# Algebra Patterns and Functions

Related process categories:

## Teacher planning resources

- Assessment Sorting
- Authentic Assessment for functions & patterns - Bridges
- Teacher Directed Assessment for functions & patterns - Bridges
- Assessment - process proof and conjecture - content zero and properties of zero - addition and subtraction - with teacher reflection
*Concepts, misconceptions*,*&*outcomes- Articulating, Editing, and Refining Conjectures in a Second or Third Grade Classroom
- Plan for teaching graphing. Solving for two unknowns four ways. (8-12 Grade)
- Primes and composites. A study of whole numbers 1 - 40 to invent the Fundamental Theory of Arithmetic
- Vocabulary: algebra related list K-3, 4-8, 9-12
- Statistics timeline and history

## Activities

- Activities and reflections from ESU #1 workshop
- Arithmetic Properties
- Beaded necklace activity - and - worksheet - repeating patterns primary grades
- Beaded necklace
- Calendar math problems: topics include: factors, primes, relatively prime, pi, triangle numbers, square numbers, palindromes, perfect number, reciprocals, reciprocal numbers.
- Candle problems rate
- Consecutive numbers adding
- Equal sign & Equality scoring guide or rubric all grades
- Envelopes with cash
- Even or odd - concrete - pictoral - symbolic representations all grades

| video of student explanation for all odd numbers added to odd being even primary grades | - Factors to 50 & 100 Activity and resources
- Planning notes
- Table with all factors for numbers 1 to 50
- Summary table for the numbers 1-50 and the total number of factors of each Sorted By the # of Factors 1-10
- Table of factors 1-100 with first 50 completed
- Summary table for the numbers 1-100 and the total number of factors of each Sorted By By the # of Factor2 1-20

- Factors of 3 & 27 variable & constant
- Fibonacci Sequence explanation for generating the sequence & Fibonacci Numbers in Nature
- Graphing Notes Coordinate graphs
- Graph, the inventor of the modern graph story and sources
- Graphing Pictures plots - Johnnie Ostermeyer
- How many toothpicks to make the pattern? Pattern, function, and equation activity
- Jo Tall and Jo Short Proportion Activity
- Magic phone number or email I received on Presidents' day.
- M&M's what colors in a package? How many M&M's of each color are in a package?
- Multiples and least common multiple - the next common multiple?
- Multiplication of whole numbers and multiplication of binomials (x+1)(x+1)
- Multiples of three and 27 - use a calculator or spreadsheet to discover an amazing pattern of numbers casting out nines.
- Pools and sidewalks - patterns and functions
- Primes and composites. A study of whole numbers 1 - 40 to invent the Fundamental Theory of Arithmetic
- Pythagorean Theorem proof
- Sack Lunches
- Simultaneous Equations proofs
- Sixteen Colored Squares in an Eight by Eight square problem how many?
- Stairways and stacking blocks problems - also known as odd squares, tower, problem
- Stem and leaf plot problems and Java plotter available on the internet
- Toothpick squares activity: patterns, equations, proof for infinite patterns, problem solving, habits of mind for mathematics and algebraic thinking
- Variables. One variable activities - ping-pong ball race experiment, collect data, analyze (ping-pong ball race, how many stars in a minute).
- Wages for Pet Care

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*Challenges*:

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One of the universal customs that man has successfully established on earth is the

*Hindu - Arabic numerals*

to record numbers.

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*Algebra* was greatly advanced by al-Khwarizmiâ€™s book

Hisab al-jabr w'al-muqabala From which the word *algebra* came.

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*Read*... Cell phone mathematics.

*The story of how Brad Parkinson*used creativity and mathematics to enable the use of cell phones.