Week Four: Division

 Big Ideas

-The concept of Division is separating a number into equal parts. This happens through two different processes of Partition and Quotition.

 

-Division is related to subtraction and division problems can be solved by repeated subtraction

-Long division is an "antiquated skill". The text recommends that students learn the algorithm for single digit divisors only and that emphasis is placed on estimation(Reys et al., 2012)

-Division by zero is not defined and this question comes up a lot in the classroom. (Facts for life Division, n.d.)  
-When teaching bracets the teacher should put emphasis on the closer in the breaks are to the middle thir the first ones to be done.
-There are three types of number sence activities Initiation, Companion and Extension 

Concept Skills and Strategies  

  The above figure reinforces the relationship between multiplication and division(Facts for life Division, n.d.)
Skip Counting backward:

                        Thinking

15÷3=⃝         15…12,9,6,3,0

                         I subtracted 3 five times

                        So 15÷3=7

Distributive Algorithm

Most common and familiar.(Reys et al., 2012)

Subtractive Algorithm

 Intuitive and straight forward method for helping students as its about repeated subtraction.(Reys et al., 2012)

Language Model

 Teaching Strategies

(Reys et al., 2012)

(Facts for life Division, n.d.)

Misconception

Division Rules:

When teaching rules teachers need to be very careful as some rules are bendable. Students need to have a high understanding the means behind the rules and this can actually see acceptation to rules.

•       Even numbers can be divided by 2 with no remainder. Numbers ending in 0, 2, 4, 6, and 8 are even and can be divided by 2.

•       Numbers ending in 5 or 0 can be divided by 5.

•       Numbers ending in 0 can be divided by 10.

•       Add the digits to see if a number can be divided by 3 e.g., 132 can be divided by 3 because 1+2+3=6 which is a multiple of 3.

• What about 4 675? What can it be divided by without leaving a remainder? 

ACARA

Mathematics / Year 2 / Number and Algebra / Number and place value / ACMNA032
("Mathematics Foundation to Year 10 Curriculum by rows - The Australian Curriculum v8.1", 2016) 

Resources and Ideas  

https://www.youtube.com/watch?v=gjqxhtjyfC4

("Learn Division for Kids - 2nd and 3rd Grade", 2016)

Synthesis Textbook 

Think multiplication when working with division

-Students do not generally lean division facts separately from multiplication facts. Example: students learn 48÷6=8 by remembering facts 6x8=48

-Most division problems in computation and real world problems do not directly involve a multiplication fact (photo from phone)

-Important that students recognise that division can be seen as repeated subtraction, as when they encounter division with multidigit numbers an understanding of division as equivalent to repeated subtraction  in order to appreciate why division algorithm involves repeated subtraction.

-A productive approach can also be ‘think multiplication’.
(Reys et al., 2012)

References

           Facts for life Division (1st ed., p. 54). Retrieved from http://leo.acu.edu.au/pluginfile.php/1486742/mod_book/chapter/32718/Why%20cant%20I%20divide%20by%200.pdf
          Mathematics Foundation to Year 10 Curriculum by rows - The Australian Curriculum v8.1. (2016). Australiancurriculum.edu.au. Retrieved 3 April 2016, from      http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1#levelF
          Reys, R., Lindquist, M., Lambdin, D., Smith, N., Rogers, A., & Falle, J. et al. (2012). Helping Children Learn Mathematics. Milton Queensland: John Wiley & Sons Australia, Ltd.