Make sense of quantities. How do quantities fit into the problem. Abstract and Recontextualize. Mathematical Practice:. Construct viable arguments and critique the reasoning of others. Build logical progression of statements to explore conjectures Recognize and use counterexamples
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
21 students need to get to the ballpark.
Each car will carry one adult and up to
5 ¼ cars please?
You can’t leave someone behind!!!!
Use appropriate tools strategically.
Attend to precision.
Teacher comments on 2-4 tests: Why do the tasks use the word angle when our textbooks use “vertex”?
Not having words to use limits the mathematics we can think about. – Harold Asturias, Lawrence Hall of Science
Teacher comments: Why did you use the word “dimensions” on the 5th grade task box of cubes? Why didn’t you just ask for length, width, and height?
Look for and make use of structure.
Seven most important words to transform education: How did you
Figure that out?
Almost 40% of the students in the sample subtracted.
Look for and express regularity in repeated reasoning.
A student noticing that all the averages are divide by 7 days should realize that comparing totals will yield some comparative results without needing to divide.
3rd GradeCore IdeasRecognize and use characteristics, properties, and relationships of two-dimensional geometric shapes and apply appropriate techniques to determine measurements.Choose appropriate units and tools for particular tasks and use these units and tools to estimate and measure (length, weight, temperature, time, and capacity).Identify and compare attributes of two-dimensional shapes and develop vocabulary to describe the attributes.Calculate perimeter and area and be able to distinguish between the two measures. (Area may be measured by covering a figure with squares.)Use visualization, spatial reasoning, and geometric modeling to solve problems.Recognize geometric ideas and relationships and apply them to problems.MARS TasksLooking Glass LandTaskRubricCore Mathematical Ideas and ChallengesQuestions for Teacher ReflectionDiscussion of Successful Examples of Student WorkDiscussion of Student MisconceptionsGraph and Analysis of the MARS Task DataSummary of Student Understandings and MisunderstandingsImplications for Instruction
TOOLS BY SUBJECTAlgebra & FunctionsAlgebraic Properties & RepresentationsData AnalysisFunctions & RelationsGeometry & MeasurementMathematical Reasoning & ProofsNumber OperationsNumber PropertiesPatterns, Functions & AlgebraProbabilityStatistics
How much longer was the longest wingspan
than the shortest?
Describe T pattern 5.
Define the pattern to explore relationships.