This lesson was written in an effort to help provide students with a solid foundation in fraction concepts that will help them, “Build the foundation to successfully apply more demanding math concepts and procedures and move into application” (Pre-K5 PACC Mathematics, p3). It also provides high-ability students with a greater in depth exploration of grade-level and above-grade level mathematics operations using fractions.

Numerator: 
The top number in a fraction.  (Shows
how many parts we have.)

Denominator: 
The bottom number in a fraction.  (Shows
how many equal parts the item is divided into.)

Mixed Numeral: 
A whole number and a fraction combined into one "mixed"
number.  (Example: 1½ (one and a half) is
a mixed fraction.)

Improper Fraction:  A fraction where
the numerator (the top number) is greater than or equal to the denominator (the
bottom number).   In other words, it is
top-heavy.  (Example: 5/3 (five thirds)
and 9/8 (nine eighths) are improper fractions.)

Common Denominator:  The
denominators in two (or more) fractions are common, or the same.

• 
  Students will find and compare fractional parts of whole objects using
  tangram pieces.
• 
  Students will apply the concept of equivalent fractions to calculate
  fractional values of multiple shapes and parts of a whole.
• 
  Students will create their own designs and calculate the fractional
  values of each color used in the designs.
• 
  Students will apply appropriate mathematical operations to analyze and
  compare the values of the parts of their design.

This lesson should take approximately three 40 minute class periods to complete.

• 
  Tangram Pattern Blocks

 

• APPLYING THE CONCEPT Handout.docx
• 
  Challenge-Window Analysis Handout.docx
• 
  Fractional Parts of a Hexagon chart.docx
• 
  Student and Teacher Evaluation.docx

W: WHERE/WHY/WHAT

Because this lesson is most appropriate for students who have demonstrated mastery
of  many or all of the Fourth Grade Mathematics/numbers and
operations – fractions skills, students will be able to not only extend and refine these grade-level skills,
but also gain experience and a better understanding of above grade-level skills
by completing the steps involved in this lesson.  This lesson is also infused with geometry,
art, writing, and speaking and listening skills as well. This will provide the
teacher with a means for both formative and summative assessment opportunities
using observation and student/teacher rubrics (Ongoing practice using gradual
release model, please do now, graphic organizers, presentation, and final product). 

 

H: HOOK

Linking this lesson to real-world personal experiences allows the students to discover
how fraction are used and calculated in their life.  Completing a “Please Do Now” during the
introduction of this lesson provides the spark for this connection.  Integrating writing, speaking and listening,
and art, gives students who would not normally choose math as their “favorite subject” a chance to explore the concepts in a way that they may find more interesting.  The hands-on activity
allows students to explore the concepts at their own pace using the option of
self-selection when creating their own geometric designs to later calculate.

 

E: EXPLORE/EXPERIENCE/EQUIP

Students will use hands-on experiences to create their own designs that will be used to
calculate fractional values.  During this exploration, students will have the opportunity to share thoughts with their
peers and listen to others’ thoughts and ideas when creating designs and calculating values.

 

R: RETHINK/REHEARSE/REVISE/REFINE

While analyzing the fractional values of their self-created window designs, students will have
to reflect on what they already know about the geometric shapes they used and
rethink how these shapes can be utilized in the calculation of fractional
values.  When completing the “Window Analysis”, students will be required to revisit these concepts and prove their calculations by reorganizing and comparing the final fractional values.

 

E: EVALUATE

Students will be formatively assessed using observation and discussion, as well as
teacher feedback of the “Please Do Now” activity and the “Fractional Parts of a
Hexagon” chart worksheet.  Teacher will use summative assessment strategies by using a student/teacher rubric to score the final product/presentation.

 

T: TAILORED

Because this lesson is focused on differentiation for the high-ability/gifted learner,
many of the steps required in this lesson involve above-grade level concepts or
greater in-depth exploration of grade-level concepts and curriculum.  During the lesson, students will be able to
self-select the shapes and designs they create and use to calculate fractional
values, thus allowing them to independently increase or decrease the level of challenge as needed.

 

O: ORGANIZED

Lesson and activities will be organized using a gradual release model, beginning with
whole group direct instruction (steps 1-3), and moving through guided
instruction (step 4), small group/partner work (step 7), and finally individual
work (steps 7- 8) involving extended thinking and real-world application.

 

 

1. 
    Using pattern blocks, Teacher will
   instruct students to locate the shape that is 1/6 of an entire hexagon.
   (Triangle)  Students will then be asked
   to write a short explanation (Please Do Now) as to why they selected the shape
   that they did.  Students will read their
   response to a partner and then discuss as a class. Teacher will complete a
   chart with the class indicating the fractional part of the hexagon for the
   following shapes: triangle, rhombus, and trapezoid. 
2. 
   Teacher will ask students to look at the larger hexagon shape on the
   handout and complete the chart again indicating the fractional part of the
   whole (4 hexagons) for the following shapes: triangle, rhombus, trapezoid, and
   hexagon.  When complete, teacher will
   discuss with class and check for understanding.
3. 
   Students will then be asked to calculate what fraction of the 4 hexagon shape would a triangle, a rhombus, and a trapezoid be all together.  Students will use addition of fractions to
   calculate this answer. (1/24 + 1/12+1/8 = ¼) 
   Teacher will remind students to simplify their final answer in lowest
   terms.  Students will demonstrate this
   both in number and picture/manipulative form and explain to a partner.  Teacher will discuss the need to have common
   denominators to calculate the problem on paper and explain that this requires
   finding equivalent fractions.  Teacher
   will provide examples if needed.
4. 
   Teacher will present students with a few more examples of addition of
   fractions using the 4 hexagon shape as the whole.  Students will independently complete
   problems.  Teacher will check for
   understanding.
5. 
   Teacher will explain that stained glass windows are an interesting way to
   study fractions because they these windows involve parts and wholes.  Teacher will share examples of stained glass
   windows by using “Applying the Concept” handout.
6. 
   Teacher will hand out “Challenge” page to students and allow each student
   to plan create and analyze the fractions of their own two stained glass
   windows.  Student and teacher will read
   through directions together and teacher will clarify any questions.
7. 
   Student will work first with a partner then independently on designing
   two stained glass windows using pattern blocks (only hexagon, trapezoid,
   rhombus, and triangle shapes).  (Window
   #1 should be completed with a partner, and Window #2 should be completed
   independently. ) Once windows are complete, student will complete the “Window
   Analysis” handout and apply the concept of adding and ordering fractions to
   their stained glass windows. 
8.  
   Students will share their final stained glass creations with the class
   discussing the fractions for each color they chose to use.
9. 
   Teacher will collect final designs, calculations, and work and score
   using project rubric.

This will provide the teacher with a means for both formative and summative
assessment opportunities using observation and student/teacher rubrics (Ongoing
practice using gradual release model, please do now, graphic organizers,
presentation, and final product). 

How Stained Glass is Made

http://www.mandywoodstainedglass.com/how-stained-glass-is-made/

Visit this website to learn
about how stained glass is made.  You’ll
have an opportunity to read about how artists design the plan for their window,
select and cut the glass, and assemble the window itself.  You can also visit the gallery to see
beautiful examples of handmade stained glass windows.

 

 

Online Pattern Blocks

http://nlvm.usu.edu/en/nav/frames_asid_169_g_1_t_2.html

Try building your window
online with these interactive pattern blocks! 
You can even print and color your window!

Gifted and Talented, Enrichment, Fractions, Numbers and Operations, IU11

Wendy Palese

June 10, 2014