Math Misconceptions

3.NF.1-3

Look closely at errors in students’ work (formative assessment) to help you reflect

and make instructional decisions to suit all students’ needs.

One of the most common misconceptions that students have when they begin to work with fractions is that they only count pieces in a whole rather than paying attention to the fact of whether or not those pieces are equal pieces to a whole. This is where teachers need to be very careful and explicit in having students experience and understand that equal pieces are necessary when partitioning a shape or number line. Equal representations of space in a shape and equal representations of space on a number line (the iterations) show that a student is attending the idea of fractions being made up of equal pieces. Be certain that the students are not just counting parts. MISCONCEPTION:

WHAT TO DO:

One misconception students believe is that fraction numerators and denominators are treated as separate whole numbers. An important step in mathematical development is that students come to see a fraction a/b as one number, even though it is written using two whole numbers, a and b. Understanding that a fraction is a numerical value is essential at this grade level. Students must see a fraction as one number, or they will not be able to place fractions on a number line. They also must attend to the relationship between the unit and the whole. MISCONCEPTION:

WHAT TO DO:

 

A very common student misconception is that with fractions, the largest denominator is the largest fraction. Unit fractions have a numerator of one, and the denominator represents the total number of equal pieces that it takes to represent that whole. Students assume this is always true because with whole numbers, they learned that a 6 is larger than a 3. The best way to eliminate this misconception is to allow students to work with math manipulatives. This allows students to visualize denominators and numerators broken down into their basic parts. Using models such as circles or rectangles, students may easily understand that in order for the whole to have more pieces, the pieces must be smaller. MISCONCEPTION:

WHAT TO DO: