When I introduce multiplying, I have them refer to 4 ways to think about it so that they understand what it really means.
- Circles and Stars - Draw it out in a picture. For 3 X 4, make 3 circles and draw 4 stars in each one. This shows the groups in picture form and we quickly find it is not that effiecient and mistakes can be made.
- Repeated Addition - 3 X 5 can be shown as 5 + 5 + 5 and skip counting can help to get the answer too.
- Number Line - Another way to demonstrate multiplication is using a number line and showing jumps. 4 X 2 can be shown with 4 jumps of 2, skip counting 2,4,6,8. Quickly some kids notice that the numbers can be reversed and 2 jumps of 4 will give the same answer but quicker.
- Arrays - drawing boxes or objects in equal rows helps students see multiplication in a concrete way. 3 X 3 can be drawn in a square 3 boxes high and 3 boxes long.