Teaching 2-digit by 1-digit multiplication and teaching 3-digit by 1-digit multiplication
Concrete: students use a place-value chart and physically make groups with base-10 blocks or with tokens that represent ones, tens, hundreds, thousands, ten-thousands, and hundred-thousands. When there are more than 9 tokens in a place, an “exchange” and “regrouping” occurs.
Pictorial: students make groups with place value charts and draw circles representing ones, tens, hundreds, etc. instead of using the physical tokens. Students make exchanges and regroup the same as in the concrete stage.
Abstract: students use a place-value chart and write numbers instead of drawing circles. Finally, they use the traditional algorithm. *Note: it is very important that students are able to UNDERSTAND the multiplication process. They should NOT just memorize the steps. Students should be able to explain and justify every step.
Place-value chart (concrete and pictorial)
23 x 2 means 2 groups of 2 tens and 2 groups of 3 ones
Students put all the tokens together to get the product: 23 x 2 = 46
Traditional algorithm - with place-value chart and without place-value chart (abstract)
23 x 2 = ?