standard_description: Apply properties of operations as strategies to add and subtract. (Students need not use formal terms for these properties.) Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)
problem_activity: Problem 1
A balance is shown below.
[IMG]
a.   Describe how you can use the balance to find the value of
$$x$$
.
b.   Write an equation to represent the situation shown in the balance.
c.   Use the equation to model the actions you did in part A with the balance.
d.   Repeat parts A–C using the balance shown below.
[IMG]
Problem 2
Yoshiro has a new puppy. She decides to create an enclosure for her puppy in her backyard. The enclosure is in the shape of a hexagon, with one pair of opposite sides running the same distance along the length of two parallel flowerbeds. A sketch of the enclosure is shown below.
[IMG]
If the perimeter of the enclosure is 137 feet, what is the length of each side that runs along the flowerbed, labeled
$$n$$
in the diagram? Write an equation to represent the situation, and solve using algebraic properties.
Problem 3
Solve the equations:
a.
$${12(x-2)=72}$$
b.
$${- {1\over3}x+4=-2}$$
c.
$${5.6-2p=13}$$


aligns: no