The following are the big ideas that were discussed in week four:
- There are two types of division:
1. Partition/sharing problems - "...a collection of objects is separated into a given number of
equivalent groups and you need to determine the number in each group...Gary had 15 shells. If
he wanted to share them equally among 5 friends, how many should he give to each" (Reys et
al., 2012, p. 203).
2. Measurement/repeated subtraction problems - "...you know how many objects are in each group
but you must determine the number of groups...Jenny had 12 grapes. She gave 3 to each
person. How many people received grapes?" (Reys et al., 2012, p. 203).
- There are four different thinking strategies for division:
1. Use counting strategy for 5s and 10s
2. Think real world for 1s and 0s
3. Use doubles for 2s, 4s and 8s
4. Build up or build down for 3s, 6s and 9s (Jamieson-Proctor, 2016).
- BEDMAS is the correct order in which mathematics operations should be performed (Smith, 2014)
* B = brackets
* E = exponents (i.e. squared, cubed)
* D = division
* M = multiplication
* A = addition
* S = subtraction
- Rules for division:
* Even numbers can be divide by 2 without a remainder
* Numbers that end in 5 or 0 can be divided by 5 evenly
* Numbers ending in 0 can be divided by 10 evenly
* By adding the digits of a number together you can tell if a number will be able to be divided by 3,
if the total is a multiple of three than it will divide equally in to 3 with no remainders (Jamieson-
Proctor, 2016).
My understanding of the weekly topic has changed in the following ways:
- My understanding of BEDMAS has changed after this week. This is because when I was in school
I learnt BIMDAS and I didn't realise that it had changed.
- My understanding of division has also changed because I never knew how to find out if a number
is able to be divided by 3 without doing the division.
Demonstrate your understanding of the mathematical concept and related skills and strategies children need to assimilate and be able to use, that are related to division
- The concept this week was division. Division is seperating a number in to equal parts (Jamieson-
Proctor, 2016).
- The concept of division is applied using the skill of division algorithm. The division algorithm can
be seen in figure 1.11 (Jamieson-Proctor, 2016).
- There are four different strategies for division:
1. Use counting strategy for 5s and 10s
2. Think real world for 1s and 0s
3. Use doubles for 2s, 4s and 8s
4. Build up or build down for 3s, 6s and 9s (Jamieson-Proctor, 2016).
 |
| Figure 1.12: Jamieson-Proctor, R. (2016). EDMA202/262 Mathematics Learning and Teaching 1: Week 4 Part 2. Brisbane, Australia: Australian Catholic University. |
Language Model for Division
 |
| Figure 1.13: Language Model for Division |
- A specific teaching strategy that could be used for children to understand the concept of division
is the skip counting strategy. Skip counting is something that occurs in everyday life fro children
and adults therefore it is an essential strategy to learn (Reys et al., 2012).
- An example of skip counting is 3, 6, 9, 12, 15, 18, 21, 24. This skip counting pattern is the a
sequence of the 3 times tables. An example of skip counting for division can be seen in the
following video.
- When teaching skip counting a hundred chart would be helpful for students to visualise the normal
number pattern and then figure out what the next number in their skip sequence would be. An
example of a hundred chart can be seen in figure 1.10 in the week 3 blog.
Describe/demonstrate a specific misconception children might have in relation to division. How would you avoid or remediate this misconception?
- A common misconception about division is that division will always make a number smaller. When
dividing rational numbers that are lower than one, this will not always be the case (Graeber &
Campbell, 1993).
- It is important that children don't always believe that division makes numbers smaller as this will
effect their mathematics skills in the later years of school.
- A way to remediate this would be to ensure that when teaching division children are never taught
that division makes numbers smaller.
Provide appropriate URL links to the ACARA year, strand, substrand, content description, elaborations and Scootle resources for the earliest mention of division
- Division is first seen in the Australian Curriculum in Year 2 number and algebra strand, number
and place value substrand.
- The content description for ACMNA032 is "recognise and represent division as grouping into equal
sets and solve simple problems using these representations" (ACARA, 2016).
- The elaborations for ACMNA032 are "dividing the class or a collection of objects into equal-sized
groups" and "identifying the difference between dividing a set of objects into three equal groups
and dividing the same set of objects into groups of three" (ACARA, 2016).
- Scootle resources for division
Provide appropriate links to resources and ideas you have sourced personally to assist students to develop concepts, skills and/or strategies related to division
- Resource/s for students to understand the concept of division:
* Concept of division
- Resources for students to understand the skill of division:
* Short division
* Long division
- Resources for students to understand the strategy of division:
* Use counting strategy
* Use doubles
* For build up and build down the same videos that were used for multiplication can be used for
division with teachers reiterating the relationship but difference between the two.
Provide a concise synthesis of the textbook chapter/s related to the weekly topic
- There are two types of division problems:
* Measurement/repeated subtraction problems
* Partition/sharing problems
- Thinking strategies for division - think multiplication and repeated subtraction
- Skills for division:
* Division with 1 digit divisor
e.g. 52 ÷ 7
"52 divided by 7 is close to 49 divided by 7, which is 7. But there are 3 left over. So the
answer is 7 remainder 3" (Reys et al., 2012, p. 263).
* Distributive algorithm
e.g.
 |
| Figure 1.14: Reys, R., Lindquist, M., Lambdin, D., Smith, N., Rogers, A., Falle, J., Frid, S., & Bennett, S. (2012). Helping children learn mathematics. Queensland, Australia: John Wiley & Sons Australia, Ltd. |
e.g.
 |
| Figure 1.15: Reys, R., Lindquist, M., Lambdin, D., Smith, N., Rogers, A., Falle, J., Frid, S., & Bennett, S. (2012). Helping children learn mathematics. Queensland, Australia: John Wiley & Sons Australia, Ltd. |
don't need to spend months with students developing this skill (Reys et al., 2012).
References
Australian Curriculum and Assessment, Reporting Authority [ACARA].
(2016). Mathematics.
Retrieved from http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1
Education Services Australia. (2016). Scootle: Mathematics.
Retrieved from http://www.scootle.edu.au/ec/search?accContentId=ACMNA032&userlevel=(2)
Graeber, A. & Campbell, P. (1993). Misconceptions about multiplication
and division. The Arithmetic Teacher, 40(7),
408-411.
Howard, C. (2015). EDX1280
use doubles strategy for multiplication and division. Retrieved from https://www.youtube.com/watch?v=xQdkzhYZQd0
Iken Edu. (2011). Division
made easy: Math video to learn division basics. Retrieved from https://www.youtube.com/watch?v=wBSVDxqCTWw
Jamieson-Proctor, R. (2016a). EDMA202/262 Mathematics
learning and teaching 1: Week 4 part 2. Brisbane, Australia: Australian
Catholic University.
MathsMaster.Org. (2011). Short
division. Retrieved from https://www.youtube.com/watch?v=oWyTxq5mewo
Mr Judy’s Class. (2013). Skip
counting for division. Retrieved from https://www.youtube.com/watch?v=bOBKsnkUGx4
Reys, R., Lindquist, M., Lambdin, D., Smith, N., Rogers, A., Falle, J., Frid, S., & Bennett, S. (2012). Helping children learn mathematics. Queensland, Australia: John Wiley & Sons Australia, Ltd.
Smith. (2014). Maths quest 8
for Victoria: Australian curriculum edition. Retrieved from http://leo.acu.edu.au/pluginfile.php/1486742/mod_book/chapter/32719/BODMAS%20example.pdf
Tecmath. (2011). Long
division: easy. Retrieved from https://www.youtube.com/watch?v=vzI3bqk2_fg
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