Math, Grades 5-8

Piecing it Together: Adding & Subtracting Fractions

1998 Master Teacher Tonya Aitken, Hampshire Regional School High School, Westhampton, MA

 

Overview

This lesson teaches students to add and subtract fractions and mixed numbers with unlike denominators. The students "fish" for and solve a number of fraction problems requiring adding, subtracting, finding equivalent fractions, renaming whole numbers into fractions, and using mixed numbers.  As a preliminary activity to demonstrate why fractions are necessary in real life, the teacher may show the Executive Chef portion of the video The Eddie Files #4 - Fractions: Any Way You Slice (Foundation for Advancements in Science and Education).  Students should also be comfortable with adding and subtracting fractions with like denominators.

 

ITV Series

The Eddie Files—Fractions:  Any Way You Slice It. (FASE)

Math Works—Fractions 2: Unlike Denominators (AIT 1985)

 

Learning Objectives

Students will be able to: find equivalent fractions; add and subtract fractions and mixed numbers with unlike denominators; and explain why they need to be able to do this.

 

Materials

construction paper in different colors (one large circle for every 2-3 students and several smaller pieces to cut into props)

glue sticks (one per group of two-three students)

scissors (one per group of two-three students)

poster board (a few large pieces, different colors preferred)

paper clips

scotch tape

large coffee can or small bucket

game spinner  (optional)

hole punch (optional)

 

Vocabulary

sum—the result when you add two or more numbers together

numerator—the top number in a fraction, represents how many parts we are interested in

denominator—the bottom number in a fraction, represents how many parts the item is divided into

equivalent—having the same value (representing the same amount)

rename—give another name for a number or fraction (change a whole number into a fraction)

multiple—multiply that number by any other integer (multiples of 3 would include 3,6,9,12...)

LCM (Lowest Common Multiple)—the smallest non-zero number that is a multiple of two or more whole numbers

 

Pre-Viewing Activities

As a preliminary activity to demonstrate why fractions are necessary in real life, the teacher may show the Executive Chef portion of the video. Introduce the concept of equivalent fractions using an activity from the video The Eddie Files #4 - Fractions: Any Way You Slice It  (FASE)  Divide students into groups of two-three.  Give each student a round piece of construction paper (pizza-sized) and a selection of pre-cut paper pizza "toppings" (mushrooms, pepperoni, peppers, tomatoes, etc. - should have 8-10 toppings).  Have each group "top" their pizza by gluing their choice of toppings with glue sticks (same toppings all over).  Assign each group a number (2, 3, 4, 6, 8, 12).  Each group is then to evenly divide their pizza into that number of pieces, becoming fractions (1/2, 1/4, 1/8, 1/3, 1/12).  Talk about how one piece from the 1/2 group would equal two pieces from the 1/4 group, etc.  Then tell the students that they will have five minutes to trade pieces with other groups to try to come up with as diverse a pizza as they can without having any less or any more than one (whole) pizza.  Time the activity.  At the end, discuss the outcome and how term "equivalent fractions" applies to this lesson.

 

Focus for Viewing

The focus for viewing is a specific responsibility or task(s) students are responsible for during or after watching the video to focus and engage students' viewing attention.  Say, "We are going to watch part of a video about fractions.  As you watch, it will be your responsibility to find out why fractions need to have common denominators before we add or subtract them, and what steps you need to take to add or subtract fractions that don't already have common denominators."

 

Viewing Activities

Begin the video Math Works—Fractions after the introductory credits.  Pause after the first Math Fair section when the man says, "It looks like the girls are going to have to add fractions with unlike denominators."  Ask the students, "What is a denominator?  What does he mean by unlike denominators?"  Then have the students brainstorm ideas as to how the girls may approach the problem.  Resume the video.

 

Pause after the man says, "5 cats and 3 dogs = 8 what?"  Ask for responses.  Give the students other examples of adding objects which are not alike but could belong to a common group and ask them to name the common group.  For example: boys and girls = students; pears and oranges = fruit.  Have students come up with a few examples of their own.  Briefly discuss the concept of needing to change categories of the objects so that they have a common category.  Resume the video.

 

Pause after the man says, "What is a number common to both denominators?"  Briefly ask students to identify what he means by "common to both denominators".  Write the problem shown on the screen on the board in class (3/4 + 5/8 = ?).  Ask class for ideas as to how to solve it.  Tell students, "Watch to see how the students solve the problem."  Resume video.

