Warm Up: Fraction Challenge!

Instructions: Look at the shapes below. Each shape is divided into equal parts. Write down the fraction that represents the shaded portion of each shape.

1. 
   Fraction:
   
   
   

2. 
   Fraction:
   
   
   

3. 
   Fraction:
   
   
   

Think about it: What does the top number (numerator) tell us? What does the bottom number (denominator) tell us?

Fraction Funhouse Script

Introduction & Warm-Up (10 minutes)

Teacher: "Good morning, everyone! Get ready to step into the 'Fraction Funhouse' today, where we're going on an exciting adventure with fractions! Our goal today is to become masters of equivalent fractions and comparing fractions. We'll learn how fractions can look different but be worth the same, and how to tell which fraction is bigger or smaller."

"Let's start by getting our brains warmed up with a quick Warm Up: Fraction Challenge. Please take out your warm-up sheet and look at the shapes. Your task is to write down the fraction that represents the shaded portion of each shape. Don't worry if it feels tricky, just do your best!"

(Allow students a few minutes to complete the warm-up. Circulate and observe.)

Teacher: "Alright, let's go over our answers. Who would like to share the fraction they wrote for the first shape? (Call on a student). What about the second? (Call on another). And the third? (Call on a third)."

"Fantastic! Now, let's quickly review: What does the top number of a fraction, the numerator, tell us? (Pause for answers). That's right, it tells us how many parts we are counting. And the bottom number, the denominator, what does that tell us? (Pause for answers). Exactly! It tells us the total number of equal parts in the whole."

"Keep that in mind as we move forward. Today, we're going to explore fractions that might look different but actually represent the same amount, and then we'll learn some clever ways to compare fractions to see which one is bigger or smaller!"

(Transition to Slide Deck: Fraction Funhouse - Slide 3: Equivalent Fractions: Same, But Different!)

Exploring Equivalent Fractions (15 minutes)

Teacher: "Our first stop in the Funhouse is all about equivalent fractions. The word 'equivalent' sounds a bit fancy, but it just means 'equal in value' or 'the same amount.' So, equivalent fractions are fractions that look different but represent the exact same portion of a whole."

"Imagine we have a delicious pizza. If I eat 1/2 of the pizza, how much have I eaten? (Pause for answers, maybe mime taking half). Now, what if I told you I ate 2/4 of the exact same pizza? Have I eaten more, less, or the same amount? (Take suggestions, guide towards same amount). That's right! 1/2 and 2/4 represent the same amount of pizza!"

(Transition to Slide Deck: Fraction Funhouse - Slide 4: Fraction Bar Fun!)

Teacher: "To see this in action, let's do our Fraction Bar Activity! I've given each of you some paper strips. Please take one strip and fold it in half. Open it up, and label each part '1/2'. Now, take another strip and fold it in half, and then fold it in half again. How many equal parts do you have now? (Fours). Label each of those parts '1/4'. And for a third strip, fold it into halves, then halves again, then halves one more time. How many parts this time? (Eights). Label each '1/8'."

(Give students time to fold and label. Circulate to assist.)

Teacher: "Now, look at your strips. If you take your 1/2 strip and hold it next to your 1/4 strip, how many 1/4 pieces fit exactly over the 1/2 piece? (Two). So, what does that tell us about 1/2 and 2/4? (They are equivalent/the same). Excellent! What about your 1/8 strip? How many 1/8 pieces fit over 1/2? (Four). And how many 1/8 pieces fit over 2/4? (Four). This shows us that 1/2, 2/4, and 4/8 are all equivalent fractions!"

(Transition to Slide Deck: Fraction Funhouse - Slide 5: The Golden Rule of Equivalent Fractions)

Teacher: "So, how can we mathematically find equivalent fractions without always drawing or folding? There's a golden rule! To find an equivalent fraction, you must multiply both the numerator (the top number) AND the denominator (the bottom number) by the same non-zero number. It's like multiplying by a special version of 1!"

"Let's look at our example: 1/2. If we multiply the numerator (1) by 2, we get 2. And if we multiply the denominator (2) by 2, we get 4. So, 1/2 becomes 2/4! It works! Let's try another one together: If we have 2/3, and we want to find an equivalent fraction, what number could we multiply both the top and bottom by? (Take suggestions, e.g., 3). If we multiply by 3, we get (2 x 3) = 6 and (3 x 3) = 9. So, 2/3 is equivalent to 6/9!"

