#### Stop Saying…

Sometimes we say things in order to help students **do** the math rather than **understand** the math. Those statements can create misconceptions and confusion when the statements no longer hold true at later grades.

#### “Whatever you do to the top, you do to the bottom.”

##### When does it fall apart?

A student is asked to find an equivalent fraction for 3/5 and ends up with 4/6. The student has added 1 to the top and 1 top the bottom.

##### Why?

This statement applies to a limited number of situations when working with fractions. Students will over-generalize this and apply it to all operations.

##### Instead say:

We do not have an appropriate replacement for the statement at this time.

#### “Reduce the fraction 2/6.”

##### When does it fall apart?

If you were told you needed to reduce your expenses or your paycheck is being reduced, how would you react?

##### Why?

Reducing implies the fraction is getting smaller. 1/3 is not smaller than 2/6. They are equivalent.

##### Instead say:

“Simplify the fraction.” or “Rename it in its simplest form”.

#### “Top number and bottom number.” (in reference to numerator and denominator)

##### When does it fall apart?

Students who see the numerator and denominator as numbers rather than digits significantly struggle when working with the length model (number lines).

##### Why?

Prior to fractions, every time students see a number / numeral, it has represented that number. In whole numbers, the number has a value of its own. (ie: 2 = 2 things). “Fraction size is relative. A fraction by itself does not describe the size of the whole or the size of the parts. A fraction tells us only about the relationship between the part and the whole.” Source

##### Instead say:

Numerator and demonimator