## The Wonderful World of Chocolate and Maths!

It’s chocolate week this week – a time when you actually have an excuse for indulging!

And at the same time, Ireland are enjoying maths week . . . maybe a less pleasurable experience for most people!

So, let’s mix it together and take a look at the importance of maths in chocolate.

We are all used to seeing the percentages on the front of more high-end chocolate bars, saying for example “70% cocoa”. But what does that actually mean?

The percentages on the front of chocolate bars refer to weight: they refer to how much of the total weight of the chocolate bar is made up of actual cocoa bean products. By cocoa bean products, we mean cocoa butter and cocoa solids. So, “70% cocoa” means that 70% of the weight of the chocolate bar is made up of cocoa bean products, while the rest is mostly sugar (yikes!) with a touch of vanilla, lecithin (this makes it smooth and creamy) and milk solids if it’s milk chocolate or white chocolate.

A typical cocoa bean is made up of 54 percent cocoa butter and 46 percent cocoa solids (the solids are often ground down and used to make cocoa powder). Different amounts of the cocoa butter and cocoa solids will be used depending on what type of chocolate you eat. White chocolate, for instance, contains cocoa butter without the cocoa solids.

So, as you sit back and tuck in to a chocolate-y treat, spare a thought for those clever chocolatiers who have mixed the right percentages together to make it!

## New National Curriculum for Maths

The new curriculum came into force this month for everyone except Years 2 and 6. Although it may seem a little daunting, the new maths curriculum is nothing to be afraid of! It seems much harder than the previous curriculum, but in reality, they are just learning topics at a slightly earlier age so that they can build on that knowledge for a longer period of time. In maths, some topics have actually been removed from the Key Stage 2 curriculum, such as probability.

By starting the teaching earlier, the theory is that they can then go into much more detail and ensure that children are able to get to the stage where they understand the methods and can solve problems rather than just perform calculations.

Take a look at our Year 1 Maths page to see the topics Year 1 students will be covering. And don’t forget to try our brand new Year 1 Fractions test!

## Careers In Maths

So, what good is maths to you in the real world? It can sometimes seem as though maths is just one of those subjects you have to do at school, then immediately forget once all the exams are over (except for the odd bank statement you have to analyse!).

And, for those with a passion for maths, you may ask yourself what pursuing maths can actually do for you. Surely the only thing you’d end up being would be an accountant or a maths teacher. But, maths is used more than you may think in working life. Every day, we make calculations that we may not even be aware of. And some places of work involve more mathematics than others. This site has some great videos showing how some people use maths in working life: mathscareers.org

There are a whole range of sectors that like to employ graduates with mathematical skills:

Aerospace, Automotive companies, Construction, Engineering, Environmental work, Healthcare, IT, Manufacturing, Scientific Research, Telecoms, Transport, Utility companies . . . and that’s just naming a few!

There are so many apprenticeship schemes and graduate schemes out there for people who have a knack for maths. This site lists some of the options available: maths careers

So, maybe maths isn’t the dead-end option you may think it is; in fact, it opens a whole world of opportunities.

## The Logic of Maths

May 26, 2014 § 1 Comment

Part of mathematical ability comes down to logic. People who are logical are able to follow mathematical processes and understand the mechanisms behind the question. This is especially helpful when it comes to solving word problems, a particular obstacle to lots of maths students.

Here’s one of the word problem questions from a GCSE Higher Maths Mock Paper:

Janice asks 100 students if they like biology or chemistry or physics best.
38 of the students are girls.
21 of these girls like biology best.
18 boys like physics best.
7 out of the 23 students who like chemistry best are girls.
Work out the number of students who like biology best.

This question can easily get you in a tangle! It needs to be tackled logically. Often, diagrams and charts are a good way to order your thought processes. For this particular question, a two-way table is helpful. We know that there are 100 students in total. 38 are girls, so 62 are boys. 21 girls like biology, 18 boys like physics, 7 girls like chemistry and 16 boys like chemistry. If we put those numbers into a table, we can then work out the rest.

## Don’t Be Negative – A Common GCSE Maths Mistake!

Okay so this might be a bit of a boring blog post! But, with the GCSE exams round the corner, I thought I would highlight one of the most common mistakes seen when marking GCSE maths papers.

That problem is negative numbers. They just get students in a right old pickle! And that’s why they crop up every year in the exam papers! But they won’t be obvious . . . . they are often very sneaky and catch people off guard. For instance, you will see minus signs when expanding brackets or in substitution or indices questions.

So, here are the simple rules:

MINUS X MINUS = PLUS

MINUS X PLUS = MINUS

Take this past paper question as an example:

V = 3b + 2b2

Find the value of V when b = –4

First, substitute the number into the equation.

