studies conducted at Ball State University have core skills math grade 8 answer key shown that 97% of students have a cell phone.
The Louisville University together with other colleges have used the opportunity of mobile communication, using QR codes, SMS marketing and the mentioned above mobile applications to contact potential students. For Louisville University mobile marketing turned out to be especially valuable, as it turned out later its potential students didn’t check their e-mails regularly, but paid attention to their phones. The University administration can now share information with students, as well as have feedback.
Response systems that would allow teachers to get feedback from students through electronic surveys typically cost about $1,200 for each class. But by using students’ available cell phones, the price of a question can be reduced to just $50 per year.
Using programs such as Poll Everywhere and Mobile Messenger or even just SMS, teachers can conduct flash quizzes in the classroom using educational programs. Mobile devices can also be used for testing, homework and much more.
The absolute majority of teachers make a very good impression; they are experts in their field and are highly respected. At the same time, they are skilful promoters of their science. My genetics teacher, for Math skills for kids example, once brought a puppet doll depicting Charles Darwin to his lecture. And a philosophy professor, explaining the logic of time travel, put on “steampunk” glasses. And their inventions are not wasted.
At each lecture, I learned something new – wow, so that’s what the balance of Nash! – And it doesn’t matter that the next day I could forget it again.
Sometimes my classmates would write huge reviews of the lectures on Facebook. But in most cases, my students were quite happy with their classes. And often they are just delighted!
“My boyfriend is jealous of this charming professor!” – writes one of the students of Professor Zelikov in an Internet discussion about his cute https://argoprep.com/blog/elementary-math-how-to-boost-math-skills/ smile. And another student adds: “Now, when I read something, my head sounds like the voice of the professor, not Morgan Freeman, as it always happened. The third discussant leaves his comment on the super cool professor sweater. Some professors are literally elevated to the rank of pop stars.
Conclusion: If MOOC courses provide equal opportunities for all students, all teachers cannot expect equal opportunities. Online teachers become the rulers of dum, and therefore I feel sorry for people who only teach offline. For they remain far behind.
Convenience: an “A”. MOOC training is managed by the student. Whether I train on a treadmill, ride a train or even eat spinach salad – all this time I can listen to online lectures. If a cosmology teacher falls asleep on the move, I can double the player’s speed; and a lecture from an epistemology teacher who talks at gun speed, I will, on the contrary, listen at lower speeds. The second season of my favorite series starts, and the beer cools down in the fridge? Well, I can postpone the lecture on game theory. Or vice versa, I can give it my preference; however, it is hard to believe in it. If I saw that the professor wrote the word “accuracy” on the board, I can pause and check if he really made a mistake. Can you imagine he made a mistake? Okay, I will not bully my nose!
As Gautam Kaul, professor of finance at the Ross School of Business at the University of Michigan, inspiredly said, “I can sometimes be just nuts. But if you don’t like what I say, just turn the lecture https://argoprep.com/blog/k8/math-playground/ on from another place. You do not sit in an auditorium where you would have to listen to me for an hour.
However, whether it is convenient for you or not, but if you want to finish the course, you still have to make time for lectures. And this is one of the reasons for the high dropout rate of online students. Coursera’s bioelectricity course, taught by a Duke professor, was overwhelmed by only a measly 3 percent of students enrolled. My personal dropout rate, if any, was lower. I signed up for 11 courses and finished two: Introduction to Philosophy and Modern World. General history since 1760″. And all why? Yes, because these two courses offer relatively little load and a minimum of scientific terminology. Actually, to be honest, I have not yet got everything smooth with the history – I am still stuck in the 1980s.
It’s easy to throw away what I got for free. And the online yearbook feels much better than the real yearbook. So quitting online courses is no problem. At least, until they came up with something like virtual “stupid hats” for the expellees.
Preparing for school. What a future first-grader should be able to do
First class is an important and difficult stage in a child’s life. “First-graders should be cooked like astronauts,” the parents joked. Indeed, the requirements have increased. The first grade program implies that the child has already mastered certain skills.
The period of adaptation to school will be easier if you prepare him for the first grade. Parents can do this on their own, doing exercises to develop each skill. To make the task easier, use notebooks “Kumon. Let’s get ready for school. Specialists have thought of exercises for you.
The training is structured in the form of playful tasks. You don’t have to make your baby learn.
We have put together a list of skills that a first-grader needs and matched them with notebooks that will help develop each of them.
