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A grid is drawn up, and each cell is split diagonally. The two multiplicands of the product to be calculated are written along the top and right side of the lattice, respectively, with one digit per column across the top for the first multiplicand (the number written left to right), and one digit per row down the right side for the second multiplicand (the number written top-down).
If a positional numeral system is used, a natural way of multiplying numbers is taught in schools as long multiplication, sometimes called grade-school multiplication, sometimes called the Standard Algorithm: multiply the multiplicand by each digit of the multiplier and then add up all the properly shifted results.
Opponents of inquiry-based methods such as the three-part lesson state that students are not learning the basics such as multiplication tables. In Ontario, Canada, where the Ministry of Education has promoted the three-part lesson, the curriculum was changed in the late 1990s in favour of "problem solving based on open-ended investigations ...
Bar modeling is a pictorial method used to solve word problems in arithmetic. [21] [25] These bar models can come in multiple forms such as a whole-part or a comparison model. With the whole-part model, students would draw a rectangular bar to represent a "whole" larger quantity, which can be subdivided into two or more "parts."
This is the "grid" or "boxes" structure which gives the multiplication method its name. Faced with a slightly larger multiplication, such as 34 × 13, pupils may initially be encouraged to also break this into tens. So, expanding 34 as 10 + 10 + 10 + 4 and 13 as 10 + 3, the product 34 × 13 might be represented:
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