Fractions
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