# ALGEBRA 2

### Chapter 1: Essential Questions

How can you use the properties of real numbers to simplify algebraic expressions?

How do you solve an equation or inequality?

Remember

you

are responsible for knowing all these terms! They are key to your success in Math

 Vocabulary Word Definition Examples Variable Numerical Expression Algebraic Expression Constant

ATTERNS AND

### E

XPRESSIONS  Some patterns can be represented using diagrams, words, numbers or algebraic expressions.

 Variables can represent different quantities in real world situations and in patterns.

 This lesson communicates that searching for patterns is a proven problem solving technique and is a foundation for mathematical knowledge.

ATTERNS AND

### E

XPRESSIONS  Please look at the arithmetic sequences below.

1.

1, 2, 4, 8, 16, 32, 64 … 2.

1, 4, 9,16 …     Look at the patterns and draw what you think is the 9 th number in the first sequence?

What do you think the 6 th second sequence?

number is in the What is the pattern for the 1 st and 2 nd sequence?

Can you write a rule for each sequence.

ATTERNS AND

### E

XPRESSIONS  Please look at the arithmetic sequences below.

1.

2, 4, 8, 16, 32, 64 … 2.

1, 4, 9,16 …    Look at the patterns and draw what you think is the 8 th number in the first sequence? 256 What do you think the 6 th second sequence? 36 number is in the In words, what is the pattern for the 1 st sequence? Doubling/Perfect squares and 2 nd

P ROBLEM 1  Look at the figures from left to right. What is the pattern? What should the next figure in the pattern look like?

  The pattern shows regular polygons with the number of sides increasing by one.

The last figure shown above has six sides, so the next figure would have seven sides.

OT IT

AGE

### 4

 Look at the patterns from left to right. What is the pattern? Draw the next figure in the pattern.

Did you write your definitions? Remember you are responsible for knowing all these terms! They are key to your success in Math

 Vocabulary Word Definition Examples Variable A symbol, or letter that represents one or more numbers n r x etc Numerical Expression 3 + 5 Algebraic Expression Constant A mathematical phrase that contains numbers and operation symbols (No equal sign: that is equation) A mathmatical phrase containing one or more variables A quantity whose value does not change (5 – 2) + 8 6n + 8 3(2x - 3) + 7 3 2.5 1/2

ROBLEM

XPRESSING A

LGEBRA

AGE

### 5 P

ATTERN WITH

Figure Number (Input) Process Column Number of Toothpicks

1 2 3 : n 20 1(4) 2(4) 3(4) ?

: ?

4 8 12 ?

: ?

Got it? # 2. How many tiles are in the 25 th pattern? Create a table like the one above.

Figure in this

ROBLEM

SING A

RAPH

AGE

ROBLEM

AGE

### 6

Input(Fish Length) Process (Formula)

0 5 10 0 + 2 0 + 5 0 + 10

Output (Capacity)

2 5 10 Output = Input + 2 = 17 + 2 = 19 So which tank will you buy??

OT IT

AGE

OT IT

AGE

### 6

 The graph shows the total cost of platys at the aquarium shop. Use a table to answer the questions.

  A. How much do 6 platys cost?

B. How much to 10 platys cost?

 C. Why is the graph in Example 3, while the graph regarding platys is a set of points?

ET

### ’

S LOOK AT SOME QUESTIONS

ESSON

### 1-1

 Text p 7, 1-7 working in pairs    Practice workbook, p 3-4 all Finish for homework / Remember homework will not be accepted if ALL work is not shown.

******If you think it in your head or enter it in a calculator, you MUST write it down.**********