9/5/13 Warm-up1.)

2.)

3.)

CHALLENGE:

ANSWERS 1.) 24 2.) -24 3.) 56 CHALLENGE: zero

ALGEBRA 1P GAME PLAN

Date 9/5/13 Thursday

Section / Topic

Notes: 1-4 & 1-5: Adding & Subtracting Real Numbers(Day 1)

Goal SWBAT add & subtract real numbers using a number line model and properties of addition.

Algebra California Standard

1.0 Students identify and use the arithmetic properties of real numbers 2.0 Students understand and use such operations as taking the opposite

Homework Choose 2 problems from each set:P. 27 #5-12 P. 28 #28-35P. 34 #1-12 P. 34 #30-37

Announcement

• Quiz Wednesday, 9/11

VocabularyIdentity Property of Addition:The sum of a number and zero is that number

Example: 5 + 0 = 5 Example: 0 + -5 = -5

Additive Inverse: The opposite of a number Example: The additive inverse of 7 is -7.

Inverse Property of Addition:The sum of a number and its additive inverse is zero.

Example: -4 + 4 = 0 or 4 + (-4) = 0

-3 -2 -1 0 1 2 3 4 5 6 7 8 9

1. 2 + 6

2. 2 + (-6)

3. -2 + 6

4. -2 + (-6)

5. -6 + 4

6. -3 + (-8)

7. -5 + 3

8. -2 + 9

Solve

Adding Real Numbersusing a number line

Same sign: Simply add them together keep the sign.

Example: 2 + 6 = 8 -2 + -6 = -8

Different signs:Subtract the numbers and keep the sign of the number with the greater absolute value (the “bigger” one).

-2 +6 = 4 2 + (-6) = -4

Adding Real Numbers

Double negatives!!

I am healthyunnot

- (-5)8- (-4) = 12

Applying AdditionEvaluating Expressions

Evaluate

-n + 8.9 Step 1

Substitute a value for the variablen = -2.3- ( -2.3) + 8.9Step 2 Add a line, Change the sign, bam bam

= 2.3 + 8.9

11.2

Step 3Simplify

Try This Evaluate the Expression

V = 7

1. v – 13

2. -2 + v

3. 8 – v

4. 8 + v – 6 + v

- 6

5

-1

16

ALGEBRA 1

Use a number line to simplify each expression.

a. 3 + (–5)

3 + (–5) = –2

b. –3 + 5

–3 + 5 = 2

Start at –3.Move left 5 units.

Start at –3.Move right 5 units.

c. –3 + (–5)–3 + (–5) = –8

Start at –3.Move left 5 units.

Adding Real NumbersLESSON 1-4

Additional Examples

ALGEBRA 1

Simplify each expression.

a. 12 + (–23)

b. –6.4 + (–8.6)

The difference of the absolute values is 11. The negative addend has the greater absolute value, so the sum is negative.

Since both addends are negative, add their absolute values. The sum is negative.

Adding Real NumbersLESSON 1-4

Additional Examples

=- 11

= -15.0

ALGEBRA 1

The water level in a lake rose 6 inches and then fell 11 inches. Write an addition statement to find the total change in water level.

6 + (–11) = –5   The water level fell 5 inches.

Adding Real NumbersLESSON 1-4

Additional Examples

ALGEBRA 1

Evaluate 3.6 + (–t) for t = –1.7.

3.6 + (–t) = 3.6 + [–(–1.7)] Substitute –1.7 for t.

= 3.6 + [1.7] –(–1.7) means the opposite of –1.7, which is 1.7.

= 5.3 Simplify.

Adding Real NumbersLESSON 1-4

Additional Examples

ALGEBRA 1

A scuba diver who is 88 ft below sea level begins to ascend to the surface.

Define: Let r = the number of feet the diver rises.

a.  Write an expression to represent the diver’s depth below sea level after rising any number of feet.

Write: –88 + r–88 + r

b.  Find the new depth of the scuba diver after rising 37 ft.–88 + r = –88 + 37 Substitute 37 for r.

= – 51 Simplify.The scuba diver is 51 ft below sea level.

Relate: 88 ft below sea level  plus  feet diver rises  

Adding Real NumbersLESSON 1-4

Additional Examples

Subtracting Real Numbers

-3 -2 -1 0 1 2 3 4 5 6 7 8 9

To subtract a number, add its opposite

Example: 3 – 5 = 3 + (-5) = 2 Example: 3 – (-5) = 3 + 5 = 8

1. 4 – 7

2. -1 – 4

3. -3 –( -8)

4. 8 + (-5)

5. -4 – (-9)

6. - 0.5 + ( -1.3)

7. 3.7 – ( -4.3)

8. -3 + 8

-4Solve

ALGEBRA 1

Find –3 – 2 using a number line.

