Reading
Fraction Vocabulary
- Fraction: A part of a whole. It shows how many parts of a certain size there are.
- Numerator: The top number in a fraction. It tells you how many parts you have.
- Denominator: The bottom number in a fraction. It tells you how many equal parts the whole is divided into.
- Unit Fraction: A fraction where the numerator is 1 (e.g., 1/2, 1/3, 1/4). It represents one part of a whole.
- Number Line: A line where numbers are placed in order.
- Whole: All of the parts put together, or one entire object or group.
use Lenny to create lessons.
No credit card needed
Reading
Fraction Sentence Stems
- "The fraction ______ represents ______ equal parts out of ______ total equal parts."
- "The numerator ______ tells me that I have ______ part(s)."
- "The denominator ______ tells me that the whole is divided into ______ equal parts."
- "I can locate ______ on the number line by dividing the whole into ______ equal parts and marking ______ of those parts from zero."
- "This fraction is a unit fraction because its numerator is ______."
Lesson Plan
Unit Fractions: Halves & Thirds
Students will be able to define unit fractions and accurately represent 1/2 and 1/3 on a number line, recognizing that each part has a size of 1/b.
Understanding unit fractions on a number line helps students visualize fractions as numbers, building a strong foundation for more complex fraction concepts and enhancing their number sense.
Audience
Grade 4 Small Group (3 students)
Time
30 minutes
Approach
Direct instruction, guided practice, and independent application.
Materials
Whiteboard or chart paper, Markers, Fraction Vocabulary, Fraction Sentence Stems, Unit Fractions: Halves & Thirds Slide Deck, Unit Fractions: Halves & Thirds Script, Halves & Thirds Worksheet, and Unit Fractions Cool Down 1
Prep
Gather Materials & Review
10 minutes
- Gather all necessary materials: whiteboard/chart paper, markers, and printouts of the Fraction Vocabulary, Fraction Sentence Stems, Halves & Thirds Worksheet, and Unit Fractions Cool Down 1.
- Review the Unit Fractions: Halves & Thirds Slide Deck and Unit Fractions: Halves & Thirds Script to familiarize yourself with the content and flow of the lesson.
- Ensure the projector or screen is ready for the slide deck presentation.
Step 1
Warm-Up (5 minutes)
5 minutes
- Begin by asking students: "What is a fraction? Can you give an example of when you might use a fraction in real life?" Allow for brief discussion.
- Introduce the Fraction Vocabulary and review key terms: fraction, numerator, denominator, whole. Focus on 'unit fraction' as the new concept for today.
Step 2
Introduction to Unit Fractions (10 minutes)
10 minutes
- Use the Unit Fractions: Halves & Thirds Slide Deck with the Unit Fractions: Halves & Thirds Script to introduce unit fractions.
- Explain what a unit fraction is (numerator is 1).
- Demonstrate how to partition a whole into two equal parts to represent 1/2, and into three equal parts to represent 1/3. Show how to represent 1/2 and 1/3 on a number line.
Step 3
Guided Practice (10 minutes)
10 minutes
- Distribute the Halves & Thirds Worksheet.
- Work through the problems for 1/2 and 1/3 together as a group, using the Fraction Sentence Stems to guide student responses.
- Encourage students to articulate their thinking as they divide the number line and place the unit fractions.
Step 4
Independent Practice & Check for Understanding (3 minutes)
3 minutes
- Have students complete any remaining problems independently from the Halves & Thirds Worksheet.
- Circulate and provide individualized support and feedback. Ensure students are correctly partitioning the number line and placing the unit fraction at the correct point.
Step 5
Cool Down (2 minutes)
2 minutes
- Distribute the Unit Fractions Cool Down 1.
- Students will answer a quick question to demonstrate their understanding of representing a unit fraction on a number line.
Slide Deck
What's a Unit Fraction?
Fractions on a Number Line!
Today, we're going to learn about a special type of fraction and how to put it on a number line.
Let's review:
- What is a fraction?
- Numerator: Top number (how many parts we have)
- Denominator: Bottom number (total equal parts in the whole)
Welcome students and briefly review what a fraction is. Introduce the idea of a 'number line' as a way to see numbers in order.
Unit Fractions: The Building Blocks
Unit Fractions
- A unit fraction is a fraction where the numerator is 1.
- It represents one equal part of a whole.
- Think of it like a single slice of a pizza, if the pizza is divided into equal slices!
Examples: 1/2, 1/3, 1/4
Clearly define a unit fraction. Emphasize that the numerator is always 1. Give several examples and ask students to identify them.
Fractions Live on a Number Line!
The Number Line: Our Fraction Ruler
- A number line helps us see where numbers belong.
- For fractions, we focus on the space between 0 and 1.
- This space is our WHOLE!
Introduce the number line concept for fractions. Explain that the space between 0 and 1 is our 'whole'.
Putting Unit Fractions on the Line
How to place 1/b on a number line:
- Draw a number line from 0 to 1.
- Look at the denominator (b). This tells you how many equal parts to divide the whole (from 0 to 1) into.
- Make marks to divide the line into 'b' equal parts.
- The first mark after 0 is where 1/b goes!
Demonstrate how to partition the number line. Use a simple example like 1/2. Show how to divide the line into 2 equal parts. Explain that the point marks the fraction.
Let's Practice: 1/2 and 1/3
Let's try placing these unit fractions!
- 1/2: How many equal parts do we need between 0 and 1?
- 1/3: How many equal parts do we need between 0 and 1?
Practice with 1/2 and 1/3. Ask students to describe the steps. Use the sentence stems.
Lesson Plan
Unit Fractions: Quarters & Fifths
Students will accurately represent unit fractions 1/4 and 1/5 on a number line, reinforcing the concept that each part has a size of 1/b.
Continued practice with different unit fractions solidifies students' understanding of partitioning a whole into equal parts and accurately locating fractions on a number line, which is crucial for building robust fraction sense.
Audience
Grade 4 Small Group (3 students)
Time
30 minutes
Approach
Review, guided practice, and independent application.
Materials
Whiteboard or chart paper, Markers, Fraction Vocabulary, Fraction Sentence Stems, Unit Fractions: Quarters & Fifths Slide Deck, Unit Fractions: Quarters & Fifths Script, Quarters & Fifths Worksheet, and Unit Fractions Cool Down 2
Prep
Gather Materials & Review
10 minutes
- Gather all necessary materials: whiteboard/chart paper, markers, and printouts of the Fraction Vocabulary, Fraction Sentence Stems, Quarters & Fifths Worksheet, and Unit Fractions Cool Down 2.
- Review the Unit Fractions: Quarters & Fifths Slide Deck and Unit Fractions: Quarters & Fifths Script to familiarize yourself with the content and flow of the lesson.
- Ensure the projector or screen is ready for the slide deck presentation.
Step 1
Warm-Up/Review (5 minutes)
5 minutes
- Review unit fractions 1/2 and 1/3 by asking students to quickly draw a number line and place one of them. Discuss their reasoning, reinforcing the concept of dividing the whole into equal parts.
Step 2
Introduction & Guided Practice (15 minutes)
15 minutes
- Use the Unit Fractions: Quarters & Fifths Slide Deck with the Unit Fractions: Quarters & Fifths Script to introduce and guide students through representing 1/4 and 1/5 on a number line.
