Week 4 - Division

Concept, Skills and Strategies
Division is separating a number into equal groups, however children need to understand the division process can be undertaken in 2 different ways;  partition and quotition3.

• Partition (sharing) - know the total number of groups, we have to find the total. A partition map can be used to demonstrate this and can make inverse links between multiplication and division by turning it around⁵. 
• Quotition (repeated subtraction)- know the total and the number in each group, we have to find the number of groups⁵.

The division algorithm is part of the skills and can be shown using MAB blocks

There is a strong relationship between division and multiplication because division can be stated in terms of multiplication therefore there are several thinking strategies that are similar to multiplication such as: The array model, counting strategy, use of doubles, build up or down5.

Language Model

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Teaching Strategy - Resource

This is an excellent resource that can be used in the classroom to demonstrate either multiplication or division using partition and quotition4. 

Misconceptions

There are many difficulties students might encounter such as there are multiple division symbols where students may get confused. Dividing anything by 0 as it is an undefined operation, children need to understand they cant do the operation. Remainders is also another difficulty students might not understand the concept and become confused, MAB blocks are a good way to show this because we can physically see the remainders2. 

ACARA

Division is introduced into the Australian curriculum as early as year 2 1. 

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References

1. Australian Curriculum and Assessment Reporting Authority. (2014). Foundation to Year 10 Curriculum: Mathematics. Retrieved from http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1#cdcode=ACMNA004&level=F 

2. Harris, Andrew. (2001). Mulitplication & Division. Retrieved from http://ictedusrv.cumbria.ac.uk/maths/pgdl/unit5/A&S.pdf

3. Reys, R., Lindquist, M., Lambdin, D., Smith, N., Rogers, A., Falle, J., Frid, S., & Bennett, S. (2012). Helping children learn Mathematics (1st Australian ed.). Milton: John Wiley & Sons. 

4. Osmond, K (2015, August 28). EDX1280- Learning Resource for Multiplication, Partition Division and Quotition Division. Retrieved from https://www.youtube.com/watch?v=KAOo6wamuso 

5. Week 4 Lecture