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Method in Multiplying Madness?

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

Grid Multiplication

 


$23 \times 21$



$246 \times 34$

 

Column Multiplication

 


$23 \times 21$



$246 \times 34$

 

Multiplying with Lines

 


$23 \times 21$



$246 \times 34$

 

Gelosia Multiplication

 


$23 \times 21$



$246 \times 34$

 

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?

 


Extension challenge

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?