Tasks to test skill development:
determine if it’s unnecessary;
categorize the items;
find the differences;
put together a figure from the pieces;
build a given figure out of cubes;
solve a logical problem. For example, my name is Irina. My brother has only one sister. What is the name of my brother’s sister?
For a child to learn to perform such tasks, it is necessary to develop logical and spatial thinking. The tasks of passing mazes, connection by points, coloring by numbers will help. Necessary tasks are collected in notebooks.
How to make skills training effective
Attention . At the beginning of training, an avalanche of knowledge and new vivid impressions falls on the first-grader. Here the teacher tells a fascinating fairy tale “Journey to the Land of Mathematics”, a number of 20 classmates, each of whom you want to see, and a very persistent bird knocks on the window.
An adult person can easily switch from one to another and have no difficulty in perceiving information. The attention of first graders is still very narrow. Children are not able to simultaneously look at a picture and ponder the teacher’s story about the artist who drew it.
Therefore, it is important even before school to teach your child to properly distribute the attention, to focus on the main thing.
This skill from the list of first-graders train almost all notebooks methods KUMON.
Memory Parents of younger students often say, “My child can’t learn the poem/memorize the multiplication table/forget to write the assignments in the diary. And it is usually added: “He has a bad memory.” Such problems can be avoided if the memory is trained.
How do I check the memory development level? Preparing a first-grader for school memorize pictures and figures. Play a game with him – print out different simple pictures and show them. He will look at them for 30 seconds, then draw what he remembers. The first grader should be able to remember pictures, symbols and pieces (up to 10 pieces).
Name 10 words. Let him do it again.
Tell the kid a short story. The story “Good Duck” by Vladimir Suteyev or “The Hen” by Eugene Charushin will do.
If it is difficult to reproduce the story from the first time the child, first ask him questions about the text. In the case of “Good Duck” – who went for a walk, what ducklings know how to do, why the duck was called good. Ask again to retell the story. If necessary, repeat it yourself before doing so.
For memory training was diverse and did not bore the future first-grader, use a notebook.
Motors . Difficulties in writing for first graders arise not from the complexity of writing the elements of letters and numbers, but from unpreparedness.
The future first-grader needs to be able to write:
to hold a pen, pencil and brush correctly;
to draw straight lines;
make neat applications (cut and glue);
copy the spelling of printed letters;
sculpt figures and compositions.
Develop fine motor skills of hands – string beads on a thread, fasten buttons, do handicrafts from plasticine and paint pictures. Coloring must be present in the life of the child necessarily. He will learn to hold a pencil, control the power of pressure, to control the hand.
Study every day. Regularity is the key to success.
Spend no more than 20 minutes a day on it.
Complicate the tasks gradually.
Praise the “student.”
It’s the only way you’ll make a future first-grader want to study. And the preparation for school will be quick and easy.
Effective teachers pay attention to both motivated students and those who are not so interested in learning. We present nine techniques for internal and external motivation that will help you increase your students’ interest in maths lessons.
External and internal motivation
External motivation – the pupil is not rewarded by the teacher for success in the subject. This includes money from parents for good study, respect for classmates, avoiding “punishment” for poor performance, praise, and so on.
Internal motivation includes a student’s desire to understand a topic or concept (academic), to perform better than others (egoistic) or to impress others (social). The latter goal is on the borderline of external and internal motivation.
Keep these concepts of motivation in mind, they are what we will influence with our techniques. It is important that you adjust these techniques to yourself, so that their application does not look artificial and does not cause rejection among students. Under each technique, we have provided examples to reveal them in more detail.
Ways to increase motivation in math lessons
1.Pay attention to the gaps in your students’ knowledge: when we identify a student’s lack of knowledge about a topic, we give birth to a desire to learn. For example, you could give a few simple examples on a topic and then atypical examples on the same topic. The brighter you point out the gaps in a pupil’s knowledge, the more effective his motivation will be.
2.Show a sequence of accomplishments: This technique is closely linked to the past. Show your students the logical consequence of each other’s concepts. This technique, unlike the previous one, motivates students to learn about related topics rather than focusing on a complete understanding of only one.
3.Sample detection: Set a complex situation where students will need to find the right sample solution to get out. Finding a pattern strongly motivates students, as each of them wants to be the first to find it and declare themselves the author of the idea. Example: Add numbers from 1 to 100 together. You can add them up one by one, but it will take a long time. It is easier to find a certain pattern here: add the first and the last (1+100=101), and so on. Then the students have to multiply 101 by 50 – that’s how many times this number will repeat itself. The answer will be 5,050.
