The Distributive Law the Case of Who Flew the Coop

The Distributive Law – The Case of Who Flew the Coop?

Farmer Brown has a rectangular poultry coup filled with chickens and ducks. When he counts them he sees that he has more ducks than chickens. One day he observes that they are starting to fight each other, so he decides to put a fence across the yard to separate them. The dimensions of the coop are shown below. How much area does each get? 18 ft

10 ft 8 ft

How much area is the entire coop?

Is it true that the area of the entire coop is equal to the sum of the two smaller areas? Introducing the Distributive Law

Ducks + Chicks = Everyone

8 x 10 + 8 x 8 = 8 x ( 10 + 8 ) The point is, it don’t matter which way you go

What is the rule? And Now the Pigs and the Cows

Now farmer Brown has the same problem with his pigs and cows. He sees more cows than pigs. To stop them from fighting each other, he decides to put a fence across the yard to separate the cows from the pigs. The dimensions of the corral are shown below. How much area does each get?

45 yds

12 yds

40 yds 5 yds

Determine the areas for each and the entire area.

Make a number sentence that shows the use of the distributive law. Tricks with the Distributive Law – Mental Multiplication

Trick Time: What is 8 x Break 42 into two friendly numbers 42?

8 x 42 = 8 x ( _____ + ______)

The beauty of the distributive law!

How about 9 x 81 ? How about 15 x 22 ?

Friendly numbers for 81 = ____ + ____ Friendly numbers for 22 = ____ + ____

Now use the Distributive law: Now use the Distributive law: So, How Does the Distributive Law Help You? In Science Class, Justus, Nerisa and Alexis were finishing their measurement activity. They had to determine the number of ounces of soup in a case of 12 soup cans. Each can weighed 1 pound or 16 ounces. So they knew they had to multiply 12 cans times the 16 ounces. As Nerisa started to write out the multiplication problem, Alexis yelled “I know the answer, I did it in my head.” “How”, they asked? “That Dissed law”, she replied.

So how did she do it?

More Tricks with the Distributive Law

Trick Time: What is 9 x Break 29 into two friendly numbers 29?

9 x 29 = 9 x ( ______)

Is this not the distributive law?

How about 5 x 38 ? How about 7 x 42 ?

Friendly numbers for 38 = ______Friendly numbers for 42 = ______

Now use the Distributive law: Now use the Distributive law: