Chapter 1 Review – Guided Notes



Chapter 7: Integers.

Galileo lived in Italy in the 1500s. He studied how to measure temperature. Galileo found that a liquid would rise or fall in a glass tube, depending on the temperature. He liquid rose or dropped, and the temperature as marked on the glass. Sounds familiar? Glass and alcohol or [pic]mercury thermometers are really number lines, just like you use in math. They’re marked by degrees of temperature. Alcohol or mercury expands up into the positive numbers when heated and shrinks into the negative numbers when cooled. Those positive and negative numbers are called integers. In math, integers can be a real hot topic.

Goals for learning:

To identify the absolute value of integers

To compare the values of negative and positive

To add, subtract, multiply, and divide integers.

Watch Movie:



Lesson 1: The Real Number Line and Integers

In arithmetic, you learned to add, subtract, multiply, and divide whole numbers greater than zero. In algebra, you will also use whole numbers less than zero.

Warm-Up:

What are some numbers less than zero? Where do you see these numbers?

You can use a number line to show the relation between positive and negative whole numbers, also called integers.

Vocab for Understanding:

Integer:

Real Number:

Negative Integer:

Positive Integer:

Every point on the number line corresponds to a specific real number. The arrows at the ends of the number line show that the line continues.

Numbers to the left of zero are negative integers. They are read as ‘negative one’, ‘negative two’… and so on.

Zero is neither negative nor positive.

Numbers to the right of the zero are positive integers. They are read as ‘positive one,’ positive two,’ and so on….

A negative number is always indicated by the______________________.

A positive sign is always indicated by _____________________________ or

____________________________.

The absolute value of an integer is the distance ________________________________

______________________________________________________________________.

The integer can be either to the left or to the right of zero. The symbol for absolute value is ___.

Vocab:

Opposites:

Example #1: |4| = 4 4 is 4 units from 0.

The absolute value of |4| is _______.

|-4| = 4 -4 is ________ units from 0.

The absolute value of |-4| is _____.

Every number other than 0 has an opposite number. Opposites are the same distance from zero.

Example #2

9 is the opposite of __________________.

-9 is the opposite of _________________.

9 is 9 units from 0.

Both -9 and 9 are _________ units from 0.

5 is the __________________________ of -5.

-5 is the opposite of _________.

5 is ____________ from 0.

Both 5 and -5 ____________________________.

Let’s Try Some Out!

Use the number line below to find the values.

1. You earn $6 from mowing the grass.

2. The wind chill is 12 below zero.

3. The Bears took a ten yard gain on the play.

4. We realized we lost five dollars.

5. A mailbox post rises 4 feet above the ground; it is set 2 feet into the ground.

In Class:

Find the absolute value:

1. |3| 2. |-12| 3. |-3|

Name the opposite of each integer:

4. 4 5. 8 6. -7

Solve these problems using the number line.

7. Which letters represent positive real numbers?

8. Which letters represent negative real numbers?

9. Which letter is the greatest distance from zero?

10. Which letter represents the greatest absolute value?

Give an integer that describes each situation.

11. A gain of 3 yards in football.

12. A loss of 15 yards in football.

13. A withdrawal of $40 from a bank account.

14. A deposit of $100 in a bank account.

15. A temperature of 13˚ F below zero.

Watch the first couple minutes of

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Lesson 2: Comparing Integers- Greater Than

To compare 2 numbers and determine which is greater.

To use the symbol > to identify the larger of two integers.

Warm-Up: Here is a list of basketball scores.

102 54

42 56

12 59

84 76

Lesson:

Integers can be arranged in an increasing or decreasing order. Consecutive integers are integers arranged from least or greatest or greatest to least without any missing integers. The integers on a number line are consecutive integers.

You can use a number line to compare two integers. On a number line, the greater of two numbers is the number to the right.

Example 1: Compare 2 and -3

_________ is to the __________ of ______________ on the number line.

______ is greater than -3.

Example 2: Compare -1 and -5.

Remember: The symbol >, read “is greater than,” is used to show that one integer is greater than another.

2 > -3 -1 > -5

Example #3: Compare |-5| and |-3|

-5 is _________________________, so |-5| = 5.

-3 is 3 units from zero, so _______________________.

________ is farther to the right than ____, so | | > | -3 |.

Let’s try it out!

Compare each pair. Use > or =.

1. 5 2 2. |-2| 2

3. |8| -3 4. |-8| |-3|

All Class: Each student will get a note card with an integer. Try to arrange yourselves from least on the left and the greatest on the right.

Lesson 3: Less Than

Objective:

To compare two numbers and decide which is smaller.

To use the symbol < to identify the smaller of two numbers.

Warm-Up:

What does this mean?

>

Try writing a true number sentence using that sign.

What do you think this means?

<

You can use a number line to compare to integers. On a number line, the lesser of two numbers is the number farthest to the left.

Example #1: Compare -3 and 1.

Example #2: Compare -5 and -3

Remember the symbol ‘ ................
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