Interactive Audio Lesson
Listen to a student-teacher conversation explaining the topic in a relatable way.
The Juice Box Order
Unlock Audio Lesson
Signup and Enroll to the course for listening the Audio Lesson
Today, we're going to work on a practical problem involving ordering juice boxes. The school has 250 students heading to a field trip, and each student gets one juice box. How can we calculate how many packs we need to order?
We need to divide the total number of students by the number of juice boxes in each pack, right?
Exactly! The juice boxes come in packs of 6, so we will take 250 and divide that by 6. Let's do it together!
Isn't that just about 41.67 packs? We can't order a fraction of a pack!
Great observation! In this case, we would round up to ensure we have enough juice boxes. So how many packs should we order?
We should order 42 packs!
Correct! And if each pack costs $3.50, what will be our total cost?
That would be 42 packs times $3.50, which is $147.
Exactly! So, to summarize, we need 42 packs of juice boxes and the total cost will be $147. Well done!
The Runner's Speed
Unlock Audio Lesson
Signup and Enroll to the course for listening the Audio Lesson
Let's move on to our next problem about a student who runs 5 kilometers in 30 minutes. How would we find the average speed in meters per second?
We first need to convert kilometers to meters and minutes to seconds.
Exactly! There are 1,000 meters in a kilometer, so how many meters did the student run?
That would be 5,000 meters.
Perfect! And to convert 30 minutes to seconds, how will we do that?
We multiply by 60 seconds! So, 30 minutes would be 30 times 60, which is 1,800 seconds.
Right! Now to find the average speed, we divide the distance by the time. So what's our calculation?
5,000 meters divided by 1,800 seconds gives us about 2.78 meters per second.
Excellent! In summary, the average speed of the runner is approximately 2.78 meters per second.
The Swimming Pool
Unlock Audio Lesson
Signup and Enroll to the course for listening the Audio Lesson
Now, letโs look at our final problem about filling a swimming pool that measures 10 meters long, 5 meters wide, and 2 meters deep. Whatโs the first step to find out how long it takes to fill it with water?
We need to find the volume of the pool first.
That's right! The volume of a rectangular prism is length times width times height. Can someone calculate that?
The volume is 10 times 5 times 2, which equals 100 cubic meters!
Well done! Now, if the water flows in at a rate of 2.5 cubic meters per minute, how can we find out how long it will take to fill the pool?
We can divide the volume of the pool by the flow rate. So, 100 cubic meters divided by 2.5 cubic meters per minute.
Exactly! Now what calculation does that give us?
That would be 40 minutes!
Right! So in summary, it will take 40 minutes to fill the pool. Great job, everyone!
Introduction & Overview
Read a summary of the section's main ideas. Choose from Basic, Medium, or Detailed.
Quick Overview
Standard
This section provides a set of practice problems designed to integrate concepts from previous units of mathematics, allowing students to engage in multi-step problem-solving using real-life contexts. The problems encourage critical thinking and the application of mathematical skills learned throughout the course.
Detailed
Practice Problems 2.1 Summary
In this section, students are presented with several practical scenarios that require them to apply various mathematical concepts learned in previous units. The problems provided are not merely theoretical; they simulate real-world situations where mathematical tools and concepts can advocate for effective solutions to common challenges.
The problems include:
1. Calculating the number of packs of juice boxes needed for a school event based on student numbers, requiring division and multiplication.
2. Determining a runner's average speed in meters per second from a distance covered in kilometers and time taken in minutes, engaging concepts of unit conversion and division.
3. Figuring out how long it will take to fill a swimming pool given its dimensions and the rate of water flow, which involves volume calculations and rates.
Through these exercises, students will not only practice their math skills but also understand the importance of translating real-world problems into mathematical language, enhancing their ability to think critically and justify their solutions.
Audio Book
Dive deep into the subject with an immersive audiobook experience.
The Juice Box Order
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
A school needs to order juice boxes for a field trip. They have 250 students going. Each student gets one juice box. The juice boxes come in packs of 6. Each pack costs $3.50.
โ Problem: How many packs of juice boxes should the school order, and what will be the total cost?
โ Concepts: Division, multiplication, rounding (to ensure enough packs).
Detailed Explanation
To determine how many packs of juice boxes the school should order, we start with the total number of students. Since each student receives one juice box, the school needs a total of 250 juice boxes. Juice boxes are sold in packs of 6, so we divide the total number of juice boxes by the number of juice boxes per pack. This can be calculated as 250 divided by 6, which equals approximately 41.67. Since the school cannot order a fraction of a pack, we round this number up to 42 packs. To find the total cost, we multiply the number of packs (42) by the cost per pack ($3.50). This results in a total cost of $147.00.
