Early algebra and solving simple linear equations:
The big ideas:
Week 10 extended upon week 9. An algebraic equation is a statement of a relationship. ACARA introduces algebra in the foundation year, with a focus on identifying patterns in the world around us. As mentioned by Reys et al., (2020) research indicated that student in the primary years would be better prepared to study algebra with a solid understanding of patterns and relationships.
the symbols and terms of algebra:
Fordummies. (2009, June 26). Understanding the vocabulary of algebra [Video] YouTube. https://www.youtube.com/watch?v=BHtE3JyZ-UQ
Student language
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Material Language
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Mathematical language
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Symbolic Language
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Language
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Same as, less, more,
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Balance, same as, less, more
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Equivalent, formula, equality, variable, equation
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= + - x ≠ y z
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Materials
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Familiar objects, toys
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Substituted objects, counters, scale mats, unifix cubes
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Substituted objects, counters, scale mats, unifix cubes
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Substituted objects, counters, scale mats, unifix cubes
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Recording
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Drawing
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Drawing
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Stating the relationship, drawing
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5x + 6 = 4x + 11
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Personal reflection:
I remember always struggling through algebra lessons, but with the lecture slides and Reys et al. (2020) comments about how the foundation of patterns and relationships will assist in the mental processes of algebra in high school, I found the connection very interesting, and will certainly remember this in my own teaching.
Concept, skills and strategies:
Balancing the scales is a concrete hands-on strategy to assist in the conceptualisation that = means both sides are balanced. It is noted that the = sign can be misidentified, so this activity should assist students in practising balancing both sides of an equation through visual methods.
This is my interpretation of a 'balance the scales' strategic activity.
A possible misconception:
A misconception is mistaking the variable x for the operation x as they have likely encountered x previously with multiplication concept. To remedy this, ensuring that mathematical language is connected with symbolic language, particularly the use of variables, is important for the student to grasp this concept.
ACARA:
Algebra: Foundation year / Number and algebra / Patterns and algebra / ACMNA005
Elaboration:
- Observing natural patterns in the world around us
- Creating and describing patterns using materials, sounds, movements or drawings.
Scootle resource: sites2see: patterns and algebra https://fuse.education.vic.gov.au/Resource/LandingPage?ObjectId=6cd9cff3-7ba7-4590-847d-994303299ba9&SearchScope=All this interactive website encompasses algebraic concepts and formulas, I would use with students in the symbolic language stage.
Resources:
Youcubed is a maths website with an algebra section which outlines number sense, functions, patterns and connecting visuals. https://www.youcubed.org/algebra/
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