Comparing Fractions (15 minutes)

(Transition to Slide Deck: Fraction Funhouse - Slide 6: Comparing Fractions: Who's Bigger?)

Teacher: "Now that we know about fractions that are the same, what about when they're not the same? How do we know which one is larger or smaller? We use special comparison symbols: greater than (>), less than (<), and equal to (=)."

"Think about our pizza again. Is 1/2 of a pizza greater than (>) or less than (<) 1/4 of a pizza? (Pause for answers). That's right, 1/2 is greater than 1/4! We write it as 1/2 > 1/4."

(Transition to Slide Deck: Fraction Funhouse - Slide 7: Strategy 1: Common Denominators)

Teacher: "One powerful strategy for comparing fractions is to make the bottoms the same! This means finding a common denominator. A common denominator is a number that both denominators can multiply into. Once you have a common denominator, you convert both fractions to equivalent fractions with that new denominator, and then it's easy to compare the numerators."

"Let's compare 1/3 and 2/6. What's a number that both 3 and 6 can multiply into? (Six). Yes! Six is a common multiple. 2/6 already has a denominator of 6. How can we make 1/3 have a denominator of 6? (Multiply the top and bottom by 2). So, 1/3 becomes 2/6. Now we compare 2/6 and 2/6. What do we find? (They are equal!). So, 1/3 = 2/6."

"Let's try another: Compare 1/2 and 3/8. What's a common denominator for 2 and 8? (Eight). How do we change 1/2 to have a denominator of 8? (Multiply top and bottom by 4). So 1/2 becomes 4/8. Now compare 4/8 and 3/8. Which is bigger? (4/8). So, 1/2 > 3/8."

(Transition to Slide Deck: Fraction Funhouse - Slide 8: Strategy 2: Benchmark Fractions (like 1/2))

Teacher: "Sometimes, you can use a shortcut! We can compare fractions to a benchmark fraction, like 1/2. Is the fraction more or less than half?"

"Let's compare 3/8 and 5/6. Is 3/8 more or less than 1/2? (It's less, because 4/8 would be 1/2). Is 5/6 more or less than 1/2? (It's more, because 3/6 would be 1/2). So, if 3/8 is less than 1/2 and 5/6 is more than 1/2, what does that tell us about comparing 3/8 and 5/6? (5/6 is greater than 3/8). Very good!"

Practice & Application (15 minutes)

(Transition to Slide Deck: Fraction Funhouse - Slide 9: Time to Practice!)

Teacher: "You've learned some great strategies today! Now it's time to put them into practice. First, you'll work on the [Worksheet: Equivalent Fractions & Comparison]. You can work independently or with a partner. Remember to use the strategies we just discussed!"

(Distribute worksheets. Circulate to provide help and check understanding. After a few minutes, introduce the game.)

Teacher: "After you've had some time with the worksheet, we'll play the [Fraction Comparison Game] to make sure those comparison skills are super sharp! I'll explain the rules once everyone has had a chance to start the worksheet."

(Once most students have worked on the worksheet for a bit, explain and facilitate the game.)

Conclusion & Wrap-Up (5 minutes)

(Transition to Slide Deck: Fraction Funhouse - Slide 10: Fraction Funhouse Farewell!)

Teacher: "Wow, what a journey through the Fraction Funhouse! You've done an amazing job today. Let's quickly review: Can someone tell me, in your own words, what equivalent fractions are? (Call on student). And how can we find them? (Call on student)."

"What about comparing fractions? What are some strategies we learned to figure out if one fraction is greater than or less than another? (Call on students for common denominators or benchmark fractions)."

"Excellent work, mathematicians! You've built a strong foundation for understanding fractions, and these skills will help you with so much more math in the future. Give yourselves a pat on the back!"

Equivalent Fractions & Comparison Worksheet

Name: ________________________
Date: _________________________

Part 1: Finding Equivalent Fractions

Instructions: For each fraction, draw a visual model and then write two equivalent fractions. You can use multiplication to help you!

1. 1/2
   Visual Model:
   
   
   
   
   
   
   
   
   
   
   
   
   Equivalent Fractions:

   1. ---

   2. ---

2. 2/3
   Visual Model:
   
   
   
   
   
   
   
   
   
   
   
   
   Equivalent Fractions:

   1. ---

   2. ---

3. 1/4
   Visual Model:
   
   
   
   
   
   
   
   
   
   
   
   
   Equivalent Fractions:

   1. ---

   2. ---

Part 2: Comparing Fractions

Instructions: Use the symbols < (less than), > (greater than), or = (equal to) to compare the fractions. Show your work using common denominators or by comparing to a benchmark fraction (like 1/2).

