The formal written method for Y4 all the way to Y6 is column addition.
Here is a fantastic website that explains column addition. It has short animations (click the play button) for each stage of the calculation. https://www.mathsisfun.com/numbers/addition-column.html
Here is a poster that explains column addition on one page. The only variation with column addition is where you put the ‘carry over’. The poster shows it carrying under the next column whereas the website shows it going over. It is up to the children what they prefer but my preference is always over. Column Addition
Finally, here are some youtube videos that also show column addition.
Column subtraction is trickier than addition as it involves more understanding of place value. The tricky part is where the bottom number is bigger than the top number, e.g. 3-5. This process is called lots of things: transfer, exchange, regroup, borrow etc.
Here is the same website as before that explains column subtraction. It has short animations (click the play button) for each stage of the calculation. https://www.mathsisfun.com/numbers/subtraction-regrouping.html
Here is a poster that explains column subtraction on one page. Column Subtraction
Here is a YouTube video explaining column subtraction.
Short multiplication is when you are multiplying a 2, 3 or 4 digit number by 1 digit, e.g. 376 x 4 or 56 x 3. Long Multiplication (which they learn in Y5), is where you multiply a 2, 3 or 4 digit number by 2 digits, e.g. 376 x 45 or 56 x 32.
BBC Bitesize has an explanation of it here: https://www.bbc.co.uk/bitesize/articles/zjbyvk7
Here are some youtube videos that show short multiplication.
Short division, sometimes called the ‘bus stop method’, is the formal method for dividing by a one digit number, e.g. 453 divided by 3 (Long division is dividing by 2 digits, e.g. 453 divided by 35).
One of the things children find difficult is knowing how many x go into y when there is a remainder. For example, how many 5s go into 47. Get the children to draw a number line in jumps of the divisor (5 in this case).