Lesson Plans: Adding and subtracting fractions with unlike denominators

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Adding and Subtracting fractions with unlike denominators


  1. Objectives: In a 40-50 minute lesson the students will be asked to add and subtract fractions with different denominators.  In order to do this, the students will have to identify the least common denominator ( LCD).  Once the LCD is identified, the students will add or subtract the numerators and simplify the fractions.  The students will then be able to complete a worksheet once they’ve initially learned the topic.


  1. Standards/Performance indicators: I will be using performance indicator 6.N.16 Adding and subtracting fractions with unlike denominators.  Quick Review Math Handbook Book 1: 113-114, 119, 162 #6.


  1. Anticipatory Set:  To “hook” the students into wanting to learn about unlike denominators, I will open the page http://teacher.scholastic.com/maven/pirate on the smart board.



Detectives, you are about to join me on a most exciting case. My old friend and world-famous treasure hunter Frieda Finditall has discovered the wrecked ship of the legendary Pirate Ringold – right here in Point Logos Bay!

For many years, people in Point Logos have told the story of Pirate Ringold's lost ship, the Grand Looter. Legend has it that the pirate hid exactly 100 ounces of gold throughout his ship. I decided to help Frieda go through the ship's loot – and find out if there's any truth to this golden legend!

It didn't take long before Frieda found the first treasure. "Math Maven, come quick!" she yelled, pulling an old leather pouch from inside the ship's cannon.

She opened the pouch and exclaimed, "My goodness! These are pure gold coins! Math Maven, how much is here?"

I quickly weighed the coins. "19 1/2 ounces," I announced. "There's still plenty of gold hidden around this ship."


We decided to search the pirate's quarters next. Frieda knew just where to look. Without a word, she opened the pirate's desk and found a secret compartment containing an old compass and a black telescope.

She closed one eye and inspected the compass closely. "We found another treasure!" she announced. "This compass is solid gold."

The compass weighed 26 2/3 ounces. "There's bound to be more gold on this ship – but where?" said Frieda, idly tapping the old telescope against the pirate's desk.

Suddenly, we heard a "clink" from inside the telescope. "Ah, ha!" she exclaimed, removing the telescope's lens. Out fell an intricate key.

"Hooray!" yelled Frieda. "This must be the key to the pirate's treasure chest!"

"Hold on there, Frieda!" I laughed. "Take a closer look at that key." She was so excited, she didn't notice that the key was shiny gold.

"Well, I'll be! This is a little treasure all by itself!" she said, weighing the key. "That's another 5 1/6 ounces of gold."


We couldn't wait to open the treasure chest. Frieda and I expected to find mounds of gold jewelry and coins inside, but instead there was just a pile of pirate clothes: a red silk scarf, a black eye patch, shiny knickers, a black and white shirt, and an old metal hook covered with barnacles.

"Look, Frieda!" I exclaimed. "This must be Pirate Ringold's hook. The legend says that he lost his hand in a great pirate battle."

"Big deal!" said Frieda with a pout. "There's no gold in here."

"Not so fast, Frieda," I said, spotting a glimmer of light on the old metal hook. We scraped away the barnacles and discovered the old pirate's hook was made of shiny gold. It weighed 48 1/3 ounces.

"All that time Pirate Ringold's most clever hiding place was right out in the open," Frieda laughed. "Well, I guess our work here is done. We've found the legendary 100 ounces of hidden gold."

"I wouldn't jump ship yet," I warned her. "I have a sneaking feeling we haven't found the whole treasure."


Solve the Mystery


Super sleuths, if the legend of the 100 ounces of gold is true, help Frieda figure out how much gold is still hidden on the ship.

Remember, if you add or subtract fractions, they must share the same denominator. If you're adding fractions with different denominators – like 1/4 and 1/2 – first change the fractions so they all share a least common denominator – like 1/4 and 2/4. Then you can add or subtract the numerators to find the total sum or difference. (For example, 1/4 + 2/4 = 3/4.)

Okay, detectives: How much of Pirate Ringold's treasure is still missing? (Here's a Math Maven Hint: Reduce the fraction to its lowest terms.)


a)   1/3 ounce

b)    2/3 ounce

c)   1 1/6 ounce

d)   99 2/3 ounce



This activity will engage the class in a treasure hunt and not be all about basic math. After pulling the website up on the smart board the students will be asked if any of them know how to solve the problem.  This will show me previous knowledge.  I will distribute tangible gold coins to the class and allow them to try on their own before we solve it together as a class.


  1. Teaching:

A)    Input-  I will start by leaching the class on how to solve the problem on the smart board.  I will go through the 5 steps we will be suing to solve these kinds of problems as well as describing why it is important to do so.

B)    Modeling- The problem will be illustrated to show how to work out the problem.  The students will watch/ observe but not take notes at this time.  First they will learn how to stack their work to avoid errors.  Then I will illustrate how to identify least common denominators.  From here they will see how to multiply each part to get the problem with the LCD.  Once the problem is re-written I will have them drag over the denominator and either add or subtract the numerator.  The last step they will be taught is how to make sure the answer is in simplest form.

C)    Check for Understanding- I will verbally ask the students if anyone has any questions.  If nobody responds I will hand out mini white boards to each student and have them perform a problem.  I will give them a set amount of time to complete the problem before asking them to raise their boards.  I will look around to see how many students got the correct answer.  If a sufficient number got it incorrect I will once again go over the process, if they do understand, we will move on to the worksheet.   This gives the students another opportunity to see how the problem is done while also checking the understanding of the class.


  1. Guided Practice: A worksheet about adding fractions with unlike denominators will be distributed to the class.  The will be asked to do only the odd problems.  As the children complete the worksheet, I will walk around checking that the students individually understand the concept that was taught.  I will also answer any questions the students have while I circulate the classroom


  1. Closure: Once the students complete all the odd problems on the worksheet, I will reinforce the major concepts of solving a problem with unlike denominators.  Before the students are able to leave the classroom I will ask them to hand in an exit slip listing the five steps of adding and subtracting unlike denominators.


1)      Stack the Equation

2)      Find the LCD

3)      Rewrite the Equation

4)      Add or subtract numerators

5)      Simplify the final answer


  1. Independent Practice: For independent practice I will ask the students to complete a homework assignment on their own to refresh their understanding, and keep the concept fresh in their minds.  I will do this by asking the students to complete the even problems on the worksheet distributed during class.



       8. Lesson Modifications: The students who are above and beyond could help the students who are not grasping the concepts as easily.  Once they finish their problems, and can try to help those who need it.  By another student modeling the problem, it might be easier for the student to pick up.  This gives both students more practice and understanding of the lesson.

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Ryann McCarty
Last Updated: December 07, 2009 10:35 PM
Ryann McCarty 2009