standard_description: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
problem_activity: Problem 1
Four expressions are shown in the chart below. For each one, write all the ways to read the expressions that you can think of.
{"table": [{"_attributes": {"align": "Center", "class": ["table", "table-bordered"], "style": "width:70%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "strong": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${x+2}$$"}]}]}, {"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${x-2}$$"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "p": [{}, {}, {}]}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${2x}$$"}]}, {"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "strong": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${x\\div2}$$"}]}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "p": [{}, {}, {}]}, {}]}]}]}]}
Problem 2
Two tape diagrams are shown below. The shading indicates subtraction.
[IMG]
Statements a–h below can be used to describe either Diagram 1 or Diagram 2. Match each statement to one of the diagrams.
a.   The difference of
$$4$$
and
$$m$$
b.   The difference of
$$m$$
and
$$4$$
c.
$$4$$
less than
$$m$$
d.
$$m$$
less than
$$4$$
e.
$$4$$
less
$$m$$
f.
$$m$$
less
$$4$$
g.   Subtract
$$4$$
from
$$m$$
h.   Subtract
$$m$$
from
$$4$$
Problem 3
For each verbal statement, write the algebraic expression it describes.
a.   The sum of
$$e$$
and
$$f$$
subtracted from
$$g$$
b.
$$g$$
less than the sum of
$$e$$
and
$$f$$
c.
$$g$$
more than twice
$$f$$


aligns: no