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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2002-032002-03

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