Pre-Algebra Room 424 Ms. Miller
Please sign in next to your name on the sheet by the door.
I have pencils, pens, paper, if you need it.
I will be available in my room from 12:00 - 12:30 for tutoring on Mondays and Wednesdays if you ever want extra help. (PLEASE LET ME KNOW AHEAD OF TIME)
The day’s lesson and the homework will be posted to my website by the end of each day.
www.mrsmillersmathtutoring.com
Always feel free to email me with any questions or concerns.
jmiller1@camdencc.edu
Warm Up: You have 5 minutes to work on these problems. Then, we will go over them.
Shortening
Numbers and Properties
Have you ever noticed the patterns numbers make? For example, some numbers can be divided exactly by two, while other can’t. When you count by fives, the numbers always end with zero or five. In this unit, you’ll learn the number patterns that you will need to solve algebra problems.
You’ve already learned how to work with numbers greater than zero. In this unit, you’ll learn how to perform operations with signed numbers, which includes numbers greater than and less than zero. You’ll also learn the basics of a few new operations such as powers and roots.
Everything you will do in algebra is based on certain properties, or rules. Properties tell you what you can and can’t do as you solve problems. In this unit, you will learn the properties that make algebra work.
Workbook page 14
Using Numbers and Properties
You use the properties of numbers when you:
Workbook page 15
Workbook page 15
The Number Line
One way to show numbers and their relationship to each other is on a number line. The markings on a number line divide the line into equal spaces. The arrows on a number line show that the numbers continue.
Workbook page 16
The number line to the right shows the whole numbers from 0 to 10. The set of whole numbers starts at 0 and includes the numbers you use for counting. On this number line, each mark represents 1.
Workbook page 16
Values increase as you move to the right along the number line.
What happens when you move to the left?
Algebra includes the use of signed numbers. Signed numbers are either positive or negative. A negative number is written with a (–) sign.
A negative number has a value less than 0. Negative numbers are written to the left of 0.
NOTE: 0 is neither positive or negative.
They decrease.
Workbook page 16
Workbook page 16
Workbook page 17
Number lines can also be drawn vertically. On a vertical number line, numbers above 0 are positive and numbers below 0 are negative.
Workbook page 17
Core Connections: Positive or Negative
As you have seen, positive and negative numbers are used to show whether a number is greater than or less than zero. You already apply this kind of thinking in your everyday life.
He will have enough in the bank to cover the check, so his account balance will be positive.
Workbook page 17
For each situation, describe the outcome.
#1 – 4 HOMEWORK
Workbook page 18
Comparing and Ordering Integers
The dots (…) on each end of the list show that the integers continue forever in both directions.
You can use a number line to decide whether one integer is greater than or less than another.
Workbook page 18
Comparing and Ordering Integers
Find both integers in a number line.
Find both integers in a number line.
Workbook page 18
Thinking about the number line will help you avoid making mistakes.
For example, you are used to thinking that 8 is greater than -5, so you might also think that -8 is greater than -5.
However, the opposite is true.
Because -5 is to the right of -8 on the number line, -5 is greater.
If you aren’t sure of an answer, try sketching a number line.
Workbook page 18
To compare the values of numbers, use the symbols shown here.
Symbol | Meaning | Example |
| Is equal to | |
| Is less than | |
| Is greater than | |
Workbook page 19
Ordering Integers
Step 1:
Think about the negative integers. The negative integers must be less then the positive integers.
Step 3:
Put it together.
Workbook page 19
Fill in each blank with a symbol (=, <, or >) that makes the statement true.
Workbook page 19
In the blanks, write the list of integers in order from least to greatest.
In the blanks, write the list of integers in order from greatest to least.
Workbook page 19
Use this information for problems 7 an 8.
#7-11 HOMEWORK
Workbook page 19
#7-11 HOMEWORK
Tonight’s homework:
Page 17, Core Connections
Page 19, Numbers 7-11