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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

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Warm Up: You have 5 minutes to work on these problems. Then, we will go over them.

Shortening

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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

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Using Numbers and Properties

You use the properties of numbers when you:

  • Withdraw or deposit money in a bank account
  • Find a common denominator
  • Play a game with scores below zero
  • Check whether a number is divisible by a certain number

Workbook page 15

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Workbook page 15

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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.

 

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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.

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Workbook page 16

 

 

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Workbook page 16

 

 

 

 

 

 

 

 

 

 

 

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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.

 

 

 

 

 

 

 

 

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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.

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Workbook page 17

For each situation, describe the outcome.

 

 

 

 

#1 – 4 HOMEWORK

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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.

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Workbook page 18

Comparing and Ordering Integers

 

Find both integers in a number line.

 

 

Find both integers in a number line.

 

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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.

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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

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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.

 

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Workbook page 19

Fill in each blank with a symbol (=, <, or >) that makes the statement true.

 

 

 

 

 

 

 

 

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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.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Workbook page 19

Use this information for problems 7 an 8.

  1. Of the states on the table, which had the lowest temperature?
  1. Explain: Craig says that the locations with the highest elevation have the lowest temperatures. Do you agree? Explain your thinking.

#7-11 HOMEWORK

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Workbook page 19

  1. How many integers are greater than -8 and less than 0?
  1. How many integers are less than 9 and greater than 4?
  1. How many integers are greater than -1 and less then -3?

#7-11 HOMEWORK

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Tonight’s homework:

Page 17, Core Connections

Page 19, Numbers 7-11