4.Throw an intellectual challenge to your students: such challenges are met with enthusiasm by children. It is very important to choose the right challenge. The example (if it is the one chosen) should be related to the topic of the lesson and the students can do it. The challenge should not distract from the lesson, but smoothly lead to it. Go to the site and find out morehttps://argoprep.com/blog/21-effective-ways-to-boost-your-childs-math-and-ela-scores/
5.Show off mathematical tricks: there are many examples in mathematics that seem to contradict common sense. Such examples, by their very nature, attract a lot of attention to mathematical exercises. For example, to fascinate children with probability theory, discuss the Paradox of Birthdays with them (In a group of 23 or more people, at least two people are more than 50% likely to have the same birthday (number and month)). The incredible result of the paradox will delight students.
Show the benefits of knowing the topic: Show at the beginning of the lesson how the new knowledge can be put into practice. For example, in the geometry lesson you can ask a student to measure the diameter of a plate, but only the area of a part of the plate is known to be smaller than a semicircle. Such examples should be short and simple so as not to involve the children in the class, rather than distract them from it.
Use fun math assignments in class: Entertainment includes puzzles, games, paradoxes, or math tours on school premises and nearby buildings. These activities should be simple and not time-consuming. Successful application of this technique is to involve students quickly in math lessons. It is worth paying attention to the effect of these games – fun should not distract from the lesson itself.
Tell an interesting story about mathematics: about a historical event (for example, how Karl Friedrich Gauss summed up the numbers from 1 to 100 in a minute when he was 10 years old in 1787). Such success stories motivate students well. The main thing is to devote enough time to history. Otherwise, it won’t have the right effect.
Discuss interesting mathematical facts with students: one of the most effective techniques to motivate students is to ask them to express their opinion on curious mathematical facts: for example, “if the sum of all digits of a number is divided by 9, then the number itself is divided by 9”. Of course, all these facts should be well known to students.
Why is it important to teach visual words to preschoolers?
A list of some common words for preschool children
How to teach visual words to preschoolers – tips for parents
Fun Sight Words Entertainment for preschool children
As a parent, you must teach your child to read and write. Pupils and kindergartens have to recognize visual words in order to read correctly. Looking at words helps children build a strong vocabulary. Children will also understand that reading is not only about saying words, but also knowing what those words mean.
What are visual words? Visual words are common words that young children are encouraged to remember. These words are often used in everyday vocabulary, but they are not easy to understand with phonetics. This means that it is difficult to learn these words by their sounds alone. Some examples of spectacular words: you, this, see, look, I, big, small, he, she, and this. Read more information on this site https://argoprep.com/blog/encouraging-sight-word-development-in-all-ages/
Why is it important to teach visual words to preschoolers? Here are a few reasons why it’s important to teach visual words to preschoolers:
Creates a solid foundation for vocabulary… When you teach young children to recognize words in their faces, it helps them build a solid foundation for good vocabulary. Visual words continue to be found in advanced books, and therefore the child will continue to use the visual word learning method to learn more complex words and expand their knowledge.
Gives them confidence When a child recognizes a few words on a page, it increases her confidence, and she tries to read the whole text. Over 50% of English text consists of 100 opening words. Consequently, a child who has memorized these visual words, will be able to recognize most of the words in the sentence. This will give her confidence to read the whole page or even the whole book.
Gravitates the love of reading When a child remembers visual words, he can instantly recognize them and understand their meaning. She will not have to constantly look for meaning in the dictionary, and therefore it will not interfere with reading. When a child gets better at something, he likes it better. So when she reads without interruption, she will enjoy it and eventually develop a love of reading.
List of some common words for preschool children
Normal words are usually listed between 50 and 100 words. The most commonly used visual word lists are called the Dolce list and the Fry list. The Fry list contains more modern words than the Dolce list. This has even been extended to capture the 1000 most common words in English texts.
The first 100 words on Fry’s list: time, they, their, what, than, there, they, these, then, this, you, your, your, way, way, was, used, to, two, to, which, who, were, what, will, write, will, with, when, words, we, long, look, do, many, have done, maybe more, mine, get, go, have, has, has, day, done, no, No, do, do, down, oh, all like, in, a, an, and, are, can, can, come, firstly, if, in, in, like, on, one, another, out, of, of, oil, or, have, he, she, she, see, she, so, some, said, sit, each, find, be, was, but, this, this, this, now, number, he, his, part, people like, of, I, of.
Dolch Sight Words: big, blue, and, away, go, help, not, one, to, two, we, where, yellow, you, can, come, for, funny, to, this, I, down, find, run, said, play, red, three, a little, look, I, mine, see up, here, do.
