# Algebra Patterns and Functions

## Knowledge base & tools to develop mathematical literacy

### Knowledge base

Mathematical knowledge base with concepts necessary for learners to conceptualize to become mathemtically literate and misconceptions that must be over come. Particularly important for how learners develop their understanding for algebra, patterns, and functions are:

Concepts related to:

### Pedagogy: information to develop literacy in algebra, patterns, & functions & some tools to achieve it

• Assessment
• Functions & patterns - Work sheet of a sample of Authentic Assessment for a Bridge pattern
• Functions & patterns - Work sheet of a sample of a Directed Assessment for a Bridge pattern
• Assessment - process proof and conjecture - content zero and properties of zero - addition and subtraction - with teacher reflection
• Scoring guides
• Classification or Sorting - Activities to assess by 1, 2, & 3 properties; use of Venn diagrams to represent intersecting & disjoint groups.
• Conjectures - Articulating, Editing, and Refining Conjectures in a Second or Third Grade Classroom
• Equality and equal sign in equations - Discusses equality, equals symbol, its big ideas, supporting concepts, development, scoring guide, & ideas to facilitate understanding. Includes the use of an equal arm balance to discover equality. With photos and different models made from K'Nex.
• Graphing - Instructional Plan for teaching graphing & solving for two unknowns four ways. (8-12 Grade)
• Justification & proof - 3 examples for Even or odd at the concrete, pictoral, & symbolic levels of representation
• Multiples, common multiples, & FTA - Discussion script includes: least common multiple, the next common multiple, fundamental theory of arithmetic (FTA) see FTA chart in activities.
• Primes and composites - Diagram to use to explore the primes of whole numbers 1 - 40 & invent the Fundamental Theory of Arithmetic (FTA)
• Reflections from ESU #1 workshop

## Activities to facilitate algebra, patterns, & functions literacy

#### Ratio & proportion

• Jo Tall and Jo Short - Work sheet ratio & proportion activity, historical research problem used to investigate the develop of reasoning as suggessted by Piaget
• Candle problems - Work sheet with sample rate & proportion problem and solution with follow up problem and questions.
• Sack Lunches - Teacher randomly passes out lunches. What are the odds? - Work sheet with hints & discussion ideas.
• Wages for Pet Care
• Acrobats Logic Problem - Work sheet draw a diagram, proportion & problem solving diagrams

Page Overview:

Other math knowledge base & activity pages

Process dimensions

Content dimensions

Challenges:

One of the universal customs that man has successfully established on earth is the
Hindu - Arabic numerals
to record numbers.

Algebra was greatly advanced by al-Khwarizmiâ€™s book:
Hisab al-jabr w'al-muqabala From which the word algebra came.