TITLE:   
 Adding and Subtracting with Common Fractions (461-469 in math book)

CONTENT  AREAS:   
 Lowest common denominator (least common multiple) (469-471)

GRADE  LEVEL:   
7th

MATERIALS   NEEDED:   
fraction kits, calculators, paper, pencils 

KEY   CONCEPTS:   
 How to find the lowest common denominator

EALR'S :   
1.1 understand the concepts of prime and composite numbers, factors and multiples, and divisibility rules

add, subtract, multiply, and divide non-negative fractions and decimals using rules for order of operation

GOALS (Remember the difference between goals and objectives):   
 Students will understand how to add and subtract fractions with different denominators by finding the lowest common denominator.

OBJECTIVES:   
 After solving some problems as a class, with the teacher, students will practice adding and fractions with different denominators and demonstrate understanding of multiple strategies by showing work on some problems they work out individually.

PROCEDURES:  (Label each step in the process:  Activating Prior Knowledge, Disequilibration, Elaboration, Crystallization)

• Introduction/Pre-assessment

  Activate prior knowledge:

Hand out calculators (if students don’t have own)

Write “¼ + 2/4 =” on board

Ask students to tell you the answer.  Then ask how they know that.  “Can you tell me the rule we discovered that helps us come up with that answer?” (you are looking for them to tell you about the denominator being the same)

“Today we are going to solve some math problems that have fractions that contain different denominators.”

• Activity

Disequilibrium:

Write “1/3 + 5/6 =” on board.

“Can we figure this out using our fraction kits? How?”

Ask for students to attempt this and have them give suggestions on how to solve.

 “What we do to solve this is we find the lowest common denominator, also called the least common multiple.  We have to find a way to make the denominators the same so we can solve the problem.”

Elaboration:

“We can do this a few different ways.  One way, which we can use for this problem (see above) is that we first see if one of the denominators will go into the other number.  Will 3 go into 6 evenly?  How many times?”

Allow a few students to answer.  Then show how to change the denominator:

1/3 (you multiply the bottom by 2 to make the denominator 6. WHAT YOU DO TO THE BOTTOM YOU DO TO THE TOP. You then multiply the top by two.  Your new fraction will be 2/6.  Now you are ready to add 5/6 to 2/6 to get 7/6.

“What do we do if the denominators won’t fit into one another?  One way is we can multiple the denominators together.  If we have ¾ - 1/3 = ? we can simply multiple the denominators by each other to get 12.  What we do to the top we do to the bottom, so we will end up with 9/12 – 4/12 = 5/12.” (show this on the board.  Show how to multiply to top and bottom – hard to do on computer)

“What if the result of multiplying the denominators is too large?  Then we can make a factor tree for each denominator.  (see page 470 because can’t make them on computer)  To add 7/24 to 5/36 we must find the common factors of the two denominators.  (24 is 6x4, 6 is 3x2 and 4 is 2x2: 36 is 9x4, 9 is 3x3 and 4 is 2x2: so, the common factors are 2,2,3 (numbers that are the same at the bottom of each factor tree).  So…the least common multiple is (2 x 2 x 2 x 3 x 3 = 72) you multiply the common factors together with the left over factors

• Closure

List different ways you can get different denominators to be the same.

When do we use these different strategies?
 

POST-ASSESSMENT   
   Have students complete a handout shown below.

Teacher will then assess to see what concepts students understand and which they need to have more experience with.