Cutting A Bar: Math Problem For 5th Graders

Nov 18, 2025 by Admin 44 views

Hey guys! Let's dive into a fun math problem perfect for 5th graders. We're going to break down a bar and figure out how to cut it just right. This involves using segments, which are super helpful visual tools. So grab your pencils, and let's get started!

Understanding the Problem

First, let's really get what the problem is asking. We have a bar that's 124 dm long. Dm stands for decimeters, which is just a unit of length. Now, this bar needs to be cut into two pieces. Here's the tricky part: one piece has to be longer than the other by 34 dm. Our mission, should we choose to accept it, is to find out the length of each of these pieces. We're going to solve this using segments, also known as bar models, which makes the whole process a lot clearer and easier to understand.

So, to recap, the key information is: the total length of the bar which is 124 dm and the difference in length between the two pieces which is 34 dm.

Visualizing with Segments

Okay, let's bring out the visual aids! Using segments, or bar models, is a fantastic way to see what's going on in the problem. Think of each piece of the bar as a rectangle. We'll draw two rectangles, one for each piece. Since one piece is longer, its rectangle will be longer than the other. Now, the difference in length, that 34 dm, is super important. On our drawing, we'll show that difference clearly. This visual representation helps us organize the information and makes it easier to figure out the steps we need to take.

How to Draw the Segments:

Draw a shorter rectangle for the shorter piece.
Draw a longer rectangle for the longer piece, making sure it extends beyond the shorter one.
Mark the extra length of the longer rectangle as 34 dm. Label the entire combined length of both rectangles as 124 dm. Visually, you'll see the total length and the difference, setting you up for the next steps in solving the problem.

Solving the Problem Step-by-Step

Now for the fun part: solving the problem! Here’s how we can do it, using the segment model we just created:

Eliminate the Difference:
- Since we know one piece is 34 dm longer than the other, let's temporarily remove that difference from the total length. This gives us a new total length as if both pieces were equal. Subtract 34 dm from the total length:
```
124 dm - 34 dm = 90 dm
```
Find the Length of the Shorter Piece:
- Now that we've removed the difference, we can find the length of the shorter piece. Since the remaining length (90 dm) represents two equal pieces, we simply divide by 2:
```
90 dm / 2 = 45 dm
```
- So, the shorter piece is 45 dm long.
Find the Length of the Longer Piece:
- To find the length of the longer piece, we add the difference (34 dm) back to the length of the shorter piece:
```
45 dm + 34 dm = 79 dm
```
- Therefore, the longer piece is 79 dm long.

Checking Our Work

It's always a good idea to double-check our answers to make sure they make sense. Here’s how:

Add the lengths of the two pieces together:
```
45 dm + 79 dm = 124 dm
```
- This matches the total length of the original bar, so that’s a good sign!
Confirm the difference in length:
```
79 dm - 45 dm = 34 dm
```
- The difference is indeed 34 dm, as the problem stated. This confirms our solution is correct.

Writing Out the Solution Clearly

To make everything crystal clear, let’s write out the solution in a neat and organized way:

Length of the shorter piece: 45 dm
Length of the longer piece: 79 dm

Why This Method Works

You might be wondering, why does this segment method work so well? It's all about visualization. By drawing those rectangles, we turn an abstract problem into something concrete. We can see the relationships between the lengths and the difference, making it easier to understand the steps needed to solve the problem. Plus, it's a great way to keep track of the information and avoid confusion.

Real-World Applications

This kind of problem-solving isn't just for math class. It pops up in real life all the time! Imagine you’re sharing a pizza with a friend, and you want to give them a bigger slice. This is the same idea. You're dividing something into two parts, with one part being larger than the other. Or think about cutting a ribbon for a craft project where you need two different lengths. Understanding how to solve these problems helps you in all sorts of situations.

Practice Problems

Want to become a segment-solving superstar? Here are a couple of practice problems to try:

A rope of 150 cm is cut into two pieces. One piece is 20 cm longer than the other. Find the length of each piece.
John and Mary have a total of $80. John has $15 more than Mary. How much money does each person have?

Conclusion

So, there you have it! We've successfully cut that bar into two pieces using segments. Remember, the key is to visualize the problem, break it down into steps, and double-check your work. Keep practicing, and you'll become a math whiz in no time! Keep up the great work guys! We'll see you in the next math adventure! Peace out!