- Emphasize looking at the denominator to determine the number of equal parts.
- Distribute the Quarters & Fifths Worksheet and work through the first few problems for 1/4 and 1/5 together, using the Fraction Sentence Stems.
Step 3
Independent Practice & Check for Understanding (8 minutes)
8 minutes
- Have students complete the remaining problems independently from the Quarters & Fifths Worksheet.
- Circulate and provide individualized support and feedback. Pay attention to how students partition the number line, ensuring equal spacing.
Step 4
Cool Down (2 minutes)
2 minutes
- Distribute the Unit Fractions Cool Down 2.
- Students will represent a new unit fraction (e.g., 1/6) on a number line.
Slide Deck
More Unit Fraction Fun!
Remembering Unit Fractions
- What is a unit fraction?
- How did we place 1/2 and 1/3 on a number line?
Today, we'll explore even more unit fractions!
Briefly review the previous lesson on 1/2 and 1/3. Ask students what a unit fraction is.
Discovering 1/4
Placing 1/4 on a Number Line
- What does the denominator (4) tell us?
- How many equal parts do we need between 0 and 1?
- Where does 1/4 go?
Introduce 1/4. Guide students to explain how they would place it on a number line.
Making Room for 1/5
Putting 1/5 on the Line
- What does the denominator (5) tell us?
- How many equal parts for our whole?
- Where do we mark 1/5?
Introduce 1/5. Guide students through the process.
Practice Time: 1/4 and 1/5
Let's ensure our number lines are perfectly partitioned!
- How many segments for 1/4? Count from zero!
- How many segments for 1/5? Count from zero!
Quick practice with both 1/4 and 1/5. Encourage using sentence stems.
Script
Unit Fractions: Quarters & Fifths Script
Warm-Up/Review (5 minutes)
Teacher: "Welcome everyone! Let's quickly remember our last lesson. Who can draw a number line from 0 to 1 and show us where 1/3 goes? Remember to explain your thinking, perhaps using one of our Fraction Sentence Stems."
Teacher: "Fantastic review! It sounds like you're all experts at placing 1/2 and 1/3. Today, we're going to keep exploring unit fractions and learn to place a couple more on our number line."
Introduction & Guided Practice (15 minutes)
Teacher: "Let's open our Unit Fractions: Quarters & Fifths Slide Deck. We'll start with 1/4. Looking at the denominator, what does it tell us we need to do to our whole, the space between 0 and 1?"
Teacher: "That's right! We divide it into four equal parts. And where does 1/4 go on that number line?"
Teacher: "Exactly! It's the first mark after zero when the whole is divided into four equal parts. Let's practice drawing this on our Quarters & Fifths Worksheet. Go ahead and draw your number line and place 1/4."
(Pause for students to draw and place.)
Teacher: "Now let's think about 1/5. What does the denominator tell us for this unit fraction?"
Teacher: "You got it! Five equal parts. And where do we mark 1/5?"
Teacher: "Excellent! The first mark after zero when we have five equal parts. Let's do the first 1/5 problem on our worksheet together. Remember to make your parts as equal as possible."
Independent Practice & Check for Understanding (8 minutes)
Teacher: "Now, for the next few minutes, I'd like you to work independently on the remaining problems on your Quarters & Fifths Worksheet. I'll be walking around to see your progress and offer help if you need it. Remember our sentence stems if you get stuck on how to explain your placement!"
Cool Down (2 minutes)
Teacher: "Alright, let's wrap up with our cool down. Please grab your Unit Fractions Cool Down 2 sheet. I want you to draw a number line and represent 1/6, and then explain your reasoning. Think carefully about the denominator!"
Worksheet
Quarters & Fifths on a Number Line
Directions: For each problem, draw a number line from 0 to 1. Then, partition the number line into the correct number of equal parts and mark the given unit fraction.
-
Represent 1/4 on the number line.
-
Represent 1/5 on the number line.
Challenge Question: If you divide a number line into more equal parts, what happens to the size of each part?
Cool Down
Unit Fractions Cool Down 2
Directions: Draw a number line below and represent the unit fraction 1/6.
Explain your reasoning: How did you decide where to place 1/6 on the number line?
Script
Unit Fractions: Halves & Thirds Script
Warm-Up (5 minutes)
Teacher: "Good morning, everyone! Let's start by thinking about what a fraction is. Can anyone tell me, in your own words, what a fraction means?"
Teacher: "Great ideas! Fractions are all around us, like when we share a pizza or measure ingredients for baking. Today, we're going to dive deeper into fractions and learn about a special type called 'unit fractions.' Look at our Fraction Vocabulary sheet. Let's quickly review 'fraction,' 'numerator,' and 'denominator.' What does the numerator tell us? What does the denominator tell us?"
Teacher: "Excellent! Now, let's look at 'unit fraction.' A unit fraction is a fraction where the numerator is always 1. It means we're talking about just one of the equal parts of a whole."
Introduction to Unit Fractions (10 minutes)
Teacher: "Now, let's look at our Unit Fractions: Halves & Thirds Slide Deck. We're going to learn how to put these unit fractions on a number line. Think of a number line like a ruler for numbers. The space between 0 and 1 is our 'whole'."
Teacher: (Display slide 4: 'Putting Unit Fractions on the Line') "When we want to place a unit fraction like 1/2 on a number line, we look at the denominator, which is 2. This tells us to divide the whole, from 0 to 1, into 2 equal parts. Let's draw a number line and do that together. Where would the mark for 1/2 go?"
Teacher: (Guide students to make a mark exactly in the middle) "That's right! The first mark after 0 is where 1/2 goes. We've divided our whole into two equal parts, and we're looking at one of those parts."
Teacher: "Now, what about 1/3? Using our Fraction Sentence Stems, how would we describe 1/3? 'The fraction 1/3 represents ______ equal part out of ______ total equal parts.'"
Teacher: "Exactly! The denominator, 3, tells us to divide the whole into three equal parts. So, on our number line, we'll make two marks to create three equal sections. Where would 1/3 go?"
Teacher: (Guide students to place 1/3) "Fantastic! It's the first mark after 0 when the whole is divided into three equal parts."
Guided Practice (10 minutes)
Teacher: "Let's get some practice with our Halves & Thirds Worksheet. We'll do the first few together. For problem 1, representing 1/2, what's the first thing we do to the number line?"
Teacher: "Right, divide it into two equal parts! And where do we mark 1/2?"
Teacher: "Excellent! Now try problem 2, representing 1/3. Remember our sentence stems to help you explain your thinking."
Independent Practice & Check for Understanding (3 minutes)
Teacher: "Now, I'd like you to complete the rest of the worksheet on your own. I'll be walking around to see how you're doing and offer help if you need it. Remember to divide the number line into equal parts and mark the correct spot for your unit fraction."
Cool Down (2 minutes)
Teacher: "Time for our cool down! Please take out your Unit Fractions Cool Down 1 sheet. I want you to represent 1/4 on a number line and explain your reasoning. This will show me what you've learned today!"
