Fraction Fun: Equivalency! Script

Warm-Up: What's a Fraction? (5 minutes)

(Teacher displays Equivalent Fractions Slide Deck - Slide 2)

"Good morning, class! Today, we're going to dive into the world of fractions, but with a fun twist. Before we get started, can anyone remind me what a fraction is? You can give an example, or tell me what its parts are."

(Allow students to share. Encourage think-pair-share if there's silence.)

"Great job! A fraction is simply a way to represent a part of a whole. It has a top number, the numerator, which tells us how many parts we have, and a bottom number, the denominator, which tells us how many total parts make up the whole. Think about when you've shared a pizza, or perhaps seen a recipe. Fractions are all around us!"

Introducing Equivalent Fractions (10 minutes)

(Teacher displays Equivalent Fractions Slide Deck - Slide 3)

"Now, sometimes, fractions can be a little tricky because they can look different but actually mean the same thing. Has anyone ever heard the word 'equivalent' before? What do you think it might mean?"

(Allow students to share ideas, guiding them towards 'equal in value' or 'the same as'.)

"That's right! When we talk about equivalent fractions, we're talking about fractions that represent the same value or same amount, even if they use different numbers. They might look different on paper, but they are exactly equal!"

(Teacher displays Equivalent Fractions Slide Deck - Slide 4)

"Let's look at an example. Imagine you have a delicious pizza. If I eat one-half of the pizza, how much is left? Now, what if I cut that same pizza into four equal slices? How many slices would I need to eat to have eaten the same amount as one-half?"

(Guide students to understand that 2 out of 4 slices is the same as 1 out of 2 slices.)

"Exactly! One-half of a pizza is the same amount as two-quarters of a pizza. The numbers are different (1/2 vs. 2/4), but the amount of pizza is exactly the same!"

(Teacher displays Equivalent Fractions Slide Deck - Slide 5)

"Here's another visual. Look at these fraction bars. Can you see how the bar showing one-third covers the exact same space as the bar showing two-sixths? They are equivalent fractions because they cover the same portion of the whole."

(Teacher displays Equivalent Fractions Slide Deck - Slide 6)

"So, how do we actually find equivalent fractions? It's like a secret trick! To find an equivalent fraction, you can multiply both the numerator (that's the top number) and the denominator (that's the bottom number) by the same non-zero number. The key is: what you do to the top, you must do to the bottom!"

(Teacher displays Equivalent Fractions Slide Deck - Slide 7)

"Let's try one together. If we have the fraction 1/2, and we want to find an equivalent fraction, we can multiply the top and bottom by, let's say, 2. So, 1 times 2 is 2, and 2 times 2 is 4. That gives us 2/4. We just saw this with our pizza! What if we multiplied by 3 instead? 1 times 3 is 3, and 2 times 3 is 6. So, 3/6 is also equivalent to 1/2! This means 1/2, 2/4, and 3/6 are all just different ways of writing the same amount."

(Teacher displays Equivalent Fractions Slide Deck - Slide 8)

"Let's try another one together. How about the fraction 3/5? What number could we multiply the numerator and denominator by to find an equivalent fraction?"

(Allow students to suggest numbers. Work through the example on the slide.)

"Excellent! So, 3/5, 6/10, and 12/20 are all equivalent. See how many different ways we can represent the same value?"

Guided Practice: Finding Equivalents (Numerical) (15 minutes)

"Now it's your turn to practice with numbers! I'm going to hand out the Equivalent Fractions Worksheet. We'll do the first few problems together on the board."

(Distribute the worksheets. Work through the first 3-4 problems on the board, explaining the steps and using the Equivalent Fractions Answer Key as a reference. Ensure students understand how to apply the multiplication rule.)

"Alright, you've got the hang of it! Now, continue working on the rest of the worksheet independently. I'll be walking around to help if you have any questions."

(Circulate and provide support. Check for common misconceptions.)

