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Promoting Algebraic Reasoning (1.Structures in the Number System:…
Promoting Algebraic Reasoning
Strands of Algebraic Reasoning
Study of patterns, relations, and functions
Process of mathematical modeling
Study of structures in the # system
Connecting Number and Algebra
Generalization with # combinations
A, One Up and One Down w/ +
"Frogs on a pond"
Generalization with Place Value
A. Diagonal Sums
Generalization with Algorithms
3.Meaningful Use of Symbols
=
A. Ten and then some
A. Different but the same
"Balance"
A. Tilt or Balance
builds understanding for equations: 5x-24=54
A. What Do you know about the shapes
Relational Thinking
Relates to Diagonal Sums
True/False and Open Sentences
A. T or F equations
open sentences next
A. What's Missing?
Variables
Unknown Values
A. Toys, Toys, Toys
Quantities that vary
Misconception: Variable means Label
1.Structures in the Number System: Properties
Making Sense of Properties
A. Five Ways to Zero
Use property, explain property, use symbols to describe
Making and Justifying Conjectures
Even and Odd Conjectures
A. Fair Share of Two
A. Bumps or no bumps
A. Broken Calculator: Can you fix it?
A. Convince Me Conjectures
Most common form: examples
Patterns and Functions
Repeating
A. Can you Match it?
A. Predict Down the Line
A. Same Pattern, Different Stuff
Growing Patterns/Sequences
Recursive
Functional Thinking
A. What is my Rule
A. What's Next and Why?
A. Calculator Skip Counting
Reinforces invented strategies
Number Patterns
*Use Physical Objects
Sense-making activity vs. right or wrong
Patterns can be extended to any length
5 Properties
Table 13.1
Common Misconceptions with Algebraic Reasoning
5 from Table 13.2