# Number Sense

The philosophy behind Number Sense is that students should learn how to do mental math quickly and accurately:
• Because of the emphasis on mental math, no calculators or scratch paper are allowed. Scratchwork on the test is highly discouraged because successful Number Sense students often find that it is faster to do all calculations in their head. In addition, students in Texas should note that when they move to middle school and high school, the rules regarding scratchwork are MUCH stricter, so it's in their best interest not to develop a habit of working their answers out on the test that could harm them later.
• Because of the emphasis on speed, students are given only 10 minutes to complete as many of the 80 problems as they can.
• Because of the emphasis on accuracy, answers must be completely legible, exactly correct, entirely numerical, fully computed, and in simplest form (see below). If the form of an answer is specified in the problem, the answer must adhere to that form.
The student's intended answer for a given problem is interpreted to be the entirely numerical portion of anything written in the answer blank that is not marked out or erased. Note that, in contrast to other Number Sense rules you may have seen, markouts or erasures are not counted as incorrect in this version of the test, but nothing that is marked out or erased will be counted as the student's answer either. The "entirely numerical" portion of an answer will consist of any digits (0-9), decimal points, commas, negative signs, and pi symbols (π) that appear in the answer blank without being marked out or erased. Unless the specific form of an answer is specified in a problem, the following forms of an answer are equivalent if they can be expressed exactly and in simplest form using only the approved symbols: decimals, mixed numbers, and improper fractions. Every tenth problem is an estimation problem, for which the answer must be an integer and must be within 5% of the exact answer to earn credit. Problems that ask for an answer in dollars must include a decimal point and be precise to the exact cent. Thus if the answer is twelve dollars the correct answer is 12.00, not 12 or 12.0 (in this context 12.00 is considered simplest form because the question deals with currency that is defined to require two decimal places). Note that there was a major revision to the rules at the beginning of the 2013-2014 season, so tests from earlier years may have symbols in the answer keys that do not conform to the guidelines listed here.

At the end of 10 minutes, the tests are collected and each student's answers are graded, starting from question 1 and proceeding to the last question for which any intended answer is visible in the answer blank (i.e. the last question attempted). Each answer blank with a correct answer and nothing else nets the student 5 points, and each answer blank without a correct answer or with anything other than a correct answer nets the student -4 points (in particular it doesn't matter whether a wrong number is in the blank or nothing at all is in the blank; neither one of these is a correct answer). Note that problems beyond the last question attempted are not counted against the student.

Below are SOME examples of what would and would not be counted correct on Number Sense for a problem where the question asks the student to divide 600 by 800 but the form of the answer is not specified:

 Answer Outcome Notes 3/4 CORRECT this is one of only two possible answers that would be accepted at Texas middle and high school contests .75 CORRECT this is one of only two possible answers that would be accepted at Texas middle and high school contests 0.75 CORRECT this is considered a fully simplified equivalent to the preferred answer of .75 0,75 CORRECT this is allowed as some students use commas in place of decimal points .75 miles per hour CORRECT although this is not entirely numerical, the entirely numerical portion is .75, which is correct .750 INCORRECT this is not in simplest form and conveys information that is not equivalent in every way to .75 6/8 INCORRECT this is not in simplest form 600/800 INCORRECT this is not in simplest form 75% INCORRECT this is not entirely numerical, as % is not an approved symbol; according to the rules above, this answer would be interpreted as 75, which is not correct 3:4 INCORRECT this is not entirely numerical, as : is not an approved symbol; according to the rules above, this answer would be interpreted as 34, which is not correct 3 ÷ 4 INCORRECT this is neither entirely numerical nor fully computed; according to the rules above, this answer would be interpreted as 34, which is not correct three fourths INCORRECT this is not entirely numerical; according to the rules above, this answer would be interpreted as a non-answer, which is not correct 6/8 = 3/4 INCORRECT this is not entirely numerical (note that if the student scratches out the "6/8=" part and leaves the 3/4, it would be counted correct); at best, this response looks like the student intended to give two answers to the question, which is not allowed 42 INCORRECT this is not exactly correct

Finally, please note that we solicit the help of volunteer graders at our contests, and they sometimes make mistakes. We are always happy to correct students' scores in our database if we are notified of grading errors in a timely fashion according to the policies outlined on our results page. In the event that an incorrect response is marked correct in violation of these rules, that does not obligate mathleague.org to accept any similarly incorrect responses at future contests. Students are required to be familiar with the current version of the rules regardless of what the rules were in the past or how their tests were graded in the past.

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