standard_description: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.
problem_activity: Problem 1
a.   Write two equivalent expressions to represent the total area of the rectangle shown. Justify that your two expressions are equivalent.
[IMG]
b.   Expand the expression below using a rectangular array.
$${\frac{1}{3}(9x-12y-18)}$$
Problem 2
a.   What could be the missing dimensions of the rectangular array? Which set of dimensions uses the greatest common factor of the two terms?
[IMG]
b.   Factor the expression below using a rectangular array. Use the greatest common factor as the representation of the width.
$${24d-8e+6}$$
Problem 3
The table below includes expressions that are written in expanded form and in factored form. Complete the table. Use rectangular arrays as needed.
{"table": [{"_attributes": {"align": "center", "class": ["table", "table-bordered"], "style": "table-layout:fixed; width:50%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "strong": [{"_value": "Factored Form"}]}, {"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "strong": [{"_value": "Expanded Form"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$3(x-14y)$$"}]}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$2x+3x$$"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{3}{4}(8a+16b)$$"}]}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$24m+8n-12p$$"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{1}{2}\\left(\\frac{1}{3}x-8y+\\frac{2}{3}z\\right)$$"}]}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$5xy+15y$$"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$2x(-3+y)$$"}]}, {"_attributes": {"style": "text-align:center"}}]}]}]}]}


aligns: no