few_shots: 
Example:
Concept/skill: 
Analyze and solve pairs of simultaneous linear equations.

Problem/activity:
Problem 1
The table below contains single equations in a single variable, single equations in two variables, and pairs of simultaneous equations in two variables. Check the appropriate box to show whether there is no solution, exactly 1 solution, or if there is an infinite number of solutions.
{"table": [{"_attributes": {"align": "center", "class": ["table", "table-bordered"], "style": "table-layout:fixed; width:70%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "strong": [{"_value": "No solution"}]}, {"_attributes": {"style": "text-align:center"}, "strong": [{"_value": "Exactly 1 solution"}]}, {"_attributes": {"style": "text-align:center"}, "strong": [{"_value": "Infinite number of solutions"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${9=4x+7}$$"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${y=3y+5}$$"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${y={x\\over2}}$$"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"p": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${3x+6y-9=0}$$"}]}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"p": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${x=y}$$"}]}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${1.25x=1.25y}$$"}]}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"p": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${9.9=6x+8y}$$"}]}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${9x=2.5y-8.8}$$"}]}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"p": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${11x-2y=1.5}$$"}]}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${11x-2y=2.5}$$"}]}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {}]}]}]}]}
Problem 2
Kim has a small container and a large container as shown.
[IMG]
It takes 16 of the small containers to fill the large container. Three small containers leave 1.95 gallons of space in the big container.
What is the size of each of the two containers?


Answer: 
Yes. The last three rows of the table in the first problem involves solving pairs of simultaneous linear equations. The second word problem can also be represented as two simultaneous linear equations.

Now, assess whether the following problem or activity is 'aligned' with the given Common Core standard in Mathematics.

shot_info: fl_problem_001392_pos_0

8
standard_description: Use place value understanding to round whole numbers to the nearest 10 or 100.
problem_activity: Problem 1
Ms. Holcombe buys 850 snacks for Monday and Tuesday. After handing out one snack to each student on Monday, she wants to make sure there will be enough snacks on Tuesday without having to count all of them. Since there are 438 students at Match Community Day, she says, "There are about 400 students at MCD. That means we have about 450 snacks left after handing out Monday’s snack. That’ll be enough for Tuesday!"
a.   Explain why Ms. Holcombe is not correct.
b.   How could Ms. Holcombe have used rounding to estimate more accurately?
c.   What is the exact number of snacks leftover for Tuesday?
Problem 2
Millie has 403 pennies in her piggy bank. Paulina has 185 pennies in her piggy bank. How many more pennies does Millie have than Paulina? Solve. Then assess the reasonableness of your answer.
Problem 3
Ms. Dowling’s class knows there are 149 students in Grades 11 and 12, and 317 students at Match High School in total. Three students are trying to figure out about how many students are in Grades 9 and 10 at Match High School. Here’s how each of them computed:
{"table": [{"_attributes": {"align": "Center", "class": ["table", "table-bordered"], "style": "table-layout:fixed; width:50%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "strong": [{"_value": "Student"}]}, {"_attributes": {"style": "text-align:center"}, "strong": [{"_value": "Computation"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "Matt"}, {"_attributes": {"style": "text-align:center"}, "_value": "300 - 100"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "Beatriz"}, {"_attributes": {"style": "text-align:center"}, "_value": "320 - 150"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "Alicia"}, {"_attributes": {"style": "text-align:center"}, "_value": "317 - 100"}]}]}]}]}
Whose estimate is closest to the actual solution? How do you know?


aligns: yes