1. Using Mathematics to Analyze an Invention
ENGR 7-2 Lesson 4
Written by Roland Williams

2. GPS:
ENGR-II-4: Students will invent or innovate a technological product.
M7A3. Students will understand relationships between two variables.
M7D1. Students will pose questions, collect data, represent and analyze the data, and interpret results.

3. Critical Knowledge/Elements
G) Evaluate the invention or innovation
C) Describe how change in one variable affects the other variable.
C) Analyze data using measures of central tendency (mean, median, and mode), including recognition of outliers.

4. Essential Question
How are mathematics used to evaluate an invention?

5. Word Wall
Mean
Median
Mode
Break-Even Point

6. Your candy dispenser was to dispense 4 – 8 candies
Your candy dispenser was to dispense 4 – 8 candies. What was the mean, median and mode of your candy dispenser?

7. Mean
Add all the numbers together then divide the answer by the amount of numbers.
EX: 4,7,6,7,4,8,4,8

8. Mean
Ans:
=48
48 ÷ 8 = 6
Mean = 6

9. Median
List all the numbers in correct order, being sure to include an doubles and find the middle number. If you have an even amount of numbers, the median is found by adding the middle two numbers together and dividing by 2.
EX: 4,7,6,7,4,8,4,8

10. Median
Ans:
4,7,6,7,4,8,4,8
4,4,4,6,7,7,8,8
(6 + 7) ÷ 2 = 6.5
Median = 6.5

11. Mode
List all numbers in order, the mode is that number which appears the most times. There can be more than one mode.
EX: 4,7,6,7,4,8,4,8

12. Mode
Ans:
4,7,6,7,4,8,4,8
4,4,4,6,7,7,8,8
Mode = 4

13. You have now added a place to deposit money in your candy dispenser and you are going to sell your dispenser. You must be a good salesman and know how what the Break-Even Point is for a candy manufacturer.

14. Break-Even Point
The point at which cost or expenses of your device and revenue or profit made from the sale of candies are equal.
X = Y ÷ Z
(Total number of candies that must be sold (X) = Dispenser Price (Y) ÷ Profit per Candy (Z)

15. Break-Even Point X = Y ÷ Z
(Total number of candies that must be sold (X) = Dispenser Price ($100) ÷ Profit per Candy ($2)
EX: X = Y ÷ Z
X = $100 ÷ $2
X = 50
BEP = 50

16. Now is your chance, complete the Candy Dispenser Analysis Worksheet

17. Candy Dispenser Analysis Worksheet Review

18. Essential Question
How are mathematics used to evaluate an invention?

19. Conclusion
ENGR 7-2 Lesson 4