TTL Spring 2003:TTL Spring 2003:Electronic Showcase for Electronic Showcase for
Understanding by Design Understanding by Design UnitUnitbyby
Pat LarsenPat LarsenWilson Elementary SchoolWilson Elementary School
Rapid City, SDRapid City, SD
MultiplicationMultiplication
In conjunction withIn conjunction with
Handheld Computer ProjectHandheld Computer Project
IntroductionIntroduction During the 2002 Summer TTL Academy, I developed a During the 2002 Summer TTL Academy, I developed a
strategic, nine-week long Understanding By Design Unit for 3strategic, nine-week long Understanding By Design Unit for 3rdrd grade multiplication. The essential understandings students grade multiplication. The essential understandings students will possess upon completion of this unit are: (1) multiplication will possess upon completion of this unit are: (1) multiplication is a critical step in their “Math Learning Stairs” and (2) their is a critical step in their “Math Learning Stairs” and (2) their success in all future math learning is contingent upon success in all future math learning is contingent upon acquisition of this skill.acquisition of this skill.
In the fall of 2002, one requirement of our TTL class was In the fall of 2002, one requirement of our TTL class was the completion of the Association for Supervision of Curriculum the completion of the Association for Supervision of Curriculum Development class entitled, “Differentiating Instruction.” This Development class entitled, “Differentiating Instruction.” This class focused on ways to address individualized learning needs. class focused on ways to address individualized learning needs. It was through the process of this class that I was able to It was through the process of this class that I was able to analyze my original UBD in terms of its effectiveness for analyze my original UBD in terms of its effectiveness for addressing each student’s learning styles and differences. addressing each student’s learning styles and differences. Based upon my new understanding of how children learn, I was Based upon my new understanding of how children learn, I was able to add key components and tiered activities to enhance my able to add key components and tiered activities to enhance my UBD.UBD.
Also in the fall of 2002, my students and I began a pilot Also in the fall of 2002, my students and I began a pilot project with handheld computers. We have been experimenting project with handheld computers. We have been experimenting with the use of these devices in all content areas. We have with the use of these devices in all content areas. We have discovered that handhelds can be extremely useful for math in discovered that handhelds can be extremely useful for math in terms of developing fluency with the basic multiplication facts.terms of developing fluency with the basic multiplication facts.
Since there are so many facets to my UBD, I have chosen Since there are so many facets to my UBD, I have chosen to address only segments of Stage 2: “Determine Acceptable to address only segments of Stage 2: “Determine Acceptable Evidence” for my presentation. The following pages highlight Evidence” for my presentation. The following pages highlight just a few features of the entire unit in order to showcase just a few features of the entire unit in order to showcase artifacts of my students’ learning opportunities and artifacts of my students’ learning opportunities and experiences. To view my UBD in its entirety, enter my website experiences. To view my UBD in its entirety, enter my website (pl031.k12.sd.us) and follow the link on my Welcome Page for (pl031.k12.sd.us) and follow the link on my Welcome Page for TTL 2002 Projects.TTL 2002 Projects.
Stage 2: Stage 2: Determine Acceptable Determine Acceptable EvidenceEvidence
PerformancePerformanceTask:Task:
Each student will be able to Each student will be able to demonstrate concrete demonstrate concrete understanding of the understanding of the concept of multiplication by concept of multiplication by building, drawing, or building, drawing, or discovering arrays around discovering arrays around the classroom.the classroom.
(The Math Stations are a new (The Math Stations are a new addition to my UBD. The addition to my UBD. The concept for these stations arose concept for these stations arose from the fall 2002 ASCD on-line from the fall 2002 ASCD on-line course entitled: course entitled: Differentiating Differentiating InstructionInstruction. These stations . These stations were created as tiered activities were created as tiered activities to address student differences.)to address student differences.)
Math Stations Math Stations (Activity #2)(Activity #2)
In this activity, students In this activity, students build given multiplication build given multiplication problems concretely. They problems concretely. They can do this several ways:can do this several ways:
Make arrays Make arrays using paper using paper plates to plates to represent represent the groups the groups and unifix and unifix cubes to cubes to represent represent the objects the objects in a group.in a group.
5 x 4 Array5 x 4 Array
Tiered Activities:Tiered Activities:
Make arrays using Make arrays using beans and cups and beans and cups and
paper plates and paper plates and monkeys.monkeys.
