EDMA 262 - Task 1 Part 2 - Week 6

1. Number Sense, Numeration and
Mental Computation and Place
Value
Week 6

2. Weekly Synthesis
This week was based on a series of concepts. The concepts included, number sense,
numeration and mental computation. From studying these concepts within the lecture, tutorial
and textbook readings, my understanding and knowledge of these concepts developed. I had
gained an understanding upon how critical it is that children have number sense, knowledge
of numeration and place value, before learning formal concepts as they are are foundation to
all other concepts.
As a teacher I would ensure that my student’s understand these concepts before I introduce
them to any formal mathematical concepts such as addition and subtraction. This would be
done to establish student understanding and knowledge then progress to concepts and teach
appropriate thinking strategies for mental computation for addition and various other concepts
that are to be taught.

3. Concepts, Skills and
Strategies
 Number Sense: https://www.youtube.com/watch?v=gVc-0jBM39o- this video depicts a detailed concept of number sense.
 https://www.youtube.com/watch?v=KrmI_bO0Ru4 - this clip depicts various number sense teaching and thinking strategies
within a kindergarten setting and also displays strategies that can assist children with mental computation.
 Numeration- The formal understanding of number and number notation. (specifying reading, writing, interpreting and
processing numbers)
 Mental Computation – The understanding of operations in order to organise thinking as well as a foundation of knowledge of
basic number facts and strategies to process information. (Romina and Julie had explained within both lectures and tutorials
that children are able to use any thinking strategy they wish as long as it is effective, quick and accurate)
 - https://www.youtube.com/watch?v=6ICQHxgL5ek
https://www.youtube.com/watch?v=9NX6-VXQ_Ew - Both of these clips depicted, portray mental computation in perspectives
using addition and subtraction.
 Place value: The location of a digit in a number; the value of the digit is determined by its place.

4. The Language Model in Relation to Place Value
Symbolic
VerbalConcrete/Visual
Student Language
Materials Language
Mathematics Language
Symbolic Language
MAB blocks, matchsticks, bottle
caps (can represent different
numbers), sticks, paddle pop
sticks, toys (anything that can
be modeled)
Ones, tens, houses, places, how many,
trade, place holder, expand, out back
together
Introduction of term place value rather
than that of place value houses
Using place value mats, MAB
blocks, unifix cubes, charts,
visual representations of
strategies (charts – count-back
strategy, use ten etc) of concepts
Once children gain an understanding
upon numbers within place value house
they can learn to write the numerals.
(children build, read and write numbers
in a new house)
None are needed.
(place value mat &
MAB blocks are to
always be available if
children need them)
Concept: Place value refers to the location of a digit in a numeral.
Skills: children must have, number knowledge, numeration skills and mental computation skills
Thinking Strategies: Foundation of understanding upon the four base mathematical concepts
(+/-/x & division)
(For yr 3’s) This resource is an animation with
audio that models and compares sizes of three
numbers based on place value -
http://skwirk.com.au/esa/Place_Value.html
This source depicts various challenges
children are to solve with place value. -
http://www.bbc.co.uk/bitesize/secondle
vel/mathematics/number_money_and_
measure/place_value_headings/play/

5. Teaching Strategies
 This source may prove to extremely useful for teachers as it is a 16 page guidance module that on introducing the concept of place value to years 1, 2, 3, and 4 students -
http://www.amsi.org.au/teacher_modules/Counting_and_place_valueK-4.html
 This source assists students in building their understanding of place value by making and regrouping numbers and using those representations to then use +/- to solve them (ipad is
needed). - https://itunes.apple.com/au/app/number-pieces-basic-by-math/id611452042?mt=8
 This resource is an interactive website that assists students in learning whole number and place value concepts through an adding game. -
http://www.curriculumsupport.education.nsw.gov.au/countmein/children_arrow_card.html
 This source identifies numeration and the big ideas of what student’s learn and are to understanding within each year level from years 4 to 6,
http://eworkshop.on.ca/edu/resources/guides/NSN_vol_1_Big_Ideas.pdf
 In relation to number sense, within this video a mathematics coach depicts ways in which number sense is defined and depicted within regular classrooms and how children can be
assisted within their developmental learning. - https://www.youtube.com/watch?v=HZdH6t7thfU
 A useful resource that teachers can use is a resource called ‘Top Drawer teachers: Mental computation’, it contains sections that cover, the big ideas, teaching practices, student activities
and a section for downloads - http://topdrawer.aamt.edu.au/Mental-computation/Big-ideas
An example of a transcript of a question
being proposing to a child and observing
their responses and thinking strategies of
their mental computation. (in relation to
the last teaching strategy source linked)

6. Misconceptions
 http://www.merga.net.au/documents/RP_Price_1998.pdf - This source identifies a common misconception that children
may have in relation to face value and place value. – e.g. 24 – a misconception that children may have may be that the
2 in 24 is viewed by only it’s face value rather than it’s place value.
 Many misconceptions with mental computation are linked to both numeration and number sense as these two concepts
are to be understood to children before they develop mental computation strategies.
 http://topdrawer.aamt.edu.au/Mental-computation/Misunderstandings/Learning-issues - this source depicts are variety
of detailed learning issues and misconceptions that student’s have in relation to mental computation that are linked to
numeration and number sense. Some of them including, number sense, place value, counting, pattern and structure.
 Resolution to learning difficulties and misconceptions- This source depicts a diverse variety of strategic resolutions for
student’s misconceptions with mental computation. (Refer to the image below for some examples)