Worksheet
Halves & Thirds on a Number Line
Directions: For each problem, draw a number line from 0 to 1. Then, partition the number line into the correct number of equal parts and mark the given unit fraction.
-
Represent 1/2 on the number line.
-
Represent 1/3 on the number line.
Challenge Question: Explain in your own words how you know where to place 1/2 on a number line.
Cool Down
Unit Fractions Cool Down 1
Directions: Draw a number line below and represent the unit fraction 1/4.
Explain your reasoning: How did you decide where to place 1/4 on the number line?
Lesson Plan
Non-Unit Fractions: Exploring Thirds & Fourths
Students will deepen their understanding of non-unit fractions by accurately representing 2/4 and 3/3 on a number line, recognizing that a/b is 'a' lengths of 1/b from 0.
Practicing with different non-unit fractions helps students generalize their understanding of fraction placement and recognize equivalent fractions (like 2/4 = 1/2) and whole numbers (like 3/3 = 1) on the number line, strengthening their number sense.
Audience
Grade 4 Small Group (3 students)
Time
30 minutes
Approach
Review, guided practice, and independent application.
Materials
Prep
Gather Materials & Review
10 minutes
- Gather all necessary materials: whiteboard/chart paper, markers, and printouts of the Fraction Vocabulary, Fraction Sentence Stems, Exploring Thirds & Fourths Worksheet, and Non-Unit Fractions Cool Down 2.
- Review the Non-Unit Fractions: Exploring Thirds & Fourths Slide Deck and Non-Unit Fractions: Exploring Thirds & Fourths Script to familiarize yourself with the content and flow of the lesson.
- Ensure the projector or screen is ready for the slide deck presentation.
Step 1
Warm-Up/Review (5 minutes)
5 minutes
- Review non-unit fractions 2/3 and 3/4 by asking students to quickly draw a number line and place one of them. Discuss their reasoning, reinforcing the two-step process (partition, then count).
Step 2
Introduction & Guided Practice (15 minutes)
15 minutes
- Use the Non-Unit Fractions: Exploring Thirds & Fourths Slide Deck with the Non-Unit Fractions: Exploring Thirds & Fourths Script to introduce and guide students through representing 2/4 and 3/3 on a number line.
- Emphasize the connection between the numerator and denominator and how it relates to the whole (e.g., 3/3 = 1 whole, 2/4 = 1/2).
- Distribute the Exploring Thirds & Fourths Worksheet and work through the first few problems together, using the Fraction Sentence Stems.
Step 3
Independent Practice & Check for Understanding (8 minutes)
8 minutes
- Have students complete the remaining problems independently from the Exploring Thirds & Fourths Worksheet.
- Circulate and provide individualized support and feedback. Encourage students to identify if a fraction represents a half or a whole.
Step 4
Cool Down (2 minutes)
2 minutes
- Distribute the Non-Unit Fractions Cool Down 2.
- Students will represent a new non-unit fraction (e.g., 3/6) on a number line.
Slide Deck
More Non-Unit Fractions!
Reviewing Non-Unit Fractions
- What is a non-unit fraction?
- What are the two steps to place it on a number line?
Today, we'll practice with more examples and find some interesting connections!
Briefly review the previous lesson on 2/3 and 3/4. Ask students what a non-unit fraction is and the two steps to place it.
Placing 2/4
Let's place 2/4 on the number line!
- How many equal parts for our whole?
- How many parts do we count from 0?
- What do you notice about where 2/4 lands? (Hint: Think about 1/2!)
Introduce 2/4. Discuss how it relates to 1/2.
What About 3/3?
Placing 3/3 on the Number Line
- How many equal parts for our whole?
- How many parts do we count from 0?
- Where does 3/3 land? What does that mean?
Introduce 3/3. Discuss how it relates to a whole number.
Practice Time: 2/4 and 3/3
Show me where these fractions belong!
- 2/4: Divide into 4, count 2.
- 3/3: Divide into 3, count 3. What number is that?
Quick practice with 2/4 and 3/3. Reinforce the concept of equivalent fractions and whole numbers.
Script
Non-Unit Fractions: Exploring Thirds & Fourths Script
Warm-Up/Review (5 minutes)
Teacher: "Good morning, team! Let's quickly review from last time. Who can draw a number line from 0 to 1 and place 2/3 on it? Remember to tell us your steps using our Fraction Sentence Stems."
Teacher: "Excellent review! You're all doing a wonderful job with non-unit fractions. Today, we're going to keep practicing and explore a couple of special non-unit fractions on our number line. We'll also see if we can find some interesting connections!"
Introduction & Guided Practice (15 minutes)
Teacher: "Let's open our Non-Unit Fractions: Exploring Thirds & Fourths Slide Deck. We're going to start with 2/4. What does the denominator tell us to do first?"
Teacher: "Right! Divide the whole into four equal parts. And then, what does the numerator tell us to do?"
Teacher: "Exactly, count two of those parts from zero! Let's draw that on the board. (Draw number line and mark 2/4). Now, what do you notice about where 2/4 lands on the number line? Does it look familiar to another fraction we know?"
Teacher: "Great observation! It lands right at the same spot as 1/2! That's a super important connection we'll explore more later. For now, let's try problem 1 on our Exploring Thirds & Fourths Worksheet and place 2/4."
(Pause for students to draw and place.)
Teacher: "Now let's look at 3/3. What does the denominator tell us?"
Teacher: "Three equal parts! And the numerator?"
Teacher: "Count three of those parts! Where does 3/3 land on our number line?"
Teacher: "Amazing! It lands right on the 1! That's because 3/3 is another way to say one whole. Let's practice placing 3/3 on our worksheet now."
Independent Practice & Check for Understanding (8 minutes)
Teacher: "For the next few minutes, please work independently on the rest of your Exploring Thirds & Fourths Worksheet. Remember to first divide the whole, then count the parts. And see if you notice any other interesting connections!"
Cool Down (2 minutes)
Teacher: "Time for our cool down! Please get your Non-Unit Fractions Cool Down 2 sheet. I want you to represent 3/6 on a number line and explain your reasoning. Think about what we discussed today about where some fractions land!"
Worksheet
Exploring Thirds & Fourths on a Number Line
Directions: For each problem, draw a number line from 0 to 1. Then, partition the number line into the correct number of equal parts and mark the given non-unit fraction.
-
Represent 2/4 on the number line.
-
Represent 3/3 on the number line.
Challenge Question: Can you think of another fraction that lands at the same spot as 2/4 on the number line? Explain why.
Cool Down
Non-Unit Fractions Cool Down 2
Directions: Draw a number line below and represent the non-unit fraction 3/6.
Explain your reasoning: How did you decide where to place 3/6 on the number line? What do you notice about its placement?
Lesson Plan
Defining the Fractional Whole: 0 to 1
Students will solidify their understanding of the interval from 0 to 1 as the designated 'whole' when representing fractions on a number line.
Clearly defining the 'whole' on a number line is fundamental for accurately placing fractions. This lesson ensures students understand the boundaries within which they partition and locate fractional parts.
Audience
Grade 4 Small Group (3 students)
Time
30 minutes
Approach
Direct instruction, visual exploration, and guided discussion.
