1. What is 23+24
2. Divide 52 by 65
3. 35+67-45x35 =?
Thursday, October 9, 2014
Saturday, May 23, 2009
What is GCSE Mathematics Coursework? Information for Parents and Students
The coursework element of GCSE Maths consists of two extended tasks (investigations), each worth 10% of the final mark. Altogether coursework is worth twenty percent of the Maths GCSE. One task is an Algebraic Investigation, and one task is a Statistical Data Handling Project. Each piece is done under the teacher's supervision in the classroom, not under exam conditions, so students are allowed to discuss their ideas with each other. Extra time is usually allowed at home, and the total duration is usually about two weeks. The teacher is allowed to support and direct the students, but the students will need to work more independently and be able to think mathematically for themselves, finding their own mathematical conclusions.
(2) What does the Maths Teacher do?
The maths teacher has to work differently during GCSE coursework tasks, as it is not possible just to tell the pupils what to do, or to give undue assistance. Some students find this change hard, as it means that they have to be less dependent upon their teacher for advice. The teacher can help the students (usually by asking questions) so the students can then come to their own conclusions about the work. The teacher can help the students stay on track but if the teacher has to give assistance and has to tell a student what to do, then the student is not eligible for those marks. The teacher can note any relevant verbal contribution if it has not been written down in the final written work. Usually the students’ own class teacher marks the coursework, using the exam board guidelines, and the marks are sent off to the exam boards in April each year.
(3) Why is GCSE Maths Coursework different from normal lessons?
GCSE Maths coursework is different from normal lessons as students have to work on a larger extended task, rather than answer lots of smaller questions from a text book. They also have to come up with their own questions about the task, which they then try and answer. The students need to work consistently over a longer period and also need to write down and explain what they are doing, and what they have found, using sentences (which pupils don’t usually do in maths lessons).
(4) What are the most common problems faced by students?
Some students find adjusting to these more open-ended tasks quite difficult. Usually work in GCSE maths lessons is broken up into many smaller questions, whereas in maths coursework they have to break the task into smaller parts for themselves. (Teachers can help direct students, and help them with short term goals). Students often find it hard to think for themselves about what they should be finding out, as usually they are told what they should be doing – in GCSE coursework tasks, students need to come up with their own questions, which they can find very hard. This means it can take students longer to get started on each section. Some students also find it very difficult to write down everything that they have done and found out - it is a requirement that there is evidence of all the pupil’s work. Students often don’t finish because they take it too easy in the first week and then run out of time in the second week.
(5) How can students be helped with Maths GCSE coursework?
Although it may be tempting to help students, it is important that students are NOT told what to do by someone else. They can be asked questions about the work, and then they can use the answers they give to help them decide what to do next. It is important that undue assistance is NOT given, as their teacher needs to be sure that it is all the student’s own work.
A problem can happen when a maths tutor, or another person, has given too much help to the student, who then hands in work of a much higher standard than usual. This is a common scenario for the maths teacher to sort out if undue assistance has been given. Usually this is the case when the language and methods used are different from those that were taught by the teacher. The teacher then has to find out which parts are the student’s own work, and which parts they have had help on. If there is any doubt about whose work it is, then the coursework may be given a zero mark and the student’s conduct investigated by the exam board. The best advice is to try and avoid this situation altogether: the pupil should see their own maths teacher if they have any questions, and to ask their teacher what they should do next. This way the maths teacher stays in touch with what they are doing and how they are doing it.
(6) Plagiarism
On no account should pupils use the internet and the pieces of coursework that are available there. Plagiarism is taken very seriously by the exam boards – if discovered, this would put into jeopardy all the GCSE exams that the student is entering. Possible warning signs to look out for are:
- a sudden increase in volume of computer printed work
- a different writing style or more mature use of vocabulary
- an unusual credit card payment (as payment is usually needed)
(7) Conclusions
Although Mathematics GCSE coursework is worth twenty percent of the final overall mark, it is not worth the student jeopardising their exam future by getting undue assistance in the form of extra help, or using coursework from the internet. The difference between these extra marks, and what the pupil could actually produce themselves, is usually quite small, and worth only a few marks. In any case it is certainly not worth the risk of what would happen if they were found out, so the student should do their own coursework tasks. Students should allow more time to complete coursework tasks as they take up more time than a usual homework.
(8) Revision is Four Times more Important
Even more important is the other 80% of the marks on the GCSE Mathematics exam papers. It is essential that the students have revised enough of the syllabus in order to get enough marks on the exam. When students are revising all their GCSE subjects, it is important to choose revision materials that will enable fast and efficient revision for each subject’s exam.
About The Author
Nicholas Pinhey is a leading teacher/author, and is the designer of fast Revision Cards for Intermediate and Higher GCSE Mathematics. Visit http://www.revisioncards.co.uk/ or http://gcse-maths-revision-cards.co.uk/ for more information on unique Revision Cards and fast exam analysed gcse maths revision.
(2) What does the Maths Teacher do?
The maths teacher has to work differently during GCSE coursework tasks, as it is not possible just to tell the pupils what to do, or to give undue assistance. Some students find this change hard, as it means that they have to be less dependent upon their teacher for advice. The teacher can help the students (usually by asking questions) so the students can then come to their own conclusions about the work. The teacher can help the students stay on track but if the teacher has to give assistance and has to tell a student what to do, then the student is not eligible for those marks. The teacher can note any relevant verbal contribution if it has not been written down in the final written work. Usually the students’ own class teacher marks the coursework, using the exam board guidelines, and the marks are sent off to the exam boards in April each year.
(3) Why is GCSE Maths Coursework different from normal lessons?
GCSE Maths coursework is different from normal lessons as students have to work on a larger extended task, rather than answer lots of smaller questions from a text book. They also have to come up with their own questions about the task, which they then try and answer. The students need to work consistently over a longer period and also need to write down and explain what they are doing, and what they have found, using sentences (which pupils don’t usually do in maths lessons).
(4) What are the most common problems faced by students?
Some students find adjusting to these more open-ended tasks quite difficult. Usually work in GCSE maths lessons is broken up into many smaller questions, whereas in maths coursework they have to break the task into smaller parts for themselves. (Teachers can help direct students, and help them with short term goals). Students often find it hard to think for themselves about what they should be finding out, as usually they are told what they should be doing – in GCSE coursework tasks, students need to come up with their own questions, which they can find very hard. This means it can take students longer to get started on each section. Some students also find it very difficult to write down everything that they have done and found out - it is a requirement that there is evidence of all the pupil’s work. Students often don’t finish because they take it too easy in the first week and then run out of time in the second week.
(5) How can students be helped with Maths GCSE coursework?
Although it may be tempting to help students, it is important that students are NOT told what to do by someone else. They can be asked questions about the work, and then they can use the answers they give to help them decide what to do next. It is important that undue assistance is NOT given, as their teacher needs to be sure that it is all the student’s own work.
A problem can happen when a maths tutor, or another person, has given too much help to the student, who then hands in work of a much higher standard than usual. This is a common scenario for the maths teacher to sort out if undue assistance has been given. Usually this is the case when the language and methods used are different from those that were taught by the teacher. The teacher then has to find out which parts are the student’s own work, and which parts they have had help on. If there is any doubt about whose work it is, then the coursework may be given a zero mark and the student’s conduct investigated by the exam board. The best advice is to try and avoid this situation altogether: the pupil should see their own maths teacher if they have any questions, and to ask their teacher what they should do next. This way the maths teacher stays in touch with what they are doing and how they are doing it.
