Sunday, 11 July 2010
Sunday, 3 January 2010
New GCSE Maths Revision Forum!
Top Grade Tutoring have just launched a GCSE Maths Revision Forum! So don't suffer anymore with your GCSE Maths! Check out the forum to find solutions to your questions, exchange ideas and even make new friends!
Friday, 1 January 2010
Maths tuition certainly makes the grade
As this is the first post of 2010 I just wanted to wish every reader a happy and prosperous 2010!
Pressure to succeed academically is becoming greater and greater in the UK. Students are expected to reach stringent government targets at key stages 2,3 and 4. Teachers often do not have the time to over topics with students if they 'don't get things first time'. So invariably parents are turning to an alternative solution, private home tuition.
Private home tuition in subjects like Mathematics is becoming more popular because students are falling behind. Mathematics has traditionally been a difficult subject, the kind of subject that you either love or hate. Alas the majority of students dislike it and often require additional support.
With the continuing decline in classroom behaviour in the United Kingdom, students are missing out on the essential education that they require. Teachers are also under more pressure to meet ever increasing government targets and fill in paper work, which means that they are unable to spend enough time with students to help them them with any problems that they are encountering with their studies.
So how does private tuition work? Once you contact a private tuition agency to arrange for private tuition you will then be contacted by a home tutor, who is CRB checked in accordance with the protection of children act 1999. The home tutor who typically will be either a graduate or a teacher in a school will discuss with you your child's educational needs, in order to establish the level and frequency of tuition that they feel is necessary. Typicall the tutor will travel to your house to conduct the lessons which typically will be around an hour in length. During the lesson the tutor will address the areas of difficulty that your child is encountering within the subject that they are being tutored in and provide exam practice and preparation.
With one to one maths tuition, students are able to raise any areas of difficulty within Mathematics that they may have with their assigned tutor and have it explained in a clear and professional manner. Secondly, more able students are able to progress more quickly in their studies as more topics can be covered on a one to one basis, compared to in a classroom environment, where disruptive students can hold back more able students who wish to learn.
Typically a student will learn twice as much via a one to one private tuition approach in a single lesson compared to that of a classroom environmnent where there are many disrupitions varying from noise to other disruptive students. The cost of home tuition can be off putting for many parents, the benefits however definitely outweigh the costs. For example students are often more confident as a result of the private tuition that they receive. Students are often ahead of their peers too, as topics can be covered more quickly as a result of the maths tuition that they receive.
Top Grade Tutoring, a private mathematics tuition agency formed by Steven Britton in his home town of Halesowen West Midlands has successfully helped over 120 people in Mathematics. He claims that a staggering 85% of all people that have been taught by tutors there have moved up at least one grade in Mathematics.
So as you can see it really does make sense to invest the time and money into your child's education. You could argue that this perhaps is a sad reflection on the state of the British education system that has been ruined by the policies of the new labour government since 1997, but with every problem there is a solution. Private tuition definitely seems the way to go and an excellent alternative to private education with certainly is costly.
Pressure to succeed academically is becoming greater and greater in the UK. Students are expected to reach stringent government targets at key stages 2,3 and 4. Teachers often do not have the time to over topics with students if they 'don't get things first time'. So invariably parents are turning to an alternative solution, private home tuition.
Private home tuition in subjects like Mathematics is becoming more popular because students are falling behind. Mathematics has traditionally been a difficult subject, the kind of subject that you either love or hate. Alas the majority of students dislike it and often require additional support.
With the continuing decline in classroom behaviour in the United Kingdom, students are missing out on the essential education that they require. Teachers are also under more pressure to meet ever increasing government targets and fill in paper work, which means that they are unable to spend enough time with students to help them them with any problems that they are encountering with their studies.
So how does private tuition work? Once you contact a private tuition agency to arrange for private tuition you will then be contacted by a home tutor, who is CRB checked in accordance with the protection of children act 1999. The home tutor who typically will be either a graduate or a teacher in a school will discuss with you your child's educational needs, in order to establish the level and frequency of tuition that they feel is necessary. Typicall the tutor will travel to your house to conduct the lessons which typically will be around an hour in length. During the lesson the tutor will address the areas of difficulty that your child is encountering within the subject that they are being tutored in and provide exam practice and preparation.
With one to one maths tuition, students are able to raise any areas of difficulty within Mathematics that they may have with their assigned tutor and have it explained in a clear and professional manner. Secondly, more able students are able to progress more quickly in their studies as more topics can be covered on a one to one basis, compared to in a classroom environment, where disruptive students can hold back more able students who wish to learn.