Materials
Whiteboard or chart paper, Markers, Fraction Vocabulary, Fraction Sentence Stems, Defining the Fractional Whole Slide Deck, Defining the Fractional Whole Script, Number Line Exploration Worksheet, and Whole-Defining Cool Down
Prep
Gather Materials & Review
10 minutes
- Gather all necessary materials: whiteboard/chart paper, markers, and printouts of the Fraction Vocabulary, Fraction Sentence Stems, Number Line Exploration Worksheet, and Whole-Defining Cool Down.
- Review the Defining the Fractional Whole Slide Deck and Defining the Fractional Whole Script to familiarize yourself with the content and flow of the lesson.
- Ensure the projector or screen is ready for the slide deck presentation.
Step 1
Warm-Up (5 minutes)
5 minutes
- Draw a simple number line (0-5) on the board. Ask students: "What do these numbers tell us? What do the spaces between the numbers represent?" Engage in a brief discussion about whole numbers and intervals.
Step 2
Introduction: The Fractional Whole (10 minutes)
10 minutes
- Use the Defining the Fractional Whole Slide Deck with the Defining the Fractional Whole Script to introduce the concept of the 'whole' as the interval from 0 to 1 for fractions.
- Explain why this specific segment is important for understanding fractions on a number line.
- Discuss common misconceptions, such as extending the fraction beyond 1 when only a part of a single whole is intended.
Step 3
Guided Exploration (10 minutes)
10 minutes
- Distribute the Number Line Exploration Worksheet.
- Guide students to identify and highlight the 'whole' (0 to 1) on various number lines. Discuss how partitioning within this specific segment creates the fractional parts.
- Use Fraction Sentence Stems to articulate their observations about the 'whole'.
Step 4
Check for Understanding (3 minutes)
3 minutes
- Ask students to orally explain why the space between 0 and 1 is crucial when thinking about a fraction like 1/2 or 2/3.
- Observe their independent work on the worksheet to ensure correct identification of the 'whole'.
Step 5
Cool Down (2 minutes)
2 minutes
- Distribute the Whole-Defining Cool Down.
- Students will draw a number line and clearly mark the 'whole' for representing a fraction, explaining why.
Slide Deck
What's Our Whole?
Reviewing Number Lines
- We've used number lines for whole numbers.
- What do the numbers 0, 1, 2, 3 tell us?
- What about the spaces between them?
Start with a general discussion about number lines and whole numbers to activate prior knowledge.
The Fractional Whole: 0 to 1
For Fractions, Our "Whole" is Special!
- When we talk about fractions like 1/2 or 3/4, we're talking about parts of one whole.
- On a number line, this 'one whole' is the space between 0 and 1.
Introduce the idea that for fractions, we focus on a specific 'whole'.
Why is 0 to 1 So Important?
Keeping Our Fractions in Check!
- If we want to show 1/2, we only need the space from 0 to 1.
- We divide that space into equal parts.
- It helps us understand the size of the fraction.
Explain why it's important not to extend beyond 1 if the fraction is less than a whole.
Spot the Whole!
Let's find the "whole"!
- Look at these number lines.
- Can you point to the segment that represents our 'whole' for fractions?
- Why is that segment so important for placing fractions?
Guide students to identify the 'whole' on example number lines.
Script
Defining the Fractional Whole Script
Warm-Up (5 minutes)
Teacher: "Good morning, everyone! Let's start by looking at a regular number line. (Draw a number line from 0 to 5 on the board with integer marks.) What do these numbers, 0, 1, 2, 3, 4, 5, represent? What do the spaces between them mean?"
Teacher: "Great answers! We use number lines to put numbers in order. Today, we're going to focus on a very specific part of the number line when we talk about fractions: the 'whole'."
Introduction: The Fractional Whole (10 minutes)
Teacher: "Let's open our Defining the Fractional Whole Slide Deck. (Display slide 2: 'The Fractional Whole: 0 to 1'). When we talk about fractions, like 1/2 or 2/3, we're always talking about parts of one whole. On a number line, that 'one whole' is always the space, or interval, from 0 to 1."
Teacher: "Why do you think it's so important to think about the space between 0 and 1 as our whole when we're placing fractions?"
Teacher: "Exactly! It sets the stage for how we divide our number line. If we want to show 1/2, we divide that specific space (0 to 1) into two equal parts. We don't need to go past the 1, because 1/2 is only part of one whole. (Display slide 3: 'Why is 0 to 1 So Important?'). This helps us truly understand the size of the fraction."
Guided Exploration (10 minutes)
Teacher: "Now, let's take out our Number Line Exploration Worksheet. You'll see different number lines there. Your job is to clearly identify and highlight the 'whole' – that special segment from 0 to 1. For each number line, explain using our Fraction Sentence Stems why that segment is the 'whole'. For example, you might say, 'The whole for this fraction is from 0 to 1 because that is where we divide our parts.'"
(Circulate, provide support, and facilitate discussion.)
Check for Understanding (3 minutes)
Teacher: "Let's pause and check our understanding. Who can tell me, in your own words, why the space between 0 and 1 is so crucial when we're thinking about placing a fraction like 1/2 or 2/3 on a number line?"
Teacher: "Wonderful explanations! You're all doing a great job understanding our 'fractional whole'."
Cool Down (2 minutes)
Teacher: "Alright, for our cool down, please grab your Whole-Defining Cool Down. I want you to draw a number line and clearly mark the 'whole' for representing a fraction. Then, explain why you chose that specific segment as the 'whole'."
Worksheet
Number Line Exploration: Defining the Whole
Directions: For each number line, clearly identify and highlight the 'whole' (the segment from 0 to 1). Then, explain why this segment is important for representing fractions.
-
0 ----------- 1 ----------- 2
Explanation:
-
0 ----- 1
Explanation:
-
0 -------------------- 1
Explanation:
Challenge Question: If you were explaining to a friend why we use the space from 0 to 1 for fractions, what would you tell them?
Cool Down
Whole-Defining Cool Down
Directions: Draw a number line below. Clearly mark the 'whole' (the segment from 0 to 1) for representing a fraction.
Explain your reasoning: Why is the space between 0 and 1 considered the 'whole' when we are working with fractions on a number line?
Lesson Plan
Partitioning with Precision: Equal Parts
Students will learn and practice accurately partitioning the 'whole' (0 to 1) into a specified number of equal parts (denominator 'b') on a number line.
Accurate partitioning is critical for correctly representing any fraction on a number line. This lesson focuses on the precision needed to create equal segments, laying the groundwork for precise fraction placement.
Audience
Grade 4 Small Group (3 students)
Time
30 minutes
Approach
Direct instruction, hands-on practice, and visual feedback.
Materials
Whiteboard or chart paper, Markers, Rulers (optional, for drawing straight lines), Fraction Vocabulary, Fraction Sentence Stems, Partitioning with Precision Slide Deck, Partitioning with Precision Script, Equal Parts Practice Worksheet, and Precision Partitioning Cool Down
Prep
Gather Materials & Review
10 minutes
- Gather all necessary materials: whiteboard/chart paper, markers, rulers (optional for students), and printouts of the Fraction Vocabulary, Fraction Sentence Stems, Equal Parts Practice Worksheet, and Precision Partitioning Cool Down.
