Question

lesson 9.2 inductive and deductive reasoning
learning goal i can use inductive reasoning and deductive reasoning. (standards: preparing g.gr.4, g.gpe.5)
explain 1a using inductive reasoning
visit bigideasmath.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 counter - clockwise), 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.bigideasmathvideos.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
lifelong

Explanation:

Step1: Identify the pattern

The first figure is a single - square. The second figure is formed by adding 3 squares to the first figure to make an 'L' - shape with 4 squares. The third figure is formed by adding 5 squares to the second figure to make an 'L' - shape with 9 squares. The fourth figure is formed by adding 7 squares to the third figure to make an 'L' - shape with 16 squares. The number of squares added each time is an odd number (3, 5, 7,...) and the total number of squares in the nth figure is \(n^{2}\).

Step2: Sketch the fifth figure

To sketch the fifth figure, we need to add 9 squares to the fourth figure. The fourth figure has 16 squares. The fifth figure will have \(16 + 9=25\) squares arranged in an 'L' - shape. We start from the bottom - left corner and build the 'L' - shape by adding rows and columns of squares.

Answer:

The fifth figure is an 'L' - shaped figure made up of 25 small squares. To sketch it, start from the bottom - left corner and build an 'L' by adding rows and columns of squares such that it has 5 squares along the bottom row and 5 squares along the right - hand column.