Examples & Analogies
Think of it like planning a pizza party where you need to order pizzas for friends. If each friend is going to eat two slices and each pizza has 8 slices, you'll need to calculate how many pizzas to order based on how many friends (like students) are coming.
The Runner's Speed
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
A student runs a total distance of 5 kilometers in 30 minutes.
โ Problem: What is the student's average speed in meters per second?
โ Concepts: Distance, time, unit conversion (kilometers to meters, minutes to seconds), division for speed.
Detailed Explanation
To calculate the average speed of the student, we first need to convert the distance from kilometers to meters. Since 1 kilometer is equivalent to 1,000 meters, 5 kilometers equals 5,000 meters. Next, we need to convert the time from minutes to seconds. Since there are 60 seconds in a minute, 30 minutes equals 1,800 seconds (30 x 60). The average speed can now be calculated using the formula: speed = distance / time. Thus, the average speed is 5,000 meters divided by 1,800 seconds, which results in approximately 2.78 meters per second.
Examples & Analogies
Imagine you're timing your friend running around a track. If the track is 400 meters long, knowing how long it takes to complete a few laps allows you to find their speed, just like measuring the runner's speed helps in athletics!
The Swimming Pool
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
A rectangular swimming pool is 10 meters long, 5 meters wide, and 2 meters deep. The pool needs to be filled with water. Water flows into the pool at a rate of 2.5 cubic meters per minute.
โ Problem: How long will it take to fill the pool?
โ Concepts: Volume of a rectangular prism, rates (division).
Detailed Explanation
To find out how long it will take to fill the swimming pool, we first need to calculate the volume of the pool using the formula for the volume of a rectangular prism: volume = length x width x depth. Plugging in the values, we get 10 meters x 5 meters x 2 meters, which equals 100 cubic meters. Next, since water flows into the pool at a rate of 2.5 cubic meters per minute, we can find the time it takes to fill the pool by dividing the total volume of the pool by the flow rate. Thus, 100 cubic meters divided by 2.5 cubic meters per minute gives us 40 minutes to fill the pool.
Examples & Analogies
Think of it like filling a large bucket with a hose. If you know how fast the water flows from the hose (like the rate), and how much water the bucket can hold (the volume), you can figure out how long it will take to fill it up.
Definitions & Key Concepts
Learn essential terms and foundational ideas that form the basis of the topic.
Key Concepts
-
Unit Conversion: The process of converting between different units of measurement.
-
Volume Calculation: Determining the space occupied by a three-dimensional object.
-
Average Speed: Calculating distance over time to determine how fast something is moving.
-
Perimeter: The total length around a two-dimensional shape.
-
Flow Rate: The speed at which a fluid moves into or out of a container.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
-
Example 1: Average speed can be calculated by taking the total distance of a run and dividing it by the total time taken, e.g., running 5 km in 30 minutes.
-
Example 2: The volume of a rectangular swimming pool can be calculated by multiplying its length, width, and depth (10 m x 5 m x 2 m = 100 mยณ).
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
๐ต Rhymes Time
-
To find the speed in a race, divide the distance, keep pace!
๐ Fascinating Stories
-
Imagine filling a giant pool with water from a hose flowing at a steady rate - the joy of watching it fill reminds you to calculate the volume first, and wait for the magic number of minutes while it fills up.
๐ง Other Memory Gems
-
Every Very Awesome Person Likes (EVA P.L.) - to remember: Every (Average Speed), Very (Volume), Awesome (Amount), Person (Packs), Likes (Liters).
๐ฏ Super Acronyms
V.A.S. - Volume, Average Speed, Packing for juices!
Flash Cards
Review key concepts with flashcards.
Glossary of Terms
Review the Definitions for terms.
-
Term: Average Speed
Definition:
The total distance traveled divided by the total time taken.
-
Term: Volume
Definition:
The amount of space that a 3D object occupies, measured in cubic units.
-
Term: Perimeter
Definition:
The total distance around a two-dimensional shape.
-
Term: Flow Rate
Definition:
The volume of fluid that passes through a surface per unit time.
-
Term: Unit Conversion
Definition:
The process of converting a quantity from one system of units to another.
-
Term: Pack
Definition:
A bundle of items sold together, often in a standardized quantity.