In Dart, you can use the `MediaQuery` class provided by Flutter to manage different screen sizes and adapt your UI accordingly. `MediaQuery` allows you to retrieve information about the current device's size and orientation, which you can then use to make responsive design decisions.

Below is an example of a Dart class called `Responsive` that provides utility methods to handle different screen sizes using `MediaQuery`:

```dart
import 'package:flutter/material.dart';

class Responsive {
  static double screenWidth(BuildContext context) {
    return MediaQuery.of(context).size.width;
  }

  static double screenHeight(BuildContext context) {
    return MediaQuery.of(context).size.height;
  }

  static double blockSizeHorizontal(BuildContext context) {
    return screenWidth(context) / 100;
  }

  static double blockSizeVertical(BuildContext context) {
    return screenHeight(context) / 100;
  }

  static double textScaleFactor(BuildContext context) {
    return MediaQuery.of(context).textScaleFactor;
  }

  static bool isTablet(BuildContext context) {
    return screenWidth(context) >= 600;
  }

  static bool isMobile(BuildContext context) {
    return screenWidth(context) < 600;
  }
}

```

In this `Responsive` class, we have defined several static methods:

1. `screenWidth` and `screenHeight`: These methods return the current screen width and height, respectively, based on the `MediaQuery` data.

2. `blockSizeHorizontal` and `blockSizeVertical`: These methods divide the screen width and height by 100, respectively, to provide a percentage-based unit for responsive design.

3. `textScaleFactor`: This method returns the text scale factor, which is useful for managing text size adjustments based on system settings.

4. `isTablet` and `isMobile`: These methods provide simple checks to determine if the screen width falls within a tablet or mobile device range (600 pixels in this example). You can adjust this value based on your specific needs.

To use the `Responsive` class in your Flutter application, you can import the file where it's defined and then call its methods from within your widgets:

```dart
import 'package:flutter/material.dart';

class MyWidget extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    double screenWidth = Responsive.screenWidth(context);
    double screenHeight = Responsive.screenHeight(context);
    double blockSizeHorizontal = Responsive.blockSizeHorizontal(context);
    double blockSizeVertical = Responsive.blockSizeVertical(context);
    double textScaleFactor = Responsive.textScaleFactor(context);
    bool isTablet = Responsive.isTablet(context);
    bool isMobile = Responsive.isMobile(context);

    // Use the retrieved values to adjust your UI based on the device's size
    // For example, you can use MediaQuery and LayoutBuilder to create responsive UI.

    return Scaffold(
      appBar: AppBar(
        title: Text('Responsive Example'),
      ),
      body: Center(
        child: Text('Your content goes here'),
      ),
    );
  }
}
```

With this `Responsive` class, you can easily manage different screen sizes and create a more adaptive and user-friendly UI in your Flutter app. Adjust the logic inside the `isTablet` and `isMobile` methods as per your needs and your understanding of tablet and mobile screen sizes.