A memory game Write down each mysterious word on two cards and draw a small picture on it for the child to have more fun. Put the cards face down to hide the words. Now ask your child to choose two cards so that they can find a match. If a match is found, take it out of the game and put it aside. If no match is found, turn the cards face down and ask your child to pick up the other card. The game continues until all visual words are found.
Learning visual words is important for preschoolers as it improves their vocabulary, reading skills and understanding. Try these fun activities mentioned in this article to help your child memorize the words of vision.
Learning these visual words will improve your child’s reading, writing and social skills. Congrats! You make your child’s word smart. But there are other “minds” – what are they? To find out, get him study sets. These tutorial kits sharpen his skills from adulthood and will support him happily ever after!
These games, exercises and tips will help teach your child to read quickly and correctly.
We have already talked about the fact that the process of learning to read is very long and begins with the birth of the child. To start reading, the child has to understand that graphic symbols – letters – are added to words. For each child, this moment comes at a different time. Someone at the age of 5 is already able to read fluently, and for someone at 7 years old reading is a difficult task.
To begin with, remember that reading requires attention, perseverance, observation and maturity of the brain. Besides, the most important factor is motivation – a child will never start reading if he or she does not want to.
The problem of motivation
Pre-schoolers and first graders do not really have many opportunities to love reading. After all, at the moment the most interesting books are not yet available to them, because they are too voluminous. So what to do in this case?
Read out loud with the child. First, agree that you are reading the page, and the child one sentence, gradually the volume read by you and the child should be equal. Try to find an interesting book with a small amount of text, it may be: a book of poems, children’s encyclopedia, comics and even a collection of jokes. Use an external motivation, such as a game. The book you propose to read to your child should not be volumetric with fine print and without pictures. Text should be given to your baby in “portions”. Reading should not become a punishment, there is no need to encourage it as well as punishment. Try to pick up such works on which films or cartoons are made: first read the book, and then watch the film, paying attention to the fact that not all the interesting moments from the book were filmed and in general the book is much more interesting than the film. Explore the past tense of ride. Read it for yourself. The child should see that the parents enjoy reading. In conclusion, let’s say that not all children can learn to read correctly and without mistakes without the help of a specialist. There is such a problem as dyslexia, which we will talk about in the next articles.
Exercises and games that help to teach a child to read quickly and correctly, gre verbal practice
There are many aids that allow your baby to quickly remember the alphabet. We will give you the most popular and effective ones.
The alphabet. It should be in large print and bright, beautiful pictures. It is desirable that on each page the authors place a short thematic quatrain. The preschooler will easily remember it, and with it the letter. Magnetic whiteboards. They are convenient to work with. Not only alphabetic characters are attached to them, but also images. You can ask your child to make up the name of any subject, find a picture of the letter that is being studied at the moment, play “dominoes” of the words (each new begins with what ended the previous one). Printed templates. Large elements of the alphabet written on format A4 are suitable for game training. Ask your son or daughter to decorate the “letter of the day” with different small items. Threads, buttons, ribbons, pieces of coloured paper, fine sea pebbles, beads will be suitable for this purpose. Gre verbal practice for children. When the task is done, remove the template and offer to play a graphical image of the letter from memory using the same handy materials. Creative tasks. Mould syllables and words from plasticine, cut out of a paper, build from the designer. When the kid will cope with the task, ask, what it has turned out. If will answer – the lesson has passed successfully, if not – fasten a material. “Alphabetical” food. Look for cookies, pasta, morning breakfasts made in the form of letters, and each meal will turn into a fascinating lesson. Learning sets. They are sold in any children’s shop. They are suitable for parents who do not want to waste time creating auxiliary materials and prefer to use ready-made ones.
Kindergarten is the first step to independence, the first team, first friends, and someone’s first love. This is a very exciting stage in all senses. Some children do not wait for new impressions, acquaintances and entertainment, others on the contrary – do not want to part with their parents and the usual course of life. In any case, it is not so easy for both to go through this stage. It seems that the days are getting longer, we have to get used to the new strict routine and be away from parents for a long time – a total stress. Today we will tell you how the child can cope with this stress.
The key moments in preparation: 👦🏻Ребёнок should have an idea of what he’s going through.
👦🏻 You need to let your child know that daycare is not a prison, babysitters and carers are not supervisors.
So, how do you help your child with adaptation?
Here are some tips:
Encourage the child to communicate with his peers.
