Question

lesson 9.2 inductive and deductive reasoning
learning goal i can use inductive reasoning and deductive reasoning. (standards preparing g.co.9, g.gpe.4, g.gpe.5)
explain 1a using inductive reasoning
visit learnzillion.com, read integrated mathematics i lesson 9.2, then read the section below.
teacher voice - a conjecture is an unproven statement that is based on observations. you use inductive reasoning when you find a pattern in specific cases and then write a conjecture for the general case.
example 1 - describing a visual pattern
describe how to sketch the next figure in the pattern. then sketch the fourth figure.
a
the pattern starts with a star having only its lower right arm unshaded. in each subsequent figure going counterclockwise the shading is removed from one arm, so each star has one more unshaded arm than in the previous star.
draw the fourth figure by drawing a star with only the lower left arm shaded in.
b
the pattern starts with one ball. in each subsequent figure, a row is added so as to form a triangle.
draw the fourth figure by drawing four rows of balls to form a triangle.
visit www.highideasmathvideos.com to watch the flipped video instruction for the \try this\ problem(s) below.
try this video for extra example 1 - describing a visual pattern
describe how to sketch the next figure in the pattern. then sketch the fifth figure.

1. 1 2 3 4

integrated math 1 b credit 2
page 17

Explanation:

Step1: Analyze the pattern

The first figure has 1 square. The second figure is formed by adding 3 squares to the first - figure in an L - shape. The third figure is formed by adding 5 squares to the second figure in an L - shape. The fourth figure is formed by adding 7 squares to the third figure in an L - shape. The number of added squares follows the odd - number sequence: 3, 5, 7, and the next odd number is 9.

Step2: Sketch the fifth figure

To sketch the fifth figure, start with the fourth figure and add 9 squares in an L - shape around it.

Answer:

To sketch the next figure, add 9 squares in an L - shape around the fourth figure. The fifth figure will have a total of 1 + 3+5 + 7+9=25 squares arranged in an L - shape.