Number Line Fraction Practice

Instructions: For each problem, use the number line provided to help you add or subtract the fractions. Draw your jumps on the number line to show your work!

1. Addition

Problem: $\frac{1}{3} + \frac{1}{3} = $

(a) Draw a number line from 0 to 1. Divide it into thirds. Show your jumps.

Answer:

2. Addition

Problem: $\frac{2}{5} + \frac{2}{5} = $

(a) Draw a number line from 0 to 1. Divide it into fifths. Show your jumps.

Answer:

3. Subtraction

Problem: $\frac{3}{4} - \frac{1}{4} = $

(a) Draw a number line from 0 to 1. Divide it into fourths. Show your jumps.

Answer:

4. Subtraction

Problem: $\frac{5}{6} - \frac{2}{6} = $

(a) Draw a number line from 0 to 1. Divide it into sixths. Show your jumps.

Answer:

5. Challenge Question

Problem: If you start at $\frac{1}{2}$ on a number line and add $\frac{1}{2}$, where do you land? Draw your jumps below.

Answer:

Number Line Fraction Practice Answer Key

Detailed Solutions:

1. Addition

Problem: $\frac{1}{3} + \frac{1}{3} = \frac{2}{3}$

(a) Thought Process:

• Start at 0 on the number line.
• Move $\frac{1}{3}$ to the right.
• From $\frac{1}{3}$, move another $\frac{1}{3}$ to the right.
• You land at $\frac{2}{3}$.

(Visual representation of a number line from 0 to 1, divided into thirds, with jumps for 1/3 and then another 1/3, landing at 2/3)

Answer: $\frac{2}{3}$

2. Addition

Problem: $\frac{2}{5} + \frac{2}{5} = \frac{4}{5}$

(a) Thought Process:

• Start at 0 on the number line.
• Move $\frac{2}{5}$ to the right.
• From $\frac{2}{5}$, move another $\frac{2}{5}$ to the right.
• You land at $\frac{4}{5}$.

(Visual representation of a number line from 0 to 1, divided into fifths, with jumps for 2/5 and then another 2/5, landing at 4/5)

Answer: $\frac{4}{5}$

3. Subtraction

Problem: $\frac{3}{4} - \frac{1}{4} = \frac{2}{4}$ (or $\frac{1}{2}$)

(a) Thought Process:

• Start at $\frac{3}{4}$ on the number line.
• Move $\frac{1}{4}$ to the left (backwards).
• You land at $\frac{2}{4}$.

(Visual representation of a number line from 0 to 1, divided into fourths, starting at 3/4 and jumping back 1/4, landing at 2/4)

Answer: $\frac{2}{4}$ (or $\frac{1}{2}$)

4. Subtraction

Problem: $\frac{5}{6} - \frac{2}{6} = \frac{3}{6}$ (or $\frac{1}{2}$)

(a) Thought Process:

• Start at $\frac{5}{6}$ on the number line.
• Move $\frac{2}{6}$ to the left (backwards).
• You land at $\frac{3}{6}$.

(Visual representation of a number line from 0 to 1, divided into sixths, starting at 5/6 and jumping back 2/6, landing at 3/6)

Answer: $\frac{3}{6}$ (or $\frac{1}{2}$)

5. Challenge Question

Problem: If you start at $\frac{1}{2}$ on a number line and add $\frac{1}{2}$, where do you land? Draw your jumps below.

(a) Thought Process:

• Start at 0 on the number line.
• Move $\frac{1}{2}$ to the right.
• From $\frac{1}{2}$, move another $\frac{1}{2}$ to the right.
• You land at 1 whole.

(Visual representation of a number line from 0 to 1, divided into halves, with jumps for 1/2 and then another 1/2, landing at 1)

Answer: You land at $\frac{2}{2}$ or 1 whole.

Fraction Number Line Fun! Script

Warm-Up: Fraction Check-in (2 minutes)

Teacher: "Good morning, everyone! Today, we're going on a fraction adventure using a tool we already know: the number line! Who can remind us what a fraction is?"

Teacher: "Excellent! And what do we use a number line for?"

Teacher: "That's right! Number lines help us visualize numbers. Today, they'll help us visualize fractions, especially when we add and subtract them. Take a look at our first slide on the Slide Deck: Fraction Number Line Fun!."

(Display Slide 1: Welcome! Fraction Number Line Fun!)

Teacher: "Our goal today is to become masters at adding and subtracting fractions using number lines. This will help you really see what's happening when we work with fractions."

Modeling: Adding Fractions on a Number Line (5 minutes)

Teacher: "Let's start with adding. Imagine our number line is a track, and we're taking jumps. Look at Slide 2: Slide Deck: Fraction Number Line Fun!."

(Display Slide 2: Adding Fractions: Jump Forward!)

Teacher: "Our problem is $\frac{1}{4} + \frac{2}{4}$. When we add, we always start at zero on our number line. The denominator, in this case, 4, tells us how many equal parts the whole is divided into. So, our number line from 0 to 1 should be cut into four equal sections.

Teacher: "First, we jump $\frac{1}{4}$ of the way. So, we land right at $\frac{1}{4}$. Now, from that spot, we need to add another $\frac{2}{4}$. That means two more jumps of $\frac{1}{4}$ each. One jump... then another jump! Where do we land?"

Teacher: "Exactly! We land at $\frac{3}{4}$. So, $\frac{1}{4} + \frac{2}{4} = \frac{3}{4}$. Notice how the denominator stayed the same? We're just counting how many of those equal parts we have in total."

Modeling: Subtracting Fractions on a Number Line (4 minutes)

Teacher: "Now, what if we need to take some jumps away? Let's look at Slide 3: Slide Deck: Fraction Number Line Fun!."

(Display Slide 3: Subtracting Fractions: Jump Back!)

Teacher: "Our problem is $\frac{3}{5} - \frac{1}{5}$. This time, instead of starting at zero, we start at our first fraction, which is $\frac{3}{5}$. So, find $\frac{3}{5}$ on your number line. Again, our denominator is 5, so our whole is divided into five equal parts.

Teacher: "From $\frac{3}{5}$, we need to subtract $\frac{1}{5}$. When we subtract, we move backwards or to the left on the number line. So, from $\frac{3}{5}$, we take one jump back of $\frac{1}{5}$. Where do we land?"

Teacher: "That's right! We land at $\frac{2}{5}$. So, $\frac{3}{5} - \frac{1}{5} = \frac{2}{5}$. The denominator still stays the same because we are still talking about fifths."

Guided Practice & Independent Work (4 minutes)

Teacher: "You've seen me do it, now it's your turn to be number line masters! I'm handing out a Worksheet: Number Line Fraction Practice."

(Distribute Worksheet: Number Line Fraction Practice.)

Teacher: "Let's do the first problem together. It's $\frac{1}{3} + \frac{1}{3}$. How would you set up your number line for this problem?"

Teacher: "Good! Now, show me your jumps. What's your answer?"

Teacher: "Fantastic! Now, work through the rest of the problems on your own. Remember to draw your jumps carefully. If you get stuck, raise your hand, and I'll come help. I'll be walking around to see your amazing work!"

(Circulate, provide support, and offer feedback. Collect worksheets.)

Teacher: "Great work everyone! We'll review these next time. You all did a wonderful job using number lines to add and subtract fractions today. Remember, these visual tools can really help you understand what's happening with numbers!"