standard_description: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.
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