3b + 2b² =   3 x -4 + 2 x -4²

3 x -4 is PLUS x MINUS, so it becomes a MINUS: 3 x -4 = -12

2 x -4² is a bit more complicated because we need to do the squaring first:
-4² = -4 x -4 which is MINUS x MINUS, so it becomes a PLUS. -4 x -4 = 16

2 x 16 = 32

So, 3b + 2b² =   3 x -4 + 2 x -4² = -12 + 32 = 20

Just take it step by step and CHECK YOUR WORK! We wish everyone doing the GCSE exams all the best.

## Fractions for Five Year Olds

The new National Curriculum will soon be sailing in to schools this September. It is set to make quite a difference and it’s exciting to see whether it will be a success.

One of the biggest changes is the step-up in terms of introducing topics much earlier than before. Now, your 5-year olds will be learning simple fractions, such as halves and quarters. This may sound crazy! But, don’t forget that the younger they are, the more they are able to learn and absorb.

The Department for Education has had the new curriculum published on their website for quite some time . . . . and it looks like the kids (and the poor teachers!) are going to be packing a lot in! These links show the new primary curriculum for maths and English – it shows you the topics that are going to be covered in each year group:

Primary Maths Curriculum From 2014

Primary English Curriculum From 2014

And, if you want a heads-up on simple fraction work, we’ve got it covered: How To Do Fractions

## The Importance Of Angles

Say the word “angles” to a class of 10 year olds and everyone sighs! But without certain angles, life would be very different.

Think about this angle: 23.4 degrees. That is the size of our Earth’s axial tilt. Earth isn’t upright as it travels round the Sun; instead, it has a slight lean. And it’s quite a tilt – the Leaning Tower of Pisa only has a tilt of 4 degrees, so it’s pretty straight in comparison!

That angle of 23.4 degrees is more than just an interesting fact. Without that angle of tilt, we would not get our seasons. During summer in the Northern Hemisphere, the North Pole is tilted towards the Sun, so the Northern Hemisphere gets more sunlight and warmth than the Southern Hemisphere. Then, in winter the North Pole is tilted away from the Sun, so there is less sunlight and it becomes much colder in the Northern Hemisphere. And, of course, during autumn and spring, both hemispheres are receiving equal sunlight.

Yes, we enjoy the variation of the seasons, but more than that they are vital to our survival. If the Earth’s tilt was different, we would not get the same regulation of temperature that we have now. The extremes caused by more or less tilt would make life very difficult – impossible in certain parts of the Earth. Not just that, without seasons we would not be able to grow food in the same way. Just think about how important it is to have the variations that make seed germination and plant growth possible. Without the seasons, food production would be seriously affected.

So, yes, angles may be incredibly boring when you’re 10! But, maybe certain angles need a little respect every now and then!

## Busy Bee Geometry

“When there is no honey, the Pooh takes his tummy wherever the honey will be,” sang Pooh.

But, whilst poking his paw into the nearest beehive, did he ever stop to think about the ingenuity of the humble honey bee? Let’s hope not, a mathematical analysis surely wouldn’t make for a good Winnie the Pooh episode!

We are all used to the hexagonal shape of the cells within a beehive. But, why do the bees choose hexagons?

It was way back in the 4th century that Pappus, an Ancient Greek geometer, started to think that maybe there was more to it than just being pretty . . . it’s actually a very efficient building technique. To make the most efficient use of space, they need to use shapes that tessellate – that means shapes that fit neatly together without leaving gaps.

But, you may say, why not use other shapes that tessellate, like squares or triangles? Well, for one thing, regular hexagons have a smaller overall perimeter than squares and triangles – once they have built one hexagon, they have already built one of the walls for 6 other hexagons, so it makes the workload much quicker and easier. Plus, the regular hexagon pattern has now been proved to be the most efficient pattern for curved walls. This means that the individual cells can bulge with honey and still make the most efficient use of the space.

So, next time you are using a protractor to measure an angle, spare a thought for the worker bees that are instinctively setting the walls in their beehives at exactly 120 degrees without so much as a spirit level!

## 11 Plus Mathematics Practice Paper

October 27, 2010 § 1 Comment

Practicing papers is one of the most effective ways of preparing for the 11 plus exams. There are lots of suggestions out there about how best to use practice papers as a revision tool, but at the end of the day it comes down to each individual. Everyone has a different way of learning, so it’s best to judge according to your own child. Some children will be able to complete whole papers in one go, whereas for other children it is easier to do the papers in sections.

Whatever way of learning you choose, though, it is essential to make sure your child is comfortable working within the time constraints. Remember that many of the 11+ maths exams allow 1 minute per question, so this is what you are aiming towards. In some 11+ verbal reasoning and 11+ non verbal reasoning tests, only 45 seconds per question is allocated – no small task for a 10-11 year old! That’s why it is a good idea to make sure your child is prepared. You do not want the 11 plus exam to be a stressful ordeal.

There are many practice papers that you can buy from various bookshops, but why not try our free downloadable 11+ maths practice paper. It is 30 questions long and can be used either as a standard or a multiple choice format paper.

11+ Maths Practice Paper

### Where Am I?

You are currently browsing entries tagged with Maths at Maths Star.