pre-algebra: chapter 2 learning goal students will understand integers and exponents by being able...

Pre-Algebra: Chapter 2 LEARNING GOALStudents will understand integers and

exponents by being able to do the following:

– Add & Subtract Integers– Multiply & Divide Integers– Solve Equations Containing Integers– Solve Inequalities Containing Integers– Solve Exponents– Understand the Properties of Exponents– Find a Pattern in Integer Exponents– Solve Scientific Notation

Today’s Learning Goal Assignment

Learn to add integers.

Pre-Algebra

2-1 Adding Integers

Lesson Quiz: Part 1

Add.

1. –7 + (– 7)

2. 15 + (–9) + (–2)

4

–14

Insert Lesson Title Here

Evaluate each expression for the given

value of the variable.

3. 13 + r for r = –15

4. 2 + b + (–9) for b = –6

–2

–13

Pre-Algebra

2-1 Adding Integers

Lesson Quiz: Part 2

5. On Monday, a local dog shelter had six dogs.

By Friday they had found homes for three, but

took in two more. Then how many dogs were in

the shelter?

Insert Lesson Title Here

5 dogs

Pre-Algebra

2-1 Adding Integers

Are we ready for the FAST Track?

Pre-Algebra

2-1 Adding Integers

Pre-Algebra: 2-1 HW

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Pre-Algebra

2-1 Adding Integers

2-1 Adding Integers

Pre-Algebra

Warm Up

Problem of the Day

Lesson Presentation

Warm UpGraph each number on a number line.

1. 5 2. 7

3. 4 4. 0

Pre-Algebra

2-1 Adding Integers

0 1 2 3 4 5 6 7 8 9 10

41 35Add.5. 22 + 19 6. 17 + 18

Problem of the Day

Start at (0, 0). Walk 3 blocks west and 2 blocks north. Then walk 4 blocks south and 1 block east. What are your coordinates?(–2, –2)

Pre-Algebra

2-1 Adding Integers

Vocabulary

integer

opposite

absolute value

Insert Lesson Title Here

Pre-Algebra

2-1 Adding Integers

-5 -4 -3 -2 -1 0 1 2 3 4 5

Negative integers Positive integers

0 is its own opposite

–3 and 3 are opposites

Integers are sets of whole numbers, including 0, and their opposites. The sum of two opposite integers is zero.

Pre-Algebra

2-1 Adding Integers

To add a positive number move to the right. To add a negative number move to the left.

Helpful Hint

Additional Example 1: Using a Number Line to Add Integers

Use a number line to find the sum.

(–6) + 2

2

–6

You finish at –4, so (–6) + 2 = –4.

–6 –5 –4 –3 –2 –1 0 1 2 3 4 5

Pre-Algebra

2-1 Adding Integers

Try This: Example 1

Use a number line to find the sum.

(–3) + 7

7

–3

You finish at 4, so (–3) + 7 = 4.

–6 –5 –4 –3 –2 –1 0 1 2 3 4 5

Pre-Algebra

2-1 Adding Integers

Another way to add integers is to use absolute value. The absolute value of a number is its distance from 0. The absolute value of –4, written as |–4|, is 4; and the absolute value of 5 is 5.

Adding integers

If the signs are the same. . . If the signs are different. . .

find the sum of the absolute values. Use the same sign as the integers.

find the difference of the absolute values. Use the sign of the integer with the larger absolute value.

Pre-Algebra

2-1 Adding Integers

Additional Example 2A & 2B: Using Absolute Value to Add Integers

A. 1 + (–2)

Think: Find the difference of 2 and 1.

Add.

1 + (–2)

2 > 1; use the sign of 2. –1

B. (–8) + 5

Think: Find the difference of 8 and 5. (–8) + 5

8 > 5; use the sign of 8. –3

Pre-Algebra

2-1 Adding Integers

Additional Example 2C: Using Absolute Value to Add Integers

C. (–2) + (–4)

Think: Find the sum of 2 and 4.

Add.

(–2) + (–4)

Same sign; use the sign of the integers. –6

Pre-Algebra

2-1 Adding Integers

Try This: Example 2A & 2B

A. 3 + (–6)

Think: Find the difference of 6 and 3.

Add.

3 + (–6)

6 > 3; use the sign of 6. –3

B. (–4) + 1

Think: Find the difference of 4 and 1. (–4) + 1

4 > 1; use the sign of 4. –3

Pre-Algebra

2-1 Adding Integers

Try This: Example 2C

C. (–6) + (–7)

Think: Find the sum of 6 and 7.

Add.

(–6) + (–7)

Same sign; use the sign of the integers. –13

Pre-Algebra

2-1 Adding Integers

Additional Example 3: Evaluating Expressions with Integers

Evaluate c + 4 for c = –8.

c + 4

Replace c with –8.Think: Find the difference of 8 and 4.

8 > 4; use the sign of 8.

(–8) + 4

–8 + 4 = –4

Pre-Algebra

2-1 Adding Integers

Try This: Example 3

Evaluate d + 7 for d = –3.

d + 7

Replace d with –3.Think: Find the difference of 7 and 3.

7 > 3; use the sign of 7.

(–3) + 7

–3 + 7 = 4

Pre-Algebra

2-1 Adding Integers

Additional Example 4: Application

Katrina opened a new bank account. Find her account balance after the first four transactions listed below.

Deposits: $200, $20 Withdrawals: $166, $38

Use a positive sign for deposits and a negative sign for withdrawals.

200 + 20 + (–166) + (–38)

Group integers with same signs.(200 + 20) + (–166 + –38)

Add integers within each group.220 + (–204)

220 > 204; use the sign of 220.16

Katrina’s account balance after the first four transactions is $16.

Pre-Algebra

2-1 Adding Integers

Try This: Example 4

Michael opened a new bank account. Find his account balance after the first four transactions listed below.

Deposits: $175, $95 Withdrawals: $133, $65

Use a positive sign for deposits and a negative sign for withdrawals.

175 + 95 + (–133) + (–65)

Group integers with same signs.(175 + 95) + (–133 + –65)

Add integers within each group.270 + (–198)

270 > 198; use the sign of 270.72

Michael’s account balance after the first four transactions is $72.

Pre-Algebra

2-1 Adding Integers