Here are some basic algorithms that are commonly taught in grade 10:

1. Linear Search: This algorithm is used to find the position of a target value within an array. It starts from the beginning of the array and checks each element until the target value is found or the end of the array is reached.

2. Binary Search: This algorithm is used to find the position of a target value within a sorted array. It starts by comparing the target value with the middle element of the array. If the target value is equal to the middle element, the search is successful. If the target value is less than the middle element, the search continues on the left half of the array. If the target value is greater than the middle element, the search continues on the right half of the array. This process is repeated until the target value is found or the search range becomes empty.

3. Bubble Sort: This algorithm is used to sort an array in ascending or descending order. It repeatedly compares adjacent elements and swaps them if they are in the wrong order. This process is repeated until the array is sorted.

4. Selection Sort: This algorithm is used to sort an array in ascending or descending order. It divides the array into two parts: the sorted part and the unsorted part. In each iteration, it finds the minimum (or maximum) element from the unsorted part and swaps it with the first element of the unsorted part. This process is repeated until the array is sorted.

5. Insertion Sort: This algorithm is used to sort an array in ascending or descending order. It divides the array into two parts: the sorted part and the unsorted part. In each iteration, it takes an element from the unsorted part and inserts it into the correct position in the sorted part. This process is repeated until the array is sorted.

These are just a few examples of basic algorithms that are commonly taught in grade 10. There are many more algorithms and variations that can be explored as you progress in your studies.