Content Area: Math

 

Index: 4.1A Grade 12 CPI 3

 

Standard: 4.1 - Number and Numerical Operations

 

Strand: C - Estimation

 

Cumulative Progress Indicator: 3 - The student will develop conjectures and informal proofs of properties of number systems and sets of numbers.

 

Grade: 12

 

Sample Activities:

 

·        Students discuss whether the transitive and reflexive properties hold for different relationships, such as "is a friend of", "is perpendicular to," or "is a factor of."

 

·        Students make up a number system using symbols. They develop algorithms for adding and multiplying within their system and decide whether these operations are commutative and associative.

 

·        Students explore the properties of clock arithmetic or a modular arithmetic system.

 

·        Students examine properties involving addition of matrices, scalar multiplication, and matrix multiplication. They demonstrate that matrix multiplication is not commutative by providing a counter-example.

 

·        Students investigate transformations of the rectangle ABCD: reflection about its the horizontal line of symmetry (H), reflection about its vertical line of symmetry (V), rotation by 180 degrees (R), and rotation by 360 degrees (the identity, I). They construct an operations table which tells what happens if one of these transformations is followed by another. Thus, for example, if you reflect about the vertical line of symmetry (V) and then rotate by 180 degrees (R), the result is the same as reflecting about the horizontal line of symmetry (H); this is indicated in the table by placing H as the entry in the row for V and column for R representing the conclusion that V followed by R is H. Students investigate the properties of this operation "followed by."