Concept: The document discusses teaching algebra concepts to primary school students. Skill: Students learn algebra through understanding patterns, relationships, and using concrete materials to represent abstract concepts. Strategy: It is important for students to fully understand underlying concepts before moving to skills and strategies. Teachers should ensure students are confident in concepts through visual and hands-on learning before having them calculate abstract problems.

1. Pre-Algebra and
Algebra
Week 7

2. Weekly Reflection
Throughout this week’s tutorial and lectures I had gained an
understanding upon the underlying concepts and processes of algebra
in a simplified form that I had not been knowledgeable of prior to this
unit. Within the tutorial, as a class, we had used concrete materials to
model our understanding of what we had learnt within the lecture and
had watched a demonstration video whilst modeling our problems, so
that we were able to visually depict what the process within the
problem involved.
Within the future, I aim to ensure that all of my students understand
every underlying concept behind a topic before proceeding to skills
and strategies of the concept being taught. By doing so, students
would become confident in proceeding to calculate problems, in
contrast to my experience where I had no knowledge of the underlying
concept or patterns of the concept and had become stuck when using
skills and strategies to calculate the problems.

3. Concept, Skills and Strategies
Concept of Algebra: A symbolic representation of patterns and relationships.
Skills: Ability to find the missing element.
As well as using skills such as,
- Recognizing
- Describing
- Repeating
- Growing
- Replacing
- Translating
Strategy: Using skills we have already learnt such as that of, (Four basic
functions/concepts)
- Addition
- Subtraction
- Multiplication
- Division
- https://www.youtube.com/watch?v=NybHckSEQBI - This video clip describes the
basic concept, functions, skills and thinking strategies used for algebraic thinking
and algorithms.

4. LanguageModelinapplicationto Algebra
Student Language
Materials Language
Mathematics Language
Symbolic Language
Concrete/Visual
Verbal
Symbolic
Pattern, repeating, growing, missing, replacing,
changing
Relationship, Function, formula, expressions,
equations, variables, equality, inequality,
substituting, unknown, generalization, input,
output
Change, equal, balanced, the same,
equals, problem, question, value,
2 x y = 5
Y x 4 = 20
2y + 5 = 11
Toys, books, pattern games,
shapes, natural materials
(anything that can be
modeled)
MAB blocks, unifix cubes,
blocks, matchsticks, pencils
(any materials that can be
modeled)
- This source contains a range of links to
online resources of patterns and algebra
from the Foundation years to year 6. –
- http://www.resources.det.nsw.edu.au/Res
ource/Access/37f3cd25-eeb2-4be3-87e0-
e83f98c717b7/1
Useful resource for students – demonstration on how to write an
equation for an expression that has an input (x) and an output (y)
& demonstrates how to write equations that contain division as
well as multiplication –
http://splash.abc.net.au/home#!/media/1453524/
Scales (created by
student on paper), A
drawn chart
Concept: Algebra, an understanding of
relationships between numbers.
Skill: Find the missing element/create & grow
patterns and investigate their relationship
Thinking Strategy: Directly related to
investigation of number.

5. Teaching Resources
• This resource may be useful to the higher year levels of primary school, but also my provide some useful
points for teachers that are teaching students within younger year levels. This source provides specific
evidence-based recommendations for teaching the algebra concept to students (American originated
source) – https://ies.ed.gov/ncee/wwc/pdf/practice_guides/wwc_algebra_040715.pdf
• In conjunction with the teaching of the concept, this video series may become of use if students are
finding difficulty with a certain part of the concept. These videos can be replayed at any time and provide
a number of visual representations and numerous examples upon the concept.
• The videos are split up into various segments of which contain, depiction of the concept of algebra,
solving basic equations (2 parts), 2 step equation, what are polynomials and simplifying polynomials.
-https://www.youtube.com/watch?v=NybHckSEQBI
-https://www.youtube.com/watch?v=l3XzepN03KQ
-https://www.youtube.com/watch?v=Qyd_v3DGzTM
-https://www.youtube.com/watch?v=LDIiYKYvvdA
-https://www.youtube.com/watch?v=ffLLmV4mZwU
-https://www.youtube.com/watch?v=DKC74YKJpNY

6. Misconceptions
• The equals sign is one of the most misinterpreted aspects to algebra. Many
students commonly use the symbol to simply state their answer.
• This source depicts some examples in which students may incorrectly utilize
the symbol. - http://www-
tc.pbs.org/teacherline/courses/math175/session3/studentmisconceptions.p
df
• To resolve the issue it may be useful to have a class discussion upon the use
of the equals sign and question students upon their current thoughts upon
what the symbol is used for. To implement this, a video clip demonstrating
what the mathematical definition and use for the equal sign is may clarify
confusion and resolve the misconception altogether. -
https://www.youtube.com/watch?v=2cJbQHYTJjM

