The Big Ideas taken from this week is that both division and multiplication both stem from the concept of equal groups. Multiplication requires two equal groups added together to find the total. Whereas, division is the opposite as it requires separating the total into equal groups. Finally, both multiplication and subtraction are linked to division through the use of quotation stories.
Concepts, Skills and Strategy:
Concept- To teach children how to distribute a certain number of items or objects equally and fairly among them. In order for children to understand the concept of division they have to know how to share. The separation process consist of two processes being Partition and Quotition. Partition is the idea of sharing a large number to see how many there are in each group. Quotition is the process of repeated subtraction where small quantities are subtracted from a larger amount.
Examples
Partition - Lucy has 6 lollies to share with his 3 friends. How many lollies can each of Lucy's friends receive?
Answer: 6 divided by 3 equal 2
Quotition - There are 12 goody bags and I want to give 1 bag each to my friends. How many friends can I give goody bags to?
Answer: 12 divided by 1 equals 12
Skills- The skills required in order to do division are Multiplication and Subtraction.
Strategy- The strategy needed in division are knowing the multiples very well, being able to do multiplication. Other strategies that can be used in division include Use doubles, Properties to zeros, Counting strategy, Build up or down strategy and using real-life scenarios can also help when demonstrating division.
Misconceptions:
The misconceptions when it comes to division are that children don't often use the language of division to describe the process. They do not understand that groups and sets need to be subtracted in order to solve the problem. Another misconception is that when dividing the number 0 does not need to be added, this is false as the number should always be recorded. The language " Goes into" changes what we want students to know about division, where the total is shared out into equal groups. Unlike the other operations, there are several symbols to represent division including: ÷ / -
.Resources:
The Australian Curriculum ( ACARA), states under Minimum Standards-Numeracy that students in years 3 and onwards should be able to apply the appropriate strategies to solve problems which require multiple steps. Using mental multiplication demonstrating by using the skills of doubling and halving as well as simple multiplication and division.
Sourced Teaching Strategy:
(https://www.pinterest.com/mariehdutoit/long-division/)
Textbook Concepts, Skills and Strategy:
Similar to multiplication, the concept of division is developed through concrete, pictorial and symbolic representations. There are two situations that are considered these include: Measurement (Repeated Subtraction) and Partition (Sharing). Fluency in basic skills such as addition, subtraction and multiplication are needed for years 3, 5 and 7. Some strategies used are concrete materials or counting specifically finger counting ( Reys. R, 2012).
References
Jamieson-Proctor, R. (2019). Learning Environment Online: Log in to the site. Retrieved from https://leo.acu.edu.au/mod/book/view.php?id=2406570&chapterid=190005
Jamieson-Proctor, R. (2019). Learning Environment Online: Log in to the site. Retrieved from https://leo.acu.edu.au/mod/book/view.php?id=2406570&chapterid=190004
NAP - Minimum standards - numeracy. (2016). Retrieved from https://www.nap.edu.au/naplan/numeracy/minimum-standards
Numeracy Learning Continuum. Retrieved from https://www.australiancurriculum.edu.au/media/1077/general-capabilities-numeracy-learning-continuum.pdf
Reys, R. (2017). Helping children learn mathematics (2nd ed., pp. 267,276). Milton, Qld: Wiley.
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