(6) Plagiarism
On no account should pupils use the internet and the pieces of coursework that are available there. Plagiarism is taken very seriously by the exam boards – if discovered, this would put into jeopardy all the GCSE exams that the student is entering. Possible warning signs to look out for are:
- a sudden increase in volume of computer printed work
- a different writing style or more mature use of vocabulary
- an unusual credit card payment (as payment is usually needed)
(7) Conclusions
Although Mathematics GCSE coursework is worth twenty percent of the final overall mark, it is not worth the student jeopardising their exam future by getting undue assistance in the form of extra help, or using coursework from the internet. The difference between these extra marks, and what the pupil could actually produce themselves, is usually quite small, and worth only a few marks. In any case it is certainly not worth the risk of what would happen if they were found out, so the student should do their own coursework tasks. Students should allow more time to complete coursework tasks as they take up more time than a usual homework.
(8) Revision is Four Times more Important
Even more important is the other 80% of the marks on the GCSE Mathematics exam papers. It is essential that the students have revised enough of the syllabus in order to get enough marks on the exam. When students are revising all their GCSE subjects, it is important to choose revision materials that will enable fast and efficient revision for each subject’s exam.
About The Author
Nicholas Pinhey is a leading teacher/author, and is the designer of fast Revision Cards for Intermediate and Higher GCSE Mathematics. Visit http://www.revisioncards.co.uk/ or http://gcse-maths-revision-cards.co.uk/ for more information on unique Revision Cards and fast exam analysed gcse maths revision.
Using a Scientific Calculator In Mathematics Exams
Using a Scientific Calculator In Mathematics Exams
by: Nicholas Pinhey
Using a Scientific Calculator In Mathematics Exams
With exams approaching this is a short article with reminders and advice for anyone about to take a mathematics exam and who will need to use a scientific calculator.The most common calculator problems are:
- setting up the calculator in the right mode
- not being able to find the calculator manual !
- remembering to change calculator modes
- rounding and inaccurate answers
Why Use a Scientific Calculator?
Scientific calculators all use the same order for carrying out mathematical operations. This order is not necessarily the same as just reading a calculation from left to right. The rules for carrying out mathematical calculations specify the priority and so the order in which a calculation should be done - scientific calculators follow the same order. This order is sometimes abbreviated by terms such as BODMAS and BIDMAS to help students remember the order of doing calculations.
1st. Brackets (all calculations within bracket are done first)
2nd. Operations (eg squaring, cubing, square rooting, sin, cos, tan )
3rd. Division and Multiplication
4th. Addition and Subtraction
Being aware of this order is necessary in order to use a scientific calculator properly. This order should always be used in all mathematical calculations whether using a calculator or not.
Scientific calculator check
There are two types of scientific calculator, the most recent type being algebraic scientific calculators. Algebraic scientific calculators allow users to type in calculations in the order in which they have been written down. Older scientific calculators need users to press the mathematical operation key after they have entered the number.
For example to find the square root of nine (with an answer of three) press: [button]
Algebraic scientific calculator: [SQUARE ROOT] [9] [=]
Non algebraic scientific calculator: [9] [SQUARE ROOT] [=]
Both these types of scientific calculator are fine for exams, but make sure you know how to use your type.
If you are not sure whether you have a scientific calculator are not, type in:
[4] [+] [3] [x] [2] [=]
If you get an answer of 14, then you have a left to right non-scientific calculator.
If you get an answer of 10, then you have a scientific calculator as it has worked out the multiplication part first.
Lost Calculator Manuals
Calculator manuals tend to get lost very easily or you can never find them as an exam is approaching. A frequent request is what can you do if you have lost your calculator’s manual? If it is a relatively new model then you can download a copy from the manufacturer’s web site. If it is an old Sharp or old Casio calculator manual then you can probably find one on the internet. Even with search engines, finding these manuals can take some time - use the following quick link for Casio: website and old calculator manuals; Sharp: website and old calculator manuals; Hewlett-Packard calculators and Texas Instruments calculators:
http://www.gcse-maths-revision-cards.co.uk/maths_calculator_exam_paper
Calculator Mode
Now that you have your calculator manual you can set your calculator to the correct settings. The standard settings are usually:
COMPUTATIONAL:
(use MODE button – choose normal not stat) NOT: SD or REG
DEGREES:
(use MODE or DRG button) NOT: RAD OR GRAD
NORMAL:
(use MODE or SETUP and arrow keys) NOT: FIX, SCI, ENG
Many calculators have a reset button on the back that can be pressed in using a pen or paper clip if you want the original factory settings.
The most common mistake is to leave your calculator in a previous mode and forgetting to CHANGE IT BACK AGAIN ! (We’ve all done it, just try to avoid doing it in the exam !)
Common Calculator Mistakes
(a) Pressing the DRG button by mistake and not doing trigonometry questions in DEGREES mode. (If you are doing more advanced work then forgetting to change out of DEGREES mode !).
(b) Borrowing an unfamiliar calculator or getting a new calculator too close to the exam and not being familiar with the keys and how to change modes.
(c) Forgetting to write down and check work. Any exam with a calculator should have a warning on it! It is essential to write down the calculations that you're doing so that you can get method marks. You should also try and double check all calculations in case of pressing a wrong button.
(d) Round only at the end of a calculation. Store calculations in the memory and use all the decimal places during calculations. If you use a rounded value too soon then you will lose accuracy.
(e) Forgetting to use brackets on division calculations (e.g. when dividing by ALL the bottom part of fraction).
Many calculators are now very powerful and have amazing computational power. Some of the programmable calculators are mini computers. Although they will all calculate 100% accurately every time, unfortunately they are only as good and as accurate as their operator!
It is often the case that candidates perform better without a calculator as it is very easy to make simple mistakes when using one. If you can do so, it certainly helps to have an idea of the rough size of the answer, so that you can see if an answer is sensible or not. It is also a good idea to repeat all calculations just in case you have made a mistake.
About The Author
Nicholas Pinhey is the designer of fast GCSE Maths Revision Cards for Intermediate and Higher GCSE Mathematics. Visit http://www.revisioncards.co.uk/ or http://gcse-maths-revision-cards.co.uk/ for more information on fast GCSE Mathematics revision and the GCSE Mathematics calculator and non-calculator exam papers.
by: Nicholas Pinhey
Using a Scientific Calculator In Mathematics Exams
With exams approaching this is a short article with reminders and advice for anyone about to take a mathematics exam and who will need to use a scientific calculator.The most common calculator problems are:
- setting up the calculator in the right mode
- not being able to find the calculator manual !
- remembering to change calculator modes
- rounding and inaccurate answers
Why Use a Scientific Calculator?
Scientific calculators all use the same order for carrying out mathematical operations. This order is not necessarily the same as just reading a calculation from left to right. The rules for carrying out mathematical calculations specify the priority and so the order in which a calculation should be done - scientific calculators follow the same order. This order is sometimes abbreviated by terms such as BODMAS and BIDMAS to help students remember the order of doing calculations.
1st. Brackets (all calculations within bracket are done first)
2nd. Operations (eg squaring, cubing, square rooting, sin, cos, tan )
3rd. Division and Multiplication
4th. Addition and Subtraction
Being aware of this order is necessary in order to use a scientific calculator properly. This order should always be used in all mathematical calculations whether using a calculator or not.
Scientific calculator check
There are two types of scientific calculator, the most recent type being algebraic scientific calculators. Algebraic scientific calculators allow users to type in calculations in the order in which they have been written down. Older scientific calculators need users to press the mathematical operation key after they have entered the number.