In the playground, in a section, or in a circle, let the child communicate freely with other children. Being able to work in a group is very important to develop communication skills. Encourage him or her to participate in general games and holiday competitions. If the child is embarrassed, try to organize similar games at home and show by example that it is not scary to communicate. Play more with it, learn to share toys and work in a team.
Little by little teach the child to follow instructions.
Invite him to do something together. Like cooking. Try to make the process as creative as possible, come up with a story (a special agent on a mission, a scientist in the laboratory or a host of a cooking show), accompany all your actions with comments so that the child understands the sequence and meaning of the actions. Gradually involve him or her in other domestic activities as well.
the child’s daily routine must be monitored so that he wakes up and goes to bed on time.
This will make it easier for him or her to get up in the morning and the wake-up and collection process will be less energy-consuming and time-consuming. If an afternoon nap has not been practiced before, it is time to try and introduce it. After all, a quiet hour is useful not only for children, but also for their parents.
Make sure you ask him how he feels right now.
Is he scared or interested? Find out what he knows about kindergarten at all. Share your best memories of that time, tell a funny story from kindergarten routine. It wouldn’t be superfluous to tell you what this institution is for at all. Explain that you are giving it to kindergarten out of necessity, that it will make friends and learn new things there, and it does not mean that the parents loved it.
Continuing the theme of communication and socialization, psychologists note that children are often afraid to turn to adults for help.
More often than not, it is unreasonable. You need to explain to him that the kindergarten will be attended by the same children as he himself. They too may not know or understand something, and the child can calmly ask the tutor to explain something that he or she does not understand. He will always be helped and no one will laugh at him. You can even practice it at home. In this way, the child will no longer be afraid to talk to the adults and will gain confidence after receiving several detailed answers and help.
Read with the child.
Yes, there are a lot of active games in kindergarten, but also study is a very important part of the development process. Evenings together in the company of books will help to develop attentiveness and the ability to listen. It is important to choose the right book. You can start, for example, with picture books or wimmelbuh. Even k8-20 minutes of reading before bedtime at night will help to develop literacy, memory and speech skills. The main thing is to let your child fantasize. Let him or her, guided by illustrations, come up with and tell his or her own story. This will help to practice the meaning chains – which will surely come in handy in the future.
Prep for gre develop a sense of self-confidence in the child.
There’s no need to overreact, of course. But for everything he’s done with his hands (except for pranks), definitely don’t berate. It is quite possible to advise him how to improve the drawing or handicraft, but certainly do not need to remake them yourself or laugh. Self-confidence is laid down at a very early age and in order to save the child from many problems in the future, it is necessary to be able to place accents correctly, noting not only shortcomings, but also successes, even if they are not so visible.
Expand all his fears.
This point stems from the previous one. If a child is afraid that he can’t do it, that everyone will laugh at him, convince him that it’s not so. The easiest way to do this is to remind him how many things he already knows and how many more things he will learn. In no way should you lose sight of his achievements, even if they are very small. If he dresses up or wakes up, that’s a success! Remember that his opinion of himself is formed by the way his parents assess him.
The LifeHacker has selected simple tips, services and applications.
In addition to excellent marks in math, the ability to count in the mind gives a lot of advantages throughout life. By practicing computation without a calculator, you:
Keep your brain toned. To work effectively, the intellect, like the muscles, needs constant training. Account in the mind develops memory, logical thinking and concentration, increases the ability to learn, helps to quickly navigate the situation and make the right decisions. Take care of your mental health. Studies show Could mental math boost emotional health? that oral counting involves the areas of the brain responsible for depression and anxiety. The more active these areas are, the less risk of neurosis and black longing. You’re afraid of punctures in everyday situations. The ability to quickly calculate change, tip size, calorie count or credit interest protects you from unplanned spending, overweight and fraud. You can master the fast account techniques at any age. It’s okay if you slow down a little first. Daily practice basic arithmetic operations for 10-15 minutes and in a couple of months you will achieve noticeable results. Need to know multiplication for 4th grade.
How to learn how to put it in your mind Let’s summarize the unambiguous numbers Start your training from the elementary level – adding unambiguous numbers with a transition through the ten. This technique is mastered in first grade, but for some reason it is often forgotten with age.
Suppose you need to add up 7 and 8. Count how many seven is missing to ten: 10 – 7 = 3. Add up the eight to the sum of three and the second part: 8 = 3 + 5. Add the second part to ten: 10 + 5 = 15. Use the same method of “reliance on ten” when adding unambiguous numbers with two-digit, three-digit, and so on. Refine the simplest addition until you learn how to perform one operation in a couple of seconds.
