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 conjecturesRecognize and use counterexamplesJustify their conclusions and respond to others ideas using drawings, diagrams, actions*

5th Walls With Windows*

Draw a picture*

Use a table*

Build on previous knowledge or calculations*

Mathematical Practice:Model with mathematics.Solve problems in everyday lifeWrite equation to describe a situationSolve a design problemMake assumptions and approximations to simplify a complicated situationInterpret results to see if they make sense in terms of the situation*

Singing at the Ballpark- 4th21 students need to get to the ballpark.Each car will carry one adult and up to 4 students.5 cars please? *

Interpret results into context to check for reasonableness *

Check for Reasonableness*

Check for ReasonablenessYou cant leave someone behind!!!!*

Solve a design problem 5th*

Real Life Situation*

Write an equation to model*

Map relationships between Quantities*

Mathematical Practice:Use appropriate tools strategically.Use paper pencil, concrete models, ruler, protractor, calculator, spreadsheet, etc.Tools might also include choosing an appropriate mathematical strategy

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Strategy - Slope*

Tools - Calculator*

Tools Calculator Strategy Convert to decimals*

Mathematical Practice:Attend to precision.Communicate precisely with clear definitionsState meaning of symbolsCalculate accurately, efficiently, and use appropriate level of precision

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Have a Clear DefinitionTeacher comments on 2-4 tests: Why do the tasks use the word angle when our textbooks use vertex?*

Words are tools for thinkingNot 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 didnt you just ask for length, width, and height?*

Cognitive DemandHow many dimensions are there?*

Dimensions?*

Dimensions?*

Diagonal*

Mathematical Practice:Look for and make use of structure.Discern pattern or structureSee complicated things, such as algebraic expressions as single objects or as composed of several objects *

5th- Box of Cubes- Structure*

Making Sense of StructureSeven most important words to transform education: How did youFigure that out?*

7th Grade Freezing in FargoHow many times colder is Wednesday Feb. 25th than Tuesday Feb. 3rd? Almost 40% of the students in the sample subtracted.*

Mathematical Practice:Look for and express regularity in repeated reasoning.Look for repeated calculations in both general methods and for short cuts*

6th Freezing In FargoWhich week (Sunday through Saturday) recorded the average lowest temperature?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.*

Tools For Practices and StandardsUse MARS Tasks Define the meaning of the standards and practicesRaise expectations for teachers about what students are capable of accomplishingHelp teachers anticipate misconceptions so that they can be surfaced and addressed in class discussion and re-engagement lessons*

ResourcesSVMIMAC.org websiteInside Mathematics.org directly or through link in NCSM*

TOOLS BY SUBJECTAlgebra & FunctionsAlgebraic Properties & RepresentationsData AnalysisFunctions & RelationsGeometry & MeasurementMathematical Reasoning & ProofsNumber OperationsNumber PropertiesPatterns, Functions & AlgebraProbabilityStatistics3rd 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*

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Practices Require ContentLooking at and Understanding Number SystemUsing Place Value Strategies to Make Sense of and Solve ProblemsUnderstanding Number Line as a basic mathematical concept and tool

Butterfly and Moth CollectionHow much longer was the longest wingspanthan the shortest?

Research Suggests:Number lines help students understand fractions as a single number instead of two unique point or location on the lineNumber line concepts and reading fractions can be introduced through rulers, clocks, scalesNumber lines help students develop the ability to generalize about number and operations

Knowing Fractions

Knowing Fractions

Preparing for GeometryTo do the type of work needed to be successful in geometry, students need to have a variety of experiences at earlier grades.Ideas build over time.

Purpose of Resources

Developing Algebraic ThinkingDescribe T pattern 5.

Lattice Fence 6thDefine the pattern to explore relationships.

Aussie Fir Tree - Algebra

Proportional Reasoning

Rate Concentrate 6th

Using the 8th Grade Test

8th Grade - ToolUnderstand the 8th grade Mathematics Common Core Course and the deep rich mathematical expectations for studentsIncludes rich Algebra Strand but also works to expand and deepen understanding and facility with other strandsUse as Placement Test or Summative Test - Could your 7th graders pass this test? Could your Algebra and Geometry students meet standard on test?Facilitate Course Discussion with Staff and Parents Is this the mathematics we want students to be able to know and do?

Implementing Formative Assessment Lessons- Forming Professional Learning Communities

How do we create classroom culture?How do we facilitate staff doing mathematics together to understand purpose of the lesson, understand the mathematics before giving it to students, work as a learning community to discuss techniques, purpose of using student work, types of comments to put on student papers, how to have a plenary discussion? What are the important mathematical ideas to be drawn from students? What teacher moves help hold all students accountable for their own learning?Making time for lessons?

How will the student get from oz to boxes?*Big Idea- *Big Idea- *Big Idea- *Big Idea- *When it comes to academic language we are all second language learners? How do we provide experiences that use language for a purpose to help develop academic language acquisition?*Big Idea- *Use structure to think about how all the cubes fit together*Move to website View 1000-998 Amelia and Ana, then go to 295 students 25 to a bus MarrissaWant students who can think about appropriate strategies for numbers involved, best strategy for the situation Show sample answer cards*Big Idea- *This years tool kits will list tasks by Common core and by Mathematical practices, Could have Cindy post it on the web now if its useful.*Go to video of Phil if time. Then take a break!!!!!*Not expecting students to be able to do formal algorithm with finding common denominators and subtracting, but are expecting them to use the number line to count the distance between and 4 .Understand the idea of distance on a number line.*Other tasks with number line: Fraction Match 6th and Lets Be Real 8th and *Ordering fractions, decimals, and percents on a number line. Using those number cards to write equations*This is no simple feat! These resources are intended to provide teachers support in making the needed enhancements and changes in instruction. Below is a schematic describing a progression of geometric understanding.*2nd grade: Teachers complained about this part of the task. Important to understand the learning trajectory. What is the purpose of the question. See structure and write formula Total = 3n + 1 *Questions meant to model types of ideas that are important for conceptual development.***Find similar figures to A, students could only find largerTeachers didnt think appropriate context for proportional reasoning*Entry level ratio of length to height of A*Take a moment to look at the 8th grade test with a neighbor and review the the core standards.*PPI Patrick Callahan*