Area Cards
Goals:
  • To promote discussion of students' ideas about decimals for assessment and learning.
  • To enable students to self-correct their ordering of decimals by size - using an area representation.
  • To promote discussion on ordering of decimals: why do we consider digits from left to right?
Year level:  Year 4 to 6
Group size: This activity can be conducted as a whole class activity or small groups of 6 students
Equipment:  Overhead transparency of the 'Area card sets' for a whole class discussion (or alternatively the cards pasted on magnetic strips for the board) . Separate 'Area card sets' for small group work (6 students). Each set contains 6 pairs of cards representing decimal numbers. In each pair, there is one numerical representation and one pictorial. Photocopy masters:
Area card set 1
Area card set 2
Area card set 3
Time: 10 - 20 minutes


Activity Instructions:
1. The class is provided with 6 decimal number cards which they order from largest to smallest. Emphasise that there must be consensus and encourage students to express their reservations about any ordering. Open discussion is the key to making this activity effective.

2. Once number cards are ordered, put the cards to one side preserving the order (the teacher has control of this in a whole class activity).  

3. Produce the corresponding picture cards and have students order them from largest to smallest, based on the amount of shading. (At this stage students do not know that the decimal numbers and picture cards correspond.)

4. Students are then asked to compare their ordering of the numbers to their ordering of the pictures - matching up numbers and picture pairs and commenting on any changes they would make and why.

Comments:
The card sets are designed to create cognitive conflict, hopefully leading to students with misconceptions (see Cases) reconstructing their ideas about decimal notation.

Variations:
To promote discussion on alternate representations of the same number, the final card set includes the numbers 2.2 and 2.20 represented pictorially as both 2 and 20 hundredths and 2 and 2 tenths.