standard_description: Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
problem_activity: Task
The first three steps of two visual patterns are shown below.
[IMG]
[IMG]
The number of tiles in step $n$ of Pattern D is defined by $d(n)=(n+3)^2$. The number of tiles in step $n$ of Pattern E is defined by $e(n)=(n+1)^2-2$.
For each pattern, decide whether there is a step with 167 tiles in it. If so, which step is it? If not, explain how you know.
For each pattern, decide whether there is a step with 169 tiles in it. If so, which step is it? If not, explain how you know.
Describe and justify the steps for solving the following equation for $x$: $$a(x-h)^2=k$$


aligns: no