Problem Solving involving Variations

Group Activity: What do you call friends who love math?

​Solve for the missing variable and write the matching letter on the blank above the answer.

Objectives:

1. Discuss the process of solving word problems involving variation.
2. Solve word problems involving different kinds of variation.
3. Manifest appreciation on the use of variation in real life situation.
4. Display social responsibility while working in pairs/groups.

Identify Me!

Identify what type of variation shown on the following problems.

Multiple Choice

The area of a rectangle (A) varies jointly as its length (L) and width (W). If the area is 30 square centimeters having a length of 3 centimeters and a width of 2 centimeters, find the area if the length is 8 centimeters and width 7 centimeters.

• Direct Variation

• Inverse Variation

• Joint Variation

• Combined Variation

Multiple Choice

The taxi fare (F) varies directly as the distance (D) traveled by the taxi. When the distance traveled is 40 km, the fare amounts to 100 Pesos. How much will the taxi fare be if the distance traveled is 120 km?

• Direct Variation

• Inverse Variation

• Joint Variation

• Combined Variation

Multiple Choice

The number of people (C) working on a certain job varies inversely as the number of days (D) needed to finish the job. If it takes 10 carpenters to finish a house in 8 days, in how many days will 4 carpenters finish it?

• Direct Variation

• Inverse Variation

• Joint Variation

• Combined Variation

Multiple Choice

The time it takes to build (T) varies directly as the length of the highway (L) and inversely as the number of workers (W). If it takes 8 weeks for 50 workers to build a 5km highway, how long will it take 100 workers to build a 50km highway?

• Direct Variation

• Inverse Variation

• Joint Variation

• Combined Variation

Direct Variation

The taxi fare (F) varies directly as the distance (D) traveled by the taxi. When the distance traveled is 40 km, the fare amounts to 100 Pesos. How much will the taxi fare be if the distance traveled is 120 km?

Inverse Variation

The number of people (C) working on a certain job varies inversely as the number of days (D) needed to finish the job. If it takes 10 carpenters to finish a house in 8 days, in how many days will 4 carpenters finish it?

Joint Variation

The area of a rectangle (A) varies jointly as its length (L) and width (W). If the area is 30 square centimeters having a length of 3 centimeters and a width of 2 centimeters, find the area if the length is 8 centimeters and width 7 centimeters.

Combined Variation

The time it takes to build (T) varies directly as the length of the highway (L) and inversely as the number of workers (W). If it takes 8 weeks for 50 workers to build a 5km highway, how long will it take 100 workers to build a 50km highway?

Group Activity: “Problem Solving”

·       They will be group into 8 according to the shape of the paper strips they have.





·       Each group will be given different problems, and they are going to solve it using manila paper and they must present it to the whole class.

1.       When looking at two buildings at the same time, the length of the buildings’ shadows (S) varies directly as their height (H). If a 5-story building has a 20 m long shadow, how many stories high would a building that has a 32 m long shadow be?

2.       The time (t) it takes to travel from Cebu City to Babag National High School varies inversely as the speed (v) at which one travels. If it takes 1.5 hours to travel this distance at an average speed of 120 km/h, find the constant (k) and the amount of time it would take to drive back if you were only able to travel at 60 km/h due to an engine problem.

3.       The electrical current, in amperes (A), in a circuit varies directly as the voltage (V). When 15 volts are applied, the current is 5 amperes. What is the current when 18 volts are applied?

4.       The current in an electrical conductor (A) varies inversely as the resistance of the conductor (O). If the current is 12 amperes when the resistance is 240 ohms, what is the current when the resistance is 540 ohms?

​Problems:

5.       Hooke’s law states that the distance (D) that a spring is stretched by hanging object varies directly as the mass (M) of the object. If the distance is 20 cm when the mass is 3 kg, what is the distance when the mass is 5 kg?

6.       The volume of a gas (V) varies inversely as the pressure (P) upon it. The volume of a gas is 200 cm3 under a pressure of 32 kg/cm2. What will be its volume under a pressure of 40 kg/cm2?

7.       The number of aluminum cans (C) used each year varies directly as the number of people (P) using the cans. If 25 people use 600 cans in one year, how many cans are used each year in Timpolok, which has a population of 1,800?

8.       The time (T) required to do a job varies inversely as the number of people working for bricklayers (B). It takes 5hr for 7 bricklayers to build a park well. How long will it take 10 bricklayers to complete the job?

​Problems:

Assessment:

Direction: Solve the following problem.

Assignment:

In a short bond paper, express how you feel about solving word problems involving variations by drawing a picture. No words. Draw a picture only.

Synthesis Journal:

Reflect on what you have done and learned in this lesson. Record your reflections in the journal below.