Hi CSS25,
First thing that strikes me is that google ad. Not good, is the google ad more important than your home page? I don't like to see a google ad bar so prominently displayed on a home page. It disconnects your menu bar from the rest of your page.
I actually like the background image, its a great line, 'think maths, grow smart'. But I don't like the background image behind the main panel. It interferes with your text too much, making it hard to read, especially lower down. And it repeats too often, it makes for too much of a distraction.
The middle portion of your main contents seems a bit bare with those three graphics and the four lines of text. Perhaps a different arrangement might help, but I'm not sure. Its a lot of your front page given over just to that section. There is so much more content on the site you could be plugging. Personally I would consider moving this whole section to the bottom of the page and have the welcome statement above it.
The blue in your header has no resonance in the rest of the page, this results in it looking out of place. I love the green but maybe you should rethink it if you are going to keep the header or rethink the header.
The page looks very busy, a little crowded. You might want to increase the padding of the text and the spacing between the lines.
The menu bar, work on the spacing of the items, For Teacher, should that not be For Teachers, for consistency.
The menu panel on the left and the welcome to marthamaths.com header should be lined up, they don't appear to be.
I would lose the red in the latest news section.
It appears you have a dashed line at the bottom of the main panel, don't know if that is part of the background graphic. It looks odd.
Your copyright statement is a little hard to read.
When opening your games I would do so in the center of the screen.
Don't refer to what you are selling as 'our product'. Give it a name, use the name, make sure the name is in your visitor's mind, repeat it at least three times in the text they will read. The youtube screen shots need to be better if you are trying to sell, they are too blurry.
Overall I think you have a good foundation you just need to work on getting it all to work together. One of my big failings is to try too hard to bring everything to a visitors attention at the same time, the page ends up with a lot of conflicting items all trying to grab your eyes. Some times you have to be a little more laid back and pick just one or two main points on a page.
Your home page is the door way into your site. The vast majority of users will look at it and decide whether to continue exploring your site. You need to think carefully if you really want to give that valuable selling space to google or to use it for your own benefit. Is the money you are going to get out of it worth handicapping yourself in this way.
On a personal note...
I love the idea behind your site, the subject and your approach is close to my own heart and thinking. I was actually doing something similar in the not too distant past, but more connected with mnemonic techniques. Perhaps that is why I have written as much as I have

sorry. I wish you and the site all the very best. I would be delighted if you let me know if you need someone to have another look. I already have it book marked.
PS. I know there are a few tutoring sites, especially to do with maths, one is based in India. They provide tutorials and teachers that students can get in touch with for one on one help if they get stuck. It might be worth your while hunting them down and seeing what they are up to.