# 1-1 Patterns and Expressions

```Identify and describe patterns by
explaining its properties.

Variable


Constant


Quantities whose values do not change. (ex: 2, 67)
Numerical Expression


Symbol, usually a letter, that represents one or more
numbers. (ex: n, x)
Mathematical phrase that contains numbers and
operation symbols. (ex: 3+5)
Algebraic Expression

Mathematical phrase that contains one or more
variables. (ex: 3n + 5)


Look at the figures from left to right to
determine which figure should come next.
Try this:

Tables are an easy way to organize data to
recognize a pattern.


Input/output
Ex: how many toothpicks in the 20th figure?



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
What is the combined length?



17 inches
Make a table using some points
from the graph.
The tank should
be at least 19
gallons.
Identify properties of real numbers by
graphing and ordering.


Numbers can be classified by
their characteristics.
Some can be represented on
the number line.

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
1
nonzero number a is .
𝑎


The product of a number and its reciprocal is 1
Ex:
1
8( )
8
=1


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
natural numbers
{1,2,3,…}
0
whole numbers
{0,1,2,3,…}
0
Integers
{…,-2,-1,0,1,2,…}
0
1
5
3
11
2
Sets of Numbers
5.75


3
4
5
6

7
𝑎
𝑏
• 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.

Sets of Numbers
15


3
4
5
6
• Irrational numbers cannot be written in as a
quotient of two integers.
• Decimals are non-terminating
• Ex: 0.1010010001…, 3.141592…
7
#1
What kind of
number is -5?
integer, rational
#2
What kind of
number is 42?
natural, whole,
integer, rational
#3
What kind of number is 4.5669?
rational


Rational numbers and irrational numbers
form the set of real numbers.
Subsets of real numbers:
 Natural
 Whole
 Integer
 Rational
 Irrational
Inequalities
An inequality is a mathematical sentence
comparing the values of two expressions
using an inequality symbol.
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
8
&gt;
-6
Inequalities
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
-7
&lt;
7
#5
-7
&lt;
#6
-5 + 10
10
=
10 - 5


Odds p. 7 #13, 15, 23
p.15 #23-27, 35-39
```