7. ACARA LINKS
Earliest mention of Algebra within the
curriculum – ACMNA005
Year 1 – ACMNA018
Year 2 – ACMNA035

8. ACARA LINKS
Year 2 – ACMNA036
Year 3 – ACMNA060
Year 4 – ACMNA061

9. ACARA LINKS
Year 4 – ACMNA062
Year 4 – ACMNA083
Year 5- ACMNA107

10. ACARA LINKS
Year 5 – ACMNA121
Year 6 – ACMNA134
Year 6 – ACMNA133

11. Additional Teaching Strategies
• This source is a 16 page resource for teachers that provides an intro for teaching fractions. This
resource covers ordering, the four basic arithmetic, cancelling, writing in simplest for, the use of
area, model for multiplication and the use of the number line for ordering, adding and
subtracting. – http://www.amsi.org.au/teacher_modules/fractions.html
• This is an interactive resource called, ‘The Function Machine’ it entitles students to drag numbers
to the appropriate section and investigate the number pattern evident. –
http://www.scootle.edu.au/ec/viewing/L3527/index.html
• This resource may be useful for students when planning lessons for students. This source provides
various teaching strategy that may be useful for implementations within the classroom. It
addresses, various learning styles, working with students that need additional support and future
planning. – http://www.regentsprep.org/regents/math/algebra/teachres/Teachres.htm
• This source is an interactive resource aimed at students within the foundational years and entitles
them to extend a coloured button pattern and then to explain the pattern in words. –
http://www.scootle.edu.au/ec/viewing/L3516/index.html

12. Chapter Summary
What students are learning within the curriculum in relation to algebra.

13. Chapter Summary
Concept map for algebra -process and calculation of algebraic
algorithm
•Problems build on ideas are that essential to the curriculum
•Problems, patterns and the relations are each an essential part of primary school mathematics
•Routine Problems – exercises considered for developing algebraic concepts and thinking (+/-/x & Division)
•Non-Routine: ‘look for a pattern’ problems and number puzzles,
‘A family is building a rectangular garden that is always 1 m wide surrounded by a path made of 1m by 1m weed mats.
For a 1m by 2m garden, they need 10 mats. Draw a picture to verify the number of mats needed for these 2 gardens.
How many mats do they need for a 1m by 8m garden?

14. Chapter Summary
• Patterns – help children understand to organize their world and understand mathematics.
• Repeating Pattern – Has a ‘core element’ that is repeated over and over
• Growing patterns differ from repeated patterns
e.g. 1, 2, 4
1, 4, 9, 6, 16, 25
Properties of numbers
• Functions – a way of expressing a relation
• e.g. each number in the first set is related to 1 and only 1 number in the second set
• Language and Symbols – weave terms and symbols into your understandings – children learn about language
and symbols as they are learning about numbers
• Variables: 3 uses
- Placeholder – 3+ = 7/ 3+a= 7
- Generalizations – ‘any no. subtracted by itself is 0 and may be represented as a-a= 0’
- Function = H=2 x 13 / H & B are variables
• Modeling: concrete materials can assist children in understanding the overall and concept that are working on
• Generalizing: Finding a rule that generates the pattern
• Justifying: Having students justify the problems and their generalizations can assist them in understanding the
concept and gain confidence in their knowledge and skills.
• Relations, Functions: May be treated as patterns, alike growing patterns previous mentioned (above)
• Relations: Properties of numbers: investigating properties such as ‘distributivity’ can assist students within their
ability to construct generalizations

15. References
ABC. (2016). Show just how pro numerals you can be. Retrieved from, http://splash.abc.net.au/home#!/media/1453524/
Australian Curriculum Assessment and Reporting Authority. (2016). Curriculum. Retrieved from, http://www.australiancurriculum.edu.au/mathematics/curriculum/f-
10?layout=1
Education Services Australia Ltd. (2016). Colour Patterns. Retrieved from, http://www.scootle.edu.au/ec/viewing/L3516/index.html
Mathantics. (2015). Algebra basics: What is algebra? – Math Antics. Retrieved from, https://www.youtube.com/watch?v=NybHckSEQBI
Mathantics. (2015). Algebra basics: Solving Basic Equations part 1 – Math Antics. Retrieved from, https://www.youtube.com/watch?v=l3XzepN03KQ
Mathantics. (2015). Algebra basics: Solving Basic Equations part 2 – Math Antics. Retrieved from, https://www.youtube.com/watch?v=Qyd_v3DGzTM
Mathantics. (2015). Algebra basics: Solving basic 2-step Equations – Math Antics. Retrieved from, https://www.youtube.com/watch?v=LDIiYKYvvdA
Mathantics. (2015). Algebra basics: What are polynomials? – Math Antics. Retrieved from, https://www.youtube.com/watch?v=ffLLmV4mZwU
Mathantics. (2015). Algebra basics: Simplifying polynomials – Math Antics. Retrieved from, https://www.youtube.com/watch?v=DKC74YKJpNY
MathwithMrAlmeida. (2010). 1.0A.7 – Meaning of the Equal Sign. Retrieved from, https://www.youtube.com/watch?v=2cJbQHYTJjM
National Center for Education Evaluation and Regional Assistance. (2015). Teaching Strategies for Improving Algebra Knowledge in Middle and High School. Retrieved from,
https://ies.ed.gov/ncee/wwc/pdf/practice_guides/wwc_algebra_040715.pdf
New South Wales Department of Education. (2013). Site2see: Patterns and Algebra. Retrieved from, http://www.resources.det.nsw.edu.au/Resource/Access/37f3cd25-eeb2-
4be3-87e0-e83f98c717b7/1
Oswega City School District. (2012). Teaching Strategy Resources for Mathematics. Retrieved from, http://www.regentsprep.org/regents/math/algebra/teachres/Teachres.htm
Rubin, A. (2002). Student’s Misconceptions about the Equals Sign. Retrieved from, http://www-tc.pbs.org/teacherline/courses/math175/session3/studentmisconceptions.pdf
University of Melbourne. (2011). Fractions. Retrieved from, http://www.amsi.org.au/teacher_modules/fractions.html
Utah State University. (2009). Function Machine. Retrieved from, http://www.scootle.edu.au/ec/viewing/L3527/index.html