- Review the Partitioning with Precision Slide Deck and Partitioning with Precision Script to familiarize yourself with the content and flow of the lesson.
- Ensure the projector or screen is ready for the slide deck presentation.
Step 1
Warm-Up/Review (5 minutes)
5 minutes
- Quick review: Ask students to define 'denominator' using the Fraction Vocabulary. Briefly discuss its role in telling us 'how many equal parts the whole is divided into.'
Step 2
Introduction: The Art of Equal Parts (10 minutes)
10 minutes
- Use the Partitioning with Precision Slide Deck with the Partitioning with Precision Script to explicitly teach strategies for partitioning the number line into equal parts.
- Demonstrate techniques like estimating, folding (if using paper strips as a visual aid), or making strategic marks.
- Emphasize that the marks divide the space between 0 and 1, not just marking random points.
Step 3
Guided Practice: Precision in Action (10 minutes)
10 minutes
- Distribute the Equal Parts Practice Worksheet.
- Work through several examples together, focusing on partitioning the number line into 2, 3, 4, and 5 equal parts.
- Encourage students to use the Fraction Sentence Stems to describe their partitioning process (e.g., "I divided the whole into _____ equal parts because the denominator is _____."). Provide immediate feedback on the equality of their divisions.
Step 4
Check for Understanding (3 minutes)
3 minutes
- Have students independently partition one or two number lines on the worksheet. Circulate and observe their technique.
- Ask them to explain how they know their parts are 'equal'.
Step 5
Cool Down (2 minutes)
2 minutes
- Distribute the Precision Partitioning Cool Down.
- Students will partition a number line into a given number of equal parts and explain their strategy.
Slide Deck
The Denominator's Big Job!
Remembering the Denominator
- The denominator tells us the total number of equal parts our whole is divided into.
- It's like telling us how many slices are in the pizza!
Start with a review of the denominator's role. Ask: 'What does the bottom number of a fraction tell us?'
Making Parts Perfectly Equal!
How to Divide Our Number Line
- When we divide the space from 0 to 1, all parts must be exactly the same size.
- Think of it like cutting a cake evenly for everyone!
- Strategy 1: Estimate and adjust.
- Strategy 2: If dividing into an even number of parts, find the middle first.
Introduce the challenge of making parts 'equal' and discuss strategies.
Dividing into 2 Equal Parts
Example: Halves!
- To get 2 equal parts, we make one mark right in the middle of 0 and 1.
- This mark divides the whole into 1/2 and 1/2.
Demonstrate partitioning into 2 equal parts. Emphasize the single mark in the middle.
Dividing into 3 Equal Parts
Example: Thirds!
- To get 3 equal parts, we make two marks that split the whole evenly.
- It takes practice to make them look just right!
Demonstrate partitioning into 3 equal parts. Emphasize making two marks.
Dividing into 4 Equal Parts
Example: Quarters!
- To get 4 equal parts, we can start by finding the middle (1/2).
- Then, we divide each half into two more equal parts.
- How many marks did we make?
Demonstrate partitioning into 4 equal parts. Show how finding the middle (1/2) first can help.
Script
Partitioning with Precision Script
Warm-Up/Review (5 minutes)
Teacher: "Good morning, everyone! Let's start with a quick review. Looking at our Fraction Vocabulary, who can tell me what the 'denominator' means?"
Teacher: "Excellent! The denominator is super important because it tells us exactly how many equal parts our whole is divided into. Today, we're going to become experts at making those parts perfectly equal on our number lines."
Introduction: The Art of Equal Parts (10 minutes)
Teacher: "Let's open our Partitioning with Precision Slide Deck. (Display slide 2: 'Making Parts Perfectly Equal!'). When we divide the space between 0 and 1, it's really important that all the parts are exactly the same size. Think about sharing a chocolate bar – no one wants a smaller piece, right?"
Teacher: "It takes practice to make truly equal parts. One strategy is to estimate where the marks should go and then adjust. For example, if we're dividing into 2 equal parts (display slide 3: 'Dividing into 2 Equal Parts'), we only need one mark right in the middle. (Demonstrate on whiteboard). This mark creates two equal sections."
Teacher: "Now, for 3 equal parts (display slide 4: 'Dividing into 3 Equal Parts'), we need two marks. It's a bit trickier to make them even. I try to make them roughly the same size. (Demonstrate on whiteboard)."
Teacher: "For 4 equal parts (display slide 5: 'Dividing into 4 Equal Parts'), a trick is to find the middle first, which gives us 1/2. Then, we can find the middle of each half. This gives us 1/4, 2/4 (which is 1/2), and 3/4. (Demonstrate on whiteboard). Notice how many marks I made for 4 equal parts? Three marks!"
Guided Practice: Precision in Action (10 minutes)
Teacher: "Now it's your turn to practice on your Equal Parts Practice Worksheet. We'll work through the first few together. For the first number line, you need to partition it into 2 equal parts. How many marks will you make?"
Teacher: "Yes, one mark in the middle! Go ahead and do that. (Circulate and provide feedback). Now, for the next one, partition it into 3 equal parts. Remember to aim for equal spaces. Use our Fraction Sentence Stems to describe what you're doing, like 'I divided the whole into ______ equal parts because the denominator is ______.'"
(Continue with 4 and 5 equal parts, providing guided support.)
Check for Understanding (3 minutes)
Teacher: "Alright, for the next minute or two, try to partition one of the remaining number lines on your own. I'm looking to see how you make your marks to ensure the parts are as equal as possible. How do you know your parts are 'equal'?"
Cool Down (2 minutes)
Teacher: "Excellent work today on partitioning! For our cool down, please grab your Precision Partitioning Cool Down sheet. I want you to partition a number line into 5 equal parts and explain the strategy you used to try and make them equal."
Worksheet
Equal Parts Practice on a Number Line
Directions: For each problem, draw a number line from 0 to 1. Then, partition the number line into the given number of equal parts. Try to make your parts as equal as possible!
-
Divide the number line into 2 equal parts.
-
Divide the number line into 3 equal parts.
-
Divide the number line into 4 equal parts.
-
Divide the number line into 5 equal parts.
Challenge Question: Why is it important for the parts on a number line to be equal when representing fractions?
Cool Down
Precision Partitioning Cool Down
Directions: Draw a number line below. Partition the number line into 5 equal parts.
Explain your strategy: How did you try to make your 5 parts equal?
Lesson Plan
Unit Fraction Explorers: What is 1/b?
Students will define a unit fraction as 1/b and understand that 'b' represents the number of equal parts in the whole, with each part having a size of 1/b.
A deep conceptual understanding of unit fractions is the cornerstone for building all other fraction concepts. This lesson solidifies what 1/b truly means before students focus on its placement.
Audience
Grade 4 Small Group (3 students)
Time
30 minutes
Approach
Conceptual discussion, visual aids, and guided questioning.
Materials
Whiteboard or chart paper, Markers, Fraction circles or manipulatives (optional), Fraction Vocabulary, Fraction Sentence Stems, Unit Fraction Explorers Slide Deck, Unit Fraction Explorers Script, What is 1/b? Worksheet, and 1/b Concept Cool Down
Prep
Gather Materials & Review
10 minutes
- Gather all necessary materials: whiteboard/chart paper, markers, optional fraction manipulatives, and printouts of the Fraction Vocabulary, Fraction Sentence Stems, What is 1/b? Worksheet, and 1/b Concept Cool Down.
