Math 7 4 7 Homework Help Morgan

Mr. Morgan's Math Help

2 Nov 201823:49

EducationalLearning

32 Likes 10 Comments

TLDRThis educational video script delves into the concept of percentages, focusing on increases and decreases from a 100% baseline. It introduces the double number line as a tool for visualizing these changes, demonstrating how to calculate new values with examples such as gas tank capacities, movie theater popcorn sizes, and school populations. The script also covers how to determine original values from a given percentage decrease and discusses the importance of identifying the 100% reference point in percentage problems. It concludes with homework problems that apply these concepts to real-life scenarios, reinforcing the lesson's practical applications.

Takeaways

📚 The lesson focuses on understanding what it means to be 100% of something and how to work with percentage increases and decreases using a double number line.
📊 A double number line is introduced as a tool to visually represent and compare different percentages of a quantity, such as cups of chocolate milk representing 100%.
🔢 The script explains how to calculate 50% and 150% of a given amount using the double number line by dividing the total into segments and identifying the value of each segment.
🚗 An example is given where the gas tank in mom's truck holds 50% more than dad's car, illustrating how to find the new amount using the double number line method.
🍿 Another example discusses the decrease in the size of popcorn bags by 20% at a movie theater, showing how to determine the new size using the double number line.
📉 The script covers how to determine the percentage decrease in the number of students at a school, using the double number line to find the difference between the original and new amounts.
📈 It explains how to calculate the percentage increase in the price of gas, emphasizing the difference between the new price and the percentage increase itself.
👕 The lesson includes a problem about determining the original price of a t-shirt after a 25% discount, using the double number line to find the original 100% value.
📈 The script discusses the increase in population in a town by 25%, using the double number line to find the original population before the increase.
🧃 An example of a juice box with 20% more juice in its new packaging is used to demonstrate how to calculate the new amount of juice using the double number line.
🐢 The lesson concludes with applying the concepts to real-life scenarios, such as the increase and decrease in the number of green sea turtles nesting in sanctuaries.

Q & A

What is the main topic of the video script?
-The main topic of the video script is understanding the concept of '100 percent' in the context of percentage increase and decrease, and how to solve related problems using double number lines.
What is a double number line and how is it used in the script?
-A double number line is a visual tool used to represent and compare different quantities or percentages. In the script, it is used to illustrate how to find percentages of an original amount and to calculate increases or decreases from that original amount.
How does the script explain the concept of '100 percent' in relation to a quantity?
-The script explains '100 percent' as representing the whole or the original amount of something. For example, if a container is filled with 10 cups of chocolate milk, that is considered '100 percent' of the container's capacity.
What is the first problem presented in the script involving a gas tank?
-The first problem involves determining the capacity of mom's truck's gas tank, which holds 50 percent more than dad's car that holds 12 gallons. The script uses a double number line to find that mom's truck holds 18 gallons.
How is a 20 percent decrease in the size of popcorn bags calculated in the script?
-The script uses a double number line divided into five segments, each representing 20 percent of the original amount. By calculating that 20 percent of 15 cups is 3 cups, and then subtracting this from the original amount, the new size of the popcorn bags is found to be 12 cups.
What is the method used in the script to find the original number of students in a school before a decrease?
-The script uses a double number line divided into 10 segments, each representing 10 percent of the original amount. By knowing that the current number of students is 1080, which represents 90 percent, the original number of students is calculated to be 1200.
How does the script calculate the percentage increase in the price of gas?
-The script uses a double number line divided into five segments, each representing 20 percent. By knowing the original price was $1.25 and the new price is $1.50, the script calculates that the price increased by 20 percent, not 120 percent.
What is the approach used in the script to find the original price of a t-shirt before a 25 percent discount?
-The script sets up a double number line with three segments, each representing 25 percent of the original price. Knowing the discounted price is $12, the script calculates that 25 percent of the original price is $4, and thus the original price was $16.
How does the script handle the problem of calculating the original population of a town before a 25 percent increase?
-The script uses a double number line divided into five segments, each representing 20 percent. Knowing the current population is 6600, which represents 125 percent, the script calculates the original population by dividing 6600 by 1.25, resulting in 5280.
What is the error identified in the script regarding the setup of a double number line by a student named Claire?
-The error identified in Claire's setup is that she placed the original amount of 12 fluid ounces in the wrong position on the double number line, treating it as if it was already increased by 20 percent, which led to an incorrect representation of the problem.