For example to find the square root of nine (with an answer of three) press: [button]
Algebraic scientific calculator: [SQUARE ROOT] [9] [=]
Non algebraic scientific calculator: [9] [SQUARE ROOT] [=]
Both these types of scientific calculator are fine for exams, but make sure you know how to use your type.
If you are not sure whether you have a scientific calculator are not, type in:
[4] [+] [3] [x] [2] [=]
If you get an answer of 14, then you have a left to right non-scientific calculator.
If you get an answer of 10, then you have a scientific calculator as it has worked out the multiplication part first.
Lost Calculator Manuals
Calculator manuals tend to get lost very easily or you can never find them as an exam is approaching. A frequent request is what can you do if you have lost your calculator’s manual? If it is a relatively new model then you can download a copy from the manufacturer’s web site. If it is an old Sharp or old Casio calculator manual then you can probably find one on the internet. Even with search engines, finding these manuals can take some time - use the following quick link for Casio: website and old calculator manuals; Sharp: website and old calculator manuals; Hewlett-Packard calculators and Texas Instruments calculators:
http://www.gcse-maths-revision-cards.co.uk/maths_calculator_exam_paper
Calculator Mode
Now that you have your calculator manual you can set your calculator to the correct settings. The standard settings are usually:
COMPUTATIONAL:
(use MODE button – choose normal not stat) NOT: SD or REG
DEGREES:
(use MODE or DRG button) NOT: RAD OR GRAD
NORMAL:
(use MODE or SETUP and arrow keys) NOT: FIX, SCI, ENG
Many calculators have a reset button on the back that can be pressed in using a pen or paper clip if you want the original factory settings.
The most common mistake is to leave your calculator in a previous mode and forgetting to CHANGE IT BACK AGAIN ! (We’ve all done it, just try to avoid doing it in the exam !)
Common Calculator Mistakes
(a) Pressing the DRG button by mistake and not doing trigonometry questions in DEGREES mode. (If you are doing more advanced work then forgetting to change out of DEGREES mode !).
(b) Borrowing an unfamiliar calculator or getting a new calculator too close to the exam and not being familiar with the keys and how to change modes.
(c) Forgetting to write down and check work. Any exam with a calculator should have a warning on it! It is essential to write down the calculations that you're doing so that you can get method marks. You should also try and double check all calculations in case of pressing a wrong button.
(d) Round only at the end of a calculation. Store calculations in the memory and use all the decimal places during calculations. If you use a rounded value too soon then you will lose accuracy.
(e) Forgetting to use brackets on division calculations (e.g. when dividing by ALL the bottom part of fraction).
Many calculators are now very powerful and have amazing computational power. Some of the programmable calculators are mini computers. Although they will all calculate 100% accurately every time, unfortunately they are only as good and as accurate as their operator!
It is often the case that candidates perform better without a calculator as it is very easy to make simple mistakes when using one. If you can do so, it certainly helps to have an idea of the rough size of the answer, so that you can see if an answer is sensible or not. It is also a good idea to repeat all calculations just in case you have made a mistake.
About The Author
Nicholas Pinhey is the designer of fast GCSE Maths Revision Cards for Intermediate and Higher GCSE Mathematics. Visit http://www.revisioncards.co.uk/ or http://gcse-maths-revision-cards.co.uk/ for more information on fast GCSE Mathematics revision and the GCSE Mathematics calculator and non-calculator exam papers.
Ohio Schools Award $4 Million To School Districts For Teacher Training In Mathematics And Science
In June 2006, the Ohio schools awarded more than $4 million in competitive grants to school districts across the state. The grants are funded by the U.S. Department of Education’s Mathematics and Science Partnership (MSP) program, and authorized by the federal No Child Left Behind Act.
The MSP grants, which are funded throughout the 2006-2007 school year, will give 1,800 teachers in high-need Ohio schools the opportunity to increase their knowledge of mathematics and science. If MSP funding remains at current levels, the Ohio schools grants will be renewable through June 2009, ensuring professional development for as many teachers as possible.
The program partners colleges and universities with high-need school districts to provide the needed training. Their faculty members also will work with teachers to study techniques for implementing the recent Ohio schools Mathematics and Science Academic Content Standard within their students’ coursework. Most Ohio schools teachers were trained and certified to teach curriculum that focused primarily on arithmetic. Today’s student begins learning algebra, geometry, measurement and the basic concepts of data analysis in the very early grades levels.
The need, according to Susan Rave Zelman, superintendent of public instruction for the Ohio schools, is simple — strong mathematics and science skills are necessary for today’s students to compete effectively in tomorrow’s workforce. Teachers’ own skills and knowledge must be expanded upon in order to provide the students with an effective curriculum in these crucial subjects.
The Ohio schools received 24 proposals for the grants. The ten grants will address either mathematics development, science development, or a combination of both. The grants encompass partnerships between 15 college/universities and more than 100 high-need school districts within the Ohio schools.
Other Mathematics and Science Partnerships within the Ohio schools include The Mathematics Coaches Project, K-3 Mathematics: The Early Foundation, Middle Grade Mathematics: The Critical Bridge, and the Topics Foundational to Calculus.
The Mathematics Coaches Project. In partnership with Ohio University, mathematics faculty members train kindergarten through sixth-grade teachers to become coaches. They then coach other elementary teachers in high-need Ohio schools, where student mathematics performance is low and the school is at-risk.
K-3 Mathematics: The Early Foundation. This program helps Ohio schools kindergarten through third-grade teachers obtain a deeper understanding of early-grade mathematics skills. Additionally, they are taught to use inquiry and concrete experiences of the children within their teaching.
Middle Grade Mathematics: The Critical Bridge. The Middle Grade Math program prepares Ohio schools fourth through eighth-grade teachers to help their students grasp the increasingly complex principles of mathematics. The program includes expanding the teachers’ knowledge and instructional approach.
Topics Foundational to Calculus. For Ohio schools eighth through twelfth-grade mathematics teachers, this program highlights the essential foundations of algebra, geometry and trigonometry for preparing students for calculus coursework.
Unlike previous statewide teacher development programs, the new Ohio schools initiatives emphasize sustained partnerships at the local level. They increase the training time frame to at least 80 hours in the first year and 40 hours in the second year. Programs now include measurements to determine changes in Ohio schools teachers’ content knowledge, instructional practices, and their effect upon student achievement.
About The Author
Patricia Hawke is a staff writer for Schools K-12, providing free, in-depth reports on all U.S. public and private K-12 schools. For more on Ohio schools visit http://www.schoolsk-12.com/Ohio/index.html.
The MSP grants, which are funded throughout the 2006-2007 school year, will give 1,800 teachers in high-need Ohio schools the opportunity to increase their knowledge of mathematics and science. If MSP funding remains at current levels, the Ohio schools grants will be renewable through June 2009, ensuring professional development for as many teachers as possible.
The program partners colleges and universities with high-need school districts to provide the needed training. Their faculty members also will work with teachers to study techniques for implementing the recent Ohio schools Mathematics and Science Academic Content Standard within their students’ coursework. Most Ohio schools teachers were trained and certified to teach curriculum that focused primarily on arithmetic. Today’s student begins learning algebra, geometry, measurement and the basic concepts of data analysis in the very early grades levels.
The need, according to Susan Rave Zelman, superintendent of public instruction for the Ohio schools, is simple — strong mathematics and science skills are necessary for today’s students to compete effectively in tomorrow’s workforce. Teachers’ own skills and knowledge must be expanded upon in order to provide the students with an effective curriculum in these crucial subjects.
The Ohio schools received 24 proposals for the grants. The ten grants will address either mathematics development, science development, or a combination of both. The grants encompass partnerships between 15 college/universities and more than 100 high-need school districts within the Ohio schools.
