PROMOTING ALGEBRAIC REASONING (MEANINGFUL USE OF SYMBOLS (The Meaning of…
PROMOTING ALGEBRAIC REASONING
STRANDS OF ALBEBRAIC REASONING
Study of Structures in the number system, including those arising in arithmetic
Study of patterns, relations and function
Process of mathematical modeling, including the meaningful use of symbols
STRUCTURE IN THE NUMBER SYSTEM: CONNECTING NUMBER AND ALGEBRA
Generalization with Number Combinations
Frogs on a pond problem: there are 5 frogs in a pond. some jump onto a lily pad and some jump onto a rock. how many frogs might be on the lily pad and how many might be on the rock?
Have students subtract numbers to equal 15
Generalization with Place Value
Move down two and over one, what is the new number
Ask "when is this true? Why does this work?"
Generalization with Algorithms
EX: 504-198= 504-200+2
MEANINGFUL USE OF SYMBOLS
The Meaning of the Equal Sign
As early as 1st grade
also ask studnets to find an equivalent expression
Conceptualizing the Equals Sign as a balance
Developed throu meaningful contexts
True/False and Open Sentences
use to make sense of the equal sign.
students agree with equations when an expression on one side and a single number on the other
Operational view: means to do something
Relational-computational view: symbolizes the relation between the two.
The Meaning of Variables
Variables Used as Unknown Values: EX n+n+7=n+17
found often in word problems
Variables Used as Quantities That Vary
EX: L is Legs, D is Dogs L=Dx4
STRUCTURE IN THE NUMBER SYSTEM: PROPERTIES
Properties: Commutative- associative - additive identity - additive inverse- invers relationship of addition and subtraction
Making Sense of properties
Ask questions such as "what do you notice?"
Make slight changes to arithmetic problems are presented can open up opportunities to examine the mathematical ideas
"is it true for any numbers?"
have students express the properties in general terms without numbers
Making and Justifying Conjectures
Students use examples of properties
PATTERNS AND FUNCTIONS
Example: red- blue- red- blue
Show by circling the core start
Sequence: Progression from step to step
Teach with visuals
Book: Two of everything
Examples: 1,2,1,2,1,2, alternating pattern -2,4,6,8, Skip counting -
2,5,11,23 double the previous number and add 1