Question

Lucas is solving this problem.

374
× 510

What are the partial products Lucas will need to solve the problem?

Answer 1

please help

Answer 2

this is my first time teaching this partial products method so bear with me

you would split 374 into its components 300 + 70 + 4
then you would split 510 into its components 500 + 10

then you would start with 300 and calculate the products with each of the two components of 510

Answer 3

so your first two partial products would be 300*500 and 300*10

you would then repeat this process with 70, and then 4

Answer 4

so basically the multiplication follows this pattern:

Answer 5

Although the partial products algorithm is based on the distributive property, students first learning multiplication this way would most likely find the distributive property concept more confusing.

here's a cool way you can think about it:

Answer 6

This rectangle idea is based on thinking about multiplication as grouping
that is 510 times 374
is
"510 groups of 374"


Here is a simpler example to show how this grouping = multiplication results in rectangles:
3 x 4 = 3 groups of 4
or
= 4 groups of 3

Answer 7

In other words, the 500 x 300 box in my first drawing is really just 500 groups of 300 circles, but represented with a rectangle to show the space it takes up (since it is tiring to draw that many circles)