Pre-Algebra and Algebra

Week 7

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.

Concept, Skills and StrategiesConcept 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.

Language Model in application to Algebra

Student Language

Materials Language

Mathematics Language

Symbolic Language

Concrete/VisualVerbal

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 = 5Y x 4 = 202y + 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/Resource/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 relationshipThinking Strategy: Directly related to investigation of number.

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

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.pdf

• 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

ACARA LINKS

Earliest mention of Algebra within the curriculum – ACMNA005

Year 1 – ACMNA018

Year 2 – ACMNA035

ACARA LINKS

Year 2 – ACMNA036

Year 3 – ACMNA060

Year 4 – ACMNA061

ACARA LINKS

Year 4 – ACMNA062

Year 4 – ACMNA083

Year 5- ACMNA107

ACARA LINKS

Year 5 – ACMNA121

Year 6 – ACMNA134

Year 6 – ACMNA133

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

Chapter Summary

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

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?

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

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