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Fraction Fiesta!

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Lesson Plan

Fraction Fiesta

Students will be able to add fractions with unlike denominators by finding a common denominator and combining the fractions numerically.

Understanding how to add fractions with different parts helps us combine ingredients in recipes, understand measurements, and solve many real-world math problems.

Audience

5th Grade Students

Time

30 minutes

Approach

Direct Instruction and Guided Practice

Materials

Whiteboard or Projector, Markers or Pens, Fraction Fiesta Slide Deck, Warm Up: Equivalent Explorations, Adding Unlike Denominators Worksheet, and Adding Unlike Denominators Answer Key

Prep

Preparation

10 minutes

Step 1

Warm-Up: Equivalent Explorations

5 minutes

  1. Distribute the Warm Up: Equivalent Explorations to students.
    2. Instruct students to complete the warm-up individually, focusing on finding equivalent fractions and adding fractions with like denominators.
    3. Review answers as a class, addressing any misconceptions before moving on. (Use the Fraction Fiesta Slide Deck for visual aid).

Step 2

Introduction: Why Unlike Denominators?

5 minutes

  1. Use the Fraction Fiesta Slide Deck to introduce the concept of adding fractions with unlike denominators.
    2. Explain why a common denominator is necessary and how it relates to having 'same-sized pieces'.
    3. Use the Fraction Fiesta Slide Deck to demonstrate finding the Least Common Multiple (LCM) to get the common denominator.

Step 3

Guided Practice: Step-by-Step Addition

10 minutes

  1. Using the Fraction Fiesta Slide Deck, work through 2-3 examples of adding fractions with unlike denominators as a class.
    2. Emphasize the steps: find common denominator, create equivalent fractions, add numerators, simplify if needed.
    3. Encourage student participation and questions throughout the examples. Refer to the Script: Fraction Fiesta for detailed talking points.

Step 4

Independent Practice: Worksheet Challenge

8 minutes

  1. Distribute the Adding Unlike Denominators Worksheet.
    2. Instruct students to work independently on the worksheet.
    3. Circulate the room to provide individual support and answer questions.
    4. Briefly review a few answers from the worksheet as a class using the Adding Unlike Denominators Answer Key if time permits or collect for grading.

Step 5

Cool-Down: Quick Check

2 minutes

  1. Ask students to solve one simple problem on adding fractions with unlike denominators on an exit ticket or small piece of paper.
    2. Collect the responses to gauge understanding and inform future instruction.
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Slide Deck

Fraction Fiesta! 🥳

Adding Fractions with Unlike Denominators

Let's get ready to combine some fractions!

Welcome students and introduce the exciting topic of the day! Build enthusiasm for understanding fractions.

Before We Start: Quick Review!

What are Equivalent Fractions?

  • Fractions that represent the same value (e.g., 1/2 = 2/4)

Adding Fractions with Like Denominators

  • When the denominators (bottom numbers) are the same, you just add the numerators (top numbers) and keep the denominator the same.
  • Example: 1/4 + 2/4 = 3/4

Begin with a quick review to activate prior knowledge. Ask students to recall what equivalent fractions are and why they are useful. Briefly touch on adding fractions with the same denominator as a lead-in.

The Big Question: What If...?

What if the denominators are different?

Imagine you have 1/2 of a pizza and your friend has 1/4 of a pizza.

How much pizza do you have together?

Can we just add 1 + 1 and say 2/something? Why or why not?

Present a problem where the denominators are different. Ask students what they notice and if they can simply add the numerators. Guide them to realize they need a common 'unit' or 'piece size'.

The Solution: Common Denominators!

We need the same-sized pieces!

To add (or subtract) fractions, their denominators must be the same.

We need to find a Common Denominator.

The best common denominator is the Least Common Multiple (LCM) of the denominators.

Explain that to add fractions, the 'pieces' must be the same size. This means finding a common denominator. Introduce the concept of the Least Common Multiple (LCM) as the most efficient common denominator.

How to Find the LCM (Least Common Multiple)

Steps:

  1. List the multiples of each denominator.
  2. Find the smallest number that appears in both lists.

Example: Find the LCM of 3 and 5

  • Multiples of 3: 3, 6, 9, 12, 15, 18...
  • Multiples of 5: 5, 10, 15, 20, 25...

The LCM of 3 and 5 is 15!

Walk students through the steps of finding the LCM using a simple example (e.g., 2 and 4, or 3 and 5). Emphasize listing multiples.

Step 1: Make Them Equivalent!

Once you have the common denominator, you need to rewrite both fractions as equivalent fractions with that new denominator.