5 x 4 Array5 x 4 Array
6 x 2 Array6 x 2 Array
Math Stations: (Activity #2)Math Stations: (Activity #2)Showing multiplication concretelyShowing multiplication concretely
Make arrays using Make arrays using string and horses and string and horses and fishing line and lures.fishing line and lures.
2 x 2 Array2 x 2 Array
4 x 4 Array4 x 4 Array
Tiered Activities:Tiered Activities:
Drawing ArraysDrawing Arrays
3 x 8 Array3 x 8 Array(Multiplication as (Multiplication as
repeated addition)repeated addition)
Math Stations: (Activity #3)Math Stations: (Activity #3)Showing multiplication semi-abstractlyShowing multiplication semi-abstractly
Drawing ArraysDrawing Arrays
6 x 4 Array6 x 4 Array
2 x 6 Array2 x 6 Array
Tiered Activities:Tiered Activities:
Arrays Around the Arrays Around the ClassroomClassroom
2 x 3 Array2 x 3 Array
Math Stations: (Activity #4)Math Stations: (Activity #4)Showing multiplication abstractlyShowing multiplication abstractly
Performance Task:Performance Task:Learning Learning
Essential Essential
Vocabulary Vocabulary
TermsTerms
Each student willEach student will
define factors, define factors,
products, products, multiples,multiples,
common factors,common factors,
and least and least commoncommon
factors.factors.
Performance Task:Performance Task:Learning Learning
Multiplication Multiplication Facts The Fun Facts The Fun
Way!Way!
Each student willEach student will
acquire basic factsacquire basic facts
through the use ofthrough the use of
Miss Larsen’sMiss Larsen’s
StrategicStrategic
MultiplicationMultiplication
flashcards.flashcards.
Performance Task:Performance Task:Learning Learning
Essential Essential
RulesRules Each student willEach student will
analyze theanalyze the
multiplication tablemultiplication table
and apply the and apply the
(a) Commutative(a) Commutative
Property of Property of
Multiplication and Multiplication and
(b) the 0, 1, 2, 5,(b) the 0, 1, 2, 5,
and 9 times rules.and 9 times rules.
Performance Task:Performance Task:
Each student willEach student will
progress progress through through
the the multiplicationmultiplication
unit at their ownunit at their own
pace.pace.
Performance Task:Performance Task:
Each student willEach student will
progress through progress through
the the multiplicationmultiplication Learning SheetsLearning Sheets..
Quizzes, Tests, and Quizzes, Tests, and Prompts:Prompts:
P.M.P.M.
UnitUnitSample Sample
WrittenWritten
TestTestSample Sample HandhelHandheld Testd Test
Each student Each student willwill
progress progress throughthrough
leveled leveled PrecisionPrecision
Math Tests.Math Tests.
Quizzes, Tests and Quizzes, Tests and Prompts:Prompts:
Precision Math Precision Math tests to assess tests to assess acquisitionacquisition of basic facts of basic facts through nine.through nine.
Precision Math Precision Math tests to assess tests to assess
fluencyfluency of of basic facts basic facts
through nine.through nine.
HandheldHandheld ComputersComputers in in the Learning the Learning
CenterCenter
HandheldHandheld ComputersComputers in in
the General the General Education Education
SettingSetting
Quizzes, Tests and Quizzes, Tests and Prompts:Prompts:
By using handheld computers, students By using handheld computers, students have the capability of instantly “beaming” have the capability of instantly “beaming”
their results to their teacher.their results to their teacher.
Through a handheld software program Through a handheld software program called “Quizzler Pro,” teachers have the called “Quizzler Pro,” teachers have the
capability of automatically exporting these capability of automatically exporting these test scores into their electronic grade book.test scores into their electronic grade book.
ConclusionConclusion
Upon completion of this nine-week long Upon completion of this nine-week long unit, the vast majority of students at Wilson unit, the vast majority of students at Wilson Elementary have not only experienced Elementary have not only experienced success in their understanding of the success in their understanding of the concept of multiplication and their concept of multiplication and their acquisition of the basic facts, but have also acquisition of the basic facts, but have also come to recognize how multiplication is a come to recognize how multiplication is a critical step in their “Math Learning Stairs.” critical step in their “Math Learning Stairs.” This vital step is This vital step is essentialessential for all future for all future math learning.math learning.
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