Let’s summarize the multi-digit numbers The main principle is to break down the summed up numbers into digits (thousands, hundreds, tens, units) and sum up the same ones among themselves, starting with the largest ones.
Suppose you add 1,574 to 689.
1,574 is expanded into four digits: 1,000, 500, 70 and 4. 689 to three: 600, 80 and 9. Now add up: thousands with thousands (1,000 + 0 = 1,000), hundreds with hundreds (500 + 600 = 1,100), dozens with dozens (70 + 80 = 150), units with units (4 + 9 = 13). Group the numbers as we like, and add up what we have: (1,000 + 1,100) + (150 + 13) = 2,100 + 163 = 2,263.
The main difficulty is to keep all intermediate results in mind. Exercising in this way, you also train your memory.
How do you learn to subtract in your mind Subtract unambiguous numbers. Once again we return to the first class and sharpen the skill of subtracting a single digit number with a transition through the ten.
Suppose you want to subtract 8 from 35.
Imagine 35 as the sum of 30 + 5. You can’t subtract 8 from 5, so spread out 8 to the sum of 5 + 3. We subtract 5 out of 35 and get 30. Then we take the remaining three from 30: 30 – 3 = 27. We subtract the multi-digit numbers. In contrast to addition, when subtracting multi-digit numbers into digits, you only need to break down what you take away.
For example, you are asked to subtract 347 from 932.
A number 347 consists of three digit parts: 300 + 40 + 7. First we subtract hundreds: 932 – 300 = 632. Let’s go to dozens: 632 – 40. For your convenience, 40 can be represented as a sum of 30 + 10. First we subtract 30 and get 632 – 30 = 602. Now we will take the remaining 10 from 602 and get 592. It remains to deal with the units, using the same “reliance on the ten”. First, we subtract the two from 592: 592 – 2 = 590. And then what’s left of the seven: 7 – 2 = 5. We get it: 590 − 5 = 585. How do you learn to multiply in your mind LifeHacker has already written about how to quickly master the multiplication table.
Let us add that the greatest difficulty for both children and adults is the multiplication of 7 by 8. There is a simple rule that will help you never make a mistake in this matter. Just remember: “five, six, seven, eight” – 56 = 7 × 8.
Now, let’s move on to more complicated cases.
Multiply unambiguous numbers by multi-digit… In fact, everything here is elementary. We break down a multi-digit number into digits, multiply each by an univocal number and sum up the results.
Let’s take a case study: 759 × 8.
Break 759 into digits: 700, 50 и 9. Multiply each digit individually: 700 × 8 = 5,600, 50 × 8 = 400, 9 × 8 = 72. Add up the results by dividing them into digits: 5 600 + 400 + 72 = 5 000 + (600 + 400) + 72 = 5 000 + 1 000 + 72 = 6 000 + 72 = 6 072. Multiply two-digit numbers Here, the hand is already reaching out to the calculator or at least to the paper and pen to take advantage of the good old bar multiplication. Although there’s nothing super-complicated about this operation. It just needs a little short-term memory training.
Let’s try to multiply 47 by 32 by a few steps.
47 × 32 is the same as 47 × (30 + 2) or 47 × 30 + 47 × 2. First, multiply 47 by 30. It is nowhere easier: 47 × 3 = 40 × 3 + 7 × 3 = 120 + 21 = 141. Ascribute zero to the right and get: 1 410. Let’s move on: 47 × 2 = 40 × 2 + 7 × 2 = 80 + 14 = 94. It remains to add up the results: 1 410 + 94 = 1 500 + 4 = 1 504.
This principle can be applied to numbers with a large number of discharges, but to keep in mind so many operations not everyone can.
We simplify multiplication. In addition to the general rules, there are several lifehaks that make it easier to multiply by certain unambiguous numbers.
Multiplication by 4. You can multiply a multi-digit number by 2 and then again by 2.
Multiplication by 11 The reception comes down to the following: at the front and back we put the first and last digits of the original number. And between them, we sequentially sum up all the numbers.
When multiplied by a two-digit number, everything looks very simple.
An example: 36 × 11 = 3(3+6)6 = 396.
If the sum goes through a decade, the digit of units remains in the center, and to the first digit we add one.
Here is an example: 37 × 11 = 3(3+7)7 = 3(10)7 = 407.
It is a bit more difficult with multiplication by larger numbers.
Example: 543 × 11 = 5(5+4)(4+3)3 = 5 973.
