PRESENTATION ABOUT JOINT VARIATION .pptx

The presentation is about Joint Variation. It consist of description of the concept, examples and activities.

1. MATHEMATICS 9 ROSE ANNE C TORRES QUARTER 2

2. The area (a) of the wall to be painted varies directly to the numbers of workers (w). What will be the mathematical equation of the given statement above? a = kw What type of variation is shown in the situation? Direct Variation

3. Compare the first and second situation. How will you describe the relationship between the area, worker and pails? How can you translate the situation into mathematical equation? The area (a) of the wall to be painted varies jointly to the number of workers (w) and the pail (p) needed to do the task.

4. Translate the situation into mathematical equation a = kwp The area (a) of the wall to be painted varies jointly to the number of workers (w) and the pail (p) needed to do the task.

5. JOINT VARIATION

6. Illustrate situations that involve joint variation Identify examples of situations that involve joint variation Appreciate the concept of joint variation in real-life situation

7. It occurs when a quantity varies directly as the product of two or more quantities JOINT VARIATION y varies jointly as x and z y is jointly proportional to x and z

8. JOINT VARIATIONS y varies jointly as x and z y = kxz

9. JOINT VARIATIONS Example 2 a = kbh The area (a) of triangle varies jointly as its base (b) and height (h)

10. LEARNING TASK Translate each statement into mathematical sentence. Use k as constant of variation. p varies jointly as q and r v varies jointly as l and w The area a of parallelogram varies jointly as the base b and altitude h. The volume of a pyramid v varies jointly as the area of the base b and the altitude h. The force f applied to an object varies jointly as the mass m and the acceleration a. P= kqr V = klw A = kbh v = kbh F = kma

11. QUIZ Read each item carefully. Write the letter of the correct answer. 1. What kind of variation is similar to direct variation but composed of two or more variables? a. combined c. inverse b. direct d. joint 2. If z varies jointly as x and y, which of the following represents this relationship? a. c. z = kxy b. z = kx + y d. 3.   To get 14, we add 2.

12. Relationship of Constant of Variation for Joint Variation The constant of variation is equal to dependent/independent variable. y = dependent variable x and z = independent variable  

13. Example: SOLUTION Find the equation of variation where y varies jointly as x and z, and y = 36 when x = 3 and z = 4 y = kxz 36 = k (3)(4) 36 = k (12)   k = 3 Equation of Variation: y=3xz

14. SEATWORK NO. 3 y varies jointly as x and z . If y = 3 when x = 3 and z = 15 , find y when x = 6 and z = 9 d varies jointly as h and g . If d = 15 when h = 14 and g = 5 , find g when h = 21 and d = 8 y varies jointly as x and z . If y=60 when x=3 and z=4 , find z when y=80 and x=2 c varies directly as a and b . If c=45 when a =15 and b=3 , find c when a=21 and b=8 If t varies jointly with m and b and t=80 when m=2 and b=5 , find t when m=5 and b=8 Translate each statement into mathematical sentence. Use k as constant of variation.

15. Multiplying by 1 A number multiplied by 1 will result in the same number.

16. Multiplying by 0 Any number multiplied by 0 will result in 0.

17. References Mathspace. ‘Properties of multiplication (10x10) | Grade 4 Math | UK Primary (3-6)’. Accessed 7 December 2023, https://mathspace.co/textbooks/syllabuses/Syllabus-452/topics/Topic-8347/subtopics/Subtopic-109695/?bookType=textbook&searchString=&activeTab=theory

18. Activity A. B . Key in the answer for each letter. C . D . What’s the Passcode? The box containing the donated clothes is secured with a lock. Key-in the passcode by finding the missing values mentally. A B C D

19. 5 1 8 What’s the Passcode? The box containing the donated clothes is secured with a lock. Key-in the passcode by finding the missing values mentally. A. B . A B C D Key in the answer for each letter. C . D . Answer Key Activity

20. Commutativity or changes in the position of numbers will result in the same answer. A number multiplied by 1 will result in the number itself. Deriving facts is getting new information from what we already know. A number multiplied by 0 will result in 0. Summary

21. 6 cans per box Assignment Thirty boxes of canned soup are donated. Each box contains 6 cans of soup. If these are to be evenly distributed to 6 different families, how many will each family get? Share your solution with the class in the next session.

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24. N + 6 = 2 N - 16 = 38 4a-7 = 6 7(8+m)=10 6(4-y)=8

25. 2x = 6 3x - 9 = 100 3x + 7 = 98 25 -2x = 12 2x + y = 15