NOMA Northern Ontario Math Association Satellite Site: New Liskeard Board Office, Saturday, October 22, 2011
PD at DJPS NOMA Saturday, October 22, 2011
GROWING LINEAR PATTERNS
InputOutput WHAT IS ADDITIVE THINKING? When students use additive thinking, they consider the change in only one set of data. For instance, in the examples below, students can recognize that the pattern increases by 3 blue tiles each time, or that the value in the right column increases by 3 each time. Students who utilize only additive thinking do not recognize the co-variation between the term number and tiles, or between the two columns in the table.
MULTIPLICATIVE THINKING Understanding the co-variation of two sets of data For instance, in this pattern, the mathematical structure can be articulated initially by a pattern rule, number of tiles = term number x3+1 In older grades more formal symbolic notation can be used, y=3x+1 This allows students to confidently predict the number of tiles for any term of the pattern 123
Multiple Representations of Growing Linear Patterns
GROWING LINEAR PATTERNS
Tiles = position number x1+1 Tiles = position number x3+1 Tiles = position number x5+1 What is similar in the 3 rules? What is different? What is similar in the 3 patterns? What is different? What is similar about the trend lines on the graph? What is different?
Tiles = position number x3+2 Tiles = position number x3+6 Tiles = position number x3+9 What is similar in the 3 rules? What is different? What is similar in the 3 patterns? What is different? What is similar about the trend lines on the graph? What is different?
GENERALIZATION STRATEGIES StrategyDescription CountingDrawing a picture or constructing a model to represent the situation to count the desired attributes RecursiveBuilding on the previous term or terms in the sequence to determine subsequent terms (Additive thinking) Whole- object Using a portion as a unit to construct a larger unit by multiplying. There may or may not be an appropriate adjustment for over-or-undercounting. Guess- and-check Guessing a rule without regard to why this rule might work. Usually this involves experimenting with various operations and numbers provided in the problem situation. ContextualConstructing an explicit rule that expresses the co-variation of two sets of data, based on information provided in the situation. An explicit rule can allow for the prediction of any term number in the pattern.
Landscape of Learning Patterning and Algebra K-8
Student Achievement OutcomeData ProcessData Summative Data Observation Data EQAO, Report Card Implementation
SUMMER INSTITUTE: AUGUST, 2011
SUMMER INSTITUTE GETS TEACHERS FROM ACROSS THE BOARD SHARING
SUMMER INSTITUTE PROMOTES COLLABORATIVE PLANNING
NETWORKING BETWEEN SCHOOLS
FLUENCY IN OPERATIONS THROUGH MATH ACTIVITIES
SUMMER INSTITUTE 2011: GROWING LINEAR PATTERNS FOR THE CLASSROOM
OUR GOALS: Focus on student achievement Build trust with principals, teachers, families Collective efficacy Build mathematics leadership capacity Increasing student comfort/enthusiasm for math Respect for specialization and diversity Collective learning Support each other with challenges Build on each other’s learning
LEADERSHIP “The heart of school improvement rests in improving daily teaching and learning practices in schools, including engaging students and their families.” Ben Levin, 2008