What is the
Connection between
the Distributive
Property and the
Order of Operations?
“Distribute”
Definition:
multiplying a sum by a number gives the same result
as multiplying each addend by the number and then
adding the products together
Example:
5 × (2 + 3) = 5 × 2 + 5 × 3
Arrays
An Area View of Distribution
Distribution Views Connected
What is the role or
purpose of grouping
symbols?
What would you do first?
3+7•5
How much money would Luz
have if she had 3 pennies and
7 nickels?
How much money would the
students have if Renardo has
3 nickels and Kirk has 7
nickels.
3+7•5
(3 + 7) • 5
Why Distribute?
Why not: 4 × (2 + 3) = 4 × 5 ?
Why: 4 × (2 + 3) = 4 × 2 + 4 × 3?
The Museum of Mathematics offers a $3 student
discount on admission.
Prices for 2015, when the trip will be taken, are not posted
yet. So, use A to represent the regular admission price. Write
two equivalent expressions for the total price for the 25
students in class to go to the museum. One expression
should use parentheses and the other should not.
Now you can take a look at different possible costs.
Evaluate the expression if the price for admission is $27.
If the cost for the whole class is $300, what is the price of
admission at the museum?
Mental Math uses the Distributive Property
46
x 35
46
x 35
230
+1380
1610
5(40 + 6)
40 + 6
x
5
30
+ 200
230
40 + 6
x 30 + 5
5(40 + 6)
30
200
30(40 + 6)
180
+ 1200
1610
Birthday Cupcakes
Blessing baked chocolate cupcakes
that filled 2 muffin tins with 6 spots
each and yellow cupcakes that
filled 3 muffin tins with 6 spots
each. Once they were cooled and
frosted, she arranged them evenly
on 3 plates.
Holiday Baking
Quantey baked three dozen
frosted sugar cookies and six
dozen double chocolate mint
cookies. The family ‘sampled’ 15
of the cookies before she got to
freeze them for Christmas.
Halloween Candy
Eight nursing students and fifteen
construction students are each
going to get 2 candies. Their
teachers, Frank and Marcel, will get
one each.
“Mathematics is not
just solving for x; it’s
also figuring out why!”
–Arthur Benjamin
revisit
What is the
Connection Between
the Distributive
Property and the
Order of Operations?