**Mathematics N7.1 Nature of Division Rubric**

**Characteristic / Level**/ 1 / 2 / 3

**What it means to be divisible.**/ Cannot explain what division or divisibility mean. / Understands division as equal sharing, but cannot explain why some whole numbers are not divisible by other whole numbers. / Describes division as equal sharing or partitioning.

Recognizes and explains the meaning of a remainder.

Can explain what it means to say a whole number is divisible by another whole number.

**Relating division to factors.**/ Does not know how to relate division to multiplication. / Can identify factors by using division, but cannot explain what a factor is. / Explains whether a number is a factor of a whole number by relating the problem to division of the two numbers.

Explains the relationship between divisibility and factors.

**Rules for divisibility.**/ Has no strategies for determining whether one whole number is divisible by another. / Has memorized a few divisibility rules, but generally resorts to doing the entire division to determine divisibility.

Sometimes when they do the entire division to determine divisibility they forget that the focus was on divisibility and not on finding the quotient. / Has created own strategies and rules for determining the divisibility of numbers and can provide examples to verify the strategies and rules.

**Division by zero.**/ Writes the answer as being the number that was being divided by zero. / Believes that dividing by zero gives a quotient of zero.

Cannot provide an explanation (oral or symbolic) for the conclusion. / Knows that division by zero is undefined and can explain what this means.

**Mathematics N7.1 Nature of Division Rubric (con’t)**

**Characteristic / Level**/ 1 / 2 / 3

**Relating Numbers by their Factors.**/ Identifies common digits for two given whole numbers rather than common factors. / Can identify one common factor for two given whole numbers.

Or

Unsure how to verify that a given factor is common to two whole numbers. / Identifies all common factors for two or more whole numbers.

Is able to explain the meaning of the term common factors and can verify whether a given whole number is a common factor for two or more other whole numbers.

Nature of Division Rubric.doc 1