Ordering Fractions

Designed by:  Jeanna Hoffman and Christi Jones
Satchel Ford Elementary School

Core Curriculum Objective: Compare and order fractions using
manipulatives and pictorial representations.  (2NR5-2)

Grade level:    Second          Subject:  Math

Overview:  Students will compare and order fractions using fraction square sets after being shown fractional parts from a pattern block web page and discussing how to compare fractions.  Students will compare and order fractions by making fractions out of paper and using them to represent foods they like and dislike.

Focus Question: How can we compare fractions to put them in order from the smallest to the largest?

Time Frame:  two 55-minute class periods

Resources/ Materials: 

fraction square (or circle) set for each student*

Averkey

overhead projector and pen

overhead fraction  squares (or circles)

9" X 12" manila paper (4 pieces per child)

12" X 16" construction paper (light-colored)

student supplies: crayons, scissors, glue http://www.pacificnet.net/~mandel/Math.html

www.distance.vic.edu.au/maths/9MaLWk10/9ML10.html#Examplethree

  www.valpo.edu/home/student/scatlin/fractions.html

  math.rice.edu/~lanius/Patterns/design.html

  www.best.com/~ejad/java/patterns/patterns_j.shtml

*Use Ellison cutters to prepare the following fraction square set:  whole - brown, ½ - red, 1/3 " purple, ¼ - yellow, 1/6 " orange, 1/8" green.

6) Culminating Assessment:  Students will compare and order fractions by making fraction squares out of paper, coloring and cutting them out, and gluing the parts to show order from smallest to largest.  The teacher will use the following rubric to score student papers:

Fraction Rubric  

7) Instructional Activities:

Activity One:  (Students should have had prior instruction on fractions.)  Ask the students to define a fraction.  Remind students of previous class lessons regarding fractions.  Facilitate the discussion to conclude that fractions tell the part of a whole.

Show students the web site http://www.best.com/~ejad/java/patterns/patterns_j.shtml  Use an Averkey to show the site on a TV screen so that students will be able to see the picture.  Place a hexagon on the page.  Ask how many triangles it would take to make one hexagon.  Build a hexagon out of the triangles on the yellow hexagon.  Repeat this procedure using the trapezoid.  Ask the students to name the fraction for one part of each hexagon (1/6, 1/3). Ask them to compare the two fractions.  Which is larger? smaller?  Lead a discussion to clear up the misconception that a larger number in a fraction means it’s a larger fraction.

 Give each student a fraction square set.  Instruct students to build each square on the top of their desks.  They should have a total of six squares.  Model using overhead fraction squares if necessary.  Have students hold up one piece of the red square.  Ask for the fraction that names it.  Record it on the overhead.  Repeat this procedure with the remaining squares so all are listed.

Tell the students that these squares represent cakes and they are all chocolate cakes.  Tell students they can eat one part of one of the cakes, have them hold up that part, and explain why they choose it.   Everyone will probably have the whole brown square.  Instruct them to put this piece away.  Erase 1 whole from the overhead list.  Now have students  select a part they would eat, hold it up, and let someone explain why.  Circle the fraction ½ on the overhead.  Now tell students that all the cakes are mud cakes and they had to eat one part of one of the cakes.  Have them hold up the part and explain why it was chosen.  Circle the fraction 1/8 on the overhead. 

Ask students to look at the fractions ½ and 1/8.  Discuss why ½ is larger than 1/8. Facilitate the discussion to conclude that the larger the bottom number, the smaller each part will be because the whole will be split into more parts.

Instruct the students to work with a partner and take one part of each fraction square, including the brown one, and put them in order from the smallest to largest on their desks.  Circulate the room and assist students as needed.  Call on students to tell the smallest fraction (using both the fraction name and the color), next smallest, and so on.  Write them on the overhead in order.  Tell students they can make changes.

Close by presenting the following "important" scenarios to your students and letting them answer and explain their answers:

-Your mom asks if you want to eat 1/3 or 1/5 of your vegetables.

-Your teacher asks if you want to write ½ or ¼ of a page in your journal.

-Your dad asks if you want to eat ¼ or 1/8 of his ice cream.

-Your brother asks if you want 1/6 or 1/13 of his Halloween candy

-Your sister asks if you want to clean 1 whole room or 1/3 room.

Activity Two: Review the activity from the previous day. Pass out the manila paper (4 per student).  Model how to fold paper in half and open it, creating 2 parts.  Ask students to name the fraction for one of the parts.  Instruct students to write ½ on each part with a black crayon.

Repeat the procedure with each of the remaining three pieces of paper to make 4, 8, and 16 squares.  Have the students write the fractional parts (1/4, 1/8, 1/16) for each square on each piece of paper.

Give students a piece of construction paper.   Instruct them use a crayon to write the following title:  "What Fractions I Would Eat."

Students will choose fours colors to represent four different foods that they select (i.e. brown for chocolate candy, red for strawberry cake, purple for plum pie, yellow for lemons, orange for rhubarb pie, and green for spinach).  Discuss how to choose the colors (based on  likes and dislikes) and how to decide what color to use on which fractional paper (better-liked foods would be ½ and ¼, disliked foods would be 1/8 and 1/16).  Students will color the fractional papers.

Instruct them to cut out one part of each fraction and then glue them on the construction paper in order from the smallest to the largest.  Circulate the room and assist as needed. Students will write the foods that the fractional parts represent under each one.  Collect and assess these using the rubric.  Correct papers can be displayed in the hall or bound into a class book and displayed on the school’s web page.

Close the activity  by leading a discussion about how fractions are used in the world (cooking, sharing with friends).

Extension Activities: Use the following web sites as center activities for the students:

A fractional tutorial site www.distance.vic.edu.au/maths/9MaLWk10/9ML10.html#Examplethree

Interactive site for students to make fractions 

                                                                           www.best.com/~ejad/java/patterns/patterns_j.shtml

 This site has lots of activities for students to do online.  It starts out with basic activities about shapes and then moves on to more challenging activities.

math.rice.edu/~lanius/Patterns/design.html

Teaching Ideas: Visit the web sites http://www.pacificnet.net/~mandel/Math.html  http://www.lessonplanspage.com/javaframe.htm   http://www.valpo.edu/home/student/scatlin/fractions.html for more ideas on teaching fractions.