Warm Up: Share & Compare!

Question: Can you show two different ways to represent the fraction 1/2? Explain why they are equivalent.

Bonus: How does finding a common multiple help you understand equivalent fractions?

Script: Adding Fractions

Warm-Up: Share & Compare! (5 minutes)

(Display Warm Up: Share & Compare! / Slide 2: Warm-Up: Share & Compare!)

"Good morning, everyone! Let's get our brains warmed up for some fraction fun today. Look at the screen for your warm-up question. Your task is to show two different ways to represent the fraction 1/2. Think about what we already know about equivalent fractions. You have about 2-3 minutes to think and write down your ideas individually.


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(After 2-3 minutes)

"Now, turn to your partner and share your responses. Discuss how your representations show that the fractions are equivalent. You have 2 minutes for this discussion.


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(After 2 minutes, bring the class back together)

"Alright, let's hear some of your brilliant ideas! Who would like to share one way they represented 1/2? (Call on students). Excellent! And how did you show they were equivalent? (Prompt for multiplication/division or visual representation). Great job! The key takeaway here is that equivalent fractions represent the same amount, even if they have different numbers. We often find them by multiplying or dividing the numerator and denominator by the same number. Keep this in mind as we move forward."

Introduction: The Denominator Dilemma (5 minutes)

(Display Slide 3: The Denominator Dilemma)

"Today, we're going to tackle a super important skill: adding fractions! But not just any fractions – we're going to learn how to add fractions when their bottom numbers, their denominators, are different. Look at the example on the screen: 1/2 + 1/3. Can we just add the top numbers and the bottom numbers directly? (Pause for responses). Why not? Think about it like this: if you have half a pizza and a third of a different pizza, can you easily say how much pizza you have in total if the slices are different sizes? No! It's much easier if all the slices are the same size."

"That's where common denominators come in! A common denominator is a shared multiple of the denominators of two or more fractions. It's like finding a way to cut both pizzas into slices of the same size so we can easily count them all up. Our goal is to make sure our fraction pieces are the same size before we add them together. Does that make sense? Thumbs up if you're with me!"

Guided Practice: Let's Do It Together! (10 minutes)

(Display Slide 4: Finding a Common Denominator)

"Let's break down the process with our first example: 1/2 + 1/3. The first step, just like we discussed, is to find the Least Common Multiple (LCM) of the denominators. Remember, the LCM is the smallest number that is a multiple of both numbers. For 1/2 + 1/3, our denominators are 2 and 3.

"Let's list the multiples of 2: 2, 4, 6, 8, 10...
And the multiples of 3: 3, 6, 9, 12...

"What's the smallest number they both share? That's right, 6! So, our common denominator for 1/2 and 1/3 will be 6."

(Display Slide 5: Creating Equivalent Fractions)

"Now for Step 2: Convert our original fractions into equivalent fractions using our new common denominator. We need to figure out what to multiply the numerator and denominator by to get 6 as the new denominator.

"For 1/2, how do we get a denominator of 6? We multiply 2 by 3. So, we must also multiply the numerator, 1, by 3! What does 1/2 become? (Wait for responses). Yes, 3/6! Great.

"Now for 1/3. How do we get a denominator of 6 from 3? We multiply 3 by 2. So, we must also multiply the numerator, 1, by 2! What does 1/3 become? (Wait for responses). You got it, 2/6!"

"So now our problem 1/2 + 1/3 has become 3/6 + 2/6. See how much easier that looks?"

(Display Slide 6: Add the Numerators!)

"Finally, Step 3: Add the numerators together and keep the common denominator. We just add the top numbers, and the bottom number, the denominator, stays the same because our pieces are now the same size.

"So, 3 + 2 equals 5. And our denominator stays 6. This means 3/6 + 2/6 = 5/6! So, 1/2 + 1/3 = 5/6! Give yourselves a pat on the back, that's a big step!"

(Display Slide 7: Let's Practice Together!)

"Let's try another one together. This time, I want you to help me lead the steps. The problem is 1/4 + 2/5.

"Who can tell me the first thing we need to do? (Call on student - Find the LCM). Excellent! What are our denominators? (4 and 5). What's the LCM of 4 and 5? (List multiples if needed: 4, 8, 12, 16, 20... 5, 10, 15, 20...). Yes, 20!

"Now for the second step? (Call on student - Create equivalent fractions). How do we change 1/4 into twentiehts? What do we multiply by? (5). So 1/4 becomes... (5/20). Perfect!

"And how about 2/5? What do we multiply by to get 20? (4). So 2/5 becomes... (8/20). Fantastic!

"Alright, last step! What do we do now? (Call on student - Add the numerators). So, 5/20 + 8/20 equals...? (13/20). You've got it! So 1/4 + 2/5 = 13/20."

