Finding Number Relationships
using Tangrams

by Renato Montaño

Introduction

Standards

Objectives

Activities

Assessment

Results

Resources

Introduction
Having a hard time teaching relationships between fractions, decimals and percents concretely to your students?  In this lesson students read Chinese Mythologies that present problems about tangrams and are then asked to give fractional representations to each piece as it relates to a whole. Students will also be asked to convert fractions to different measures such as decimals and percents to represent tangram pieces and explain the relationship between the three measures.

Subject:  Mathematics
Topic: Number Relationships
Grade Level:  Fifth Grade
Student Lesson name and URL:
http://ctap295.ctaponline.org/~rmontano/student/

Standards Addressed
Fifth Grade
Math: Number Sense

1.0  Students compute with very large and very small numbers, positive integers, decimals, and fractions and understand the relationship between decimals, fractions, and percents.  They understand the relative magnitudes of numbers:

1.2  Interpret percents as a part of a hundred: find decimal and percent equivalents for common fractions and explain why they represent the same value; compute a given percent of a whole number.

Instructional Objectives 

1. After reading "The Magic Window", retold by Sarah A. Keith, students will be able to re-arrange the seven tangram pieces to create, color and name at least 3 different beautiful creatures.
2. Students will be able to write and type, in Microsoft Word, a 5-sentence paragraph myth based on one of their created creatures and present it orally to the class.
3. After reading "The Chinese Tile Maker", paired students will be able to give a monetary value to each of the seven tangram pieces and covert to fractional representations.
4. Paired students will be able to convert fractions to different measures such as decimals and percents and plot the results on an Excel spreadsheet table to represent tangram pieces with 90% accuracy.
5. After students have converted fractions to decimals and percents, paired students will be able to orally explain the relationship between the three measures and determine which measure best applies to the problem posed on "The Chinese Tile Maker". 
   
   

Student Activities

Introductory Activity
1.  Students will read

2.  Also, students will be asked to write and type, in Microsoft Word, a 5-sentence paragraph myth based on one of their created creatures and present it orally to the class.  Their selected tangram illustration and typed myth will be glued on a 11 x 18 construction paper and posted around the classroom to encourage student involvement in future activities.

Enabling Activities)
1.  Administer pre-assessment on number relationships.  Have students convert the monetary values to fractions, decimals and percents and plot on table (Pre-Assessment).

2.  Students will read "The Chinese Tile Maker".  Students will then be asked to print a copy of the seven tangram pieces and cut out all the pieces.   In pairs, students will give each tangram piece a monetary value and share it with the class on the overhead.

3.  Discuss how monetary representations can be converted to fractions such as $.50 = 50/200 = 1/4 in a whole that equals $2.00.  Then, have paired students convert all of their original answers in the form of money to fractions and have them share some examples with the class.  Students can check their answers on the on-line Converting Machine (Decimal to Fraction Converter).

Culminating Activity
1.  Discuss and give examples on how to convert fractions to other measures such as decimals (remind students that money representations are in form of decimals and that they would only have to remove the dollar or cents symbol)  and percents.  Have paired students find the relationships for the tangram pieces and plot results on an Excel spreadsheet table.  Students can check their answers on the on-line Percent Calculators.

2.  Students will illustrate their spreadsheet on a projected screen (LCD Projector) and orally explain the relationship between the three measures and which measure best applies to the problem posed on "The Chinese Tile Maker".

3.  Administer the post-assessment on number relationships.  Have students convert the monetary values to fractions, decimals and percents and plot on table (Post-Assessment).
 

Assessment
1.  Click here for Pre-Assessment

Results
After implementing your lesson (sometime between January & March), insert a chart of your pre-test, post-test, and culminating assessment data.
 

Web Resources & Supplementary Materials

Web Resources
1.  "The Magic Window"
http://www.ajkids.com/KidsFinalAnswer.asp?qCategory=KIDS&Link=http%3A%2F%2Fwww%2Egeocities%2Ecom%2FEureka%2FSuite%2F3789%2FPAGE4%2EHTML&Title=Picture+This&Answers=1&site_name=Kids&origin=0&ask=Where+can+I+make+Tangram+puzzles%3F&aj_ques=snapshot%3Dkids1%26kbid%3D1229363&aj_logid=085951D1AA61D4118A390090276A5452&aj_rank=1&aj_score=0%2E8

2.  Converting Machine
http://www.math.com/students/converters/online_converters.htm

3.  Percent Calculators
http://www.math.com/students/calculators/source/3percent.htm

Supplementary Materials
1.  Myth Template (Myth Template.doc)

2.  Pre-Assessment (Pre-Test.xls)

3.  Pre-Assessment answers (Pre-Test Answers.xls)

4.  "The Chinese Tile Maker" (Chinese Tile Maker.doc)

5.  Number Relationship Conversion Table (Number Relationship Table.xls)

6.  Post-Assessment (Post-Test.xls)

7.  Post-Assessment answers (Post-Test Answers.xls)

8.  Grading Rubric (Rubric.doc.)

Desert Garden Elementary School
1900 South 6th Street 
Renato Montaño: rmontano@ecsd.k12.ca.us
Last Revised: 09/12/00