Adding Mixed Numbers with Unlike Denominators

Camille Gales                  Edward Coles Elementary School
2901 S. Michigan Ave.          8441 S. Yates Blvd.
Chicago IL 60616               Chicago IL 60617
                               (773) 535-6550

Objective:

This is a seventh grade activity designed to provide students with practice in 
adding mixed fractions with unlike denominators. 

Materials:

tape measures; water soluble marking pens; 12 inch rulers; teacher made block 
letters of equal height but widths containing fractional parts including 1/16, 
1/8, 1/4, 1/3, 1/2 (or any fractional part that can be measured by using a 12 
inch ruler); long strips of fadeless paper or a roll of drywall tape; scissors; 
glue  

    
Strategy:

Review addition with mixed numbers, first at the board, then at the desk using 
individual worksheets.  When seatwork is complete pair the students.  Using a 
tape measure, each student will measure distance from his/her wrist to the tip 
of the longest finger.  Make a dot, with the marker, at that spot on the wrist 
where the measurement began.  Record the distance.  Next, measure the distance 
from the spot on the wrist to the inside fold in the arm where the forearm and 
upper arm meet.  Put a dot on that spot in the fold.  Record that distance.  
Measure the distance from the inside fold in the arm to the shoulder joint.  
Record it.  Sum the three measurements.  Measure the distance from the shoulder 
joint to the inside fold in the arm.  Compare the added length to the measured 
length. 

In the second activity students will select the precut letters to form such 
things as school name, first name or nickname.  Students will measure the width 
of each letter, allocate 1/4 of an inch space between each letter, and then add 
all letter widths and spaces.  Once the students have calculated the width of 
letters and spaces they will cut fadeless paper or drywall tape to equal the 
width of the calculated letters and spaces.  Paste the letters onto the 
fadeless paper or drywall tape. 

Performance Assessment:

In the first activity, if the students have measured and added correctly, the 
sum of the three measurements should equal the distance measured from shoulder 
joint to finger tip.  In the second activity, the length of the fadeless paper 
or drywall tape should be equal to the sum of the letters and spaces.  Both 
activities are self checking.
Grading Rubric    
If the error in measurement is within 1/4 of an inch a grade of A should be 
awarded.  If the error in measurement is within 1/2 of an inch a grade of B 
should be awarded.  If the error in measurement is within 1 inch a grade of C 
should be awarded.  If the error in measurement is within 1 1/2 of an inch a 
grade of D should be awarded.  If the error in measurement is greater the 
activity should be redone. 

Conclusions:

This activity enables the student to put math concepts to practical use.  It 
also motivates the student to measure correctly.  Finally, the self-checking 
mechanism makes the activities easy to grade.