Example: 1/3 + 1/5

  • We found the LCM of 3 and 5 is 15.
  • To change 1/3 to have a denominator of 15, we multiply 3 by 5. So we must multiply the numerator (1) by 5 too! (1 x 5) / (3 x 5) = 5/15
  • To change 1/5 to have a denominator of 15, we multiply 5 by 3. So we must multiply the numerator (1) by 3 too! (1 x 3) / (5 x 3) = 3/15

Demonstrate how to convert fractions to equivalent fractions with the common denominator. Connect this back to what they learned in the warm-up.

Step 2: Add and Simplify!

Now that the denominators are the same, you can add them just like before!

Example: 1/3 + 1/5 becomes 5/15 + 3/15

  • Add the numerators: 5 + 3 = 8
  • Keep the denominator: 15

So, 5/15 + 3/15 = 8/15

Don't forget to simplify if you can!

Now, combine the steps. Show how to add the newly equivalent fractions. Remind them to simplify if possible.

Let's Practice Together! Example 1

Add: 1/2 + 1/3

  1. Find the LCM of the denominators (2 and 3):

    • Multiples of 2: 2, 4, 6, 8, 10...
    • Multiples of 3: 3, 6, 9, 12...
    • LCM = 6

  2. Rewrite with common denominators:

    • 1/2 = (1 x 3) / (2 x 3) = 3/6
    • 1/3 = (1 x 2) / (3 x 2) = 2/6

  3. Add the fractions:

    • 3/6 + 2/6 = 5/6

Our answer is 5/6!

Work through a full example with the class, step-by-step. Encourage students to participate in each step.

Let's Practice Together! Example 2

Add: 1/4 + 3/8

  1. Find the LCM of the denominators (4 and 8):

    • Multiples of 4: 4, 8, 12...
    • Multiples of 8: 8, 16...
    • LCM = 8

  2. Rewrite with common denominators:

    • 1/4 = (1 x 2) / (4 x 2) = 2/8
    • 3/8 = 3/8 (already has the common denominator)

  3. Add the fractions:

    • 2/8 + 3/8 = 5/8

Our answer is 5/8!

Work through a second example, perhaps slightly more challenging or requiring simplification.

Your Turn! Independent Practice

Now it's time to show what you know!

  • You will receive a worksheet with more problems.
  • Work quietly and carefully.
  • Remember the steps: Find LCM, rewrite, add, simplify!
  • If you get stuck, try to remember our examples.

Introduce the independent practice. Explain expectations for the worksheet.

Wrap Up: What Did We Learn?

Today we learned to add fractions with unlike denominators!

Key Steps:

  1. Find the Least Common Multiple (LCM) of the denominators.
  2. Rewrite each fraction as an equivalent fraction using the LCM as the new denominator.
  3. Add the numerators and keep the common denominator.
  4. Simplify the answer if possible.

Conclude the lesson by asking students to summarize the main steps or to try one last problem. This serves as the cool-down.

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Warm Up

Warm Up: Equivalent Explorations

Welcome mathematicians! Let's get our brains ready for some fraction fun!

Part 1: Equivalent Fractions

Find the missing number to make the fractions equivalent.

  1. 1/2 = ?/4


  2. 2/3 = ?/9


  3. 3/5 = 6/?


  4. 1/4 = 2/?


Part 2: Adding Like Fractions

Add the fractions. Remember to simplify your answer if possible!

  1. 1/5 + 2/5 = ?


  2. 3/8 + 1/8 = ?


  3. 2/7 + 3/7 = ?


  4. 5/10 + 3/10 = ?


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Script

Script: Fraction Fiesta!

Warm-Up: Equivalent Explorations (5 minutes)

(Teacher says:) "Good morning, mathematicians! Let's kick off our math adventure today with a quick warm-up to get our brains buzzing. I'm handing out a Warm Up: Equivalent Explorations worksheet. Please work quietly on your own for about 3-4 minutes to complete it. Focus on what you remember about equivalent fractions and adding fractions with the same bottom number. When you're done, put your pencil down so I know you're ready."

(Allow students to work. Circulate and observe.)

(Teacher says:) "Alright, pencils down! Let's review our warm-up together. We'll use our Fraction Fiesta Slide Deck to check our answers."

(Display Slide 2: Before We Start: Quick Review!)

(Teacher says:) "Who can tell me, in your own words, what an equivalent fraction is? Yes, [Student Name]? Excellent! They are fractions that look different but have the same value. And when we add fractions with the same denominator, what do we do? That's right, we just add the top numbers and keep the bottom number the same. Great job everyone!"

Introduction: Why Unlike Denominators? (5 minutes)

(Display Slide 3: The Big Question: What If...?)

(Teacher says:) "Now, here's our big question for today. Look at the problem on the slide: 'What if the denominators are different?' Imagine you have 1/2 of a pizza, and your friend has 1/4 of a pizza. If you put your slices together, how much pizza do you have? Can we just add 1 + 1 and say 2/something? Why or why not? Turn and talk to a partner for 30 seconds about this."