Other Mathematics and Science Partnerships within the Ohio schools include The Mathematics Coaches Project, K-3 Mathematics: The Early Foundation, Middle Grade Mathematics: The Critical Bridge, and the Topics Foundational to Calculus.
The Mathematics Coaches Project. In partnership with Ohio University, mathematics faculty members train kindergarten through sixth-grade teachers to become coaches. They then coach other elementary teachers in high-need Ohio schools, where student mathematics performance is low and the school is at-risk.
K-3 Mathematics: The Early Foundation. This program helps Ohio schools kindergarten through third-grade teachers obtain a deeper understanding of early-grade mathematics skills. Additionally, they are taught to use inquiry and concrete experiences of the children within their teaching.
Middle Grade Mathematics: The Critical Bridge. The Middle Grade Math program prepares Ohio schools fourth through eighth-grade teachers to help their students grasp the increasingly complex principles of mathematics. The program includes expanding the teachers’ knowledge and instructional approach.
Topics Foundational to Calculus. For Ohio schools eighth through twelfth-grade mathematics teachers, this program highlights the essential foundations of algebra, geometry and trigonometry for preparing students for calculus coursework.
Unlike previous statewide teacher development programs, the new Ohio schools initiatives emphasize sustained partnerships at the local level. They increase the training time frame to at least 80 hours in the first year and 40 hours in the second year. Programs now include measurements to determine changes in Ohio schools teachers’ content knowledge, instructional practices, and their effect upon student achievement.
About The Author
Patricia Hawke is a staff writer for Schools K-12, providing free, in-depth reports on all U.S. public and private K-12 schools. For more on Ohio schools visit http://www.schoolsk-12.com/Ohio/index.html.
The Mathematics of Persuasive Communication
At first glance mathematics and persuasive communication – writing, and particularly public speaking - would seem to have little in common. After all, mathematics is an objective science, whilst speaking involves voice quality, inflection, eye contact, personality, body language, and other subjective components.
However, under the surface they are very similar.
Above anything else, the success of an oral presentation depends on the precision of its structure. Mathematics is all about precision. It is therefore not so odd to think that applying some of the concepts of mathematics to oral presentations could make them substantially more effective.
As they say in the film industry, three key factors go into making a successful movie: the script, the script, and the script. Likewise, three key factors go into making a successful speech: the structure, the structure, and the structure.
Not convinced? Then let's start with something less radical.
I think we can all agree that good speaking is related to good writing. If you can write a good text, then you are well on your way to preparing a good oral presentation. Therefore, if you improve your writing, you will also improve your speaking.
To simplify matters, from now on we will talk mainly about good writing, because in most cases the same ideas apply directly to good speaking.
Know what you are doing
Many commercial companies do not live up to their potential - and sometimes even go bankrupt - because they fail to correctly define the business they are in.
Perfume companies, for example, do not sell fragrant liquids, but rather love, romance, seductiveness, self-esteem, etc. Bio-food companies do not sell organic produce, but rather honesty, purity, nature, etc. Automobile manufacturers do not sell transportation, but rather freedom, adventure, spontaneity, prestige, etc. The fact is, each industry, even each individual product, may have to determine what it is truly all about - and there are thousands of them!
Writers are lucky. There are numerous variations to what we do, but there are really only two fundamental types of writing. It is important to recognise this, because not only are they quite different, in some respects they are exactly opposite. So unless we clearly recognise which type of writing we are doing - and how it differs from the other one - we will almost certainly commit serious errors.
What are the two types? And how do they differ?
Creative Writing
Texts such as short stories, novels, poems, radio plays, stage plays, television scripts, film scripts, etc.
The fundamental purpose of creative writing is to amuse and entertain. Expository Writing
Texts such as memos, reports, proposals, training manuals, newsletters, research papers, etc.
The fundamental purpose of expository writing is to instruct and inform.
Essential attitude towards expository writing
Because the objectives of creative and expository writing are so different, before striking a key you must adopt the appropriate attitude towards the type of writing you are doing.
Creative writing attitude
Everyone wants to read want what you are going to write.
After all, who doesn't want to be amused and entertained?
Expository writing attitude
No one wants to read what you are going to write.
Most people don't like to be instructed and informed. They probably would much prefer to be doing something else.
The importance of recognising and adopting the "expository writing attitude" cannot be over-stated, because it can dramatically change the very nature of what you are writing. Here are a couple of examples.
A. Corporate image brochure
I was once commissioned to write a corporate image brochure. Two things are certain about these expensive, glossy booklets:
• Almost all companies of any size feel compelled to produce them.
• Virtually no one ever reads them.
Starting from the attitude that no one would want to read what I was about to write, I created a brochure that people not only read. They actually called the company to request additional copies to give to friends, clients and professional colleagues!
B. Stagnating product
On another occasion, I was commissioned to develop an advertising campaign to revitalise a product with stagnating sales. Applying the expository writing attitude, I discovered that three of the product's key benefits were not being properly exploited. Why? The manufacturer felt that everything about their product was important, so for years they had been systematically burying these three key benefits under an avalanche of other information of less interest to potential buyers. The new campaign sharply focussed on the key benefits; virtually all other information was moved to the background or eliminated. As a result, sales shot up some 40% in the first year.
With some nuances, this self-same expository writing attitude can be - and should be - applied to speaking, as well.
Essential approach to expository writing
Because creative writing and expository writing have essentially different objectives and attitudes, they require essentially different approaches.
Creative writing approach
Play with language to generate pleasure.
In other words, use your mastery of the language to amuse and entertain.
Expository writing approach
Organise information to generate interest.
Clever use of language will never make dull information interesting; however, you can organise the information to make it interesting. Forget about literary pyrotechnics. Concentrate on content.
We are now going to leave creative writing, because most of what we write, and say, is expository.
What do we mean by "good writing"?
We are now ready to return to the notion of how mathematics applies to good writing, and by extension to good speaking.
When someone reads an expository text or listens to an expository speech, they are likely to judge it as good or not good. You probably do this yourself. But what do you actually mean when you say a text or a speech is "good".
After some struggling, most people will usually settle on two criteria: clear and concise.
Mathematics depends on unambiguous definitions; if you are not clear about the problem, you are unlikely to find the solution. So we are going to examine these criteria in some detail in order to establish objective definitions - and even quasi-mathematical formulae - for testing whether a text or a presentation truly is "good".
A. Clarity
How do you know that a text is clear?
If this sounds like a silly question, try to answer it. You will probably do something like this:
Question: What makes this text clear?
Answer: It is easy to understand.
Question: What makes it easy to understand?
Answer: It is simple.
Question: What do you mean by simple?
Answer: It is clear.
You in fact end up going around in a circle. The text is clear because it is easy to understand . . . because it is simple . . . because it is clear.
"Clear", "easy to understand", and "simple" are synonyms. Whilst synonyms may have nuances, they do not have content, so you are still left to your own subjective appreciation. But what you think is clear may not be clear to someone else.
This is why we give "clear" an objective definition, almost like a mathematical formula. To achieve clarity -i.e. virtually everyone will agree that it is clear - you must do three things.
1. Emphasise what is of key importance.
2. De-emphasise what is of secondary importance.
3. Eliminate what is of no importance.
In short: CL = EDE
Like all mathematical formulae, this one works only if you know how to apply it, which requires judgement.