 

Pause after the girl says, "Since 8 is the lowest common denominator, why don't we just multiply the 4 by the 2?" and circles the two 8s.  Ask students, "What does she mean by lowest common multiple?  How did she find it?  Did anyone notice what she did to numerator and the denominator?"  (She multiplied both by the same number.)   Resume the video.

 

Pause after the girl says, "...so we have 6/8."  Ask students, "Why did she multiply both the numerator and denominator by 2?"  Resume video.

 

Pause after the girl says, "I'll write 1 3/8 as our answer."  Briefly discuss the term "mixed number.”  Ask students to review the steps of how the girl got from 1 1/8 to 1 3/8.  Resume the video.  Fast Forward the videotape after the girl says, "Let's see what the boys are doing at the penny toss."  Continue to Fast Forward through music section (music section can be used in Extension section with related activity).  Resume the video when the boy throws a dart at the board. 

 

Pause after the boy says, "Hey Robert, you can't do it that way."  Write the problem on the board in the classroom (2/3 - 1/2).  Ask the students, "What was Robert doing incorrectly?  What do you think he should do and why?"  After discussion, tell the students, "In this next section, watch for the problem the 'fraction family' faces and how they solve it."  Resume video.  Write down on the chalkboard the mixed number problems the students "fish" out as the problems are shown in written format on the screen.

 

Pause the videotape after Robert (student) says, "You take one whole number and rename it as 8/8."  Ask the students what he means by "rename" and why does he need to rename it?  Resume video. Stop the video after the students declare a truce.

 

Post-Viewing Activities

Using an activity similar to one seen on the video, the students will "fish" for fractions to create problems to solve.  Divide the students into small groups or pairs.  Provide each group with a "fishing pole" made by taping a paper clip bent to form a "fish hook" to a small stick or to a student's pencil.  Students will then pull fraction "fish" out of a large coffee can or small bucket.  Fish should be made out of poster board and either have a hole punched in one end or a paper clip taped to one side so that the end of the clip extends over the edge of the fish, providing students with a place to "hook" the fish.  A variety of fractions, whole numbers and mixed numbers should be written on the "fish".  Students can also "fish" for an addition or subtraction sign out of a similar can, or spin for the operation using a regular game spinner with “+” and “- “ written on paper placed under the spinner.  Students then solve their problems.  A competition between groups, such as on the video, can be set up; or students can be required to fish and solve a given amount of problems.  "Fish wardens" can check for correct answers. 

 

Action Plan

Have students meet with cafeteria staff and discuss how fractions are used when reducing or increasing a recipe.  Sample recipes can be used in a classroom activity.  Invite a chef from a local restaurant to speak with the class.

 

Extensions

Music:  Show the students the portion of video The Eddie Files #4  - Fractions: Any Way You Slice (Foundation for Advancements in Science and Education) in which the drummer demonstrates the sound of different beats (quarter notes, eighth notes, etc.).  Discuss how the notes came more quickly (more notes per measure) as the fractions became smaller.  Follow this by showing the music portion of the video Math Works #20 - Fractions 2: Unlike Denominators (AIT).  Using music used by students in their band or chorus class, divide the music into measures and beats by drawing the measures on 1/4 inch graph paper (two square equals one quarter note).  Help the students to mark the beats of the notes from the music on the graph paper.  Have the students identify each note as a fraction (half note, quarter note, whole note, etc.).  Look for any "carry" marks telling the students to hold a note over several beats.  Write those beats as fractions and add them together to show how long the note should be held.  Percussion students can identify the fractions relating to the beats their music shows them to play.

 

Science:  Have the students complete a survey and give the results in fraction format.  For example: Six out of 24 trees studied have serrated leaves, while three have long and smooth leaves.  Students can find equivalent fractions (reduce to lowest terms) and draw a circle or other graphs representing the fraction portions, and to demonstrate the addition of those portions.  Students find weights of a variety of objects adding fractions of kilograms.

 

Interesting Internet sites

http://MathCentral.uregina.ca/RR/index.html
Resource Room section of the above site includes  "teacher prepared math materials" and lesson plans organized by grades (Elementary, Middle, and Secondary) and then further divided by curriculum standards. 

http://www.planemath.com/
"Lessons and activities to learn cool things about math and aeronautics on the Internet."