–3 – 2 = –5

Start at –3.

Move left 2 units

Subtracting Real NumbersLESSON 1-5

Additional Examples

ALGEBRA 1

Simplify each expression.

a. –11.6 – (–14)

= 2.4 Add.

= + Use common denominators.49

69

= Add.10 9

= or 1 Write in simplest form.10 9

19

10 9

b. – (– )23

49

= –11.6 + 14 The opposite of –14 is 14.

23

49

49

49

= + The opposite of – is .

Subtracting Real NumbersLESSON 1-5

Additional Examples

ALGEBRA 1

Simplify | –13 – (–21) |.

| –13 – (–21) | = | –13 + 21 |   The opposite of –21 is 21.

= | 8 | Add within absolute value symbols.

= 8 Find the absolute value.

Subtracting Real NumbersLESSON 1-5

Additional Examples

ALGEBRA 1

Evaluate x – (–y) for x = –3 and y = –6.

x – (–y) = –3 – [–(–6)] Substitute –3 for x and –6 for y.

= –3 – 6 The opposite of –6 is 6.

= –9 Subtract.

Subtracting Real NumbersLESSON 1-5

Additional Examples

ALGEBRA 1

The temperature in Montreal, Canada, at 6:00 P.M. was –8°F. Find the temperature at 10:00 P.M. if it fell 7°F.

Find the temperature at 10:00 P.M. by subtracting 7°F from the temperature at 6:00 P.M.

–8 – 7 = –8 + (–7) Add the opposite.

= –15 Simplify.

The temperature at 10:00 P.M. was –15°F.

Subtracting Real NumbersLESSON 1-5

Additional Examples

More Real World Examples

A football team gains 2 yd and then loses 7yd in two plays. You express a loss of 7 yd as -7. Use addition to find the result of the two plays.

2 + (-7) = -5 The result of the two plays is a loss of 5 yd

Try thisThe temperature falls 15 degrees and then rises 18 degrees. Use addition to find the change in temperature.

-15 + 18 = 3

There is a rise of 3 degrees

ALGEBRA 1

–5 11 –12

–1 7

Simplify each expression.

1. 7 – 12 2. 3 – (–8) 3. –7 – 5

Evaluate each expression for x = 3 and y = 4.

4. x – y 5. | – y – x| 6. | y – x – 5|

4

Subtracting Real NumbersLESSON 1-5 Ticket Out The Door (TOD)

ALGEBRA 1

Simplify.

1. 15 + (– 10) 2. – 57 + (– 11) 3. – 42 + 19

4. – 1 + (– 3 )

Evaluate each expression for x = –5.

5. – 11 + (– x)

6. 25 + 4x

5 –68 –23

–4 715

15

4 15

5

– 6

Adding Real NumbersLESSON 1-4 9/6/13 Warm Up

ALGEBRA 1P GAME PLAN

Date 9/6/13 Friday

Section / Topic

Notes: 1-4 & 1-5: Adding & Subtracting Real Numbers(Day 2)

Goal SWBAT add & subtract real numbers with fractions & decimals.

Algebra California Standard

1.0 Students identify and use the arithmetic properties of real numbers 2.0 Students understand and use such operations as taking the opposite

Homework Choose 2 problems from each set:P. 27 #13-24 P. 28 #25-27, 36, & 37P. 34 #13-20 P. 34-36 #38, 51, 55 & 61

Announcement

• Quiz Wednesday, 9/11

Find the sum.1) -2.304 + (-0.26)Line up the decimals and add (same

signs).-2.564

2) +58

34

Get a common denominator and subtract.

58

68

18

+

Find the difference.

3)5 3

9 5

35

59

2545

2745

245

Change subtraction to adding the opposite.

Get a common denominator.

Subtract and keep sign of the larger number.

+

Find the difference.

4)12

67

612 7

714

1214

514

Get a common denominator and subtract.

Change subtraction to adding the opposite.

_

+ -

Substitute for y: 6.32 - (-3.42)6.32 + 3.42

9.74

5) Evaluate 6.32 – y for y = -3.42

Find the solution6.5 – 9.3 = ?

Answer Now

A. -3.2B. -2.8C. 2.8D. 3.2

Find the solution

Answer Now

2 1 ?3 4

17

1112

512

37

A.

B.

C.

D.