1. 1/2 _______ 3/8
   Show Your Work:
   
   
   
   
   
   
   

2. 2/3 _______ 5/6
   Show Your Work:
   
   
   
   
   
   
   

3. 1/4 _______ 2/8
   Show Your Work:
   
   
   
   
   
   
   

4. 3/5 _______ 1/2
   Show Your Work:
   
   
   
   
   
   
   

5. 2/7 _______ 2/5
   Show Your Work:
   
   
   
   
   
   
   

Part 3: Fraction Comparison Graphic Organizer

Instructions: Choose two fractions from the list below and compare them using the graphic organizer. Explain your reasoning.

Fractions to Choose From: 3/4, 1/3, 5/8, 1/2

Fraction 1: ____________
Fraction 2: ____________

Fraction Bar Activity: Seeing is Believing!

Materials: 3-4 strips of paper (same size) per student, markers or pencils.

Instructions: Follow along with your teacher to create your own fraction bars and discover equivalent fractions!

Step 1: The Whole

Take your first strip of paper. This strip represents one whole. Do not fold it, just write "1 Whole" on it.

Step 2: Halves

Take your second strip of paper.

1. Fold this strip exactly in half. Make a crisp crease.
2. Open it up. How many equal parts do you see?
3. Label each part "1/2". You have made a "Halves" fraction bar.

Step 3: Fourths

Take your third strip of paper.

1. Fold this strip in half, then fold it in half again. Make crisp creases.
2. Open it up. How many equal parts do you see now?
3. Label each part "1/4". You have made a "Fourths" fraction bar.

Step 4: Eighths (Optional)

Take your fourth strip of paper (if you have one).

1. Fold this strip in half, then half again, then half one more time. Make crisp creases.
2. Open it up. How many equal parts do you see now?
3. Label each part "1/8". You have made an "Eighths" fraction bar.

Reflection Questions:

1. Place your "Halves" bar above your "Fourths" bar. How many "1/4" pieces are equal to one "1/2" piece?
   
   
   
   

2. Write an equivalent fraction based on your observation from Question 1:
   1/2 = ________
   
   
   
   

3. If you made an "Eighths" bar, place it above your "Halves" bar. How many "1/8" pieces are equal to one "1/2" piece?
   
   
   
   

4. Write another equivalent fraction based on your observation from Question 3:
   1/2 = ________
   
   
   
   

5. What do you notice about the numbers in equivalent fractions? How do they relate to each other? Think about multiplication and division.
   
   
   
   
   
   
   

Fraction Comparison Game: Greater Than, Less Than, or Equal!

Materials:

• Index cards with various fractions written on them (e.g., 1/2, 3/4, 1/3, 2/5, 5/8, 2/2, 1/4, 4/6, etc.). Make sure to include some equivalent fractions and fractions that can be easily compared using benchmarks.
• Comparison symbols cards: one > card, one < card, one = card per group.

Players: 2-4 students per group

Objective: Be the first to correctly compare two fractions and win the round!

How to Play:

1. Preparation:

   • Shuffle the fraction cards and place them face down in a stack in the center of the group.
   • Place the >, <, and = symbol cards face up where everyone can reach them.

2. Starting the Round:

   • Each player draws one fraction card from the stack and places it face up in front of them.

3. Comparing Fractions:

   • Players then look at their own fraction and compare it to another player's fraction (e.g., Player A compares their fraction to Player B's fraction). The teacher can specify which two players compare, or groups can decide.
   • All players in the group mentally (or on scratch paper) determine the correct comparison symbol (> , <, or = ) between the two chosen fractions. They can use any strategy they've learned: common denominators, benchmark fractions, or drawing visual models.

4. Showdown!

   • On the count of three (or a signal from the teacher), all players reveal their chosen comparison symbol by grabbing and holding up the correct card (> , <, or =).

5. Scoring:

   • Players who correctly identified the relationship between the two fractions (and can explain why) earn a point. If there's a tie, all correct players get a point.
   • The player with the larger fraction (if comparing two different fractions) also explains their reasoning. If the fractions are equivalent, both players explain.

6. New Round:

   • Return the fraction cards to the bottom of the stack. Shuffle if needed. Start a new round.