- Review the Unit Fraction Explorers Slide Deck and Unit Fraction Explorers Script to familiarize yourself with the content and flow of the lesson.
- Ensure the projector or screen is ready for the slide deck presentation.
Step 1
Warm-Up/Review (5 minutes)
5 minutes
- Draw a shape (e.g., a circle) and divide it into 4 equal parts, shading one part. Ask students: "What fraction does the shaded part represent? How do you know?" Connect to previous lessons on identifying the numerator and denominator.
Step 2
Introduction: The 1/b Concept (10 minutes)
10 minutes
- Use the Unit Fraction Explorers Slide Deck with the Unit Fraction Explorers Script to explicitly define a unit fraction as 1/b.
- Emphasize that the '1' in the numerator means one single part, and 'b' means the total number of equal parts the whole is divided into.
- Connect this to the idea that each of those 'b' parts has a size of 1/b.
Step 3
Guided Exploration: Manipulatives & Discussion (10 minutes)
10 minutes
- Distribute the What is 1/b? Worksheet.
- Use fraction circles or draw models on the board to visualize unit fractions like 1/2, 1/3, 1/4.
- For each unit fraction, use the Fraction Sentence Stems to articulate: "The unit fraction 1/______ represents one equal part out of ______ total equal parts. Each part has a size of 1/______."
- Guide students to complete the worksheet by drawing and labeling parts of wholes.
Step 4
Check for Understanding (3 minutes)
3 minutes
- Ask students to orally explain what the 'b' in 1/b tells them.
- Circulate and check their drawings and explanations on the worksheet.
Step 5
Cool Down (2 minutes)
2 minutes
- Distribute the 1/b Concept Cool Down.
- Students will define 1/b and provide an example, explaining its components.
Slide Deck
What's in a Fraction?
Remembering Our Fraction Basics
- What is a fraction? (Part of a whole)
- Numerator: How many parts we have
- Denominator: Total equal parts in the whole
Today, we're diving deeper into the special fraction with a '1' on top!
Start with a quick review of basic fraction identification using a visual model.
Unit Fractions: Always 1 on Top!
Meet the Unit Fraction: 1/b
- A unit fraction is a fraction where the numerator is always 1.
- It represents one single piece of a whole that has been divided into equal parts.
- The 'b' in 1/b tells us how many equal pieces make up the whole.
Explicitly define a unit fraction as 1/b. Emphasize the numerator of 1.
The Size of Each Part is 1/b
Each Piece Has a Name and a Size!
- If you divide a candy bar into 2 equal pieces, each piece has a size of 1/2.
- If you divide it into 3 equal pieces, each piece has a size of 1/3.
- The denominator 'b' tells us the name of each equal part, and its size!
Explain that each part has a size of 1/b. Use examples like a pie cut into 4 slices, each slice is 1/4 of the pie.
What Does 'b' Tell Us?
Let's figure out the 'b'!
- For 1/4, the 'b' is 4. What does that mean?
- For 1/6, the 'b' is 6. What does that tell us?
- For 1/8, the 'b' is 8. What does that tell us?
Practice identifying the 'b' and what it means for various unit fractions.
Script
Unit Fraction Explorers Script
Warm-Up/Review (5 minutes)
Teacher: "Good morning, fraction explorers! Let's start with a quick warm-up. (Draw a circle divided into 4 equal parts, shade one part on the board). What fraction does the shaded part represent? And how do you know?"
Teacher: "Fantastic! You're all experts at identifying fractions. Today, we're going to talk more about those special fractions with a '1' on top, called 'unit fractions,' and what they really mean."
Introduction: The 1/b Concept (10 minutes)
Teacher: "Let's open our Unit Fraction Explorers Slide Deck. (Display slide 2: 'Unit Fractions: Always 1 on Top!'). Remember, a unit fraction always has a '1' as its numerator. It means we're talking about just one single, equal piece of a whole. The 'b' in 1/b is our denominator, and it tells us how many equal pieces the whole is divided into."
Teacher: "Now, here's an important idea: each of those 'b' parts actually has a size of 1/b. (Display slide 3: 'The Size of Each Part is 1/b'). Imagine you have a delicious apple pie, and you cut it into 4 equal slices. Each individual slice has a size of 1/4 of the whole pie. It's not just a 'piece'; it's a '1/4 piece'."
Teacher: "So, if you have 1/5 of a pizza, what does the '5' (our 'b') tell you about the pizza and the size of your slice?"
Teacher: "Exactly! It means the pizza was divided into 5 equal parts, and your slice has a size of 1/5. That 'b' gives us the name and the size of each equal part!"
Guided Exploration: Manipulatives & Discussion (10 minutes)
Teacher: "Let's take out our What is 1/b? Worksheet. We'll draw some models and practice describing these unit fractions. For the first one, let's think about 1/2. Using our Fraction Sentence Stems, how would you complete this: 'The unit fraction 1/2 represents one equal part out of ______ total equal parts. Each part has a size of 1/______.'"
Teacher: "Perfect! The denominator is 2, so it's 2 total parts, and each part has a size of 1/2. Let's draw a model for 1/2 on our worksheet. (Guide students in drawing). Now let's do the same for 1/3 and 1/4. Remember, the 'b' always tells you the total number of parts and the size of each individual part."
(Circulate and provide support as students draw and label.)
Check for Understanding (3 minutes)
Teacher: "Let's pause. In your own words, what does the 'b' in 1/b tell us about a unit fraction? Why is that important?"
Teacher: "Wonderful! You're really thinking about the meaning behind the numbers."
Cool Down (2 minutes)
Teacher: "Time for our cool down! Please grab your 1/b Concept Cool Down sheet. I want you to define what a unit fraction 1/b means and then provide an example, explaining what the '1' and the 'b' represent in your example."
Worksheet
What is 1/b? Exploring Unit Fractions
Directions: For each unit fraction, draw a model (circle or rectangle) and shade one part. Then, complete the sentences to explain what the '1' and the 'b' represent.
-
Unit Fraction: 1/2
Draw your model here:
The unit fraction 1/2 represents ______ equal part out of ______ total equal parts. Each part has a size of ______.
-
Unit Fraction: 1/3
Draw your model here:
The unit fraction 1/3 represents ______ equal part out of ______ total equal parts. Each part has a size of ______.
-
Unit Fraction: 1/4
Draw your model here:
The unit fraction 1/4 represents ______ equal part out of ______ total equal parts. Each part has a size of ______.
Challenge Question: If you know the unit fraction is 1/8, what does that tell you about the whole object and the size of one piece?
Cool Down
1/b Concept Cool Down
Directions: In your own words, define what a unit fraction 1/b means.
Provide an example: Give a unit fraction and explain what the '1' and the 'b' represent in your example.
Lesson Plan
Unit Fractions: Comparing Sizes on a Line
Students will compare the sizes of different unit fractions by observing their positions on a number line, understanding that as the denominator increases, the size of the unit fraction decreases.
