We learned how to find the product of a three-digit number and a two-digit number. We first represented the products with diagrams. The diagrams help us break the product into parts by place value.

Example:

This diagram breaks apart the product by place value. To find the product of , we multiply and then add all the partial products.

Then we learned a new algorithm to multiply numbers, the standard algorithm for multiplication.

Example:

multiply. four hundred twelve times 32. 5 rows. First row: four hundred twelve. Second row: multiplication symbol, 32. Horizontal line. Third row: eight hundred twenty four. Fourth row: plus twelve thousand three hundred sixty. Horizontal line. Fifth row: thirteen thousand one hundred eighty four.

Partial products are organized in a different way. 824 represents the partial product for , and 12,360 represents the partial product for .

We noticed that sometimes we need to compose a new unit when we use the standard algorithm. We represent that unit with a number over the place value to the left of the digit we are multiplying. We may have to compose more than one new unit.

multiply. two hundred sixteen times 43. 5 rows. First row: two hundred sixteen. Second row: multiplication symbol, 43. Horizontal line. Third row: six hundred forty eight. Fourth row: plus eight thousand six hundred forty. Horizontal line. Fifth row: nine thousand two hundred eighty eight

The 1 above the 1 in 216 represents the ten from the product . The 2 represents 2 hundreds from the product .