inductive and deductive reasoning
comparing rates
radicals
deductive reasoning
inductive and deductive reasoning
100

A student notices that every Friday,the school cafeteria serves pizza.This has happened for the last 6 Fridays.

Using inductive reasoning,what can the student predict will be served next Friday?

Answer:

The student can predict that pizza will probably be served next Friday 

why?

Inductive reasoning uses patterns from observations to make predictions.

200

Two ride-share drivers are comparing how much they earn:

  • Driver A earns $96 in 6 hours
  • Driver B earns $120 in 8 hours

    Question:

who earns more money per hour?

Answer:

Driver A:

96÷6=16

= $16/hour

Driver B:

120÷8=15

= $15/hour

Driver A earns more money per hour.

300

A contractor is building a square garden with an area of 81 m².

Question:
What is the length of one side of the garden?

(Hint: Use square roots.)

Answer:

The area of a square is:

s2=81

Take the square root:

s=square root of 81

 s=9

 The side length is 9 m.

400

At a school tournament:

  • All basketball players must wear team jerseys.
  • Marcus is wearing a team jersey.

Question:
Can you conclude that Marcus is definitely a basketball player? Explain why or why not using deductive reasoning.

Answer:

 No, we cannot conclude Marcus is definitely a basketball player.

Why?

The statement only says:

  • All basketball players wear jerseys.

But other athletes could also wear jerseys.

This is not enough evidence to guarantee Marcus plays basketball.

500

A delivery company compares two bike couriers:

  • Courier A travels 45 km in 1.5 hours
  • Courier B travels 64 km in 2 hours

The company predicts Courier A will always be faster because they were faster today.

Question:

  1. Compare both couriers’ rates of speed.
  2. Is the company using inductive or deductive reasoning?
  3. Explain whether the conclusion is guaranteed to be true


Step 1: Compare Rates

Courier A:

45÷1.5=30

= 30 km/h

Courier B:

64÷2=32

= 32 km/h

Courier B is actually faster.

Step 2: Type of Reasoning

The company is using inductive reasoning because they are making a prediction based on one observation.

Step 3: Is the Conclusion Guaranteed?

No, the conclusion is not guaranteed to be true.

Why?

Inductive reasoning makes predictions, but predictions can sometimes be incorrect.



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