Celebration Party Problem - Algorithm
Your algorithm is correct and will be very efficient. Note that it assumes that the array of float values is sorted ascendingly. To make sure of that, you could explicitely sort the array before entering the while loop, or document that the method must take a pre-sorted array.

The comments I have are concerning the presentation of the code itself:


Consider adding white-spaces before and after each parentheses and curly braces. For example

while(currentChild&lt;lastChild){


could be read easier with

while (currentChild &lt; lastChild) {


where extra spaces have been added.
You have added a lot of vertical spaces. Adding a line break with an empty line can indeed help readability but having 2 empty lines is too much: this is what you have after your while loop and between the two if statements. Consider having only a single empty line where you think it adds to clarity.
Be consistent with your usage of white-spaces. Statements like

startingPoint=currentChild ;


are a bit weird. There is a space before the semi-colon and no spaces around the = operator.


An IDE can usually reformat your code automatically. For example, taking directly your code into Eclipse and reformatting it by selecting it and hitting Ctrl+Shift+F let me to 

static int getGroups(float[] children) {

    int lastChild = children.length;
    int currentChild = 1;
    int startingPoint = 0;
    int groups = 0;

    while (currentChild &lt; lastChild) {

        if (children[currentChild] - children[startingPoint] &gt; 1) {
            startingPoint = currentChild;
            groups++;
        }

        if (currentChild == lastChild - 1) {
            groups++;
        }
        currentChild++;
    }

    return groups;
}




Also, I noticed that you used wildcard import statement:

import java.io.*;
import java.util.*;


This is generally not a good practice. You want to import the specific classes with which you are interacting. In this case, it is actually not a lot, you just one import statement:

import java.util.Scanner;


There is no need for any class under java.io.