7. Winning: The game continues for a set amount of time (e.g., 10-15 minutes) or until a player reaches a certain number of points. The player with the most points at the end wins!

Example Round:

• Player A draws: 3/4

• Player B draws: 1/2

• Player A thinks:

Answer Key: Equivalent Fractions & Comparison Worksheet

Part 1: Finding Equivalent Fractions

Instructions: For each fraction, draw a visual model and then write two equivalent fractions. You can use multiplication to help you!

Note: Visual models may vary, but should accurately represent the fractions. Equivalent fractions provided are examples; others are possible.

1. 1/2
   Visual Model: (Example: A rectangle divided into 2 equal parts, 1 shaded)

   Thought Process: To find equivalent fractions, multiply the numerator and denominator by the same non-zero number.
   Equivalent Fractions:

   1. 2/4 (1x2 / 2x2)
   2. 3/6 (1x3 / 2x3) or 4/8 (1x4 / 2x4)

2. 2/3
   Visual Model: (Example: A rectangle divided into 3 equal parts, 2 shaded)

   Thought Process: To find equivalent fractions, multiply the numerator and denominator by the same non-zero number.
   Equivalent Fractions:

   1. 4/6 (2x2 / 3x2)
   2. 6/9 (2x3 / 3x3) or 8/12 (2x4 / 3x4)

3. 1/4
   Visual Model: (Example: A circle divided into 4 equal parts, 1 shaded)

   Thought Process: To find equivalent fractions, multiply the numerator and denominator by the same non-zero number.
   Equivalent Fractions:

   1. 2/8 (1x2 / 4x2)
   2. 3/12 (1x3 / 4x3) or 4/16 (1x4 / 4x4)

Part 2: Comparing Fractions

Instructions: Use the symbols < (less than), > (greater than), or = (equal to) to compare the fractions. Show your work using common denominators or by comparing to a benchmark fraction (like 1/2).

1. 1/2 > 3/8
   Show Your Work:

   • Common Denominator: Convert 1/2 to 4/8 (multiply numerator and denominator by 4). Compare 4/8 to 3/8. Since 4 > 3, then 4/8 > 3/8.
   • Benchmark Fraction: 1/2 is exactly 1/2. 3/8 is less than 1/2 (because 4/8 would be 1/2). Therefore, 1/2 > 3/8.

2. 2/3 < 5/6
   Show Your Work:

   • Common Denominator: Convert 2/3 to 4/6 (multiply numerator and denominator by 2). Compare 4/6 to 5/6. Since 4 < 5, then 4/6 < 5/6.
   • Benchmark Fraction: Both are greater than 1/2. 2/3 is equivalent to 0.66... and 5/6 is equivalent to 0.83.... So 2/3 < 5/6.

3. 1/4 = 2/8
   Show Your Work:

   • Common Denominator: Convert 1/4 to 2/8 (multiply numerator and denominator by 2). Compare 2/8 to 2/8. They are equal.
   • Equivalent Fractions: 1/4 and 2/8 are equivalent fractions.

4. 3/5 > 1/2
   Show Your Work:

   • Common Denominator: Convert 3/5 to 6/10 (multiply by 2) and 1/2 to 5/10 (multiply by 5). Compare 6/10 to 5/10. Since 6 > 5, then 6/10 > 5/10.
   • Benchmark Fraction: 1/2 is the benchmark. 3/5 is greater than 1/2 (because 2.5/5 would be 1/2). Therefore, 3/5 > 1/2.

5. 2/7 < 2/5
   Show Your Work:

   • Common Numerator (or Common Denominator): When numerators are the same, the fraction with the smaller denominator is larger. If you have 2 slices of a pizza cut into 5 pieces (2/5), those slices are bigger than 2 slices of a pizza cut into 7 pieces (2/7). So 2/7 < 2/5.
   • Common Denominator: Convert 2/7 to 10/35 (multiply by 5) and 2/5 to 14/35 (multiply by 7). Compare 10/35 to 14/35. Since 10 < 14, then 10/35 < 14/35.

Part 3: Fraction Comparison Graphic Organizer

Instructions: Choose two fractions from the list below and compare them using the graphic organizer. Explain your reasoning.

Fractions to Choose From: 3/4, 1/3, 5/8, 1/2

Example Solution (Student answers will vary depending on chosen fractions and strategies):

Fraction 1: 3/4
Fraction 2: 1/3