How do you learn to divide in your mind math grade 3
It is an operation inverse to multiplication, so success depends largely on knowledge of the same school table. The rest is a matter of practice. All you need to know about math grade 3.
We divide it by an unambiguous number. To do this, break down the original multi-digit number into convenient parts, which will be exactly divided into our unambiguous.
Let’s try to divide 2,436 by 7.
Out of 2,436, we will divide the largest part, which will be divided into 7. In our case, that’s 2,100. We get (2 100 + 336) / 7. We continue in the same way, only now with the number 336. Obviously, there will be 280 divided by 7. And the balance will be 56. Now we divide each part by 7: (2 100 + 280 + 56) / 7 = 300 + 40 + 8 = 348. We divide it by a two-digit number. It’s already aerobatics, but we’ll still try. Suppose you divide 1,128 by 24.
Let’s estimate how many times 24 can fit in 1,128. Obviously, 1 128 is about half the size of 24 × 100 (2,400). So for “shoot” we’ll take the multiplier 50: 24 × 50 = 1,200. Up to 1,200, our division of 1,128 is missing 72. How many times does 24 fit in 72? That’s right, three. Which means 1 128 = 24 × 50 – 24 × 3 = 24 × (50 – 3) = 24 × 47. That’s 1128 / 24 = 47. We did not take the hardest example, but using the method of “shooting” and crushing into convenient parts, you will learn to perform more complex operations.
Which will help you learn the oral count For the exercises you will have to come up with new examples every day, only if you want to do it yourself. Otherwise, use other available methods.
Board games Playing those where you need to constantly calculate in your mind, you do not just learn to count quickly. And combine useful things with a pleasant pastime in the circle of family or friends.
Card fun like “Uno” and all sorts of options for mathematical dominoes allow schoolchildren playyuchi learn a simple addition, subtraction, multiplication and division. More complex economic strategies a la “Monopoly” develop financial flair and sharpen complex skills in counting.
What to buy “Uno.” “seven by nine.” “seven by nine multi.” “Traffic Jam.” “Hekmek; “Mathematical dominoes.” “Multiplyjarium.” “Pharaoh’s code.” “Super Farmer.” “Monopoly.” Mobile applications With them you will be able to bring the oral score to automatic. Most of them offer examples for addition, subtraction, multiplication and division in the junior program. But you’d be surprised how difficult it is. Especially if you have to click tasks for a while, without a pen or paper.
Mathematics: oral counting, multiplication table. Covers oral counting assignments that correspond to grades 1-6 of the school curriculum, including percentage assignments. Allows you to train the speed and quality of the score, as well as to adjust the complexity. For example, you can go from a simple multiplication table to multiplication and division of two and three-digit numbers.
It’s hard to think, sometimes we don’t want it, sometimes we get distracted, and sometimes we just don’t need it.
Today I read about a study by scientists at the University of California, according to which it takes about 23 minutes for a person to concentrate on an idea, gather his thoughts in a pile and immerse himself in the subject. And if you get distracted, even for a short while, it will take the same amount of time to check the news feed at the WC, for example, to get your attention back.
If it’s so hard, if it’s so hard to get the gears in your head spinning, then why do you even need it? We rarely ask this question, but it would be very useful to know the answer to it.
What is thinking?
There’s no unambiguous answer. You can use a scientific dictionary or Wikipedia, but I like the variant of Russian psychotherapist Andrey Kurpatov:
Thinking is the ability to build models of reality. By model, we mean our idea of the world around us and ourselves. Human psychology means that much of what we think about doesn’t reflect the real picture, which is why it is called a model.
For example, a person is obsessed with thinking, “This is all America’s fault!” It doesn’t matter exactly what we’re talking about. His model of the world consists of evil America and good Sweden, for example. He does not need to know history, political science or the world economy to think so, just his thinking corresponds to the model.
It turns out that the more complex the model we try to build, the more effective our thoughts are. I remember an interview with the famous scientist Jacques Fresco, where he expressed this idea:
I am often asked: “Why do you give a whole lecture to every question?”. I answer, “Because they ask me such questions.” So a man comes and asks for help:
Tell me, why is my brother annoyed? If it were up to you, I would answer:
Because something is annoying to him. But the people I talk to ask me questions differently:
Can you explain, step by step, what makes my brother annoyed? Then I try to help them. Someone is looking for simple answers according to their thinking, should they expect to find the right one among them? It is important to emphasize one fact: thinking is not equal to the amount of knowledge. Knowledge is a building material, and thinking is the ability to build. Therefore, despite the fact that today all knowledge about the world is at a distance of one reference, not everyone tries to think.