(Allow brief partner discussion.)

(Teacher says:) "What did you and your partner discuss? [Call on a student]. That's a really good point! When we're talking about pizza, 1/2 a pizza slice looks very different from 1/4 of a pizza slice, right? They're not the same size. So, to really combine them, we need to think about them in terms of pieces that are the same size."

(Display Slide 4: The Solution: Common Denominators!)

(Teacher says:) "Exactly! We need the same-sized pieces! To add or subtract fractions, their denominators must be the same. So, our goal today is to learn how to change fractions so they have a Common Denominator. The best common denominator is often the Least Common Multiple, or LCM, of the denominators. This might sound tricky, but we'll break it down."

Guided Practice: Step-by-Step Addition (10 minutes)

(Display Slide 5: How to Find the LCM (Least Common Multiple))

(Teacher says:) "Let's start with how to find that Least Common Multiple, or LCM. It's like finding the smallest number that both denominators can divide into evenly. The easiest way is to list the multiples of each denominator until you find the first one they share."

"Look at our example: finding the LCM of 3 and 5. What are the multiples of 3? (Pause for answers). Good: 3, 6, 9, 12, 15... And for 5? (Pause). Right: 5, 10, 15, 20... What's the smallest number that's in both lists? Yes, 15! So, our common denominator for fractions with 3 and 5 on the bottom will be 15."

(Display Slide 6: Step 1: Make Them Equivalent!)

(Teacher says:) "Once we have our common denominator, we need to rewrite both fractions as equivalent fractions. This means we make them look different, but still mean the same thing, just like we did in the warm-up!"

"Let's go back to our example of 1/3 + 1/5. We know the LCM is 15. How do we change 1/3 into an equivalent fraction with a denominator of 15? What do we multiply 3 by to get 15? (Pause). By 5! And remember, whatever we do to the bottom, we must do to the top! So, 1 times 5 is 5. 1/3 becomes 5/15."

"Now, for 1/5. What do we multiply 5 by to get 15? (Pause). By 3! So, we multiply the top number, 1, by 3 as well. 1/5 becomes 3/15. See how we now have 5/15 and 3/15? They both have 15 on the bottom!"

(Display Slide 7: Step 2: Add and Simplify!)

(Teacher says:) "Now that our fractions have the same denominator, adding them is easy! Just like in our warm-up, we add the top numbers and keep the bottom number the same."

"So, 5/15 + 3/15. What's 5 + 3? (Pause). 8! And we keep the denominator, 15. So our answer is 8/15. Can we simplify 8/15? Are there any numbers other than 1 that divide evenly into both 8 and 15? (Pause). No! So 8/15 is our final, simplified answer."

(Display Slide 8: Let's Practice Together! Example 1)

(Teacher says:) "Let's try another one together. Let's add 1/2 + 1/3. Who can tell me the first step? [Call on a student]. Yes, find the LCM of 2 and 3! What are the multiples of 2? And 3? What's the smallest they share? (Guide students to 6). So, our common denominator is 6."

"Next, we rewrite. How does 1/2 become an equivalent fraction with 6 on the bottom? (Guide students to 3/6). And 1/3? (Guide students to 2/6). Excellent!

"Now, add them! What's 3/6 + 2/6? (Guide students to 5/6). Can we simplify 5/6? (Guide to no). So, our answer is 5/6!"

(Display Slide 9: Let's Practice Together! Example 2)

(Teacher says:) "One more together! 1/4 + 3/8. What's our first step? Find the LCM of 4 and 8. What are the multiples of 4? What are the multiples of 8? What's the LCM? (Guide to 8). Great! Notice that sometimes one of the denominators is already the LCM."

"Now, rewrite. How does 1/4 become an equivalent fraction with 8 on the bottom? (Guide to 2/8). And 3/8? It already has 8 on the bottom, so it stays 3/8!"

"Finally, add! What's 2/8 + 3/8? (Guide to 5/8). Can we simplify 5/8? (Guide to no). Fantastic!"

Independent Practice: Worksheet Challenge (8 minutes)

(Display Slide 10: Your Turn! Independent Practice)

(Teacher says:) "You've done a wonderful job practicing together! Now it's your turn to show what you know. I'm handing out the Adding Unlike Denominators Worksheet. You will have about 8 minutes to work on this independently. Remember to follow our steps: Find the LCM, rewrite the fractions, add the numerators, and simplify if needed. If you get stuck, try to remember the examples we just did on the slides. Work quietly and carefully. If you have a question, raise your hand, and I will come to you."

(Distribute worksheets. Circulate to provide support and answer questions. Keep an eye on the time.)