In this case, you must first decide what is of key importance, i.e. what are the key ideas you want your readers to take away from your text? This is not always easy to do. It is far simpler to say that everything is of key importance, so you put in everything you have. But there is a dictum that warns: If everything is important, then nothing is. In other words, unless you first do the work of defining what you really want your readers to know, they won't do it for you. They will get lost in your text and either give up or come out the other end not knowing what it is they have read.
What about the second element of the formula, de-emphasise what is of secondary importance?
That sounds easy enough. You don't want key information and ideas to get lost in details. If you clearly emphasise what is of key importance - via headlines, Italics, underlining, or simply how you organise the information - then whatever is left over is automatically de-emphasised.
Now the only thing left to do is eliminate what is of no importance.
But how do you distinguish between what is of secondary importance and what is of no importance? Once again, this requires judgement, which is helped by the following very important test.
Secondary importance is anything that supports and/or elaborates one or more of the key ideas. If you judge that a piece of information in fact does support or elaborate one or more key ideas, then you keep it. If not, you eliminate it.
B. Conciseness
How do you know that a text is concise?
If this once again sounds like a silly question, let's try to answer it.
Question: What makes this text concise?
Answer: It is short.
Question: What do you mean by short?
Answer: It doesn't have too many words.
Question: How do you know it doesn't have too many words?
Answer: Because it is concise.
So once again we end up going around in a circle. The text is concise because it is short . . . because it doesn't have too many words . . . because it is concise.
Once again, we have almost a mathematical formula to solve the problem. To achieve conciseness, your text should meet two criteria. It must be as:
1. Long as necessary
2. Short as possible
In symbols: CO = LS
If you have fulfilled the criteria of "clarity" correctly, you already understand "as long as necessary". It means covering all the ideas of key importance you have identified, and all the ideas of secondary importance needed to support and/or elaborate these key ideas.
Note that nothing is said here about the number of words, because it is irrelevant. If it takes 500 words to be "as long as necessary", then 500 words must be used. If it takes 1500 words, then this is all right too. The important point is that everything that should be in the text is fully there.
Then what is meant by "as short as possible"?
Once again, this has nothing do to with the number of words. It is useless to say at the beginning, "I must not write more than 300 words on this subject", because 500 words may be the minimum necessary.
"As short as possible" means staying as close as you can to the minimum. But not because people prefer short texts; in the abstract the terms "long" and "short" have no meaning. The important point is that all words beyond the minimum tend to reduce clarity.
We should not be rigid about this. If being "as long as necessary" can be done in 500 words and you use 520, this is probably a question of individual style. It does no harm. However, if you use 650 words, it is almost certain that the text will not be completely clea r- and that the reader will become confused, bored or lost.
In sum, conciseness means saying what needs to be said in the minimum amount of words. Conciseness:
• Aids clarity by ensuring best structuring of information.
• Holds reader interest by providing maximum information in minimum time.
C. Density
Density is a less familiar concept than clarity and conciseness, but is equally important. In mathematical form, density consists of:
1. Precise information
2. Logically linked
In other words: D = PL
Importance of precise information
Suppose you enter a room where there are two other people and say, "It's very hot today." One of those people comes from Helsinki; in his mind he interprets "hot" to mean about 23°C. The other one comes from Khartoum; to him "hot" means 45°C.
You are off to a rather bad start, because each one has a totally different idea of what you want to say. But suppose you say, "It's very hot today; the temperature is 28° C." Now there is no room for confusion. They both know quite clearly that it is 28° C outside and that you consider this to be very hot.
Using as much precise information as possible in a text gives the writer two significant advantages:
• Mind Control
Let's not be embarrassed by the term "mind control", because this is precisely what the good expository writer wants to achieve. He needs for the reader's mind to go only where he directs it and nowhere else.
Because they can be interpreted in unknown ways, ambiguous terms (so-called "weasel words") such as "hot", "cold", "big", "small", "good", "bad", etc., allow the reader's mind to escape from the writer's control. An occasional lapse is not critical; however, too many weasel words in a text will inevitably lead to reader confusion, boredom and disinterest.
• Reader Confidence
Using precise information generates confidence, because it tells the reader that the writer really knows what he is talking about.
Reader confidence is important in any kind of text, but it is crucial in argumentation. If you are trying to win a point, the last thing you want is the reader to challenge your data, but this is the first reaction imprecise writing will provoke. Precise writing ensures that the discussion will be about the implications of the information, i.e. what conclusions should be drawn, not whether the whole thing needs to go back for further investigation.
Importance of logical linking
Precise data (facts) by themselves are insufficient. To be meaningful, data must be organised to create information, i.e. help the reader understand.
There are two important tests to apply when converting data into information:
1. Relevance
Is a particular piece of data really needed? As we have seen, unnecessary data damages understanding and ultimately undermines confidence. Therefore, any data that do not either aid understanding or promote confidence should be eliminated.
2. Misconceptions
The logical link between data must be made explicit to prevent the reader from coming to false conclusions. For example: a specific situation may be confused for a general one; credit for an achievement may seem to belong to only one person when it really belongs to a group; a company policy may appear to apply only in very specific circumstances rather than in all circumstances, etc.
To ensure that a logical link is clear, place the two pieces of data as close to each other as possible, preferably right next to each other.
When data are widely separated, their logical relationship is masked and the reader is unlikely to make the connection.
What do you want? What do your readers want?
I frequently ask non-professional writers what they are thinking when they sit down at the keyboard to compose their text. The answer is usually something like, "How do I want to present my material?" "What tone and style should I use?" "In what order should I put my key ideas?" And so on.
However, if you start with the correct attitude, i.e. no one wants to read what you write, your first task is none of these. Ahead of anything else, you must find reasons why people should spend their time to read what you write.
In general, you cannot force people to read what they don't want to, even if they are being paid to do so.
For example, you produce a report defining opportunities for increased sales and profits. However, if it is not well written, even people who must read it as part of their job are unlikely to give it their full attention. On the other hand, if they immediately see their own self-interest in reading what you have written, they will do so gladly and with full attention. In fact, you probably couldn't stop them from reading it!
There are various methods to generate such a strong desire to read, depending on the type of readers and the type of information. Whatever the most appropriate device, the crucial thing is to recognise the imperative need to use it. Until this need is met, nothing else is of any importance.
Editor's note: Reading is an isolated activity and listening to a speech is a social one. Therefore, whilst the underlying principles of good writing and good speaking are constant, the way they are applied can be markedly different. In the 'I' of the Storm: the Simple Secrets of Writing & Speaking (Almost) like a Professional, Mr. Yaffe's recently published book, clearly explains these differences. It also offers several appendices with cogent examples and pertinent, effective exercises.
Philip Yaffe is a former reporter/feature writer with The Wall Street Journal and a marketing communication consultant. He currently teaches a course in good writing and good public speaking in Brussels, Belgium. In the 'I' of the Storm is available either in a print version or electronic version from Story Publishers in Ghent, Belgium (www.Storypublishers.be) and Amazon (www.amazon.com).
About The Author
Philip Yaffe is a former writer with The Wall Street Journal and international marketing communication consultant. Now semi-retired, he teaches courses in persuasive communication in Brussels, Belgium. Because his clients use English as a second or third language, his approach to writing and public speaking is somewhat different from other communication coaches. He is the author of In the “I” of the Storm: the Simple Secrets of Writing & Speaking (Almost) like a Professional. Contact: phil.yaffe@yahoo.com.
However, under the surface they are very similar.
Above anything else, the success of an oral presentation depends on the precision of its structure. Mathematics is all about precision. It is therefore not so odd to think that applying some of the concepts of mathematics to oral presentations could make them substantially more effective.
