Real-World Applications
Presentation
•
Science
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6th Grade
•
Practice Problem
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Medium
Standards-aligned
Barbara White
Used 1+ times
FREE Resource
8 Slides • 8 Questions
1
Middle School
2
Use proportions to calculate percentages for sales tax and gratuities.
Use the Pythagorean theorem to find unknown side lengths in right triangles.
Calculate the area of a circle to solve real-world problems.
Identify key information in word problems to find the correct solution.
3
Key Vocabulary
Proportions
The equality of two ratios, used here to solve percent problems like taxes or tips.
Sales Tax
A percentage of the cost of goods that is added on to the final price.
Gratuities
A tip or percentage of a bill that is given to a server for their service.
Pythagorean Theorem
A formula, a2 + b2 = c2, for finding an unknown side of a right triangle.
Area of a Circle
The total space enclosed within a circle, calculated using the formula A = πr2.
Radius
The distance from the center of a circle to any point on its circumference boundary.
4
Applications of Proportions: Sales Tax & Gratuity
5
Multiple Choice
Your family's dinner bill was $42.00, and your parents want to give the waiter a 15% tip. What is the amount of the tip?
$42.15
$48.30
$6.30
$5.00
6
The Pythagorean Theorem in Action
7
Multiple Choice
How can the Pythagorean Theorem be used to find the distance between two points on a graph?
By calculating the percentage of the distance.
By using the formula for the area of a circle.
By treating the distance as the area of a square.
By using the 'rise' and 'run' between the points as the legs of a right triangle.
8
Finding the Area of a Circle in Real-World Problems
9
Multiple Choice
A circular clock face has a diameter of 10 inches. What is the first and most critical step to find the area of the clock face?
Multiply the diameter by π.
Square the diameter.
Divide the diameter by 2 to find the radius.
Use 10 as the radius in the area formula.
10
Misconception | Correction |
|---|---|
Using diameter instead of radius to find the area of a circle. | Always use the radius, which is half the diameter, for the area formula. |
Forgetting to add tax or tip to the original total for the final price. | Add the calculated percentage amount back to the subtotal to find the final cost. |
Confusing the hypotenuse and legs when using the Pythagorean theorem. | The hypotenuse is the longest side and is opposite the right angle. |
A 20% discount on $100 means the final price is $20. | The discount is $20. The final price is $100 - $20, which equals $80. |
11
Multiple Choice
A $250 suede jacket is on sale for 20% off. Which choice correctly shows how to calculate the final price of the jacket?
$250 - ($250 x 0.20)
$250 x 0.20
$250 + ($250 x 0.20)
$250 / 0.20
12
Multiple Choice
A 14-foot ladder is set up against a building with its base 4 feet from the wall. How does the Pythagorean theorem apply to this situation?
It determines the total sales tax for the ladder.
It calculates the area of the wall.
It treats the ladder as the hypotenuse to find how high it reaches on the wall.
It finds the distance between the top and bottom of the ladder.
13
Multiple Choice
Analyze the following situations: 1) A dinner bill is $65, and you leave a 20% tip. 2) A $44 bracelet is 25% off. How does the final calculation differ between finding the total cost of the dinner versus the final price of the bracelet?
The tip is subtracted from the bill, while the discount is added to the price.
There is no difference in the calculation method.
The tip amount is added to the bill, while the discount amount is subtracted from the price.
The tip is found using the Pythagorean theorem, while the discount is found with proportions.
14
Multiple Choice
A large, circular window has a diameter of 6 meters. If the glass costs $50 per square meter, how would you set up the problem to find the total cost of the glass?
($50 / 6) x π
(π x 32) x $50
(2 x π x 6) x $50
(π x 62) x $50
15
Use proportions to solve real-world percent problems like sales tax and tips.
The Pythagorean theorem, a2 + b2 = c2, finds unknown side lengths and distances.
To find the area of a circle, use the formula Area = πr2 with the radius.
Read word problems carefully to identify keywords and choose the correct formula.
16
Poll
On a scale of 1-4, how confident are you about applying these math concepts to real-world problems?
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Middle School
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