Order of operations and division:
The big ideas:
Division is defined as separating a number into equal parts, and can be undertaken in two different ways.
Reys et al., (2020) notes the importance of communication throughout the process of concrete -> pictorial -> abstract representations in division.
Partition
Student language
Material Language
Mathematical language
Symbolic Language
Language
Shared
Shared
8 divided between 4 is 2
8 ÷ 4 = 2
Materials
Familiar objects, photos
Substituted objects, photos
Substituted objects, photos,
graphics, diagrams
Non-word symbols
Recording
Drawings
Drawings
8 divided between 4 is 2
8 ÷ 4 = 2
Quotition
Student language
Material Language
Mathematical language
Symbolic Language
Language
How many groups of 8 are there?
How many groups of 8 are there?
How many 8's in 32?
32 ÷ 8 = 4
Materials
Familiar objects, photos
Substituted objects, photos
Substituted objects, photos,
graphics, diagrams
Non-word symbols
Recording
Drawings
Drawings
How many 8's in 32?
32 ÷ 8 = 4
Video demonstrating partition and quotition division.
Mcintosh. (2015, April 20). Demonstrating Multiplication, Partition and Quotition Division [Video] YouTube. https://www.youtube.com/watch?v=sx5h16Af5l0&t=32s
Personal reflection:
I had no previously knowledge of the difference between partition and quotition division. I now understand the distinct way each is undertaken and taught, which will be vital when I am teaching.
Concept, skill or strategy:
The strategy of using equal groups is hands-on and visual. This strategy would only be suitable for a student in the mathematical or symbolic language stage, as it veers away from familiar objects and uses symbols. This video demonstrates its use in the classroom.
Blackman. (2015, October 28). Division using equal groups [Video] YouTube. https://www.youtube.com/watch?v=IeN0kj5wb9I
A possible misconception:
0 ÷ 3 = 3 students may fail to recognise that division by 0 is impossible. Example: If I don't share any, I still have 3 left. To remedy, modelling with concrete objects would be beneficial.
I have created an example division lesson plan below:
ACARA:
Division: Year two / Number and Algebra / Number and place value / ACMNA032
Elaboration:
- Dividing the class or a collection of objects into equal-sized groups
- Identifying the difference between dividing a set of objects into three equal groups and dividing the same set of objects into groups of three.
Scootle resource: What is a quarter? https://education.abc.net.au/home#!/media/2119277/ This short video demonstrates how to quarter groups of things with the help of visuals.
Resources:
Mathsframe is an interactive website featuring multiplication and division games and worksheets. https://mathsframe.co.uk/en/resources/category/7/multiplication-and-division would be suited for students in the material language stage, as some require operations with substituted objects.
Word Count: 268
The big ideas:
Division is defined as separating a number into equal parts, and can be undertaken in two different ways.
Reys et al., (2020) notes the importance of communication throughout the process of concrete -> pictorial -> abstract representations in division.
Partition
|
Student language
|
Material Language
|
Mathematical language
|
Symbolic Language
|
Language
|
Shared
|
Shared
|
8 divided between 4 is 2
|
8 ÷ 4 = 2
|
Materials
|
Familiar objects, photos
|
Substituted objects, photos
|
Substituted objects, photos,
graphics, diagrams
|
Non-word symbols
|
Recording
|
Drawings
|
Drawings
|
8 divided between 4 is 2
|
8 ÷ 4 = 2
|
Quotition
|
Student language
|
Material Language
|
Mathematical language
|
Symbolic Language
|
Language
|
How many groups of 8 are there?
|
How many groups of 8 are there?
|
How many 8's in 32?
|
32 ÷ 8 = 4
|
Materials
|
Familiar objects, photos
|
Substituted objects, photos
|
Substituted objects, photos,
graphics, diagrams
|
Non-word symbols
|
Recording
|
Drawings
|
Drawings
|
How many 8's in 32?
|
32 ÷ 8 = 4
|
Video demonstrating partition and quotition division.
Mcintosh. (2015, April 20). Demonstrating Multiplication, Partition and Quotition Division [Video] YouTube. https://www.youtube.com/watch?v=sx5h16Af5l0&t=32s
Personal reflection:
I had no previously knowledge of the difference between partition and quotition division. I now understand the distinct way each is undertaken and taught, which will be vital when I am teaching.
Concept, skill or strategy:
The strategy of using equal groups is hands-on and visual. This strategy would only be suitable for a student in the mathematical or symbolic language stage, as it veers away from familiar objects and uses symbols. This video demonstrates its use in the classroom.
Blackman. (2015, October 28). Division using equal groups [Video] YouTube. https://www.youtube.com/watch?v=IeN0kj5wb9I
A possible misconception:
0 ÷ 3 = 3 students may fail to recognise that division by 0 is impossible. Example: If I don't share any, I still have 3 left. To remedy, modelling with concrete objects would be beneficial.
I have created an example division lesson plan below:
ACARA:
Division: Year two / Number and Algebra / Number and place value / ACMNA032
Elaboration:
- Dividing the class or a collection of objects into equal-sized groups
- Identifying the difference between dividing a set of objects into three equal groups and dividing the same set of objects into groups of three.
Scootle resource: What is a quarter? https://education.abc.net.au/home#!/media/2119277/ This short video demonstrates how to quarter groups of things with the help of visuals.
Resources:
Mathsframe is an interactive website featuring multiplication and division games and worksheets. https://mathsframe.co.uk/en/resources/category/7/multiplication-and-division would be suited for students in the material language stage, as some require operations with substituted objects.
Word Count: 268