As they say in the film industry, three key factors go into making a successful movie: the script, the script, and the script. Likewise, three key factors go into making a successful speech: the structure, the structure, and the structure.
Not convinced? Then let's start with something less radical.
I think we can all agree that good speaking is related to good writing. If you can write a good text, then you are well on your way to preparing a good oral presentation. Therefore, if you improve your writing, you will also improve your speaking.
To simplify matters, from now on we will talk mainly about good writing, because in most cases the same ideas apply directly to good speaking.
Know what you are doing
Many commercial companies do not live up to their potential - and sometimes even go bankrupt - because they fail to correctly define the business they are in.
Perfume companies, for example, do not sell fragrant liquids, but rather love, romance, seductiveness, self-esteem, etc. Bio-food companies do not sell organic produce, but rather honesty, purity, nature, etc. Automobile manufacturers do not sell transportation, but rather freedom, adventure, spontaneity, prestige, etc. The fact is, each industry, even each individual product, may have to determine what it is truly all about - and there are thousands of them!
Writers are lucky. There are numerous variations to what we do, but there are really only two fundamental types of writing. It is important to recognise this, because not only are they quite different, in some respects they are exactly opposite. So unless we clearly recognise which type of writing we are doing - and how it differs from the other one - we will almost certainly commit serious errors.
What are the two types? And how do they differ?
Creative Writing
Texts such as short stories, novels, poems, radio plays, stage plays, television scripts, film scripts, etc.
The fundamental purpose of creative writing is to amuse and entertain. Expository Writing
Texts such as memos, reports, proposals, training manuals, newsletters, research papers, etc.
The fundamental purpose of expository writing is to instruct and inform.
Essential attitude towards expository writing
Because the objectives of creative and expository writing are so different, before striking a key you must adopt the appropriate attitude towards the type of writing you are doing.
Creative writing attitude
Everyone wants to read want what you are going to write.
After all, who doesn't want to be amused and entertained?
Expository writing attitude
No one wants to read what you are going to write.
Most people don't like to be instructed and informed. They probably would much prefer to be doing something else.
The importance of recognising and adopting the "expository writing attitude" cannot be over-stated, because it can dramatically change the very nature of what you are writing. Here are a couple of examples.
A. Corporate image brochure
I was once commissioned to write a corporate image brochure. Two things are certain about these expensive, glossy booklets:
• Almost all companies of any size feel compelled to produce them.
• Virtually no one ever reads them.
Starting from the attitude that no one would want to read what I was about to write, I created a brochure that people not only read. They actually called the company to request additional copies to give to friends, clients and professional colleagues!
B. Stagnating product
On another occasion, I was commissioned to develop an advertising campaign to revitalise a product with stagnating sales. Applying the expository writing attitude, I discovered that three of the product's key benefits were not being properly exploited. Why? The manufacturer felt that everything about their product was important, so for years they had been systematically burying these three key benefits under an avalanche of other information of less interest to potential buyers. The new campaign sharply focussed on the key benefits; virtually all other information was moved to the background or eliminated. As a result, sales shot up some 40% in the first year.
With some nuances, this self-same expository writing attitude can be - and should be - applied to speaking, as well.
Essential approach to expository writing
Because creative writing and expository writing have essentially different objectives and attitudes, they require essentially different approaches.
Creative writing approach
Play with language to generate pleasure.
In other words, use your mastery of the language to amuse and entertain.
Expository writing approach
Organise information to generate interest.
Clever use of language will never make dull information interesting; however, you can organise the information to make it interesting. Forget about literary pyrotechnics. Concentrate on content.
We are now going to leave creative writing, because most of what we write, and say, is expository.
What do we mean by "good writing"?
We are now ready to return to the notion of how mathematics applies to good writing, and by extension to good speaking.
When someone reads an expository text or listens to an expository speech, they are likely to judge it as good or not good. You probably do this yourself. But what do you actually mean when you say a text or a speech is "good".
After some struggling, most people will usually settle on two criteria: clear and concise.
Mathematics depends on unambiguous definitions; if you are not clear about the problem, you are unlikely to find the solution. So we are going to examine these criteria in some detail in order to establish objective definitions - and even quasi-mathematical formulae - for testing whether a text or a presentation truly is "good".
A. Clarity
How do you know that a text is clear?
If this sounds like a silly question, try to answer it. You will probably do something like this:
Question: What makes this text clear?
Answer: It is easy to understand.
Question: What makes it easy to understand?
Answer: It is simple.
Question: What do you mean by simple?
Answer: It is clear.
You in fact end up going around in a circle. The text is clear because it is easy to understand . . . because it is simple . . . because it is clear.
"Clear", "easy to understand", and "simple" are synonyms. Whilst synonyms may have nuances, they do not have content, so you are still left to your own subjective appreciation. But what you think is clear may not be clear to someone else.
This is why we give "clear" an objective definition, almost like a mathematical formula. To achieve clarity -i.e. virtually everyone will agree that it is clear - you must do three things.
1. Emphasise what is of key importance.
2. De-emphasise what is of secondary importance.
3. Eliminate what is of no importance.
In short: CL = EDE
Like all mathematical formulae, this one works only if you know how to apply it, which requires judgement.
In this case, you must first decide what is of key importance, i.e. what are the key ideas you want your readers to take away from your text? This is not always easy to do. It is far simpler to say that everything is of key importance, so you put in everything you have. But there is a dictum that warns: If everything is important, then nothing is. In other words, unless you first do the work of defining what you really want your readers to know, they won't do it for you. They will get lost in your text and either give up or come out the other end not knowing what it is they have read.
What about the second element of the formula, de-emphasise what is of secondary importance?
That sounds easy enough. You don't want key information and ideas to get lost in details. If you clearly emphasise what is of key importance - via headlines, Italics, underlining, or simply how you organise the information - then whatever is left over is automatically de-emphasised.
Now the only thing left to do is eliminate what is of no importance.
But how do you distinguish between what is of secondary importance and what is of no importance? Once again, this requires judgement, which is helped by the following very important test.
Secondary importance is anything that supports and/or elaborates one or more of the key ideas. If you judge that a piece of information in fact does support or elaborate one or more key ideas, then you keep it. If not, you eliminate it.
B. Conciseness
How do you know that a text is concise?
If this once again sounds like a silly question, let's try to answer it.
Question: What makes this text concise?
Answer: It is short.
Question: What do you mean by short?
Answer: It doesn't have too many words.
Question: How do you know it doesn't have too many words?
Answer: Because it is concise.
So once again we end up going around in a circle. The text is concise because it is short . . . because it doesn't have too many words . . . because it is concise.
Once again, we have almost a mathematical formula to solve the problem. To achieve conciseness, your text should meet two criteria. It must be as:
1. Long as necessary
2. Short as possible
In symbols: CO = LS
If you have fulfilled the criteria of "clarity" correctly, you already understand "as long as necessary". It means covering all the ideas of key importance you have identified, and all the ideas of secondary importance needed to support and/or elaborate these key ideas.
Note that nothing is said here about the number of words, because it is irrelevant. If it takes 500 words to be "as long as necessary", then 500 words must be used. If it takes 1500 words, then this is all right too. The important point is that everything that should be in the text is fully there.
Then what is meant by "as short as possible"?
Once again, this has nothing do to with the number of words. It is useless to say at the beginning, "I must not write more than 300 words on this subject", because 500 words may be the minimum necessary.
"As short as possible" means staying as close as you can to the minimum. But not because people prefer short texts; in the abstract the terms "long" and "short" have no meaning. The important point is that all words beyond the minimum tend to reduce clarity.
