Here it is. From an elementary school math test.
The math problem in the picture below deals with Reasonableness. In mathematics, reasonableness a rough and easily mentally-calculated estimate, often referred to as a "ballpark estimate." It can help to predict the numerical range the final answer should fall within. For example, if the given problem is to determine the sum of 23 plus 76, it can be estimated that the final and precise answer will be somewhere close to 100 because the known calculation of 25 plus 75 equals 100 and is close to the given problem 23 plus 76. Elementary students are often taught to check the reasonableness of their final answers by comparing them to a ballpark estimate. If the ballpark estimate is 100, and they do the math and calculate the answer to be 783, they can easily see their calculation is unreasonable, as two numbers less-than 100 cannot be added together to equal a number greater than 200, much less greater than 700.
Expediters deal with mathematical reasonableness every day, be it a ballpark estimate of the actual travel time for a 500 mile load to the amount of fuel required for a given run. We come up with some reasonable estimates without having to use precise calculations.
Kids gets a introduction to fractions and the terminologies in the first and second grade, and by the third grade they move on to comparing fractions (less than, greater than) and then late in the third grade and into the fourth grade they get into adding and subtracting fractions with the same and then different denominators. The problem below is almost certainly from the third grade.
As with all math problems, the premise is stated giving you the parameters with which to calculate or estimate the solution.
The facts:
1) Marty are 4/6 of his pizza.
2) Luis are 5/6 of his pizza.
3) Marty ate more pizza than Luis.
The solution to estimate with mathematical reasonableness:
How is that possible?
It's difficult to make out the written answer, but this third grader took the facts as presented and reasoned the correct answer, which the teacher marked WRONG.
"Marty's pizza is bigger than Luis's pizza."
We know for a fact that Marty ate 4/6 of his pizza. And we know for a fact that Luis ate 5/6 of his pizza. And we know for a fact that Marty ate more pizza than Luis. The ONLY way that is possible is for 4/6 of one pizza to be more pizza than 5/6 of another pizza. Marty's pizza was bigger to begin with than was Luis' pizza. Even the third grader could deduce that.
If the premise had stated the two pizzas were the same size and then asked the question "Who ate more pizza?" then mathematical reasonableness determines that whoever ate the 5/6 ate more. Duh.
Instead of the teacher being able to recognize the astonishingly poor English wording of the question to begin with and giving the kid credit for (A) being smart enough to figure out the correct correct answer, and (B) for thinking outside the box, she remained inside her own little "5/6 is greater than 4/6" box.
I weep for the future of America, because we have morons teaching our children.
(Incidentally, mathematical reasonableness not a concept that was invented by Obama or the Common Core. Sorry.)
The math problem in the picture below deals with Reasonableness. In mathematics, reasonableness a rough and easily mentally-calculated estimate, often referred to as a "ballpark estimate." It can help to predict the numerical range the final answer should fall within. For example, if the given problem is to determine the sum of 23 plus 76, it can be estimated that the final and precise answer will be somewhere close to 100 because the known calculation of 25 plus 75 equals 100 and is close to the given problem 23 plus 76. Elementary students are often taught to check the reasonableness of their final answers by comparing them to a ballpark estimate. If the ballpark estimate is 100, and they do the math and calculate the answer to be 783, they can easily see their calculation is unreasonable, as two numbers less-than 100 cannot be added together to equal a number greater than 200, much less greater than 700.
Expediters deal with mathematical reasonableness every day, be it a ballpark estimate of the actual travel time for a 500 mile load to the amount of fuel required for a given run. We come up with some reasonable estimates without having to use precise calculations.
Kids gets a introduction to fractions and the terminologies in the first and second grade, and by the third grade they move on to comparing fractions (less than, greater than) and then late in the third grade and into the fourth grade they get into adding and subtracting fractions with the same and then different denominators. The problem below is almost certainly from the third grade.
As with all math problems, the premise is stated giving you the parameters with which to calculate or estimate the solution.
The facts:
1) Marty are 4/6 of his pizza.
2) Luis are 5/6 of his pizza.
3) Marty ate more pizza than Luis.
The solution to estimate with mathematical reasonableness:
How is that possible?
It's difficult to make out the written answer, but this third grader took the facts as presented and reasoned the correct answer, which the teacher marked WRONG.
"Marty's pizza is bigger than Luis's pizza."
We know for a fact that Marty ate 4/6 of his pizza. And we know for a fact that Luis ate 5/6 of his pizza. And we know for a fact that Marty ate more pizza than Luis. The ONLY way that is possible is for 4/6 of one pizza to be more pizza than 5/6 of another pizza. Marty's pizza was bigger to begin with than was Luis' pizza. Even the third grader could deduce that.
If the premise had stated the two pizzas were the same size and then asked the question "Who ate more pizza?" then mathematical reasonableness determines that whoever ate the 5/6 ate more. Duh.
Instead of the teacher being able to recognize the astonishingly poor English wording of the question to begin with and giving the kid credit for (A) being smart enough to figure out the correct correct answer, and (B) for thinking outside the box, she remained inside her own little "5/6 is greater than 4/6" box.
I weep for the future of America, because we have morons teaching our children.
(Incidentally, mathematical reasonableness not a concept that was invented by Obama or the Common Core. Sorry.)