Guided Practice: Finding Equivalents (Visual) (10 minutes)

"Excellent work with the numerical fractions! Now, let's look at equivalent fractions in a different way – with pictures! I'm handing out the Equivalent Fractions Visual Worksheet."

(Distribute the visual worksheets.)

"For each problem, you'll first shade the given fraction in the first shape. Then, you'll divide the second shape into more parts to show an equivalent fraction, and shade it to match the amount of the first fraction. Finally, you'll write down the new equivalent fraction. Let's do the first problem together on the board to make sure everyone understands."

(Work through the first problem on the board or projector, demonstrating how to divide and shade a shape to create an equivalent fraction visually. Use the Equivalent Fractions Visual Answer Key as a guide.)

"Now, try the rest on your own! Remember, the goal is to show the same amount, just with more pieces. I'll be walking around to help."

(Circulate and provide support as students work on the visual worksheet.)

Wrap-Up & Cool-Down (5 minutes)

(Teacher displays Equivalent Fractions Slide Deck - Slide 9)

"Excellent work today, everyone! Let's quickly recap. What's the most important thing to remember about equivalent fractions?"

(Listen for responses like "they're the same value" or "you multiply top and bottom by the same number.")

"Fantastic! They represent the same amount, just written differently. And remember the rule: what you do to the top, you do to the bottom (or vice versa with division!)."

"Please hand in both your Equivalent Fractions Worksheet and Equivalent Fractions Visual Worksheet as you leave. For a quick cool-down, on a small slip of paper or just tell me verbally: can you give me one equivalent fraction for 1/3?"

(Collect worksheets and cool-down responses.)

"Great job today, sixth graders! See you next time!"

Equivalent Fractions Practice

Name: _____________________________

Instructions: For each fraction, find two equivalent fractions. Show your work by writing what number you multiplied the numerator and denominator by.

Example:

1/2

• Multiply by 2/2: (1 * 2) / (2 * 2) = 2/4
• Multiply by 3/3: (1 * 3) / (2 * 3) = 3/6

Problems:

1. 1/3
   
   
   
   
   
   
   
   
   
   
   
   
2. 2/5
   
   
   
   
   
   
   
   
   
   
   
   
3. 3/4
   
   
   
   
   
   
   
   
   
   
   
   
4. 1/6
   
   
   
   
   
   
   
   
   
   
   
   
5. 4/8
   
   
   
   
   
   
   
   
   
   
   
   
6. 2/7
   
   
   
   
   
   
   
   
   
   
   
   
7. 5/10
   
   
   
   
   
   
   
   
   
   
   
   
8. 3/9
   
   
   
   
   
   
   
   
   
   
   
   

Challenge Question: Explain in your own words why multiplying the numerator and denominator by the same number results in an equivalent fraction.

Equivalent Fractions: See It to Believe It!

Name: _____________________________

Instructions: For each diagram, shade the first shape to represent the given fraction. Then, divide the second shape into more parts to show an equivalent fraction, and shade it accordingly. Write down the equivalent fraction you've created.

Problem 1:

Given Fraction: 1/2

Divide this circle to show an equivalent fraction:

Equivalent Fraction: ____________

Problem 2:

Given Fraction: 1/3

Divide this rectangle to show an equivalent fraction:

Equivalent Fraction: ____________

Problem 3:

Given Fraction: 3/4

Divide this square to show an equivalent fraction:

Equivalent Fraction: ____________

Problem 4:

Given Fraction: 2/6

Divide this bar to show an equivalent fraction:

Equivalent Fraction: ____________

Equivalent Fractions: See It to Believe It! - Answer Key

Instructions:

For each diagram, shade the first shape to represent the given fraction. Then, divide the second shape into more parts to show an equivalent fraction, and shade it accordingly. Write down the equivalent fraction you've created.

Note: There are many possible ways to divide the second shape and create an equivalent fraction. Examples are provided below.