We should not be rigid about this. If being "as long as necessary" can be done in 500 words and you use 520, this is probably a question of individual style. It does no harm. However, if you use 650 words, it is almost certain that the text will not be completely clea r- and that the reader will become confused, bored or lost.
In sum, conciseness means saying what needs to be said in the minimum amount of words. Conciseness:
• Aids clarity by ensuring best structuring of information.
• Holds reader interest by providing maximum information in minimum time.
C. Density
Density is a less familiar concept than clarity and conciseness, but is equally important. In mathematical form, density consists of:
1. Precise information
2. Logically linked
In other words: D = PL
Importance of precise information
Suppose you enter a room where there are two other people and say, "It's very hot today." One of those people comes from Helsinki; in his mind he interprets "hot" to mean about 23°C. The other one comes from Khartoum; to him "hot" means 45°C.
You are off to a rather bad start, because each one has a totally different idea of what you want to say. But suppose you say, "It's very hot today; the temperature is 28° C." Now there is no room for confusion. They both know quite clearly that it is 28° C outside and that you consider this to be very hot.
Using as much precise information as possible in a text gives the writer two significant advantages:
• Mind Control
Let's not be embarrassed by the term "mind control", because this is precisely what the good expository writer wants to achieve. He needs for the reader's mind to go only where he directs it and nowhere else.
Because they can be interpreted in unknown ways, ambiguous terms (so-called "weasel words") such as "hot", "cold", "big", "small", "good", "bad", etc., allow the reader's mind to escape from the writer's control. An occasional lapse is not critical; however, too many weasel words in a text will inevitably lead to reader confusion, boredom and disinterest.
• Reader Confidence
Using precise information generates confidence, because it tells the reader that the writer really knows what he is talking about.
Reader confidence is important in any kind of text, but it is crucial in argumentation. If you are trying to win a point, the last thing you want is the reader to challenge your data, but this is the first reaction imprecise writing will provoke. Precise writing ensures that the discussion will be about the implications of the information, i.e. what conclusions should be drawn, not whether the whole thing needs to go back for further investigation.
Importance of logical linking
Precise data (facts) by themselves are insufficient. To be meaningful, data must be organised to create information, i.e. help the reader understand.
There are two important tests to apply when converting data into information:
1. Relevance
Is a particular piece of data really needed? As we have seen, unnecessary data damages understanding and ultimately undermines confidence. Therefore, any data that do not either aid understanding or promote confidence should be eliminated.
2. Misconceptions
The logical link between data must be made explicit to prevent the reader from coming to false conclusions. For example: a specific situation may be confused for a general one; credit for an achievement may seem to belong to only one person when it really belongs to a group; a company policy may appear to apply only in very specific circumstances rather than in all circumstances, etc.
To ensure that a logical link is clear, place the two pieces of data as close to each other as possible, preferably right next to each other.
When data are widely separated, their logical relationship is masked and the reader is unlikely to make the connection.
What do you want? What do your readers want?
I frequently ask non-professional writers what they are thinking when they sit down at the keyboard to compose their text. The answer is usually something like, "How do I want to present my material?" "What tone and style should I use?" "In what order should I put my key ideas?" And so on.
However, if you start with the correct attitude, i.e. no one wants to read what you write, your first task is none of these. Ahead of anything else, you must find reasons why people should spend their time to read what you write.
In general, you cannot force people to read what they don't want to, even if they are being paid to do so.
For example, you produce a report defining opportunities for increased sales and profits. However, if it is not well written, even people who must read it as part of their job are unlikely to give it their full attention. On the other hand, if they immediately see their own self-interest in reading what you have written, they will do so gladly and with full attention. In fact, you probably couldn't stop them from reading it!
There are various methods to generate such a strong desire to read, depending on the type of readers and the type of information. Whatever the most appropriate device, the crucial thing is to recognise the imperative need to use it. Until this need is met, nothing else is of any importance.
Editor's note: Reading is an isolated activity and listening to a speech is a social one. Therefore, whilst the underlying principles of good writing and good speaking are constant, the way they are applied can be markedly different. In the 'I' of the Storm: the Simple Secrets of Writing & Speaking (Almost) like a Professional, Mr. Yaffe's recently published book, clearly explains these differences. It also offers several appendices with cogent examples and pertinent, effective exercises.
Philip Yaffe is a former reporter/feature writer with The Wall Street Journal and a marketing communication consultant. He currently teaches a course in good writing and good public speaking in Brussels, Belgium. In the 'I' of the Storm is available either in a print version or electronic version from Story Publishers in Ghent, Belgium (www.Storypublishers.be) and Amazon (www.amazon.com).
About The Author
Philip Yaffe is a former writer with The Wall Street Journal and international marketing communication consultant. Now semi-retired, he teaches courses in persuasive communication in Brussels, Belgium. Because his clients use English as a second or third language, his approach to writing and public speaking is somewhat different from other communication coaches. He is the author of In the “I” of the Storm: the Simple Secrets of Writing & Speaking (Almost) like a Professional. Contact: phil.yaffe@yahoo.com.
Preschool Mathematics
My preschooler can count twice as high as your preschooler -- but does that mean she really understands number concepts? In truth, she has memorized a sequence of words. Although children can't learn math unless they know how to count, counting is only one aspect of math.
Children begin to count on their own as they grow, and they learn from everyday experiences with length, quantity, time, temperature, money, and more. Through Preschool program, children expand their true understanding of math. Adults should recognize that games such as sorting and putting objects in sequence are actually early experiments in math, even if they don't look much like geometry!
Here are some everyday opportunities for children to begin thinking about numbers:
• All about me - Teach children their own address and phone number as well as their age. Also, record their height – in centimeters and metres. Putting a child on a scale represents an opportunity to compare pounds and Kg, and heavy versus light. Children can also learn what size clothes they wear, and be able to judge what will fit and what won’t.
• Cooking -- Adults pour, measure, divide, estimate time, and read labels every time they prepare a meal. Why not include young children in on the activities? Before he can pour pancake batter or read recipes, a child can stir with a wooden spoon in a plastic bowl. Show a child how you follow a recipe step by step, and how you set the oven temperature. Remember to warn children about what's too hot to touch or eat!
• Managing money -- Children can start knowing about money even before elementary tutoring. You can start letting your child touch, count, save, sort, and spend money. What better way to teach children about the value of money than by taking them shopping and showing them how much they must pay for items -- and how much they will save with coupons!
• Around the house -- Household repairs offer children excellent opportunities to practice math skills. Let children watch as you measure a door frame, or hang a picture in the center of a wall. Children can help you make a list of items you will need to complete a project, including the number of tools. Everyday activities like setting the timer on the VCR or setting the dinner table are opportunities for children to count and work with numbers.
• Play -- Children may also race against the clock or measure the distance they can hit or throw a ball. Help children make neighborhood activities and sports more than just good exercise.
When children pretend, they often create lifelike situations in which they may check a bus schedule, or gauge how much gas is needed for a long car trip.
• Travelling -- Even a short car trip offers children experiences with math. Ask children to identify the speed limit on a passing sign. Estimate the number of minutes it takes to get to a relative's house. Remember games you played in the back seat of the car, like counting yellow school buses and adding up the numbers on license plates.
For more information on how to better prepare for you preschooler, please visit us at the Bayhill Bulletin at http://www.bayhilleducation.com. We are located in Ontario Richmond hill specialized in preschool elementary high school tutoring. And remember…we are among the leaders in York Region preschool program education.
About The Author
Maggie Duarte
Growing up in a family that placed great emphasis on education, Maggie Duarte developed her love of learning at an early age. Teaching and motivating others to achieve their best is ingrained in her character.
