Design of the application - training for solving mathematical problems

We need a website design for our application. The website is already ready and functional, but we need a beautiful design. I decided to try a contest to see some interesting ideas that we will like. 

With the winner we choose, we will continue working on the design of all other pages of the website as part of a personal project (currently 7 pages). Therefore, I set a minimum amount for the design of the main page. The final budget is up to 15000 hryvnias (which means a maximum of 10000 hryvnias remains). It's a bit unusual, but from your works, it will be clear who fits...

The task of the contest:

To create a design for the main page of our application. The application is already working: http://calculus-guru.uasite.pp.ua - the design here is only technical. But I think it will be a bit easier for you, as the functionality is visible.

Website name: CalculusGuru (www.calculusguru.com.ua, www.calculus-guru.com.ua). 

A bit about the application itself:

The target audience that will later pay for the application is the parent. The user will be the child: a student in grades 1-5. The parent will log in and view the child's (children's) results.

The user will go through daily lectures, where an embedded generator of mathematical problems will prepare tasks according to the child's progress.

The application, as a result of long-term use, makes sense in improving the child's mathematical abilities, but also enhances concentration skills. Our goal is not to teach mathematics (mathematics is not the top priority here).

In essence: we want to prove to the child that mathematics is actually easy if you understand the most basic principles and focus on the task. Every child is capable of understanding and can feel success - this is what we desire the most. Improving the ability to concentrate will help the child not only in mathematics.

The design and color scheme should be pleasant for the child, but should not be in a playful form (there should be no elements that interfere or distract: for example, animals, flowers, etc.).

A logo is needed - the website name in a good interesting font, possibly with some color play. It can also be graphic if there is a simple idea.

Interesting fonts are needed that we will use on all pages of the website.

A good color scheme is needed that fits our application.

Elements related to mathematics are allowed, but without overloading. The child should not be frightened immediately on the main page of the website.

Functionality of the main page:

A well-visible logo in the header.

A menu, as shown on the website.

Login for the parent, registration, language selection. (You can also add login windows - username).

Something between the header and the rest of the website, where there will be a well-visible and convenient login for the child - with the title "Start Lecture" - login, password, start. All this needs to be designed more beautifully than we did. One of the main tasks is for the area not to look empty, but to be convenient and noticeable.

Next, a block of icons - infographics that will briefly tell about the advantages of the application to the new user - the idea is for them to understand, register, and add their children. Of course, design it more beautifully than we did )

Each part has:

- an icon

- a title

- a short text

At the bottom footer -social networks, menu, company name and address, links to articles from the blog.

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The most important thing: I want to see the concept and idea. We will finalize all the details with the chosen performer. If anything needs to be clarified, write.