Comparing fractions on a number line provides a visual and intuitive way to understand their relative magnitudes, which is crucial for developing strong number sense and future fraction operations.
Audience
Grade 4 Small Group (3 students)
Time
30 minutes
Approach
Visual comparison, guided discussion, and number line creation.
Materials
Whiteboard or chart paper, Markers, Pre-drawn number lines (0-1) for demonstration, Fraction Vocabulary, Fraction Sentence Stems, Unit Fractions: Comparing Sizes Slide Deck, Unit Fractions: Comparing Sizes Script, Comparing Unit Fractions Worksheet, and Unit Fraction Comparison Cool Down
Prep
Gather Materials & Review
10 minutes
- Gather all necessary materials: whiteboard/chart paper, markers, pre-drawn number lines (or strips of paper for folding), and printouts of the Fraction Vocabulary, Fraction Sentence Stems, Comparing Unit Fractions Worksheet, and Unit Fraction Comparison Cool Down.
- Review the Unit Fractions: Comparing Sizes Slide Deck and Unit Fractions: Comparing Sizes Script to familiarize yourself with the content and flow of the lesson.
- Ensure the projector or screen is ready for the slide deck presentation.
Step 1
Warm-Up/Review (5 minutes)
5 minutes
- Quickly review placing a unit fraction (e.g., 1/2) on a number line. Ask: "What does the denominator tell us?"
Step 2
Introduction: What's Bigger? (10 minutes)
10 minutes
- Use the Unit Fractions: Comparing Sizes Slide Deck with the Unit Fractions: Comparing Sizes Script to introduce the concept of comparing unit fractions.
- Draw two number lines, one showing 1/2 and another showing 1/4. Ask students which looks 'bigger' or takes up more space from 0. Discuss why.
- Explicitly teach the rule: As the denominator increases, the unit fraction size decreases.
Step 3
Guided Practice: Visual Comparison (10 minutes)
10 minutes
- Distribute the Comparing Unit Fractions Worksheet.
- Work through several comparison problems together. For each pair of unit fractions, have students draw number lines and then compare their positions.
- Use the Fraction Sentence Stems to articulate comparisons (e.g., "1/2 is greater than 1/4 because 2 equal parts are larger than 4 equal parts within the same whole.").
Step 4
Check for Understanding (3 minutes)
3 minutes
- Ask students to independently compare a pair of unit fractions on the worksheet and explain their reasoning.
- Circulate and observe their number line drawings and explanations.
Step 5
Cool Down (2 minutes)
2 minutes
- Distribute the Unit Fraction Comparison Cool Down.
- Students will compare two unit fractions and explain their answer using a number line.
Slide Deck
Comparing Unit Fractions
Where Do Fractions Stand?
- We know how to place unit fractions like 1/2 and 1/3 on a number line.
- Today, we'll learn how to tell which unit fraction is bigger or smaller!
Start with a quick review of placing a simple unit fraction on a number line.
1/2 vs. 1/4: Who Wins?
Look at these number lines:
- Number line 1 shows 1/2.
- Number line 2 shows 1/4.
Which fraction is bigger? Why do you think so?
Visually compare 1/2 and 1/4 using two separate number lines or one combined visual. Ask which one takes up more space from 0.
The Denominator Rule!
Here's the Trick:
- When the numerator is the same (like '1' in unit fractions),
- The BIGGER the denominator, the SMALLER the piece!
- Think: Would you rather have 1/2 of a cookie or 1/8 of a cookie?
Introduce the rule: bigger denominator, smaller piece. Explain with examples.
Let's Practice Comparing!
Which is greater: 1/3 or 1/5?
- Draw them on number lines to check!
Which is smaller: 1/6 or 1/2?
- Use the denominator rule!
Practice comparing more unit fractions using the rule and visual confirmation.
Script
Unit Fractions: Comparing Sizes Script
Warm-Up/Review (5 minutes)
Teacher: "Good morning, everyone! Let's get our brains warmed up. Who can draw a number line from 0 to 1 and show us where 1/4 goes? Remember to explain how you divided your whole and why you placed it there."
Teacher: "Excellent job! Today, we're going to use our number lines to do something new: compare unit fractions! We'll figure out which unit fraction is bigger or smaller, just by looking at our number line."
Introduction: What's Bigger? (10 minutes)
Teacher: "Let's open our Unit Fractions: Comparing Sizes Slide Deck. (Display slide 2: '1/2 vs. 1/4: Who Wins?'). On the board, I'm going to draw two number lines, one showing 1/2 and another showing 1/4. (Draw them clearly, emphasizing the equal parts and the mark for the fraction). Now, looking at these two number lines, which fraction seems 'bigger'? Which one takes up more space from zero?"
Teacher: "Most of you said 1/2, and you're right! Even though 4 is a bigger number than 2, the fraction 1/4 is actually smaller than 1/2. Why do you think that is?"
Teacher: "Fantastic thinking! (Display slide 3: 'The Denominator Rule!'). This leads us to an important rule: When the numerator is the same (like '1' in all unit fractions), the bigger the denominator, the smaller the piece! Think about it: If you divide a cookie into 2 pieces (halves), those pieces are bigger than if you divide the same cookie into 8 pieces (eighths). The more pieces you divide the whole into, the smaller each piece becomes."
Teacher: "So, knowing this rule, would you rather have 1/3 of a cake or 1/6 of a cake? Why?"
Guided Practice: Visual Comparison (10 minutes)
Teacher: "Let's take out our Comparing Unit Fractions Worksheet. We'll work through the first few comparisons together. For problem 1, compare 1/3 and 1/5. First, draw a number line for each fraction, marking their positions. Then, tell me which is greater and why, using our Fraction Sentence Stems. You might say, '1/3 is greater than 1/5 because...'
(Guide students through drawing and comparing, reinforcing the denominator rule.)
Check for Understanding (3 minutes)
Teacher: "Now, try problem 3 on your own: Compare 1/6 and 1/2. Draw your number lines and explain your reasoning. I'll be looking to see if you remember our denominator rule!"
Cool Down (2 minutes)
Teacher: "Time for our cool down! Please grab your Unit Fraction Comparison Cool Down sheet. You'll compare 1/8 and 1/3, explain which is greater, and use a number line to help you show your answer!"
Worksheet
Comparing Unit Fractions on a Number Line
Directions: For each pair of unit fractions, draw a separate number line (from 0 to 1) for each fraction. Mark the position of each fraction. Then, use <, >, or = to compare them and explain your reasoning.
-
Compare 1/3 and 1/5.
1/3 ______ 1/5
Explanation:
-
Compare 1/2 and 1/6.
1/2 ______ 1/6
Explanation:
-
Compare 1/8 and 1/4.
1/8 ______ 1/4
Explanation:
Challenge Question: If you have 1/10 of a candy bar and your friend has 1/2 of the same candy bar, who has more? Explain using the denominator rule.
Cool Down
Unit Fraction Comparison Cool Down
Directions: Compare the unit fractions 1/8 and 1/3. Which one is greater? Draw number lines to support your answer.
1/8 ______ 1/3
Explain your reasoning: How did your number lines help you compare these fractions? What did the denominators tell you?
