Math 7 4 6 Homework Help Morgan
TLDRThis Math 7 Unit 4 Lesson 6 transcript focuses on understanding increases and decreases using percentages. It explores the concept through sports team scores, cereal box quantities, and shirt prices, illustrating percent increases and decreases with various examples. The lesson also includes activities like improving game scores and using tape diagrams to represent changes. It concludes with homework problems that challenge students to apply these concepts to real-life situations, emphasizing the importance of percentage calculations in everyday scenarios.
Takeaways
- 🏈 The football team improved their score from 22 to 30 points, showing an 8-point increase.
- 🏀 The basketball team increased their score from 100 to 108 points, also an 8-point improvement.
- ⚾ The baseball team saw the most significant relative increase, tripling their score from 4 to 12 points.
- 📈 Understanding the percentage of growth is crucial when comparing the performance increase between teams.
- 📊 A percentage increase or decrease can be calculated by adding or subtracting the percentage value from 1, then multiplying by the original amount.
- 🛒 A cereal box with 20% more cereal would have 22.2 ounces if it originally contained 18.5 ounces.
- 👕 A shirt with a 20% discount would cost 14.80 if it was originally priced at 18.50.
- 📉 A 100% decrease in a quantity would result in zero, as seen with the example of making 100 fewer cookies.
- 📈 The concept of a percent increase or decrease is about the change in quantity relative to the original amount.
- 📊 The use of tape diagrams helps visualize the changes in quantities due to percentage increases or decreases.
- 🤔 The impact of a percentage raise in salary or a discount on an item depends on the original amount, not just the percentage itself.
Q & A
What is the main topic of the lesson in the script?
-The main topic of the lesson is understanding increases and decreases using percentages to describe changes in various amounts.
What is the first activity discussed in the script?
-The first activity discussed is called 'improving their game', which involves analyzing scores from three different sports teams over two games.
How did the football team's score change between the two games mentioned in the script?
-The football team's score increased from 22 points in the first game to 30 points in the second game.
What is the difference in the basketball team's score between the two games?
-The basketball team's score increased from 100 points in the first game to 108 points in the second game, a difference of 8 points.
How much did the baseball team's score increase from the first game to the second game?
-The baseball team's score increased from 4 in the first game to 12 in the second game, which is a tripling of their score.
What is the mathematical concept used to calculate the new amount of cereal in the box after a 20% increase?
-The mathematical concept used is a percentage increase, which involves adding 20% (or 0.2 as a decimal) to the original amount and then multiplying by the original quantity to find the new amount.
What is the final amount of cereal in the box after a 20% increase from 18.5 ounces?
-After a 20% increase, the final amount of cereal in the box is 22.2 ounces.
What is the example of a percentage decrease given in the script involving the price of a shirt?
-The example given is a shirt originally priced at $18.50, which is reduced by 20% with a coupon, resulting in a new price of $14.80.
How does the script explain the difference between a 20% increase on a small and a large original amount?
-The script explains that while the absolute increase (8 points) is the same for both, the percentage growth is much larger when starting from a smaller original amount, such as going from 4 to 12 in the baseball team's score.
What is the purpose of the tape diagrams in the script?
-The tape diagrams are used to visually represent and match different situations of percentage increases and decreases to help understand the relative changes in quantities.
What is the mathematical formula used to represent a percentage increase in the script?
-The formula used to represent a percentage increase is the original amount plus the percentage increase as a decimal times the original amount (1 + (percentage/100) * original amount).
How does the script illustrate the concept of a 100% decrease?
-The script illustrates a 100% decrease by explaining that if you had 100 units of something and decreased by 100%, you would have zero units left.
What is the incorrect statement made by the cashier in the script regarding the discount on shirts?
-The incorrect statement made by the cashier is that buying two shirts with a 20% discount on each would result in a 40% discount on the total price, which is not how percentage discounts work.
How does the script use the concept of percentages to compare different quantities or situations?
-The script uses percentages to compare different quantities by showing how much more or less one quantity is compared to another, using the original amount as a reference point.