Independent Practice: Practice Makes Perfect! (7 minutes)

(Display Slide 8: Your Turn! Independent Practice)

"You've done great work following along! Now it's your turn to show what you've learned. I'm handing out the Worksheet: Fraction Addition Practice. Please work quietly and independently on these problems. Remember to show all your steps: finding the LCM, creating equivalent fractions, and then adding. If you get stuck, try to remember the steps we just practiced. I'll be walking around to help if you have questions. You have about 7 minutes for this."

(Circulate and assist students as they work.)

Cool-Down: One Question Exit Ticket (3 minutes)

(Display Slide 9: Cool Down: Exit Ticket / Cool Down: One Question Exit Ticket )

"Alright mathematicians, time is almost up for our practice! To wrap up today, I have one last quick question for you to answer on this exit ticket (or a small piece of paper). Please complete the Cool Down: One Question Exit Ticket before you leave. This will help me see what you understood today and what we might need to review. Try your best and show your work!"

(Collect cool-down responses as students finish.)

"Thank you all for your hard work today! I look forward to seeing your understanding of adding fractions with unlike denominators. Have a wonderful rest of your day!"

Fraction Addition Practice

Name: _____________________________

Date: _____________________________

Instructions: Add the following fractions. Show all your work, including finding the least common multiple (LCM) for the denominators and creating equivalent fractions before adding.

1. 1/3 + 1/4
   
   
   
   
   
   
   
   
   
   
   
   

2. 2/5 + 1/2
   
   
   
   
   
   
   
   
   
   
   
   

3. 3/8 + 1/4
   
   
   
   
   
   
   
   
   
   
   
   

4. 1/6 + 2/3
   
   
   
   
   
   
   
   
   
   
   
   

5. 3/10 + 1/5
   
   
   
   
   
   
   
   
   
   
   
   

6. 1/2 + 2/7
   
   
   
   
   
   
   
   
   
   
   
   

7. 5/6 + 1/8
   
   
   
   
   
   
   
   
   
   
   
   

8. 2/9 + 1/3
   
   
   
   
   
   
   
   
   
   
   
   

Challenge Question:

9. Sarah baked a pie. Her family ate 1/4 of the pie in the morning and 3/8 of the pie in the afternoon. What fraction of the pie did her family eat altogether?
   
   
   
   
   
   
   
   
   
   
   
   

Fraction Addition Answer Key

Instructions: Step-by-Step Solutions

1. 1/3 + 1/4

• Thought Process: To add these fractions, we need a common denominator. The least common multiple (LCM) of 3 and 4 is 12.
• Step 1: Find the LCM. Multiples of 3: 3, 6, 9, 12, 15... Multiples of 4: 4, 8, 12, 16...
  The LCM is 12.
• Step 2: Create Equivalent Fractions.
  To change 1/3 to twelfths, multiply the numerator and denominator by 4: (1 * 4) / (3 * 4) = 4/12.
  To change 1/4 to twelfths, multiply the numerator and denominator by 3: (1 * 3) / (4 * 3) = 3/12.
• Step 3: Add the Numerators. 4/12 + 3/12 = (4 + 3)/12 = 7/12.
• Answer: 7/12

2. 2/5 + 1/2

• Thought Process: We need a common denominator for 5 and 2. The LCM of 5 and 2 is 10.
• Step 1: Find the LCM. Multiples of 5: 5, 10, 15... Multiples of 2: 2, 4, 6, 8, 10, 12...
  The LCM is 10.
• Step 2: Create Equivalent Fractions.
  To change 2/5 to tenths, multiply the numerator and denominator by 2: (2 * 2) / (5 * 2) = 4/10.
  To change 1/2 to tenths, multiply the numerator and denominator by 5: (1 * 5) / (2 * 5) = 5/10.
• Step 3: Add the Numerators. 4/10 + 5/10 = (4 + 5)/10 = 9/10.
• Answer: 9/10

3. 3/8 + 1/4

• Thought Process: We need a common denominator for 8 and 4. The LCM of 8 and 4 is 8 (since 8 is a multiple of 4).
• Step 1: Find the LCM. Multiples of 8: 8, 16... Multiples of 4: 4, 8, 12...
  The LCM is 8.
• Step 2: Create Equivalent Fractions.
  3/8 already has the common denominator.
  To change 1/4 to eighths, multiply the numerator and denominator by 2: (1 * 2) / (4 * 2) = 2/8.
• Step 3: Add the Numerators. 3/8 + 2/8 = (3 + 2)/8 = 5/8.
• Answer: 5/8

4. 1/6 + 2/3

• Thought Process: We need a common denominator for 6 and 3. The LCM of 6 and 3 is 6.
• Step 1: Find the LCM. Multiples of 6: 6, 12... Multiples of 3: 3, 6, 9...
  The LCM is 6.
• Step 2: Create Equivalent Fractions.
  1/6 already has the common denominator.
  To change 2/3 to sixths, multiply the numerator and denominator by 2: (2 * 2) / (3 * 2) = 4/6.
• Step 3: Add the Numerators. 1/6 + 4/6 = (1 + 4)/6 = 5/6.
• Answer: 5/6

