1-1 PATTERNS AND EXPRESSIONS

Identify and describe patterns by explaining its properties.

Some Vocabulary Variable

Symbol, usually a letter, that represents one or more numbers. (ex: n, x)

Constant Quantities whose values do not change. (ex:

2, 67) Numerical Expression

Mathematical phrase that contains numbers and operation symbols. (ex: 3+5)

Algebraic Expression Mathematical phrase that contains one or

more variables. (ex: 3n + 5)

Identifying a Pattern

Look at the figures from left to right to determine which figure should come next.

Try this:

Using Tables

Tables are an easy way to organize data to recognize a pattern. Input/output Ex: how many toothpicks in the 20th figure?

Using a Graph

The following graph shows tank sizes in relation to the combined lengths of the fish it can hold.

If you want five 2-in goldfish, four 1-in guppies, and a 3-in loach, what is the smallest capacity tank you can buy?

What is the combined length? 17 inches

Make a table using some points from the graph. The tank should be at least 19 gallons.

1-2 PROPERTIES OF REAL NUMBERS

Identify properties of real numbers by graphing and ordering.

Types of Numbers

Numbers can be classified by their characteristics.

Some can be represented on the number line.

Inverse

The opposite or additive inverse of any number a is –a. The sum of a number and its inverse is 0 Ex: 12 + (-12) = 0

The reciprocal or multiplicative inverse of any nonzero number a is . The product of a number and its reciprocal is 1 Ex: 8(

Sets

Numbers are classified using sets.

Set- a well-defined collection of objects. Each object is an element of

the set. Subset- consists of elements

from the given set.

Sets of Numbers

0natural numbers{1,2,3,…}

0whole numbers{0,1,2,3,…}

0Integers{…,-2,-1,0,1,2,…}

Sets of Numbers

4 5 6 7

51

3

11

2

5.75

• Rational numbers can be written in the form where a and b are integers. They can also be written in decimal form.• Decimals must be terminating or

repeating.

3

Sets of Numbers

4 5 6 7

• Irrational numbers cannot be written in as a quotient of two integers.

• Decimals are non-terminating• Ex: 0.1010010001…, 3.141592…

3

15

#1 #2

integer, rational

What kind of number is 42?

What kind of number is -5?

natural, whole, integer, rational

#3

What kind of number is -4.5669?

rational

Real Numbers Rational numbers and irrational

numbers form the set of real numbers.

Subsets of real numbers:NaturalWholeIntegerRationalIrrational

Inequalities

An inequality is a mathematical sentence comparing the values of two expressions using an inequality symbol.

0 1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1-9

8 -6>

Inequalities

0 1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1-9

-7 7<

#5-7 10

<

#6-5 + 10 10 - 5

=

Assignment

Odds p. 7 #13, 15, 23 p.15 #23-27, 35-39