Decomposing Arrays and Multiples of Ten

Our students' knowledge of multiplication has come so far in so little time. We worked on finding the total number of squares (or area) in an array. An array is a multiplication model used to work toward independence and mental math strategies. 

Students discovered that by decomposing the array into smaller arrays, they could more easily find the product. We also encouraged them to record using correct algebraic notation. You'll notice in this piece of student work that 4 x 3, said, "four groups of three," can be decomposed into (2 x 3) + (2x3) = 12.

More recently, we've been exploring larger numbers, too, and recognizing relationships. The chart below was created by my co-teach partner, Ashley, during a lesson to emphasis why students have been seeing the pattern of a 0 in the ones place. Zeros aren't merely added to the ones place, rather they are in the ones place because they are a multiple of 10. Multiples of 10 have a 0 in the ones place. A student could see that 5 x 60 = 5 x 6 x 10. This helps them see why the pattern occurs.