Maths - KS3 Topics and chapters

Good news is I only have 20 more days work of maths to complete my maths KS3 text book.  THen I will be complete for Year 9/S2 maths!!!

We did a summary in MS Excel.

       

Maths KS3

We have been concentrating on maths for the past few days.  We have been through:

Decimals
Adding, subtraction - the general rule is to proceed as normal or remove decimals and then reinsert the decimals at the end.
Multiplying - remove decimals, work out and then combine the number of decimals points in the answer.
Division - make a whole number by multiplying by 10 or 100 and then do long division.  The answer will be the same as if you had not multiplied by 10 or 100.
make it a whole number

Factors
Factors of  10 are 2 x 5.  Factors of 20 are 2 x 10 + 2 x 2 x 5  = 2squared x 5.

Prime numbers
Prime numbers only have 2 factors - 1 and themselves.
2,3,5,7,11,13,17 etc. 2 s the only even prime number.  To work out if it is a prime number:  is it divisable by 2,3,5,7?    If not then its a prime number.

HCF
Take the lowest factors (all of them) and work out.
LCM
Take the higests common factors (all of them) and work out

Maths online and free help online?

  This looks like a possible site?  Though based in the US  http://math.tutorvista.com/algebra.html

Maths

Einstein, Albert (1879-1955)

Do not worry about your difficulties in mathematics, I assure you that mine are greater.

Maths: Perpendicular bisectors

I am using a Maths text book called "Maths KS3 Classbook" by Alan Smith.



My chapter today is Geometric Constructions: Using a protractor and ruler to construct triangles, using a compass and ruler to construct a triangle, perpendicular bisectors and angle bisectors.

I have done the whole chapter today but am discussing Perpendicular Bisectors in this particular blog entry.

I looked for a good definition of the word Perpendicular. This is what I found:

Perpendicular Meaning and Definition
(n.) A line at right angles to the plane of the horizon; a vertical line or direction.
(a.) At right angles to a given line or surface; as, the line ad is perpendicular to the line bc.
(a.) Exactly upright or vertical; pointing to the zenith; at right angles to the plane of the horizon; extending in a right line from any point toward the center of the earth.
(n.) A line or plane falling at right angles on another line or surface, or making equal angles with it on each side.

Read more at the source: http://thinkexist.com/dictionary/meaning/perpendicular/

- So its a vertical line that is 90 degrees to a horizontal line.

Looking at the word "bisector":

Bisector Meaning and Definition
(n.) One who, or that which, bisects; esp. (Geom.) a straight line which bisects an angle.

Bisect Meaning and Definition
(v. t.) To cut or divide into two parts.
(v. t.) To divide into two equal parts.

Read more at the source: http://thinkexist.com/dictionary/meaning/perpendicular/
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In the exercise I had to draw a horizontal line AB = 6 cm. Then with a compass, opened at approx 4-5cm (more than half of horizontal line), I marked small arcs that intersect - both below and above the line.

I then had to draw a line joining the midpoint of each of the arc. The result was a PERPENDICULAR BISECTOR which divided the line AB into two (half).

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We also discussed how one could use this in real life. 

One could build a + shaped "wind/sun" shelter for livestock in a field. In such a situation you would create a field compass using short rods joined by a piece of twine that was more than half the distance of the required line 10 or 20 meters. Driving one of the rods into the ground and creating arc with the other both above and below would allow you to create an accurate perpendicular bisector. In this way you could for example recycle used tyres by placing them along both 90 degree lines.

If you stack them like bricks and fill them with either soil or compost (aged droppings?) you can make them quite steady. Build up to approx shoulder height or hip height for say sheep. If you experience high winds or have large livestock that could bump the types over then you can look at bolting the types together or use either metal or wooden poles down the middle of each group of tyres anchoring them to the ground. Its a concept that can be adaptable and fine tuned for your application.

Using tyres means you could be recycling a product that has an extremely long lifespan and there is a huge excess of used tyres.

You could of course also use stone or brick etc. depending of where you live and what your local affordable resource is.

Where we live the majority of livestock have very little to no shelter from the elements. Thy do hide behind rock outcrops or a single rock or in the dunes during harsh windy weather. Sometimes the rain comes down sideways so they don't get wet either. In hot countries, this type of shelter would provide much needed shade.

Maths - My P7 workbook

My P7 maths book is: 

Heinemann Mathematics Textbook SPMG P7

Is quite a silly maths book which I suppose is meant to make it interesting but its a bit distracting.

For example.they talk about word problems with mixed up imaginary fruits and vegetable (Banapples and peacherries, lemoranges, plumpears, turnipeas, oniotts, caulipeas etc. )  It more like learning a new language and having to learn maths at the same time.

Its a fun idea for a kids story book but not for learning maths.

I have had other maths books that are really good and helpful but lets face it maths is a serious, straight forward subject and I prefer it like that.

I think silly stops one from learning and its difficult for the person who is marking it as they have to also learn all these silly names.

I already have my KS3 maths book and we were tempted to miss this Heineman P7 maths book altogether but we are labouring through it.  Its a real put off though.

Not sure what anyone else thinks of it?

I had a Heineman P6 book last year and it was ok.  Not done in that style at all.  I have also done the KS2 Maths book which is fine and well set out.

I have seen that its really important which textbooks you use as the way they present the work really affects how well you can learn and understand your work.

Its a pain that you cant see what the book looks like properly before you buy it over Amazon.  Very few books have previews.

I have a real lot of textbooks and because we bought them all we cant just go and buy more.

So. now its coming up for the end of the school year and I need to get through my maths.

Oh well, back to maths....

Maths: Roman Numerals

Read the full article here:  http://www.novaroma.org/via_romana/numbers.html

Extract:


"The Romans were active in trade and commerce, and from the time of learning to write they needed a way to indicate numbers. The system they developed lasted many centuries, and still sees some specialized use today.

The big differences between Roman and Arabic numerals (the ones we use today) are that Romans didn't have a symbol for zero, and that numeral placement within a number can sometimes indicate subtraction rather than addition.


Here are the basics:

I	The easiest way to note down a number is to make that many marks - little I's. Thus I means 1, II means 2, III means 3. However, four strokes seemed like too many....
V	So the Romans moved on to the symbol for 5 - V. Placing I in front of the V — or placing any smaller number in front of any larger number — indicates subtraction. So IV means 4. After V comes a series of additions - VI means 6, VII means 7, VIII means 8.
X	X means 10. But wait — what about 9? Same deal. IX means to subtract I from X, leaving 9. Numbers in the teens, twenties and thirties follow the same form as the first set, only with X's indicating the number of tens. So XXXI is 31, and XXIV is 24.
L	L means 50. Based on what you've learned, I bet you can figure out what 40 is. If you guessed XL, you're right = 10 subtracted from 50. And thus 60, 70, and 80 are LX, LXX and LXXX.
C	C stands for centum, the Latin word for 100. A centurion led 100 men. We still use this in words like "century" and "cent." The subtraction rule means 90 is written as XC. Like the X's and L's, the C's are tacked on to the beginning of numbers to indicate how many hundreds there are: CCCLXIX is 369.
D	D stands for 500. As you can probably guess by this time, CD means 400. So CDXLVIII is 448. (See why we switched systems?)
M	M is 1,000. You see a lot of Ms because Roman numerals are used a lot to indicate dates. For instance, this page was written in the year of Nova Roma's founding, 1998 CE (Common Era; Christians use AD for Anno Domini, "year of our Lord"). That year is written as MCMXCVIII. But wait! Nova Roma counts years from the founding of Rome, ab urbe condita. By that reckoning Nova Roma was founded in 2751 a.u.c. or MMDCCLI.
V	Larger numbers were indicated by putting a horizontal line over them, which meant to multiply the number by 1,000. Hence the V at left has a line over the top, which means 5,000. This usage is no longer current, because the largest numbers usually expressed in the Roman system are dates, as discussed above.

Source:   http://www.novaroma.org/via_romana/numbers.html

Maths!

I finished my maths text book yesterday and I only started it in August!   I am super happy.  

I have 2 new ones to move onto :)  Maths is cool!  I have ccaught up everything that I missed when I was ill at the beginning of the year! 

Maths: Geometry - Rotation

This is really helpful. You can use this interactive tool to rotate 3 different shapes by various degrees. You can even change the point of rotation - and then it shows you step-by-step how the shape rotates (Each point moving in a circle/arc around the centre).

http://www.mathsisfun.com/geometry/rotation.html

Symmetry Artist - Mathematics and Art together!

Check this out - it cool....

Symmetry Artist

http://www.mathsisfun.com/geometry/symmetry-artist.html

Maths Revision: Sequences/Number Patterns

It is important to be able to spot patterns.

To find a pattern work out the difference between terms (each number in the sequence). Also try multiplying/dividing.

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TEST YOUR KNOWLEDGE

Can you work out the pattern for 5,8,11,14,17?

Give your answer in the comments.

QUIZZ Question

What is the smallest square number that is the sum of two square numbers?

Submit your answers in the comments section by sleep-time tonight.

Math Revision

Multiples, factors, prime numbers...

Multiples

This is the times tables. Multiples of 5 are 10,15,20,25. Multiples of 7 are 14,28,35,42.

Factors

The factors of a number are all the numbers that go into that number EXACTLY. The factors of 30 are 1,2,3,5,6,10,15 and 30.

Prime Numbers

A prime number can only be divided by 1 and itself. Prime numbers less than 20 are 2,3,5,7,11,13,17 and 19.

A quick trick to work out prime numbers between 21 and 50 is to write out all the number and then cross out all even numbers. Also cross out mulitples of 3,5 and 7. The numbers that are left are all prime numbers.

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DID YOU KNOW:

1 is not a prime number. It only has 1 factor.

2 is the only even prime number.

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Maths Revision

Today I am doing revision on calculating temperature changes on a thermometer.

Basically its a vertical number line used to work out the sum of negative and positive numbers.

Its useful to see how one can use maths in real life for working out things like thermometers and temperature changes.

Image Ref: http://www.topnews.in/discovery-protein-thermometer-may-aid-fight-against-bacteria-2175388

The Essentials of Maths - Key Stage Two

I started on this book yesterday and did a few pages. The work was on decimals (Values, smallest to biggest and multiplication and division).

I only got stuck a couple of times but after some revision and explaining, I have it all in my head now.

The tricky bit for me was the smallest to biggest, and it was a bit confusing for some reason:

126.36, 126.4, 125.97, 126.08

=

125.97, 126.08, 126.36, 126.4

I also had a look at this website for extra practice: http://www.bbc.co.uk/schools/ks2bitesize/maths/number/decimals/read4.shtml

Its a good book, it catches your attention as its set out well and is colourful. The information and the way they set out the work is good.

Dividing by 9 - an easy trick for mental maths