Primary students (K-2): number recognition, counting, shapes, repeated addition, area
Intermediate students (3-5): patterns, multiplication, area, array model of multiplication
A visual way to represent multiplication as repeated addition is through rectangular arrays: 3 + 3 + 3 + 3 is the same as 4 x 3. Multiplication is a much more efficient way to add the same number multiple times. For this table, I just entered the length and width of different rectangles. These rectangles were also represented visually next to the table so that students could make the connection between the numbers in the table and the length and width of the rectangles. Looking for patterns in these numbers can help students discover the formula for the area of a rectangular shape: L x W = A.
" If you look at the two left columns and multiply them together you get the number on the right."
"They're all quadrilaterals."
"Square units."
"They have right angles."