Typically a student will learn twice as much via a one to one private tuition approach in a single lesson compared to that of a classroom environmnent where there are many disrupitions varying from noise to other disruptive students. The cost of home tuition can be off putting for many parents, the benefits however definitely outweigh the costs. For example students are often more confident as a result of the private tuition that they receive. Students are often ahead of their peers too, as topics can be covered more quickly as a result of the maths tuition that they receive.
Top Grade Tutoring, a private mathematics tuition agency formed by Steven Britton in his home town of Halesowen West Midlands has successfully helped over 120 people in Mathematics. He claims that a staggering 85% of all people that have been taught by tutors there have moved up at least one grade in Mathematics.
So as you can see it really does make sense to invest the time and money into your child's education. You could argue that this perhaps is a sad reflection on the state of the British education system that has been ruined by the policies of the new labour government since 1997, but with every problem there is a solution. Private tuition definitely seems the way to go and an excellent alternative to private education with certainly is costly.
Friday, 6 November 2009
L.C.M Anyone?
I was teaching fractions to a student the other day. I then got onto the topic of adding fractions, I mentioned the word LCM. The student looked at me as though I was speaking a foreign language. I then tried to elaborate saying the words "Lowest Common Multiple", the student was still bemused. So I had to explain the concept to them. So this posting is for anybody who is confused with lowest common multiples.
Lowest Common Multiple
The smallest common multiple of two or more numbers is called the lowest common multiple (LCM).
E.g. Multiples of 8 are 8, 16, 24, 32, … Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, …
In general:
To find the lowest common multiple (LCM) of two or more numbers, list the multiples of the larger number and stop when you find a multiple of the other number. This is the LCM.
Example 3
Find the lowest common multiple of 6 and 9.
Solution:
List the multiples of 9 and stop when you find a multiple of 6.
Multiples of 9 are 9, 18, …Multiples of 6 are 6, 12, 18, …
Example 4
Find the lowest common multiple of 5, 6 and 8.
Solution:
List the multiples of 8 and stop when you find a multiple of both 5 and 6.
Multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, …
Stop at 120 as it is a multiple of both 5 and 6.
So, the LCM of 5, 6 and 8 is 120.
Lowest Common Multiple
The smallest common multiple of two or more numbers is called the lowest common multiple (LCM).
E.g. Multiples of 8 are 8, 16, 24, 32, … Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, …
In general:
To find the lowest common multiple (LCM) of two or more numbers, list the multiples of the larger number and stop when you find a multiple of the other number. This is the LCM.
Example 3
Find the lowest common multiple of 6 and 9.
Solution:
List the multiples of 9 and stop when you find a multiple of 6.
Multiples of 9 are 9, 18, …Multiples of 6 are 6, 12, 18, …
Example 4
Find the lowest common multiple of 5, 6 and 8.
Solution:
List the multiples of 8 and stop when you find a multiple of both 5 and 6.
Multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, …
Stop at 120 as it is a multiple of both 5 and 6.
So, the LCM of 5, 6 and 8 is 120.
Wednesday, 21 October 2009
Negative numbers
I thought I'd post this as I have seen a lot of my students struggle with this
OK….We all know what numbers are: 1, 2, 3, 4……etc.
Did you know that numbers can also be negative? You must have heard of temperatures of being minus ten degrees before (especially if you're into snowboarding!). Minus ten as a number is written as -10. Any number with - before it can also be called a negative number.
We can have as many negative numbers as we have normal (positive or plus) numbers - the only funny number sitting on the fence is zero, which is always called zero - not negative zero or positive zero.
The numbers can be seen in a range like the one below:
………….-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6………..
Negative numbers surprisingly appear quite a lot in everyday life. If you owe your parents £8 and have no other money it could be said that you have £ -8. Similarly, it is very important for all businesses to know how much money they don't have or they could go bust.
We've already mentioned temperatures being negative, but how about the speed of a car - how can you travel at -20 miles per hour? - By going backwards of course!
Negatives of anything are opposites for the positives - such as the negatives you get when you have photographs developed. So, whenever you are dealing with negative numbers - think of them as simply being the opposite of positive numbers.
Adding
When you add two positive numbers e.g. 2 + 2 the answer will always be positive i.e. 4
When you add two negative numbers e.g. -2 + -2 the answer will always be negative i.e. -4 (this is like saying minus 2 degrees below zero plus another minus 2 degrees below zero)
Subtracting
When you subtract two positive numbers the answer could be positive e.g. 3 - 1 = 2 or negative! e.g. 3 - 7 = -4
Have a look at this on the number scale to see how it works:
………….-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6………..
