Examples in the fourth-grade scoring guide include:Imagine how these kids will be after a few more years if they get used to getting half credit just for knowing that subtraction is involved in figuring out change or that multiplication is involved in figuring out the books in boxes problem.

* A kid who answers that a 2-foot-long skateboard is 48 inches long gets half-credit for adding 24 and 24 instead of the correct 12 plus 12.

* A miscalculation that 28 divided by 14 equals 4 instead of 2 is "partially correct" if the student uses the right method to verify the wrong answer.

* Setting up a division problem to find one-fifth of $400, but not solving the problem -- and leaving the answer blank -- gets half-credit.

* A kid who subtracts 57 cents from three quarters for the right change and comes up with 15 cents instead of 18 cents still gets half-credit.

* A student who figures the numbers of books in 35 boxes of 10 gets half-credit despite messed-up multiplication that yields the wrong answer, 150 instead of 350.

These questions ask students to show their work. The scoring guidelines, called "holistic rubrics," require that points be given if a kid's attempt at an answer reflects a "partial understanding" of the math concept, "addresses some element of the task correctly," or uses the "appropriate process" to arrive at a wrong solution. Despite flubbing the answer, students can get 1 point on a 2-point problem and 1 or 2 points on a 3-pointer.

For a contrast, check out this video from Uncommon Schools of these seventh grade students being called on to answer math questions.That's what students can do if you set high expectations for them instead of giving them partial credit for figuring out that a division problem involves division.