Question

evaluate independent practice lesson 9.2 homework
complete problems 5, 7, 9, 10, 13, 14 and 23 for independent practice.
when you are finished, check the solutions with your teacher.
describe the pattern. then write or draw the next two numbers, letters, or figures. (see example 1.)

1. z, y, x, w, v, ...
2. triangle, square, pentagon

make and test a conjecture about the given quantity. (see example 2.)

1. the product of any two even integers
2. the sum of an even integer and an odd integer

integrated math 1 b credit 2
page 21

Explanation:

Problem 5

Step1: Identify the pattern

The sequence counts backward through the English alphabet, each term is the previous letter minus 1 in alphabetical order.

Step2: Find next two letters

After V (22nd letter), the next is $22-1=21$ (U), then $21-1=20$ (T).

Problem 7

Step1: Identify the pattern

Each shape has one more side than the previous: triangle (3 sides), square (4 sides), pentagon (5 sides).

Step2: Draw next two shapes

Next is a 6-sided hexagon, then a 7-sided heptagon.

Problem 9

Step1: Define even integers

Let even integers be $2m$ and $2n$, where $m,n$ are integers.

Step2: Calculate their product

$$(2m)(2n)=4mn=2(2mn)$$

Step3: Test with examples

$2 \times 4 = 8$ (even), $6 \times 8 = 48$ (even). The result is divisible by 2, so it is even.

Problem 10

Step1: Define even/odd integers

Let even integer be $2m$, odd integer be $2n+1$, where $m,n$ are integers.

Step2: Calculate their sum

$$2m + (2n+1)=2(m+n)+1$$

Step3: Test with examples

$2 + 3 = 5$ (odd), $6 + 7 = 13$ (odd). The result fits the form of an odd integer.

Answer:

1. Problem 5: Pattern: Backward alphabetical order. Next two letters: U, T
2. Problem 7: Pattern: Shapes increase by 1 side each. Next two shapes: A hexagon (6 sides), a heptagon (7 sides)
3. Problem 9: Conjecture: The product of any two even integers is an even integer (and divisible by 4).
4. Problem 10: Conjecture: The sum of an even integer and an odd integer is an odd integer.