Count backwards (right to left) from 3 through the purple numbers for 7 steps (call the gap between 3 and 2 a step, then the one between 2 and 1 and the one between 1 and 0 etc.) and you end up with the answer -4.
What is -7 + 3? Look at the number scale again and count 3 to the right from -7 and you end up with -4.
In other words -7 + 3 is exactly the same as 3 - 7.
-3 - 2 means the same as -3 + -2. By moving another 2 places to the left of the scale from -3 we get the answer as -5.
Now for the funny bit…..
What is -3 - -2 (minus 3 minus minus 2)? this is nearly always written as -3 - (-2) where the brackets just make it easier for people to see that you have written two minus signs - - and don't just have a dodgy pen and only intended to write a single minus.
Back to the question -3 minus -2 again - Think of opposites - you know that -3 -2 moves two to the left of the number scale and gives the answer -5. So -3 - (-2) being opposite must move two to the right of the number scale giving the answer -1.
Secret: If ever you see two minus signs together - treat them as a plus (positive) number e.g. -3 -(-2) is exactly the same as -3 + 2!
Back to the question -3 minus -2 again - Think of opposites - you know that -3 -2 moves two to the left of the number scale and gives the answer -5. So -3 - (-2) being opposite must move two to the right of the number scale giving the answer -1.
Secret: If ever you see two minus signs together - treat them as a plus (positive) number e.g. -3 -(-2) is exactly the same as -3 + 2!
Multiplying
There's another secret coming up here which is surprisingly similar to the one you've just learnt - wait for it.
Firstly, a negative number multiplied by a positive number is always negative e.g. -3 x 2 = -6 and likewise 3 x -2 = -6.
-3 x 2 is like saying "I'm at -3 on the number scale and need to go twice as far as -3 to get the answer - so you move on another -3 (to the left of the scale) giving you the answer -6.
Now, when a negative number is multiplied by a negative number the answer is always positive.
Secret: A minus number times a minus number always gives a plus number (e.g. -3 x -4 = 12, -10 x -3 = 30).
Dividing
Here the technique is the same as multiplying. A negative number divided by a positive number gives a negative number e.g. -6/3 = -2.
Also a positive number divided by a negative number also gives a negative numbere.g. 6 / -3 = -2.
So what do you think a negative number divided by a negative number is?
That's it you've guessed it (if you've understood the section on multiplying). Negative divided by negative gives positive.
Secret: A minus number divided by a minus number gives a plus number (e.g. -6/-3 = 2)
The bit most people forget
If you see two minus numbers together when multiplying or dividing the answer will always be plus.
When a minus number is subtracted from another minus number, the two minuses - - should be treated as if they were +.
"TWO MINUSES ALWAYS MAKE A PLUS"
Earlier we were talking about opposites - did you notice that it isn't just the positive and negative numbers which are opposite?
Subtraction is the opposite of Addition and
Division is the opposite of Multiplication
OK….We all know what numbers are: 1, 2, 3, 4……etc.
Did you know that numbers can also be negative? You must have heard of temperatures of being minus ten degrees before (especially if you're into snowboarding!). Minus ten as a number is written as -10. Any number with - before it can also be called a negative number.
We can have as many negative numbers as we have normal (positive or plus) numbers - the only funny number sitting on the fence is zero, which is always called zero - not negative zero or positive zero.
The numbers can be seen in a range like the one below:
………….-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6………..
Negative numbers surprisingly appear quite a lot in everyday life. If you owe your parents £8 and have no other money it could be said that you have £ -8. Similarly, it is very important for all businesses to know how much money they don't have or they could go bust.
We've already mentioned temperatures being negative, but how about the speed of a car - how can you travel at -20 miles per hour? - By going backwards of course!
Negatives of anything are opposites for the positives - such as the negatives you get when you have photographs developed. So, whenever you are dealing with negative numbers - think of them as simply being the opposite of positive numbers.
Adding
When you add two positive numbers e.g. 2 + 2 the answer will always be positive i.e. 4
When you add two negative numbers e.g. -2 + -2 the answer will always be negative i.e. -4 (this is like saying minus 2 degrees below zero plus another minus 2 degrees below zero)
Subtracting
When you subtract two positive numbers the answer could be positive e.g. 3 - 1 = 2 or negative! e.g. 3 - 7 = -4
Have a look at this on the number scale to see how it works:
………….-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6………..
Count backwards (right to left) from 3 through the purple numbers for 7 steps (call the gap between 3 and 2 a step, then the one between 2 and 1 and the one between 1 and 0 etc.) and you end up with the answer -4.
What is -7 + 3? Look at the number scale again and count 3 to the right from -7 and you end up with -4.
In other words -7 + 3 is exactly the same as 3 - 7.
-3 - 2 means the same as -3 + -2. By moving another 2 places to the left of the scale from -3 we get the answer as -5.
Now for the funny bit…..
What is -3 - -2 (minus 3 minus minus 2)? this is nearly always written as -3 - (-2) where the brackets just make it easier for people to see that you have written two minus signs - - and don't just have a dodgy pen and only intended to write a single minus.
Back to the question -3 minus -2 again - Think of opposites - you know that -3 -2 moves two to the left of the number scale and gives the answer -5. So -3 - (-2) being opposite must move two to the right of the number scale giving the answer -1.
Secret: If ever you see two minus signs together - treat them as a plus (positive) number e.g. -3 -(-2) is exactly the same as -3 + 2!
Back to the question -3 minus -2 again - Think of opposites - you know that -3 -2 moves two to the left of the number scale and gives the answer -5. So -3 - (-2) being opposite must move two to the right of the number scale giving the answer -1.
Secret: If ever you see two minus signs together - treat them as a plus (positive) number e.g. -3 -(-2) is exactly the same as -3 + 2!
Multiplying
There's another secret coming up here which is surprisingly similar to the one you've just learnt - wait for it.
Firstly, a negative number multiplied by a positive number is always negative e.g. -3 x 2 = -6 and likewise 3 x -2 = -6.
-3 x 2 is like saying "I'm at -3 on the number scale and need to go twice as far as -3 to get the answer - so you move on another -3 (to the left of the scale) giving you the answer -6.
Now, when a negative number is multiplied by a negative number the answer is always positive.
Secret: A minus number times a minus number always gives a plus number (e.g. -3 x -4 = 12, -10 x -3 = 30).
Dividing
Here the technique is the same as multiplying. A negative number divided by a positive number gives a negative number e.g. -6/3 = -2.
Also a positive number divided by a negative number also gives a negative numbere.g. 6 / -3 = -2.
So what do you think a negative number divided by a negative number is?
That's it you've guessed it (if you've understood the section on multiplying). Negative divided by negative gives positive.
Secret: A minus number divided by a minus number gives a plus number (e.g. -6/-3 = 2)
The bit most people forget
If you see two minus numbers together when multiplying or dividing the answer will always be plus.
When a minus number is subtracted from another minus number, the two minuses - - should be treated as if they were +.
"TWO MINUSES ALWAYS MAKE A PLUS"
Earlier we were talking about opposites - did you notice that it isn't just the positive and negative numbers which are opposite?
Subtraction is the opposite of Addition and
Division is the opposite of Multiplication
Saturday, 17 October 2009
Making the most of past papers
With mock exams looming now is the time to start preparing for them. There is no better way than to practice as many past papers as possible so as you get a feel for the exam style questions. It is important that you know what exam board is issuing the paper as well as the syllabus code and the level at which you are studying at, e.g Higher and Foundation.
Remember the better prepared you are the more likely you are to obtain higher grades. Simply reading through a text book is not adequate preparation. The more questions that you can do the better!
Past exam papers are available directly from exam board websites, also they are available from the Top Maths DVD website where you can download them free of charge.
Remember the better prepared you are the more likely you are to obtain higher grades. Simply reading through a text book is not adequate preparation. The more questions that you can do the better!
Past exam papers are available directly from exam board websites, also they are available from the Top Maths DVD website where you can download them free of charge.
Saturday, 29 August 2009
Don't forget your working out!
Why is it that a lot of students forget vital working out when answering GCSE Maths questions? Well the answer is that students think that by putting a single answer down that they will get all the marks possible for that question! How wrong is that!
The simple truth is that examiners are looking for students to demonstrate that they are able to apply a method to solve a mathematical problem, hence examiners award marks for doing so even if you arive at the wrong answer!!
Remember that Mathematics is fundamentally about accuracy, not speed. Therefore under timed examination conditions it is far better to spend time showing all working out and checking your answer and working out afterwards, than rushing the question and only putting an answer down that could potentially be wrong! So you may end up with no marks with just a single answer! So as you can see it really makes sense to show your working out!
The simple truth is that examiners are looking for students to demonstrate that they are able to apply a method to solve a mathematical problem, hence examiners award marks for doing so even if you arive at the wrong answer!!
Remember that Mathematics is fundamentally about accuracy, not speed. Therefore under timed examination conditions it is far better to spend time showing all working out and checking your answer and working out afterwards, than rushing the question and only putting an answer down that could potentially be wrong! So you may end up with no marks with just a single answer! So as you can see it really makes sense to show your working out!
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