# Scenario: Finding three fractions that adds up to one whole

## Context

The teacher has five years teaching experience. The lesson is halfway through grade seven. The competence goals in the Norwegian curriculum are not formulated for each year, but are given after the completion of grade 4, 7 and 10. The students have only met fractions like ½ and ¼ used in everyday situations prior to fifth grade. The competence goals regarding fractions after grade seven focuses on calculations using positive and negative fractions, and placing fractions on a number line.

In this case the teacher asks the students in plenary of suggestions to a task that many found difficult. The task was to find three fractions that added together was equal to one whole. One student suggested 6/12, 1/3 and 1/6, and the teacher wrote 6/12+1/3+1/6 on the blackboard. Then this followed:

SM: Yes (confirming that the teacher had written the correct fractions).

T: Yes. And how did you do now?

SM: (impossible to hear the start)… with four.

T: You expanded with four, because you wanted to have a common denominator (writes x4 behind numerator and denominator of the fraction 1/3). Yes.

SM: And then we get four twelfths.

T: Yes, if we now just write below… six twelfths (writes 6/12 on a new line below 6/12+1/3+1/6) plus four twelfth (writes +4/12 below 1/3). Yes.

SM: And then one sixth multiplied by two

T: Yes. Above and below when we expand. Yes. (writes x2 behind numerator and denominator of the fraction 1/6).

SM: And then I got two twelfths.

T: Yes… (writes +2/12 below 1/6). And then we add these (pointing at 6/12+4/12+2/12), six plus four plus two twelfths equals twelve twelfths (writes 6+4+2 as numerator and 12 as denominator on a new fraction, then =12/12=1)… and that equals one whole. Great.

The same pattern was repeated four times with different student suggestions.