1 Mathematics Tasks for Cognitive Mathematics Tasks for Cognitive Instruction Instruction Based on research from the Quasar Project found in Implementing Standards-Based Mathematics Instruction: A Casebook for Professional Development(Stein, Smith, Henningsen, & Silver, 2000).
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1 Mathematics Tasks for Cognitive Instruction Based on research from the Quasar Project found in Implementing Standards-Based Mathematics Instruction:
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Mathematics Tasks for Cognitive Mathematics Tasks for Cognitive InstructionInstruction
Based on research from the Quasar Project found in Implementing Standards-Based Mathematics Instruction: A Casebook for Professional Development(Stein, Smith, Henningsen, & Silver, 2000).
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NCTM Standards Compared to NCTM Standards Compared to Connecticut Scope and SequenceConnecticut Scope and Sequence
Connecticut Scope and Sequence
Number Sense Operations Estimation Ratio, Proportion and Percent Measurement Spatial Relations and Geometry Probability and Statistics Patterns Algebra and Functions Discrete Mathematics
NCTM Content Standards Numbers and Operations Algebra Data Analysis and Probability Geometry Measurement
NCTM Process Standards Problem Solving Reasoning and Proof Connections Communication Representation
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NCTM and CT Scope and NCTM and CT Scope and SequenceSequence
Defining Levels of Cognitive Defining Levels of Cognitive Demands of Mathematical TasksDemands of Mathematical Tasks
Higher Level DemandsHigher Level Demands Doing Mathematics: Shade 6 small squares in a 4 X 10 rectangle. Using
the rectangle, explain how to determine each of the following:
A) the percent of area that is shaded B) the decimal part of the area that is shaded C) the fractional part of the area that is shaded
Comparing Two Comparing Two Mathematical TasksMathematical Tasks
Martha’s Carpeting Task
The Fencing Task
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Martha’s Carpeting TaskMartha’s Carpeting Task
Martha was recarpeting her bedroom, which was 15 feet long and 10 feet wide. How many square feet of carpeting will she need to purchase?
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The Fencing TaskThe Fencing Task
Ms. Brown’s class will raise rabbits for their spring science fair. They have 24 feet of fencing with which to build a rectangular rabbit pen to keep the rabbits.
a) If Ms. Brown’s students want their rabbits to have as much room
as possible, how long would each of the sides of the pen be?
b) How long would each of the sides of the pen be if they had only 16 feet of fencing?
c) How would you go about determining the pen with the most room for any amount of fencing? Organize your work so that someone else who reads it will understand it.