Why don’t we like to think?
There are at least two reasons why we don’t like to think. First, thinking is energy-consuming. Evolution has taught us to act instinctively. And for its time, it was very useful.
Imagine two Neanderthals. They walk through the forest in peace, and suddenly the bushes begin to sway. One of them, obeying his instincts, runs away with a broken head. The other says to himself, “My not to be afraid of bushes, my reasonable one.” And he is eaten by a saber-toothed tiger. So, in ancient times, those who were “the smartest” lived only for a short time.
Today the situation has changed, but not too much.
It would seem that now that we are no longer threatened with being eaten, we can start thinking, but people still try to avoid it. The 21st century has given us “a variety of opportunities”, but has not taught us how to use them. It was easier for a modern person to write to WhatsApp than to call, and it used to be easier to call than to meet in person.
On the one hand, it simplifies communication, but on the other hand, it just helps to do less, think less, and create simpler pictures of the world. Why is it bad?
As Einstein said:
A problem cannot be solved at the same level of thought at which it was created. Simply put, without developing “thinking,” we run in a circle. If a person has problems in a relationship, and he is getting the third divorce in a year, it is definitely worth thinking about what he is doing wrong. And then there’s the big question.
How do you learn to think?
The methods that I will describe below are not formulated by me, but by the therapist Andrey Kurpatov, whose definition of thinking was used in the beginning. I just added some examples and tips from personal practice. Let’s move on to methods.
Build complex systems.
The ability to think is the ability to see the object in detail. When a simple person looks at a car, he sees the car, when the car mechanic looks at the car, he sees the engine, carburetor, relay, etc. He sees a complex system.
It does not follow that everyone has to become a mechanic. It follows that we should perceive ourselves and the people around us as complex systems in the first place.
Why do you want something? Why are you afraid of something?
A Neanderthal would just run away from these questions, but we need to ask them as often as possible. That goes for the people around us, too. Try to get to know the identity of the person you’re communicating with, the reasons for their actions, and understanding between you will be much more. What do you know about your loved ones, your friends? Do you know their history?
Simple explanations are convenient, but they do not give answers, moreover, they teach you not to notice the truth.
We are surrounded by the illusion of clarity. We are used to thinking that “everything is clear”: how everything is arranged, why people behave this way and not otherwise, etc. To train incomprehensibility is to admit: we know nothing.
The progress of mankind is built on the rebuttal of past discoveries. Imagine that 200 years ago, scientists would have said, “Well, it looks like we’ve discovered everything, it’s time to wrap up…” By the way, a similar case occurred in 1899, when the head of the British Patent Office resigned because he believed … that there was nothing else to discover.
Ask yourself questions that have no definite answers, and do not be afraid to admit from time to time that you were wrong.
Look for authority.
When I was little and watched a program on television about the life of African tribes, I often wondered, “Why do they not know about the existence of TV, phone or at least pants?”. In short, because they don’t ask for them, they don’t ask.
Today I understand that the same is true for people who are convinced that they know everything. This feeling is deceptive, because a person surrounded by stupidity will be stupid, he does not see himself from outside. Whatever happens, we need authority.
Authority is anything that gives us a different perspective on the world. A real person, a historical character, a book or a film – it doesn’t matter at all. What matters is that “something” makes you wonder sometimes.
Think purposefully and practice gre tests.
I have a question for you: Are you thinking about what you’re thinking about or something specific?
More often than not, we think about what we’re thinking about. Practice gre tests on thinking. We rarely have a specific goal of understanding why something happens this way or why a person does this.
Thinking must be purposeful.
If you are concerned about relationships, do not blindly follow your instincts and jump to conclusions, it is better to ask yourself a couple of questions that will help you make an informed decision. For any problem, this is enough.
For example, I want to get into classical literature. To get my brain to work in that direction, I’m gonna ask you a couple of questions:
Why would I do that?
Who should I start with?
Who can tell me authors and books?
How not to give up what you started?
Which sites should I look at?
How to make the best use of the knowledge gained?
I love doing it. With this method, any problem becomes just a set of questions to be answered.
The main reason why I want to keep moving the gears in my head was formulated by the American writer Edward Gori:
There are so many things that we’ve been taught since childhood to believe that it will take you quite a while to understand that they are not you. Take an online gre course on thinking. The only thing you want to add is not to be afraid of the unknown, welcome it, it’s just a screen that hides the real world from us.