If you are a teacher, click here for a version of the problem suitable for classroom use, together with supporting materials. Otherwise, read on...
If you had to work out $23 \times 21$ how would you do it?
What if you needed to work out $246 \times 34$?
Here are eight videos showing four different methods for working out the two multiplications. Can you make sense of them?
Multiplying with Lines
Once you have watched the videos, make up some multiplication calculations of your own and have a go at answering them using all four methods. Check that you get the same answer each time!
Here are some questions to consider:
Why does each method work?
What do the methods have in common?
What are the advantages and disadvantages to each method?
Here is a video of another multiplication method, one where no writing down is needed along the way. Can you make sense of the video, and explain how this method works?