The concept of multiplication is repeated addition where all the parts that are added are equal to each other. Or it could be said; repeated addition of equal groups or sets. There are 4 ways to picture or model multiplication:
- The set model - good way to display or model to show them the groups. Eg: I had 3 friends which I gave 6 lollies to each friend how many lollies did i give out altogether?
- The array model (area model) - Eg: the length of a rectangle is 5cms by 3cms. What is the area of the rectangle? This could be represented using materials such as counters you can use them to turn the equation around to be 3x5 instead.
- The measurement of length model - Eg: I bought 4 hair ribbons each 2 meters in length. How many meters did i buy?
- The combinations (cross products) model - Eg: I have 3 different coloured shirts and different coloured pairs of trousers. How many different outfits can i make? 5
The skills are completed through using multiplication algorithm which can be displayed using materials such as MAB blocks which is shown step by step below for 36x4 6
Thinking strategies for multiplication include3:
- Commutivity
- Counting, doubles,
- Repeated addition
- Build up (x3 & x6) or Build-down (x9),
- Turn- around 7's.
- Patterns
- Multilying by 1 or 0
Language model
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This is the language model set out in the textbook which demonstrates the language used and symbolic references. Other materials that can be used to assist with demonstrating multiplication include: counters, MAB blocks, learning mats, blocks and almost any other materials that are in quanities and can be manipulated and moved around3.
Teaching Strategy - Resource
Teaching multiplication using the array method - resource using a bus to show how many rows and how many people and then uses blocks to represent the equation4.4
Misconceptions
The misconceptions are similar in solving all mathematical equations where the child may not have fully understood the concept of the operation or they misinterpret the language or symbol2 .
ACARA
The Australian curriculum introduces multiplication in 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. Robinson, BJ (2011, August 10). Year 2 multiplication arrays. Retrieved from https://www.youtube.com/watch?v=37ejU_8lcaY
5. Week 3 Lecture
6. Week 3 Tutorial
6. Week 3 Tutorial
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