5. 3/10 + 1/5

• Thought Process: We need a common denominator for 10 and 5. The LCM of 10 and 5 is 10.
• Step 1: Find the LCM. Multiples of 10: 10, 20... Multiples of 5: 5, 10, 15...
  The LCM is 10.
• Step 2: Create Equivalent Fractions.
  3/10 already has the common denominator.
  To change 1/5 to tenths, multiply the numerator and denominator by 2: (1 * 2) / (5 * 2) = 2/10.
• Step 3: Add the Numerators. 3/10 + 2/10 = (3 + 2)/10 = 5/10.
• Answer: 5/10 (which simplifies to 1/2)

6. 1/2 + 2/7

• Thought Process: We need a common denominator for 2 and 7. Since 2 and 7 are prime numbers, their LCM is their product, 14.
• Step 1: Find the LCM. Multiples of 2: 2, 4, 6, 8, 10, 12, 14... Multiples of 7: 7, 14, 21...
  The LCM is 14.
• Step 2: Create Equivalent Fractions.
  To change 1/2 to fourteenths, multiply the numerator and denominator by 7: (1 * 7) / (2 * 7) = 7/14.
  To change 2/7 to fourteenths, multiply the numerator and denominator by 2: (2 * 2) / (7 * 2) = 4/14.
• Step 3: Add the Numerators. 7/14 + 4/14 = (7 + 4)/14 = 11/14.
• Answer: 11/14

7. 5/6 + 1/8

• Thought Process: We need a common denominator for 6 and 8. The LCM of 6 and 8 is 24.
• Step 1: Find the LCM. Multiples of 6: 6, 12, 18, 24, 30... Multiples of 8: 8, 16, 24, 32...
  The LCM is 24.
• Step 2: Create Equivalent Fractions.
  To change 5/6 to twenty-fourths, multiply the numerator and denominator by 4: (5 * 4) / (6 * 4) = 20/24.
  To change 1/8 to twenty-fourths, multiply the numerator and denominator by 3: (1 * 3) / (8 * 3) = 3/24.
• Step 3: Add the Numerators. 20/24 + 3/24 = (20 + 3)/24 = 23/24.
• Answer: 23/24

8. 2/9 + 1/3

• Thought Process: We need a common denominator for 9 and 3. The LCM of 9 and 3 is 9.
• Step 1: Find the LCM. Multiples of 9: 9, 18... Multiples of 3: 3, 6, 9, 12...
  The LCM is 9.
• Step 2: Create Equivalent Fractions.
  2/9 already has the common denominator.
  To change 1/3 to ninths, multiply the numerator and denominator by 3: (1 * 3) / (3 * 3) = 3/9.
• Step 3: Add the Numerators. 2/9 + 3/9 = (2 + 3)/9 = 5/9.
• Answer: 5/9

9. Challenge Question: Sarah baked a pie. Her family ate 1/4 of the pie in the morning and 3/8 of the pie in the afternoon. What fraction of the pie did her family eat altogether?

• Thought Process: This is a word problem requiring us to add the two fractions of pie eaten. We need to find a common denominator for 4 and 8, which is 8.
• Step 1: Identify the fractions. 1/4 and 3/8.
• Step 2: Find the LCM. The LCM of 4 and 8 is 8.
• Step 3: Create Equivalent Fractions.
  To change 1/4 to eighths, multiply the numerator and denominator by 2: (1 * 2) / (4 * 2) = 2/8.
  3/8 already has the common denominator.
• Step 4: Add the Numerators. 2/8 + 3/8 = (2 + 3)/8 = 5/8.
• Step 5: State the Answer. Sarah's family ate 5/8 of the pie altogether.
• Answer: 5/8 of the pie

Cool Down: One Question Exit Ticket

Name: _____________________________

Date: _____________________________

Question: Solve the following fraction addition problem. Show all your work, including finding the common denominator and creating equivalent fractions.

1/5 + 3/10

Explain in one sentence: Why is it important to find a common denominator before adding fractions?

Fraction Frenzy: Denominator Dash!

Objective: Be the first team to correctly add fractions with unlike denominators and reach the finish line!

Materials:

• Game Board (Teacher can draw a simple path with 10-15 spaces on the whiteboard or chart paper)
• Fraction Cards (Create cards with pairs of fractions to add, e.g., 1/2 + 1/4, 2/3 + 1/6, 3/5 + 1/10, etc. Ensure some require finding an LCM beyond just one denominator being a multiple of the other.)
• Markers or small objects for game pieces (one per team)
• Scratch paper and pencils for each team

How to Play:

1. Divide into Teams: Divide the class into 2-4 teams.
2. Set Up: Each team places their marker at the