This first topic of the Edexcel IGCSE Computer Science course is a significant one, with in-depth coverage of algorithms. Students must be able to understand the applications of algorithms, be able to read and write them, and describe the output of an algorithm (dry running). They should also be able to identify and correct mistakes in algorithms, as describe the operation of common searching and sorting algorithms. There is also a significant practical aspect to this topic, as students must be able to convert an algorithm to working code, which ties in with the skills required in Topic 2.
In the context of this topic, "algorithms" may refer to pseudo-code, flowcharts, structured English, or actual program code.
As its name suggests, Sorting Algorithms features animations of popular sorting algorithms, including Bubble, Selection, and Insertion. The animations for each sorting method are played side by side, allowing a direct comparison. The great thing about this site is that students can select the state of the starting data (reversed, random, almost sorted, etc) as well as its size - this is perfect for helping students compare the efficiency of the algorithms and understanding that there is no generic "best" algorithm for all circumstances.
Lightbot is a simple game that involves logic and basic programming techniques. Players must create a set of instructions from the list available (go forward, rotate, jump) to guide the robot to the blue squares at the end of each maze. Levels get gradually more difficult and there commands can even be grouped into functions and 'called' from different points. The game is best suited to younger players.
CS Field Guide has an extremely comprehensive page about searching and sorting algorithms, including clear explanations, animated examples, and interactives. It covers algorithm efficiency and cost.
The linear search or sequential search algorithm is very straightforward, but this video explains it. It also makes an important point that students often forget: that is, while we can see all of the numbers on display at the same time in our examples, a computer cannot. Therefore no algorithm can make 'jumps' or 'assumptions' about the data - it must be searched item by item if it is unsorted. The video also includes pseudo code for the algorithm
This Bubble Sort video does exactly as its name suggests - explaining the algorithm clearing with the aid of diagrams. Although it is labelled as "Java", it is relevant to all computer science students.
There is also a good explanation of the algorithm (including why it is very inefficient) plus step by step diagrams here.
Harvard's CS50 Merge sort video uses a really clear approach - numbered plastic cups which are moved around as we step through the algorithm. The same approach is used in all of their sorting algorithm videos, making it easy to compare different sorting algorithms.
Joe James' Merge sort algorithm video is also very clear.
For Merge sort in particular, step by step diagrams can be very helpful in understanding the algorithm. TutorialsPoint has a good set of diagrams, plus pseudocode.