# Scenario: Teaching of fractions

## Country: Norway

## Grade (student age): Year 5 (age 10-11)

## Contributed by: Ove Gunnar Drageset, University of Tromsoe, Norway

## Context

The teacher has 35 years of experience as a teacher. The lesson is taught mid-way through the school year. 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 competence goals regarding fractions after grade seven focus on calculations using positive and negative fractions, and placing fractions on a number line.

The teacher writes 1/10 on the blackboard and asks if someone knows another fraction of equal size. A student answers 10/100, and the teacher writes ‘=10/100’ to the right of 1/10. Then the teacher chooses to illustrate this by using base ten blocks, one hundred square, one ten pole and one single block (as illustrated below).

T: How many such single blocks are there in this one (holding up the pole of ten bricks).

S1: Ten

T: Yes, it is ten. So this one is one of the ten (holding up the single block). True? It is one of these ten. It is one tenth… It is one tenth.

T: How many such goes across this one (puts the ten pole on one of the columns of the hundred square, then simulates counting by moving it one column at a time a few steps)

S2: Ten

T: Then we also get ten. So this is one of ten such ones (demonstrates that the tens pole is one of the ten columns on the hundred square by moving the pole from one column to the next all the way). So ten such ones are equal to the whole square. True? Like this, one tenth.

Then the teacher continues by trying to explain the connection between one tenth as one of ten blocks and one tenth as one of ten columns, and pointing out that one of ten columns is also ten of hundred blocks. This explanation is fragmented and by no means perfect, but the aim seems clear.

Knowledge Quartet Coding Commentary

## Contributed by: Ove Gunnar Drageset, University of Tromsoe

## Knowledge Quartet Dimension: Transformation

## Knowledge Quartet Code: Use of instructional materials (UIM)

## Scenario: Teaching of fractions

The answer is already established (with the teacher writing 1/10=10/100 on the blackboard). Instead of finding the answer, the instructional material is used to explain the reason why one tenth equals ten hundredths. Used in this way, instructional materials may help students to understand the general principles of equivalent fractions.

On the other hand, it is a major challenge to understand the rather abstract idea that one strip of ten blocks also can illustrate 1/10 of the hundred square.