Term Break

Congratulations on completing 75% of your first year of high school. I hope you all have a fantastic and safe time off and come back feeling refreshed and ready to smash out this last term.

The plan for the final term of the year will be to start with Algebra, and then finish off spending some time looking at Statistics and Probability.

Adding and subtracting negative numbers

Today we had a look at how we add or subtract negative numbers. I found a webpage which I think explains it better than I ever could, so I suggest look at the examples on this page and how they explain it. They are very thorough and use easy-to-understand language. The website is:

http://www.mathsisfun.com/positive-negative-integers.html

In general, always remember that if:

• your signs are the same (i.e. + +, or - - ) we add
• your signs are different (i.e. + - , or - + ) we take away, or subtract. 

Your should now have the skills to finish off the worksheet. This needs to be completed by the end of the lesson on Thursday. Any incomplete work will decrease your mark overall on this unit. 

As always, if you do have any questions or concerns feel free to comment on this post, or email or chat to me in person. 

Addition, Subtraction, Multiplication, and Division

Today we had a look at adding, subtracting, multiplying, and dividing larger numbers. This should be covered in primary school, however if you need a refresher on any of these, the following websites are really handy.

Addition: http://www.mathsisfun.com/numbers/addition-column.html -> Look at the examples, clicking play to see how they work these out

Subtraction: http://www.mathsisfun.com/numbers/subtraction-regrouping.html -> Look at the examples, clicking play to see how they work these out

Multiplication: http://www.mathsisfun.com/numbers/multiplication-long.html -> Look at the examples, clicking play to see how they work these out

Division: When we are doing division, I don't want you to write an answer with a remainder. I want you to write it with decimals. Most of these examples show you how to do these.
http://www.wikihow.com/Do-Short-Division -> A good step by step method, although it does end with remainders.
http://www.youtube.com/watch?v=2X0Cjy7oEgw -> Starts by writing with remainder, however the last example does show how to calculate with decimals.
http://www.youtube.com/watch?v=PX6ktbFIKdM -> A short but good example showing a division problem with a decimal answer.

Continue to work through the worksheet.

If you do have any questions feel free to comment on this post, or email or chat to me in person.

Powers and Roots, and BODMAS

Today in class we had a look at what a power and a root are.

First we looked at powers. Now you may have seen something that looks kind of like this before:

5²

This just looks like a number 5 with a small number 2 on the right hand side of it. In maths, when we see something like this we say "five raised to the power of two". What this basically means is we want to multiply 5 by itself two times. So: 5 x 5 = 25

Now we could have something different, such as 6⁵

We say this one as "six raised to the power of five", and it simply means 6 multiplied by itself 5 times. So: 6 x 6 x 6 x 6 x 6 = 7776

Now we also have stuff that looks like this: 

In maths, we say this as the "square root of twenty-five". What this is basically asking us for is a number, that when multiplied by itself twice (because of the little two on the left) will equal 25. So in this case, we know 5 x 5 = 25, or 5 multiplied by itself twice is equal to 25, so the answer to our problem is 5. 

We could also get something that looks like this:

We can describe this one as the "third root of 64". In simpler terms, this is asking us what number, multiplied by itself 3 times, is equal to 64. We can work out that 4 x 4 x 4 = 64, or 4 multiplied by itself three times is equal to 64. So the answer to our problem is 4. 

Now finally today we had a look at order of operations. In maths, when we are faced with a problem we must solve it in a particular order. This is where order of operations comes in. A good acronym to remember is BODMAS. This stands for: 

Now we use this because it actually tells us the order we need to solve our problems. We must first solve any brackets, then followed by any Orders (basically what we were looking at above, so powers and roots). Next we solve any Division or Multiplication. These may be written as separate words, but they are really grouped together. Finally, we solve any Addition or Subtraction. Again, these are written separately but they are actually grouped together. 

The following website has some great examples. It does use a slightly different acronym (PEMDAS), however it is all the same in the end. 

http://www.mathsisfun.com/operation-order-pemdas.html 

For homework, continue working through the sheet. Remember this needs to be finished before the end of term. 

As always, feel free to comment on here if you have any questions, or email or chat to me in person.  

New Unit - Number Studies

We are now looking at a new unit for the rest of this term. It will just be a quick unit on numbers and how we use these. It is quite an important unit, as it provides the foundations for a lot of other maths and maths skills we use in the future.

The first things we looked at today was recapping on multiples and factors. We looked at these during our unit on fractions, however if you do need some reminding, this website is really handy:
http://www.mathsisfun.com/numbers/factors-multiples.html

We then had a chat about prime numbers and composite numbers. A prime number is a number that has only 2 factors, 1 and itself. A composite number is a number that has more that 2 factors.

Finally we had a look at factor trees. A factor tree is basically a way of visualising all of the prime factors of a number. We start with the number itself, then split this into a pair of factors. We then split each of these into pairs of factors, and so on until we are left with just prime number (which cannot be split any further). An example could be:

This shows 3 different factor trees of the number 108. You can see that each factor tree always finishes with the same set of numbers (in green). These numbers are the prime factors of 108. If we multiply all of these numbers together you will get your original number (in this case, 108). 

The work for this can be found under the "Worksheets" tab. It is one 5 page booklet that will last you for this whole unit. You should now be able to do most of the first page and a half. If you do know how to do more of the content, keep going with it. If not, we will look at some more stuff on this unit on Tuesday. 

As always, if you do have any questions feel free to comment on this post, or email or chat to me in person. 

Riddle 4

Create a number using only the digits 4,4,3,3,2,2,1 and 1. It can only be eight digits. You have to make sure the ones are separated by one digit, the twos are separated by two digits the threes are separated with three digits and the fours are separated by four digits. 

As always, have fun with this. Do not Google the answer. Try it for yourself. Have fun with it. If you cannot get it, don't worry.

The answer will be revealed in class on Tuesday. If you come up with a solution before then, let me know, but do not share it with others. Let them solve it themselves. 

Review of Measurement + Test

Today we started some revision of the unit of measurement. I have made a worksheet, which can be found in the "Worksheets" tab. This worksheet has a brief summary of our unit, followed by some revision questions with answers. Work through these as practice for the test.

We will be having a test on this topic on Tuesday the 8th of August. You will be allowed calculators for the whole test, and an A5 single sided information sheet. The test will be on the topics of:

• Converting between units of measurement (i.e. converting cm to m) 
• Finding perimeters of shapes
• Finding areas of shapes
• Finding volumes of 3D shapes

As always, feel free to comment on this post, or email or chat to me in person. 

Riddle number 3 answer

The answer to riddle number 3 is:

4 + 5 = 3²

Congratulation to Ruben and Indy for solving this one.