standard_description: Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) ^( )Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
problem_activity: Problem 1
A quadratic equation is shown below.
$${x^2=(2x-9)^2}$$
a.  Solve this equation by expanding and then factoring.
b.  Solve this equation by taking the square root of each side.
Problem 2
A physics teacher put a ball at the top of a ramp and let it roll down toward the floor. The class determined that the height of the ball could be represented by the equation
$${h=-16t^2+4}$$
, where the height,
$$h$$
, is measured in feet from the ground and time,
$$t$$
, is measured in seconds.
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What do you notice about the structure of the quadratic expression in this problem?
In the equation, explain what the
$$4$$
represents.
Determine the time it takes for the ball to reach the floor. Interpret your solution(s) in context of the problem.


aligns: no