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Transcript of Pre-Algebra: Chapter 2 LEARNING GOAL Students will understand integers and exponents by being able...
![Page 1: Pre-Algebra: Chapter 2 LEARNING GOAL Students will understand integers and exponents by being able to do the following: –Add & Subtract Integers –Multiply.](https://reader036.fdocuments.us/reader036/viewer/2022081513/56649e405503460f94b31eee/html5/thumbnails/1.jpg)
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
![Page 2: Pre-Algebra: Chapter 2 LEARNING GOAL Students will understand integers and exponents by being able to do the following: –Add & Subtract Integers –Multiply.](https://reader036.fdocuments.us/reader036/viewer/2022081513/56649e405503460f94b31eee/html5/thumbnails/2.jpg)
Today’s Learning Goal Assignment
Learn to add integers.
Pre-Algebra
2-1 Adding Integers
![Page 3: Pre-Algebra: Chapter 2 LEARNING GOAL Students will understand integers and exponents by being able to do the following: –Add & Subtract Integers –Multiply.](https://reader036.fdocuments.us/reader036/viewer/2022081513/56649e405503460f94b31eee/html5/thumbnails/3.jpg)
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
![Page 4: Pre-Algebra: Chapter 2 LEARNING GOAL Students will understand integers and exponents by being able to do the following: –Add & Subtract Integers –Multiply.](https://reader036.fdocuments.us/reader036/viewer/2022081513/56649e405503460f94b31eee/html5/thumbnails/4.jpg)
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
![Page 5: Pre-Algebra: Chapter 2 LEARNING GOAL Students will understand integers and exponents by being able to do the following: –Add & Subtract Integers –Multiply.](https://reader036.fdocuments.us/reader036/viewer/2022081513/56649e405503460f94b31eee/html5/thumbnails/5.jpg)
Are we ready for the FAST Track?
Pre-Algebra
2-1 Adding Integers
![Page 6: Pre-Algebra: Chapter 2 LEARNING GOAL Students will understand integers and exponents by being able to do the following: –Add & Subtract Integers –Multiply.](https://reader036.fdocuments.us/reader036/viewer/2022081513/56649e405503460f94b31eee/html5/thumbnails/6.jpg)
Pre-Algebra: 2-1 HW
Page 62#13-24 all
Pre-Algebra
2-1 Adding Integers
![Page 7: Pre-Algebra: Chapter 2 LEARNING GOAL Students will understand integers and exponents by being able to do the following: –Add & Subtract Integers –Multiply.](https://reader036.fdocuments.us/reader036/viewer/2022081513/56649e405503460f94b31eee/html5/thumbnails/7.jpg)
2-1 Adding Integers
Pre-Algebra
Warm Up
Problem of the Day
Lesson Presentation
![Page 8: Pre-Algebra: Chapter 2 LEARNING GOAL Students will understand integers and exponents by being able to do the following: –Add & Subtract Integers –Multiply.](https://reader036.fdocuments.us/reader036/viewer/2022081513/56649e405503460f94b31eee/html5/thumbnails/8.jpg)
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
![Page 9: Pre-Algebra: Chapter 2 LEARNING GOAL Students will understand integers and exponents by being able to do the following: –Add & Subtract Integers –Multiply.](https://reader036.fdocuments.us/reader036/viewer/2022081513/56649e405503460f94b31eee/html5/thumbnails/9.jpg)
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
![Page 10: Pre-Algebra: Chapter 2 LEARNING GOAL Students will understand integers and exponents by being able to do the following: –Add & Subtract Integers –Multiply.](https://reader036.fdocuments.us/reader036/viewer/2022081513/56649e405503460f94b31eee/html5/thumbnails/10.jpg)
Vocabulary
integer
opposite
absolute value
Insert Lesson Title Here
Pre-Algebra
2-1 Adding Integers
![Page 11: Pre-Algebra: Chapter 2 LEARNING GOAL Students will understand integers and exponents by being able to do the following: –Add & Subtract Integers –Multiply.](https://reader036.fdocuments.us/reader036/viewer/2022081513/56649e405503460f94b31eee/html5/thumbnails/11.jpg)
-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
![Page 12: Pre-Algebra: Chapter 2 LEARNING GOAL Students will understand integers and exponents by being able to do the following: –Add & Subtract Integers –Multiply.](https://reader036.fdocuments.us/reader036/viewer/2022081513/56649e405503460f94b31eee/html5/thumbnails/12.jpg)
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
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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
![Page 14: Pre-Algebra: Chapter 2 LEARNING GOAL Students will understand integers and exponents by being able to do the following: –Add & Subtract Integers –Multiply.](https://reader036.fdocuments.us/reader036/viewer/2022081513/56649e405503460f94b31eee/html5/thumbnails/14.jpg)
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
![Page 15: Pre-Algebra: Chapter 2 LEARNING GOAL Students will understand integers and exponents by being able to do the following: –Add & Subtract Integers –Multiply.](https://reader036.fdocuments.us/reader036/viewer/2022081513/56649e405503460f94b31eee/html5/thumbnails/15.jpg)
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
![Page 16: Pre-Algebra: Chapter 2 LEARNING GOAL Students will understand integers and exponents by being able to do the following: –Add & Subtract Integers –Multiply.](https://reader036.fdocuments.us/reader036/viewer/2022081513/56649e405503460f94b31eee/html5/thumbnails/16.jpg)
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
![Page 17: Pre-Algebra: Chapter 2 LEARNING GOAL Students will understand integers and exponents by being able to do the following: –Add & Subtract Integers –Multiply.](https://reader036.fdocuments.us/reader036/viewer/2022081513/56649e405503460f94b31eee/html5/thumbnails/17.jpg)
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
![Page 18: Pre-Algebra: Chapter 2 LEARNING GOAL Students will understand integers and exponents by being able to do the following: –Add & Subtract Integers –Multiply.](https://reader036.fdocuments.us/reader036/viewer/2022081513/56649e405503460f94b31eee/html5/thumbnails/18.jpg)
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
![Page 19: Pre-Algebra: Chapter 2 LEARNING GOAL Students will understand integers and exponents by being able to do the following: –Add & Subtract Integers –Multiply.](https://reader036.fdocuments.us/reader036/viewer/2022081513/56649e405503460f94b31eee/html5/thumbnails/19.jpg)
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
![Page 20: Pre-Algebra: Chapter 2 LEARNING GOAL Students will understand integers and exponents by being able to do the following: –Add & Subtract Integers –Multiply.](https://reader036.fdocuments.us/reader036/viewer/2022081513/56649e405503460f94b31eee/html5/thumbnails/20.jpg)
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
![Page 21: Pre-Algebra: Chapter 2 LEARNING GOAL Students will understand integers and exponents by being able to do the following: –Add & Subtract Integers –Multiply.](https://reader036.fdocuments.us/reader036/viewer/2022081513/56649e405503460f94b31eee/html5/thumbnails/21.jpg)
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
![Page 22: Pre-Algebra: Chapter 2 LEARNING GOAL Students will understand integers and exponents by being able to do the following: –Add & Subtract Integers –Multiply.](https://reader036.fdocuments.us/reader036/viewer/2022081513/56649e405503460f94b31eee/html5/thumbnails/22.jpg)
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