Welcome to 3rd Grade Math!

The Big Dinner - Multiplication with the Ratio Table (January 23rd - February 3rd)

This investigation addresses the following "big ideas:"

• introducing multiplication
• the distributive property of multiplication over addition:  this means that students know that factors can be broken up and distributed to make partial products, which can then be added together to get the product of the original factors.  This is the reason that the traditional multiplication algorithm works!  For example: 4 x 19 can be solved by splitting 19 into 10 and 9.  Then multiply 4 x10 and 4 x 9.  Adding those products, 40 + 36 produces the answer to 4 x 19.
• the commutative property of multiplication: 2 x 4 = 4 x 2
• proportional reasoning: the genuine hallmark of multiplicative thinking!  For example, if we know that 1 car needs 4 tires, then 2 cars need 8 tires, and so on.  We use the ratio table as strategy throughout this unit in orde r to develop this thinking.

Strategies students might use throughout this unit:

• repeated addition
• skip-countinng
• partial products
• ten-times
• t-chart or ratio table
• doubling and halving