Ms. Duarte a teacher for over fifteen years in both the public and private school systems has a diverse background in education.
Children begin to count on their own as they grow, and they learn from everyday experiences with length, quantity, time, temperature, money, and more. Through Preschool program, children expand their true understanding of math. Adults should recognize that games such as sorting and putting objects in sequence are actually early experiments in math, even if they don't look much like geometry!
Here are some everyday opportunities for children to begin thinking about numbers:
• All about me - Teach children their own address and phone number as well as their age. Also, record their height – in centimeters and metres. Putting a child on a scale represents an opportunity to compare pounds and Kg, and heavy versus light. Children can also learn what size clothes they wear, and be able to judge what will fit and what won’t.
• Cooking -- Adults pour, measure, divide, estimate time, and read labels every time they prepare a meal. Why not include young children in on the activities? Before he can pour pancake batter or read recipes, a child can stir with a wooden spoon in a plastic bowl. Show a child how you follow a recipe step by step, and how you set the oven temperature. Remember to warn children about what's too hot to touch or eat!
• Managing money -- Children can start knowing about money even before elementary tutoring. You can start letting your child touch, count, save, sort, and spend money. What better way to teach children about the value of money than by taking them shopping and showing them how much they must pay for items -- and how much they will save with coupons!
• Around the house -- Household repairs offer children excellent opportunities to practice math skills. Let children watch as you measure a door frame, or hang a picture in the center of a wall. Children can help you make a list of items you will need to complete a project, including the number of tools. Everyday activities like setting the timer on the VCR or setting the dinner table are opportunities for children to count and work with numbers.
• Play -- Children may also race against the clock or measure the distance they can hit or throw a ball. Help children make neighborhood activities and sports more than just good exercise.
When children pretend, they often create lifelike situations in which they may check a bus schedule, or gauge how much gas is needed for a long car trip.
• Travelling -- Even a short car trip offers children experiences with math. Ask children to identify the speed limit on a passing sign. Estimate the number of minutes it takes to get to a relative's house. Remember games you played in the back seat of the car, like counting yellow school buses and adding up the numbers on license plates.
For more information on how to better prepare for you preschooler, please visit us at the Bayhill Bulletin at http://www.bayhilleducation.com. We are located in Ontario Richmond hill specialized in preschool elementary high school tutoring. And remember…we are among the leaders in York Region preschool program education.
About The Author
Maggie Duarte
Growing up in a family that placed great emphasis on education, Maggie Duarte developed her love of learning at an early age. Teaching and motivating others to achieve their best is ingrained in her character.
Ms. Duarte a teacher for over fifteen years in both the public and private school systems has a diverse background in education.
Thursday, May 14, 2009
Mathematics Clock Puzzles
WHAT WAS THE TIME?
"I say, Rackbrane, what is the time?" an acquaintance asked our friend
the professor the other day. The answer was certainly curious.
"If you add one quarter of the time from noon till now to half the time
from now till noon to-morrow, you will get the time exactly."
What was the time of day when the professor spoke?
A TIME PUZZLE.
How many minutes is it until six o'clock if fifty minutes ago it was
four times as many minutes past three o'clock?
A PUZZLING WATCH.
A friend pulled out his watch and said, "This watch of mine does not
keep perfect time; I must have it seen to. I have noticed that the
minute hand and the hour hand are exactly together every sixty-five
minutes." Does that watch gain or lose, and how much per hour?
THE WAPSHAW'S WHARF MYSTERY.
There was a great commotion in Lower Thames Street on the morning of
January 12, 1887. When the early members of the staff arrived at
Wapshaw's Wharf they found that the safe had been broken open, a
considerable sum of money removed, and the offices left in great
disorder. The night watchman was nowhere to be found, but nobody who had
been acquainted with him for one moment suspected him to be guilty of
the robbery. In this belief the proprietors were confirmed when, later
in the day, they were informed that the poor fellow's body had been
picked up by the River Police. Certain marks of violence pointed to the
fact that he had been brutally attacked and thrown into the river. A
watch found in his pocket had stopped, as is invariably the case in such
circumstances, and this was a valuable clue to the time of the outrage.
But a very stupid officer (and we invariably find one or two stupid
individuals in the most intelligent bodies of men) had actually amused
himself by turning the hands round and round, trying to set the watch
going again. After he had been severely reprimanded for this serious
indiscretion, he was asked whether he could remember the time that was
indicated by the watch when found. He replied that he could not, but he
recollected that the hour hand and minute hand were exactly together,
one above the other, and the second hand had just passed the forty-ninth
second. More than this he could not remember.
What was the exact time at which the watchman's watch stopped? The watch
is, of course, assumed to have been an accurate one.
CHANGING PLACES.
The above clock face indicates a little before 42 minutes past 4. The
hands will again point at exactly the same spots a little after 23
minutes past 8. In fact, the hands will have changed places. How many
times do the hands of a clock change places between three o'clock p.m.
and midnight? And out of all the pairs of times indicated by these
changes, what is the exact time when the minute hand will be nearest to
the point IX?
Read more articles on mathematics and math puzzles at my blog www.mathtutoronline.blogspot.com and
www.articlesoneducation.blogspot.com
"I say, Rackbrane, what is the time?" an acquaintance asked our friend
the professor the other day. The answer was certainly curious.
"If you add one quarter of the time from noon till now to half the time
from now till noon to-morrow, you will get the time exactly."
What was the time of day when the professor spoke?
A TIME PUZZLE.
How many minutes is it until six o'clock if fifty minutes ago it was
four times as many minutes past three o'clock?
A PUZZLING WATCH.
A friend pulled out his watch and said, "This watch of mine does not
keep perfect time; I must have it seen to. I have noticed that the
minute hand and the hour hand are exactly together every sixty-five
minutes." Does that watch gain or lose, and how much per hour?
THE WAPSHAW'S WHARF MYSTERY.
There was a great commotion in Lower Thames Street on the morning of
January 12, 1887. When the early members of the staff arrived at
Wapshaw's Wharf they found that the safe had been broken open, a
considerable sum of money removed, and the offices left in great
disorder. The night watchman was nowhere to be found, but nobody who had
been acquainted with him for one moment suspected him to be guilty of
the robbery. In this belief the proprietors were confirmed when, later
in the day, they were informed that the poor fellow's body had been
picked up by the River Police. Certain marks of violence pointed to the
fact that he had been brutally attacked and thrown into the river. A
watch found in his pocket had stopped, as is invariably the case in such
circumstances, and this was a valuable clue to the time of the outrage.
But a very stupid officer (and we invariably find one or two stupid
individuals in the most intelligent bodies of men) had actually amused
himself by turning the hands round and round, trying to set the watch
going again. After he had been severely reprimanded for this serious
indiscretion, he was asked whether he could remember the time that was
indicated by the watch when found. He replied that he could not, but he
recollected that the hour hand and minute hand were exactly together,
one above the other, and the second hand had just passed the forty-ninth
second. More than this he could not remember.
What was the exact time at which the watchman's watch stopped? The watch
is, of course, assumed to have been an accurate one.
CHANGING PLACES.
The above clock face indicates a little before 42 minutes past 4. The
hands will again point at exactly the same spots a little after 23
minutes past 8. In fact, the hands will have changed places. How many
times do the hands of a clock change places between three o'clock p.m.
and midnight? And out of all the pairs of times indicated by these
changes, what is the exact time when the minute hand will be nearest to
the point IX?
Read more articles on mathematics and math puzzles at my blog www.mathtutoronline.blogspot.com and
www.articlesoneducation.blogspot.com
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