Outlines

00:00

📚 Understanding 100% and Percentage Problems

This paragraph introduces the concept of 100% as a base value in percentage problems, using a double number line to visualize and solve problems involving percentage increases and decreases. The script explains how to determine what 100% represents in various contexts, such as the capacity of a gas tank or the size of a popcorn bag, and how to calculate new values based on percentage changes from this base.

05:00

📉 Dealing with Percent Decrease in Student Population

The second paragraph delves into calculating percentage decreases using the example of a school's student population. It explains how to find the original 100% value when given a decreased number and the percentage of decrease, using a double number line to illustrate the process. The paragraph emphasizes the importance of identifying the initial 100% value to correctly determine the decrease.

10:02

📈 Applying Percentage Changes to Various Scenarios

This section of the script covers a range of problems involving percentage increases and decreases in different scenarios, such as gas prices, t-shirt discounts, and population changes. It demonstrates the use of double number lines and mathematical calculations to find new values based on percentage changes from a known original amount, highlighting the need for clarity on what constitutes 100% in each case.

15:03

🐢 Analyzing Turtle Population Fluctuations

The script uses the example of green sea turtles to illustrate how to calculate population changes when given a percentage increase or decrease. It explains the process of finding the original population size before the change and how to apply the percentage increase or decrease to determine the new population number, emphasizing the mathematical operations involved in these calculations.

20:03

🍞 Solving Real-World Problems with Percentages

The final paragraph of the script applies the concepts of percentages to real-world problems, such as calculating the amount of butter used by a bakery after a percentage increase and determining the price of oranges after a percentage decrease. It also addresses the difference between calculating an increase to a new total and finding the original amount before a decrease, using mathematical formulas and examples to clarify these processes.

🚶‍♀️ Calculating Distances and Areas with Percentages

This part of the script presents mathematical word problems involving percentages, such as calculating the total distance walked by Elena after an additional percentage of a distance and estimating the area of a circle given its circumference. It also includes a problem about the proportional relationship between distance and time for a snail, demonstrating how to solve for unknowns in direct proportion situations.

Mindmap

Keywords

💡Double Number Line

A double number line is a visual tool used to represent and compare quantities or percentages. In the video, it is used to illustrate the concept of 100% and how it relates to increases and decreases in various contexts, such as the capacity of gas tanks or the size of popcorn bags. For example, the script describes using a double number line to determine that 10 cups of chocolate milk represent 100%, and then how to calculate 50% or 150% of that amount.

💡Percentage Increase

A percentage increase refers to the growth of a quantity relative to its original value, expressed as a percentage. The video explains how to calculate a percentage increase using the double number line, as seen when determining that mom's truck holds 50% more gas than dad's car, which is the original 100% reference.

💡Percentage Decrease

A percentage decrease is the reduction of a quantity relative to its original value, also expressed as a percentage. The script uses the example of movie theater popcorn bags decreasing in size by 20% to illustrate how to calculate a percentage decrease and its impact on the original amount.

💡100% Value

The 100% value is the original amount or quantity that serves as a reference point for calculating increases or decreases. The video emphasizes the importance of identifying the 100% value to accurately determine changes in percentage. For instance, the initial number of students in a school or the original price of an item are both used as 100% values in different examples.