(Teacher says:) "Alright everyone, pencils down! We are going to quickly go over one or two answers as a class before we move to our cool down."

(Quickly review 1-2 problems from the worksheet, using the Adding Unlike Denominators Answer Key to guide discussion if time permits. Alternatively, simply collect the worksheets.)

Cool-Down: Quick Check (2 minutes)

(Display Slide 11: Wrap Up: What Did We Learn?)

(Teacher says:) "To wrap up our Fraction Fiesta today, I want everyone to answer one quick question on a small piece of paper or a sticky note. Please write down the answer to this problem: 1/3 + 1/6. Show your work if you can. This will help me see what you've learned today."

(Collect the cool-down responses as students leave or transition.)

(Teacher says:) "Excellent work today, everyone! You've taken a big step in becoming fraction masters!"

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Worksheet

Adding Unlike Denominators Worksheet

Name: _________________________
Date: __________________________

Instructions:

Read each problem carefully. Follow the steps we learned today to add the fractions. Remember to find a common denominator, create equivalent fractions, add, and then simplify your answer if possible.

Practice Problems:

  1. 1/4 + 1/2 = ?







  2. 2/5 + 1/10 = ?







  3. 1/3 + 2/9 = ?







  4. 3/6 + 1/3 = ?







  5. 1/2 + 2/5 = ?







  6. 3/4 + 1/6 = ?







  7. 2/3 + 1/4 = ?







  8. 5/12 + 1/3 = ?







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Answer Key

Adding Unlike Denominators Answer Key

Step-by-Step Solutions:

1. 1/4 + 1/2

  • Find LCM: Multiples of 4: 4, 8... Multiples of 2: 2, 4, 6... LCM = 4
  • Rewrite: 1/4 remains 1/4. 1/2 = (1x2)/(2x2) = 2/4
  • Add: 1/4 + 2/4 = 3/4
  • Simplify: 3/4 (already simplified)

2. 2/5 + 1/10

  • Find LCM: Multiples of 5: 5, 10, 15... Multiples of 10: 10, 20... LCM = 10
  • Rewrite: 2/5 = (2x2)/(5x2) = 4/10. 1/10 remains 1/10.
  • Add: 4/10 + 1/10 = 5/10
  • Simplify: 5/10 = 1/2 (divide numerator and denominator by 5)

3. 1/3 + 2/9

  • Find LCM: Multiples of 3: 3, 6, 9, 12... Multiples of 9: 9, 18... LCM = 9
  • Rewrite: 1/3 = (1x3)/(3x3) = 3/9. 2/9 remains 2/9.
  • Add: 3/9 + 2/9 = 5/9
  • Simplify: 5/9 (already simplified)

4. 3/6 + 1/3

  • Find LCM: Multiples of 6: 6, 12... Multiples of 3: 3, 6, 9... LCM = 6
  • Rewrite: 3/6 remains 3/6. 1/3 = (1x2)/(3x2) = 2/6
  • Add: 3/6 + 2/6 = 5/6
  • Simplify: 5/6 (already simplified)

5. 1/2 + 2/5

  • Find LCM: Multiples of 2: 2, 4, 6, 8, 10, 12... Multiples of 5: 5, 10, 15... LCM = 10
  • Rewrite: 1/2 = (1x5)/(2x5) = 5/10. 2/5 = (2x2)/(5x2) = 4/10
  • Add: 5/10 + 4/10 = 9/10
  • Simplify: 9/10 (already simplified)

6. 3/4 + 1/6

  • Find LCM: Multiples of 4: 4, 8, 12, 16... Multiples of 6: 6, 12, 18... LCM = 12
  • Rewrite: 3/4 = (3x3)/(4x3) = 9/12. 1/6 = (1x2)/(6x2) = 2/12
  • Add: 9/12 + 2/12 = 11/12
  • Simplify: 11/12 (already simplified)

7. 2/3 + 1/4

  • Find LCM: Multiples of 3: 3, 6, 9, 12, 15... Multiples of 4: 4, 8, 12, 16... LCM = 12
  • Rewrite: 2/3 = (2x4)/(3x4) = 8/12. 1/4 = (1x3)/(4x3) = 3/12
  • Add: 8/12 + 3/12 = 11/12
  • Simplify: 11/12 (already simplified)

8. 5/12 + 1/3

  • Find LCM: Multiples of 12: 12, 24... Multiples of 3: 3, 6, 9, 12, 15... LCM = 12
  • Rewrite: 5/12 remains 5/12. 1/3 = (1x4)/(3x4) = 4/12
  • Add: 5/12 + 4/12 = 9/12
  • Simplify: 9/12 = 3/4 (divide numerator and denominator by 3)
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Fraction Fiesta! • Lenny Learning