Lesson Plan
Non-Unit Fractions: Two-Thirds & Three-Fourths
Students will be able to represent non-unit fractions like 2/3 and 3/4 on a number line by partitioning the whole into 'b' equal parts and marking off 'a' lengths of 1/b from 0.
Extending their understanding from unit fractions to non-unit fractions on a number line helps students grasp the magnitude and position of any fraction, solidifying their fraction and number sense.
Audience
Grade 4 Small Group (3 students)
Time
30 minutes
Approach
Review, direct instruction, guided practice, and independent application.
Materials
Prep
Gather Materials & Review
10 minutes
- Gather all necessary materials: whiteboard/chart paper, markers, and printouts of the Fraction Vocabulary, Fraction Sentence Stems, Two-Thirds & Three-Fourths Worksheet, and Non-Unit Fractions Cool Down 1.
- Review the Non-Unit Fractions: Two-Thirds & Three-Fourths Slide Deck and Non-Unit Fractions: Two-Thirds & Three-Fourths Script to familiarize yourself with the content and flow of the lesson.
- Ensure the projector or screen is ready for the slide deck presentation.
Step 1
Warm-Up/Review (5 minutes)
5 minutes
- Review unit fractions on a number line by asking students to quickly draw a number line and place 1/3 on it. Discuss their reasoning, using sentence stems.
- Briefly revisit relevant terms from Fraction Vocabulary.
Step 2
Introduction to Non-Unit Fractions (10 minutes)
10 minutes
- Use the Non-Unit Fractions: Two-Thirds & Three-Fourths Slide Deck with the Non-Unit Fractions: Two-Thirds & Three-Fourths Script to introduce non-unit fractions.
- Explain that non-unit fractions have a numerator greater than 1 (e.g., 2/3, 3/4).
- Demonstrate how to represent 2/3 and 3/4 on a number line: first, divide the whole into 'b' equal parts, and then count 'a' of those parts from zero to find the fraction a/b. Emphasize that 2/3 is two lengths of 1/3.
Step 3
Guided Practice (10 minutes)
10 minutes
- Distribute the Two-Thirds & Three-Fourths Worksheet.
- Work through the problems for 2/3 and 3/4 together as a group, continuing to use the Fraction Sentence Stems to encourage clear explanations.
- Emphasize the two-step process: partition, then mark.
Step 4
Independent Practice & Check for Understanding (3 minutes)
3 minutes
- Have students complete any remaining problems independently from the Two-Thirds & Three-Fourths Worksheet.
- Circulate, observe, and provide targeted support to students who may be struggling with partitioning or counting segments.
Step 5
Cool Down (2 minutes)
2 minutes
- Distribute the Non-Unit Fractions Cool Down 1.
- Students will represent a non-unit fraction (e.g., 2/4) and explain their process.
Slide Deck
Beyond Unit Fractions!
Remember Unit Fractions?
- Last time, we learned about unit fractions like 1/2 or 1/3.
- What did the '1' in the numerator tell us?
- How did the denominator tell us to divide the number line?
Review unit fractions quickly from the previous lesson, perhaps by asking a student to describe how to place 1/3 on a number line.
What's a Non-Unit Fraction?
Non-Unit Fractions
- These are fractions where the numerator is GREATER than 1.
- It means we are talking about more than one of those equal parts.
Examples: 2/3, 3/4, 2/5
Introduce non-unit fractions. Explain that the numerator now tells us how many of those equal parts we have or are counting.
Placing Non-Unit Fractions on the Line
How to place a/b on a number line:
- Draw a number line from 0 to 1.
- Look at the denominator (b). Divide the whole (from 0 to 1) into that many equal parts.
- Now, look at the numerator (a). Count 'a' of those equal parts starting from 0.
- The mark where you stop is where a/b goes!
Explain the two-step process: first divide the whole into 'b' parts, then count 'a' parts from 0. Use visuals or draw on the board.
Let's Practice: 2/3 and 3/4
Let's try placing these fractions!
- 2/3: How many total parts? How many parts do we count from 0?
- 3/4: How many total parts? How many parts do we count from 0?
Practice with 2/3 and 3/4. Have students guide you through the steps. Reinforce the use of vocabulary and sentence stems.
Script
Non-Unit Fractions: Two-Thirds & Three-Fourths Script
Warm-Up/Review (5 minutes)
Teacher: "Welcome back! Let's quickly review what we learned about unit fractions. Can someone draw a number line and show us where 1/3 would go? And explain your steps using our Fraction Sentence Stems."
Teacher: "Great job remembering how to place unit fractions! Today, we're going to build on that and learn about fractions where the numerator is not 1. We call these 'non-unit fractions.' Let's quickly glance at our Fraction Vocabulary again and make sure we remember our terms like numerator and denominator."
Introduction to Non-Unit Fractions (10 minutes)
Teacher: "Take a look at our Non-Unit Fractions: Two-Thirds & Three-Fourths Slide Deck. We already know that a unit fraction is like one slice of a pizza. A non-unit fraction is when we have more than one of those slices."
Teacher: (Display slide 3: 'Placing Non-Unit Fractions on the Line') "Let's think about 2/3. The denominator, 3, tells us to divide our whole number line from 0 to 1 into three equal parts, just like with 1/3. But now, the numerator is 2. What do you think that means?"
Teacher: "Excellent! It means we count two of those equal parts from zero. So, if 1/3 is the first mark, where would 2/3 be?"
Teacher: (Guide students to mark 2/3) "You got it! It's two jumps of 1/3 from zero. Let's try 3/4. First, how many equal parts do we divide the whole into?"
Teacher: "Right, four equal parts! And then, how many parts do we count to find 3/4?"
Teacher: (Guide students to mark 3/4) "Fantastic! 3/4 is three lengths of 1/4 from zero."
Guided Practice (10 minutes)
Teacher: "Now let's work on our Two-Thirds & Three-Fourths Worksheet together. For problem 1, representing 2/3, what's our first step?"
Teacher: "And then, what do we do with the numerator?"
Teacher: "Perfect! You're really getting the hang of this. Let's try problem 2, representing 3/4. Talk me through your steps."
Independent Practice & Check for Understanding (3 minutes)
Teacher: "Okay, now it's your turn to work independently on the rest of the worksheet. Remember the two steps: divide the whole into equal parts, and then count the number of parts from zero. I'll be here to help if you have questions."
Cool Down (2 minutes)
Teacher: "For our cool down today, please complete the Non-Unit Fractions Cool Down 1 sheet. You'll represent 2/4 on a number line and explain your thinking. This will help me see how well you understand non-unit fractions on a number line!"
Worksheet
Two-Thirds & Three-Fourths on a Number Line
Directions: For each problem, draw a number line from 0 to 1. Then, partition the number line into the correct number of equal parts and mark the given non-unit fraction.
-
Represent 2/3 on the number line.
-
Represent 3/4 on the number line.
Challenge Question: How is placing 2/3 on a number line similar to placing 1/3? How is it different?
Cool Down
Non-Unit Fractions Cool Down 1
Directions: Draw a number line below and represent the non-unit fraction 2/4.
Explain your reasoning: How did you decide where to place 2/4 on the number line?