💡Proportional Relationships

Proportional relationships describe a constant ratio between two quantities. In the video, the script mentions the equation 'd = 3t' to represent the distance a snail travels in relation to time, where 'd' is distance and 't' is time, and the constant '3' indicates the snail travels at a rate of 3 inches per minute.

💡Circumference

Circumference is the measurement of the distance around a circle. The video uses the circumference of a circle to introduce the concept of estimating the area of a circle, given that the circumference is 600 meters. It explains the relationship between circumference and radius, and how to approximate the area using the formula for the area of a circle (A = πr²).

💡Area

Area is the amount of space inside a two-dimensional shape. In the context of the video, the area of a circle is approximated using the formula A = πr², after determining the radius from the given circumference. The script provides an example of how to calculate the area when the circumference is 600 meters.

💡Population Increase

Population increase refers to the growth in the number of individuals in a population. The video script discusses an example of a bison herd that has a 10% increase in population, illustrating how to calculate the new population size based on the original number of bison.

💡Population Decrease

Population decrease is the reduction in the number of individuals in a population. The script contrasts the population increase example by showing how to calculate the original population size of a bison herd that has experienced a 10% decrease, using the current population as a reference.

💡Discount

A discount is a reduction in the original price of an item. The video explains how to calculate the original price of a t-shirt after a 25% discount by understanding that the discounted price represents 75% of the original price, and then determining the full price before the discount was applied.

💡Constant of Proportionality

The constant of proportionality, often denoted as 'k', is a factor that defines the ratio between two quantities in a proportional relationship. In the video, the constant '3' in the equation 'd = 3t' represents the rate at which a snail moves, indicating that for every minute that passes, the snail travels 3 inches.

Highlights

Introduction to the concept of 100% in relation to various quantities and how it applies to percentage increases and decreases.

Explanation of a double number line as a tool for visualizing percentages in relation to a whole.

Demonstration of how to use a double number line to determine the value of 50% and 150% of a given amount.

Problem-solving approach using the double number line to find the gas tank capacity of mom's truck, which is 50% larger than dad's.

Use of division to determine the value of each segment on a double number line for calculating percentages.

Alternative method of using multiplication to find percentage differences, exemplified with the gas tank problem.

Application of the double number line to a problem involving a decrease in the size of popcorn bags by 20%.

Strategy for calculating the new amount after a 20% decrease using both pattern continuation and subtraction.

Analysis of a problem involving a decrease in the number of students at a school, emphasizing the difference between the new percentage and the decrease.

Clarification on how to determine the percentage decrease by comparing the difference between the new and original percentages.

Problem-solving with a price increase of gas, illustrating the difference between the new price percentage and the actual percentage increase.

Explanation of the importance of starting with the original 100% value when solving percentage problems.

Approach to finding the original price of a t-shirt before a 25% discount, using the double number line.

Problem involving the increase in population of a town by 25%, and how to calculate the original population.

Common mistakes in setting up a double number line and how to correct them for accurate percentage calculations.

Real-world application of percentage increase and decrease in problems involving sea turtles and juice packaging.

Final summary emphasizing the importance of identifying the 100% value in percentage problem-solving.

Homework problems involving percentage increases and decreases in various contexts, with solutions provided.

Explanation of how to calculate the area of a circle given its circumference, using approximations.

Problem involving the relation between distance and time for a snail, demonstrating the use of proportionality.

Transcripts

Browse More Related Video

Math 7 4 6 Homework Help Morgan

Math Antics - Finding A Percent Of A Number

3.5 - Max-Min Problems and Applications

Business Calculus - Math 1329 - Section 2.5 - Marginal Analysis and Differentials

Solving Percent Problems: IS/OF

Quartiles, Deciles, & Percentiles With Cumulative Relative Frequency - Data & Statistics

Related Tags

Percentage Calculation Math Education Double Number Line Increase Decrease Problem Solving Interactive Learning Educational Content Math Strategies Homework Help Concept Clarification