Outlines
📊 Understanding Percentages in Sports Scores
This paragraph introduces the concept of using percentages to describe increases and decreases in team scores across different sports. It discusses the improvement of three sports teams from one game to the next, highlighting the difference in the percentage of growth between teams. The football team's score increased from 22 to 30 points, the basketball team's from 100 to 108 points, and the baseball team's from 4 to 12 points. The discussion emphasizes the importance of considering the percentage growth rather than just the point difference, as it provides a more meaningful comparison of the teams' performance improvements.
📈 Calculating Percent Increase and Decrease
This section teaches how to calculate percentage increases and decreases with two examples. The first example involves a cereal box that originally contained 18.5 ounces and now has 20 more ounces due to an increase. The calculation shows how to find the new amount of cereal using both addition of a percentage and direct multiplication. The second example is about a shirt with a price of $18.50 that has a 20% discount when a coupon is used. The calculations demonstrate two methods to find the new price after the discount: one by subtracting the percentage decrease from the original price and the other by multiplying the original price by the remaining percentage after the discount.
📉 Applying Percent Increase and Decrease to Real-Life Situations
The paragraph explores the application of percentage increase and decrease to real-life situations using tape diagrams. It compares different scenarios such as a strawberry harvest with a 25% increase, a blueberry harvest with a 25% decrease, and a peach harvest with a 25% decrease. The paragraph also discusses how to represent these situations visually using tape diagrams and emphasizes the importance of understanding the context to determine whether a situation represents an increase or a decrease.
🤔 Critical Thinking on Percent Increases and Discounts
This paragraph challenges the viewer to think critically about statements involving percent increases and discounts. It presents scenarios where an employee receives a 50% raise and another receives a 45% raise, prompting a discussion on whether one is truly a 'bigger raise' without knowing the original salaries. Another scenario involves a misunderstanding at a store where a cashier incorrectly states that buying two shirts with a 20% discount each results in a 40% discount on the total price, which is mathematically incorrect and would lead to a different total discount calculation.
📚 Summary of Percent Increase and Decrease Concepts
The final paragraph summarizes the key concepts learned in the lesson about percent increase and decrease. It uses examples such as Andre having three-fourths more time to get to school than Jada, which translates to a 75% increase. The paragraph reiterates that percent increase and decrease describe the change in quantity relative to the starting amount. It also includes a homework assignment that asks students to determine if 'y' is an increase or decrease relative to 'x', calculate the percentage change, and draw diagrams to represent different situations involving flour and milk usage at a bakery.
📐 Mathematical Relationships and Problem Solving
This paragraph focuses on mathematical relationships, specifically the relationship between the diameter and circumference of a circle. It provides a method to find additional points that lie on the line representing this relationship using the formula for the circumference of a circle. The paragraph also includes a problem-solving exercise where the viewer is asked to select the correct equations that represent buying a certain amount of flour and then buying three-eighths more, with multiple-choice options provided to test understanding.
Mindmap
Keywords
💡Increasing
💡Decreasing
💡Percentages
💡Improvement
💡Growth
💡Percent Increase
💡Percent Decrease
💡Tape Diagrams
💡Contextual Understanding
💡Calculations
💡Proportional Reasoning
Highlights
Introduction to the concept of increasing and decreasing quantities using percentages.
Activity involving sports team scores to illustrate increases and decreases in points.
Discussion on the difference between absolute point increase and percentage growth.
Example of calculating a 20% increase in cereal box size from 18.5 ounces.
Two methods for calculating the new amount after a percentage increase: addition and direct multiplication.
Introduction to the concept of a percentage decrease with a shirt price example.
Calculating the new price after a 20% discount using both subtraction and multiplication.
Use of tape diagrams to match situations of percentage increase and decrease.
Explanation of how to represent a 40% increase in ducks at a pond using a diagram.
Illustration of an 80% decrease in mosquitoes with a corresponding diagram.
Concept of a 100% decrease resulting in zero quantity remaining.
Discussion on whether a 50% raise is larger than a 45% raise depending on the initial salary.
Misunderstanding clarified: 20% off each of two items does not equal 40% off the total.
Homework involving determining percent increase or decrease using diagrams.
Example of calculating the new amount of snow with a 40% increase from last year.
Explanation of how to write a percentage increase or decrease as a percentage of the initial amount.
Activity to find additional points on the line representing the relationship between diameter and circumference of a circle.
Problem-solving involving buying flour and calculating an additional three-eighths more.
Transcripts
5.0 / 5 (0 votes)
Thanks for rating: