How to Implement A Story of Units

Kathleen DialImagine South Lake

*commoncore.org* engageny.org

IntroductionSequenced and Comprehensive Through 3

Components:

1. Unfolding story over the student’s career – emphasizing key themes and the relation and manipulation of units.

2. Focus on meaningful assessment – well designed, quick and accurate that promote self-monitoring and self-improvement

3. Engaging lesson structure- fast paced practice, encourage perseverance and foster thoughtful development of understanding.

Design ApproachMathematics is mostly effective taught in

logical engaging storyMain character is the unitThemes like measurement, place value and

fractions run throughout the storylineSignificance of the unit: define the basic

building block – the unitProgression: numbers through 10, addition and

subtraction, place value and standard algorithms, multiplication, fractions, word problems

Instructional Shifts AddressedFOCUS

Relating every arithmetic ideas back to the understanding of a unit.

Definition varies – whole numbers, fractions, decimals, measurements

Commonalities between all units/unique features of the units (they can be added, subtracted, multiplied)

Instructional Shifts AddressedCoherence

Not a collection of topics – emphasis on mastery of cluster standards

Instructional sequence is organized to build on previous learning

Instructional Shifts Addressed

RIGOR in 3 ways

1. Fluency2. Conceptual Understanding3. Application with Dual Intensity

Shift – RigorFLUENCY

Daily, substantial, sustainedIncluded in most lessons and supported in

lesson structureEasy to administer and assess

Shift-RigorConceptual Understanding

Deep understanding- they learn more than how to get the answer right

Use writing and speaking to solve math problems, reflect on learning and analyze their thinking

SEQUENCE IS EVERYTHING! Modules build on requisite skills – Deliberate Progression

Shift-RigorApplication and Dual Intensity

Teaches students to choose and apply math concepts to read world problems

Tools and diagrams that aid problem solvingProblems are designed for a healthy mix of

PARCC Type I, II and III tasks. Fluency and application practice daily

Approach to Assessment1. Daily Assessment – activity sheets, exit

tickets, homework sheetsMid-Module Assessment Task End of Module Assessment TaskCross-Modular Assessment Task

Daily Assessment Check InsActivity Sheets – apply conceptual understanding,

can be independent, group work, or with teacher guidance, graded or not

Exit Tickets – Critical element of lesson1. Individual accountability2. Valuable evidence of the effectiveness of that day’s

instruction – for planning purposes

Homework – additional practice, not introduce brand new concepts or ideas, build student confidence and check understanding

Mid-Module Assessment

Address first ½ of a moduleRubric will provide guidance for pre-

conceptions or mis-conceptionsComplete independently

End-Of-Module Assessment Task

SummativeGauge full range of understandingTasks will help prepare them for PARCCSome items will assess specific standardsSome items will synthesize broader concepts

Cross-Modular Assessment Task

Multiple modulesImportant connections across major topicsRequire students to retain skills and also

make connections to deepen their understanding of key math topics

Rigor in AssessmentsSimple to ComplexDemonstrate procedural skill, fluency and

conceptual understandingApplication problems, including multi-step

work problems are always part of the assessments

Differentiating

Modules contain scaffold chartsMarginal notes regarding scaffolds in each

lessonPay attention to sequence – ideas move from

simple to complex throughout the lesson – can help you locate specific steps that students are struggling with

Differentiating - TIMEUtilize a “TIME FRAME” rather that a “TASK

FRAME”“Class, you have 10 minutes to work

independently.”Teacher circulates and monitors, error-

correctingAlways bonus tasks for accelerated students

PERSONAL SUCCESS IS THE GOAL! Not completion of an activity page.

Differentiating – EXIT TICKETS

Teaching practice can be firmly grounded in student learning

“Precise Error Correcting” Demonstrate, Model and Intelligent PracticeSkills are acquired incrementally

Lesson StructureFluency PracticeConcept DevelopmentApplication ProblemsStudent Debrief

Most lesson are structured for 60 minutes, can easily be stretched to 90 minutes.

Fluency PracticePromote AUTOMATICYEngaging – gets adrenaline flowingAutomaticity is critical so that students

avoid using up too many of their attention resources with lower-level skills when they need to be addressing higher-level problems.

Minimum of 10 minutes daily Use it or lose it

Concept Development

Major portion of instructional timeAt least 20 minutes of total lessonNew learning is introducedConcrete-Pictoral-Abstract

Application ProblemsStudent chance to choose and apply the

correct mathematics to solve real world problems

Beginning of the year – establishes routines, model behaviors

Differ from fluency “quick answers”Read-Draw-WriteConnect to Concept Development part of the

lesson

Student DebriefReflect back and analyze the learning that

occurredObjective of lessonSee and hear multiple perspectivesShare and analyze multiple student workExit Tickets

Team PlanningModule 1