Question

reasoning in mathematics
worksheet: inductive and deductive reasoning
part a: inductive reasoning

1. find the next number: 2, 4, 8, 16, 32
2. find the next number: 1, 4, 9, 16, ____
3. look at the pattern: monday, wednesday, friday, ____
4. the first three figures each have 4 sides. what conjecture can you make about the next figure?
5. find the next number: 3, 6, 12, 24, ____
6. observe the pattern: 1, 1, 2, 3, 5, ____
7. look at the sequence: 10, 20, 30, 40, ____
8. the sum of the first three odd numbers is even. what can you conjecture about the sum of any two odd numbers?
9. find the next number: 100, 90, 80, ____
10. a student notices that every triangle measured has interior angles adding to 180°. what conjecture can be made?

part b: deductive reasoning

1. all squares are rectangles. a figure is a square. what can you conclude?
2. if a number is divisible by 4, then it is even. 28 is divisible by 4. what can you conclude?
3. all right angles measure 90°. ∠a is a right angle. what is the measure of ∠a?
4. if two angles form a linear pair, then they are supplementary. what is the sum of their measures?
5. all equilateral triangles have three congruent sides. triangle abc is equilateral. what can you conclude?
6. if a shape has four equal sides and four right angles, what is the shape?
7. if it is raining, then the ground is wet. it is raining. what can you conclude?
8. all multiples of 10 end in 0. 70 is a multiple of 10. what can you conclude?
9. if two lines are perpendicular, then they intersect at right angles. what can you conclude?
10. all prime numbers greater than 2 are odd. 17 is prime and greater than 2. what can you conclude?

Explanation:

Answer:

1. 32
2. 25
3. Sunday
4. The next figure will have 4 sides.
5. 48
6. 8
7. 50
8. The sum of any two odd numbers is even.
9. 70
10. The sum of the interior angles of any triangle is $180^{\circ}$.
11. The figure is a rectangle.
12. 28 is even.
13. $90^{\circ}$
14. $180^{\circ}$
15. Triangle ABC has three congruent sides.
16. Square
17. The ground is wet.
18. 70 ends in 0.
19. The two lines intersect at right angles.
20. 17 is odd.