Integers & Absolute Value

MJ3

Ch 1.3 – Integers & Absolute Value

Bellwork •

Identify the Property

3. 4. 5. 6. 7.

6+1=1+6 9+0=9 4(6 + 2) = 4(6) + 4(2) 5∙1=5 3 ∙ (4 ∙ 5) = (3 ∙ 4) ∙ 5

Assignment Review • None

Before we begin… • You were awesome last week…so

before we begin lets do a little activity… • We will be going outside for about 10 minutes…it is expected that you are on task and working during this activity • I have a number line set up on the front and back stairs…we will be solving simple integer problems using the stairs…

After the activity… • Raise your hand if you liked this

activity…Why? • Raise your hand if you did not like this activity…Why? • My comments… • Raise you hand if you can answer the question…Why did I have you do this activity?....

It’s time to work…. • Please take out your notebook and

get ready to work… • Last week discussed four algebraic properties • Today we will look at numbers themselves…more specifically we will look at positive and negative numbers and how to graph them as well as absolute value

Objective • Students will graph numbers on a

number line and find absolute value

Vocabulary • Negative Number – A number less

than zero • Integers – the set of numbers that includes zero and all positive and negative numbers. • Inequality – a sentence that compares two numbers or quantities • Absolute Value – The distance a number is from zero on the number line. Note: Absolute value can never be negative!

Pre-requisite Knowledge • Its expected that you know most of

the following information… • Please bear with me as I quickly go through it to make sure that we are all on the same page… Thank you for your cooperation…

Number Line

• You should all be familiar with a number line • Zero is in the center – its neither positive nor

negative • Negative numbers are to the left of zero

– On the left side of zero the further a number is from zero the smaller it is

• Positive numbers are to the right of zero – On the right side of zero the further a number is from zero the larger it is

Writing Integers We can use integers to express real-life situations • When doing so the words like: less, minus, below, etc… are represented with a negative sign (–) Example 4. A 15 yard loss can be expressed as -15 5. 250 feet below sea level can be expressed as -250 ft •

Writing Integers The words like more, greater, higher, above, etc… can be represented with a positive sign (+) Example 3. 3 inches of rain above normal can be expressed as +3 4. A profit of $750.00 can be expressed as + $750 •

Your Turn In the notes section of your notebook write each expression and express it as an integer 2. A gain of $2.00 per share 3. 10 degrees below zero •

Graphing on a Number line • Integers can be graphed on a

number line. To do so…simply locate the number on the number line and put a dot. • The dot represents the coordinate of that number on the number line

Example • I can graph the numbers -5 and 4

on the number line like this:

-5 Negative Numbers

0

4 Positive Numbers

Inequalities • A mathematical sentence that compares two

numbers is called an inequality • Inequalities use these symbols (<) Less than, and (>) greater than • Inequalities are read from left to right and should be a true statement when comparing two numbers • In the previous example I can read the inequality as: -5<4 or 4>-5 Be careful with inequalities…sometimes I even have a hard time with them!

Comparing Two Integers • To compare 2 integers you can

graph them on a number line • Then look at the relationship to each of the numbers to determine which is bigger or smaller • Then use the appropriate inequality sign (< or >) to make the statement true

Example 1 • • • •

1 •

(- 6) First draw a number line (demonstrate on board) Then plot the numbers Since 1 is to the right of zero, it is greater than – 6. Use the > inequality sign to get the true statement > -6 This statement can also be written as 6<1

Your Turn In the notes section draw a number line and plot the following and write a true statement using the inequality signs 2. -3 2 3. -5 -6 4. -1 1 •

Absolute Value • As stated previously absolute value represents the

distance a number is from zero on the number line Example Demonstrate on board using – 3 and +3 • Absolute value is indicated with the following symbol | | Example |5| is read as the absolute value of 5, which is 5 | - 5| is read as the absolute value of negative 5, which is 5 Each of the numbers above are 5 units away from zero. The absolute value of a number is never negative

Evaluating Expressions • You can evaluate expressions with

absolute value Example |5| + | -6| 5 + 6 = 11

Evaluating Expressions •

If the expression has an absolute variable use the substitution method 1. Write the expression 2. Substitute 3. Do the math

Example 8 + |n| where n = -12 8 + | -12| 8 + 12 = 20

Strategy • Whenever evaluating or solving

problems always write the original problem out • Then as you perform each step re-write the entire problem over again • This strategy minimizes errors and allows you to easily problem solve should you make an error. • This strategy will help you maximize your grade on tests and assignments

Your Turn •

2. 3. 4. 5.

In the notes section of your notebook write and evaluate the following: |14| |-9| + |3| |-8| - | -2| 4|a| + b where a = -5 and b = 3

Summary • In the notes section of your notes

summarize the key concepts covered in today’s lesson. Keep in mind that today we discussed – How to use an integer to model a real-life situation – Graphing and comparing numbers using a number line – Absolute value

Assignment • Text p. 20 # 15 – 45

Reminder:

– I do not accept answers only for assignments – I do not accept late assignments – Write the problem and show how you got your answer – Use the examples in section 1.3 or your notes if you get stuck – Check your answers for the odd problems in the back of the text book. – If you didn’t get the same answer as the text…its safe to assume that you did something wrong….go back and figure out what you did wrong!