Lesson 3-1 and 3-2 (2011)

Yea – It’s the Algebra Unit!

My absolutely favorite unit in the whole year!!!!

Turn to Journal page 82.

Patterns & Variables

• Study the number sentences above. All three sentences show the same general pattern.

• This general pattern may be described in words: – To find 10% of a number, multiply the number by 10/100

(or 0.10 or 1/10).• This general pattern may also be described by a

number sentence that contains a variable: – 10% of n = 10/100 X n

• Number sentences like above are examples, or special cases, for the general pattern described by 10% of n = 10/100 X n

10% of 50 = 10/100 X 50

10% of 200 = 10/100 X 200

10% of 8 = 10/100 X 8

• To write a special case for a general pattern, replace the variable with a number.

• Example:– General pattern 10% of n = 10/100 X n

– Special case 10% of 35 = 10/100 X 35

Let’s Try Some!

• Here are 3 special cases for a general pattern.

• Describe the pattern in words.

• Give 2 other special cases for the pattern.

Let’s Try Another!

• Here are 3 special cases for a general pattern.

• Describe the pattern in words.

• Give 2 other special cases for the pattern.

15 + (-15 ) = 0 3 + (-3) = 0 ¼ + (-¼) = 0

Try This!

• A spider has 8 legs. The general pattern is: s spiders have s • 8 legs.

• Write 2 special cases for the general pattern.

Problem 4

Again!

• Write 3 special cases for each general pattern.

• p + p = 2 • p c • 1/c = 1 p + p + (3 • p) = 5 • p

Let’s reverse it.

• Write a general pattern for each group of 3 special cases.

General Pattern

18 • 1 = 182.75 • 1 = 2.756/10 • 1 = 6/10

What’s the general pattern?

6 • 0 = 0½ • 0 = 078.7 • 0 = 0

6 • 6 = 62

½ • ½ = (½)2

0.7 • 0.7 = (0.7)2

What about 2 variables? (p. 87)

• The general pattern below uses 2 variables. They are a and b.

• To write a special case for the general pattern:– Replace the variable a with any number.– Replace the variable b with any number.– Notice that in the third special case, the

variables a and b have been replaced by the same number.

General Pattern Special Cases

a • (b – 1) = a • b – a 5 • (4 – 1) = 5 • 4 – 5

7 • (3 – 1) = 7 • 3 – 7

6 • (6 – 1) = 6 • 6 – 6

Write 3 special cases for each general pattern.

Writing a General Pattern

1. Write everything that is the same for all of the special cases. Use blanks for the parts that change.

2. Each special case has 2 different numbers. Use different variables for the numbers that vary. Write them on the blanks.

3. Check that the special cases given fit the general pattern.

For Example

_______ + _______ = ______ + _______

Each special case has two additions and an equal sign.

___a____ + ____b___ = __b____ + ___a____

Write a number sentence with 2 variables for each general

pattern.

4 • 2/7 = 2 • 4/7

10 • 2/3 = 2 • 10/3

29• 2/8 = 2 • 29/8

(5 • 2) + (5 • 6) = 5 • (2 + 6)(5 • 4) + (5 • 1) = 5 • (4 + 1)(5 • 2) + (5 • 100) = 5 • (2 + 100)