7. ACARA Links
Foundation year-
ACMNA001
Foundation Year-
ACMNA002

8. Foundation Year-
ACMNA003
Foundation
Year-
ACMNA289

9. Year 2-
ACMNA030
The earliest mention of the use of thinking strategies and mental
computation.
Year 3 –
ACMNA053

10. Year 3 – ACMNA055
Year 3 – ACMNA057

11. Year 4 – ACMNA073
Year 4 – ACMNA078
Year 5 – ACMNA100

12. Year 5 – ACMNA101
Year 6 – ACMNA123

13. Additional Teaching
Resources
 This resource can prove to be useful for teachers as it provides
constructed lesson plans, strategies and recommended steps to take for
the future. This resource is aimed mainly at assisting students that are
developing under the achievement standards for their year level with
mental computation
http://www.scootle.edu.au/ec/viewing/S7048/pdf/tls16_using_visual_tool.p
df
 This video depicts a variety of strategies that can be used by teachers for
student enrichment within number sense and mental computation.
Throughout the video, various thinking strategies are depicted with
addition and subtraction as well as various questions and language that
teacher’s can use to encourage student development. -
https://www.youtube.com/watch?v=UYE876S_OzM

14. Chapter Summary
Concept map for Mental
Computation (processes)

15. Chapter Summary
Chapter 10
 Calculators- ‘All students should have access to appropriate technology as a means of both support and extend their mathematics learning experiences’.
 Students should be encouraged to become intelligent/fluent with ICT and to be aware of limitations of the approach. (ready to adapt and respond to changes)
 Student’s use of calculators shifts away from teacher centered approaches and reaches towards a more flexible student centered approach.
 Teachers are to educate student’s upon the use of technology as calculators can raise student achievement.
 Calculators reveal patterns which is a good method of practice for students to encompass as it will reinforce their skills and knowledge.
 Mental Computation – ‘Calculations done mentally’
 Using the ‘Big 7 Strategies’, such as, count on/back, use tens, doubles etc
 Using place value with basic addition facts, combine basic facts
 Many children apply written algorithms, mentally when asked to do mental computation
 Guidelines for developing strategies – Encourage students to do computation mentally, learn which computations students prefer to do mentally, find out if
students are applying written algorithms mentally.
 Front –end estimation – Checking the leading/front end digit in a number and the place value of that digit e.g. 4000/ 1213 + 2926 + 1578 (the answer would be
exactly 4000 if all digits except the front end ones were zeros – their not and so it must be more than 4000)
 Compatible no. – numbers that go together – e.g. 7029 is close to 6900, and 69 is divided evenly by 23, so 23 and 69 are compatible.

16. References
Australian Curriculum Assessment and Reporting Authority. (2016). Maths. Retrieved from, http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1
BBC. (2014). Place Value Headings. Retrieved from, http://www.bbc.co.uk/bitesize/secondlevel/mathematics/number_money_and_measure/place_value_headings/play/
Blackman Sparks Learning Channel. (2015). Strategies to Develop Number Sense. https://www.youtube.com/watch?v=KrmI_bO0Ru4
Commonwelth of Australia. (2014). Using Visual tools to assist low achievers with mental computation. Retrieved from,
http://www.scootle.edu.au/ec/viewing/S7048/pdf/tls16_using_visual_tool.pdf
Education Services Australia Ltd. (2015). Times Module 1: Number and Algebra: Counting and place value – teacher guide. Retrieved from, -
http://www.amsi.org.au/teacher_modules/Counting_and_place_valueK-4.html
Elphick, C. (2013). EXD 1280 Mental Computation Strategies. Retrieved from, https://www.youtube.com/watch?v=9NX6-VXQ_Ew
Family Math Night. (2012). Developing Number Sense using tiles, 10-frames and the number chart. Retrieved from, https://www.youtube.com/watch?v=UYE876S_OzM
Mathnasium Learning Centres. (2012). What is number sense?. Retrieved from, : https://www.youtube.com/watch?v=gVc-0jBM39o-

17. References
National Council of Teachers of Math. (2015). Number Pieces basic, by the Math Learning Center. Retrieved from, https://itunes.apple.com/au/app/number-pieces-basic-by-
math/id611452042?mt=8
New South Wales Department of Education and Communities. (2013). Arrow Card Game. Retrieved from,
http://www.curriculumsupport.education.nsw.gov.au/countmein/children_arrow_card.html
Ontario Education. (2006). Number sense and Numeration: Grades 4 to 6. Retrieved from, http://eworkshop.on.ca/edu/resources/guides/NSN_vol_1_Big_Ideas.pdf
Price, P. Year 3 Students’ place-value misconceptions: Another look at MAB. Retrieved from, http://www.merga.net.au/documents/RP_Price_1998.pdf
Red apple Pty Ltd. (2012). Place Value. Retrieved from, http://skwirk.com.au/esa/Place_Value.html
Shumway, J. (2011). Number Sense Routines. Retrieved from, https://www.youtube.com/watch?v=HZdH6t7thfU
Top Drawer Teachers. (n.d.) Resources for teachers of mathematics: Big Ideas Retrieved from, http://topdrawer.aamt.edu.au/Mental-computation/Big-ideas
Top Drawer Teachers. (n.d.) Resources for teachers of mathematics: Misunderstandings. Retrieved from, http://topdrawer.aamt.edu.au/Mental-
computation/Misunderstandings/Learning-issues
Van, T. (2013). Mental Computation Strategy. Retrieved from, https://www.youtube.com/watch?v=6ICQHxgL5ek