Pre-algebra (patterning) and early algebra:
The big ideas:
This week covered the use of patterns to develop algebraic thinking, specifically how to
determine relationships within a pattern. Patterns can include geometry, geometric shapes or numbers. Reys et al. (2020) states that developing an understanding of the prevalence of patterns in the world will help children clarify their learning of number, geometry and measurement.
Function: numbers that are so connected with another number that if there was to be any alteration to one number, there would be a consequence for the other.
Anderson. (2014, December 15). Find the rule for the patterns [Video] YouTube. https://www.youtube.com/watch?v=OlUBFXfLE0c
Number theory:
- odds and evens
- prime and composite
- multiples and factors
- positive and negative
- whole and fraction
- place value
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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Pattern, replacing, changing, repeating
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Pattern, replacing, changing, repeating
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Relationship, formula, function, equation, variable
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+ = -
2 + ? = 8
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Materials
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Familiar objects
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Substituted objects
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Substituted objects, photographs, graphics
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Non-word symbols
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Recording
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Drawings
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Drawings
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Writing
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Write symbols
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Personal reflection:
My first introduction to algebra was through manipulating patterns. This tutorial activity of toothpick patterns was a good demonstration of what could be done in classes.
Concept, skills and strategies:
A pre-algebra skill is being able to determine what is missing in a pattern. This skill can be practised by growing or creating patterns.
A possible misconception:
A common student misconception is seeing a pattern as a repeated block rather than individual elements within the pattern. For example 12231223, the student may believe that 1223 is the pattern being repeated rather than 1, 2, 2, 3. To remedy this, I would create an activity that involves filling in blanks so students consider each element as an individual.
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: Monster choir: making patterns http://www.scootle.edu.au/ec/viewing/L1056/index.html Make a pattern, and practice repeating to hear the monster choir sing!
Resources:
The website patternshapes https://apps.mathlearningcenter.org/pattern-shapes/ allows students to create their own patterns, and manipulate the size, shape, colour of their patterns. An excellent way to develop their thinking.
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