Problem 1:

Given Fraction: 1/2

Divide this circle to show an equivalent fraction:

Equivalent Fraction: 2/4 (or 3/6, 4/8, etc. - any equivalent fraction shown visually and numerically)

Problem 2:

Given Fraction: 1/3

Divide this rectangle to show an equivalent fraction:

Equivalent Fraction: 2/6 (or 3/9, 4/12, etc. - any equivalent fraction shown visually and numerically)

Problem 3:

Given Fraction: 3/4

Divide this square to show an equivalent fraction:

Equivalent Fraction: 6/8 (or 9/12, 12/16, etc. - any equivalent fraction shown visually and numerically)

Problem 4:

Given Fraction: 2/6

Divide this bar to show an equivalent fraction:

Equivalent Fraction: 1/3 (or 4/12, 6/18, etc. - students could also simplify by dividing by 2/2, as shown here)

Equivalent Fractions Practice - Answer Key

Instructions:

For each fraction, find two equivalent fractions. There are many possible correct answers; examples are provided below. The key is that both the numerator and denominator are multiplied (or divided) by the same non-zero number.

Problems:

1. 1/3

   • Thought Process: To find an equivalent fraction, I need to multiply both the numerator (1) and the denominator (3) by the same number.
   • Example 1: Multiply by 2/2
     (1 * 2) / (3 * 2) = 2/6
   • Example 2: Multiply by 3/3
     (1 * 3) / (3 * 3) = 3/9

2. 2/5

   • Thought Process: Multiply both the numerator (2) and the denominator (5) by the same number.
   • Example 1: Multiply by 2/2
     (2 * 2) / (5 * 2) = 4/10
   • Example 2: Multiply by 3/3
     (2 * 3) / (5 * 3) = 6/15

3. 3/4

   • Thought Process: Multiply both the numerator (3) and the denominator (4) by the same number.
   • Example 1: Multiply by 2/2
     (3 * 2) / (4 * 2) = 6/8
   • Example 2: Multiply by 5/5
     (3 * 5) / (4 * 5) = 15/20

4. 1/6

   • Thought Process: Multiply both the numerator (1) and the denominator (6) by the same number.
   • Example 1: Multiply by 2/2
     (1 * 2) / (6 * 2) = 2/12
   • Example 2: Multiply by 4/4
     (1 * 4) / (6 * 4) = 4/24

5. 4/8

   • Thought Process: Multiply both the numerator (4) and the denominator (8) by the same number. Students could also simplify by dividing.
   • Example 1 (Multiply): Multiply by 2/2
     (4 * 2) / (8 * 2) = 8/16
   • Example 2 (Divide/Simplify): Divide by 4/4
     (4 / 4) / (8 / 4) = 1/2

6. 2/7

   • Thought Process: Multiply both the numerator (2) and the denominator (7) by the same number.
   • Example 1: Multiply by 2/2
     (2 * 2) / (7 * 2) = 4/14
   • Example 2: Multiply by 3/3
     (2 * 3) / (7 * 3) = 6/21

7. 5/10

   • Thought Process: Multiply both the numerator (5) and the denominator (10) by the same number. Students could also simplify by dividing.
   • Example 1 (Multiply): Multiply by 2/2
     (5 * 2) / (10 * 2) = 10/20
   • Example 2 (Divide/Simplify): Divide by 5/5
     (5 / 5) / (10 / 5) = 1/2

8. 3/9

   • Thought Process: Multiply both the numerator (3) and the denominator (9) by the same number. Students could also simplify by dividing.
   • Example 1 (Multiply): Multiply by 2/2
     (3 * 2) / (9 * 2) = 6/18
   • Example 2 (Divide/Simplify): Divide by 3/3
     (3 / 3) / (9 / 3) = 1/3

Challenge Question:

Explain in your own words why multiplying the numerator and denominator by the same number results in an equivalent fraction.

• Explanation: When you multiply the numerator and denominator by the same number, you are essentially multiplying the fraction by another fraction that is equal to 1 (e.g., 2/2, 3/3, 4/4). Multiplying anything by 1 doesn't change its value, so the original fraction's value stays the same, even though it looks different. It's like cutting the existing pieces into smaller, equal pieces without changing the total amount.