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## PowerPoint Slideshow about ' Big Idea #3' - ahava

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### Big Idea #3

### Why Do I Need to Know This?(Motivation and Real World Applications)

### Above and Below Sea Level

### Vocabulary Words That You Need to Know

### Principles/Hypothesis Formed

### Principle

### What is -2 - -7?

### What is 5 - 7?

### What is 3 - -9?

### What is -5 - - 4?

### Principle

### Why does a positive times a negative equal a negative?

### But why does a negative times a negative equal a positive?

### Principle

### Why Do I Need to Know This?(Motivation and Real World Applications)

### Above and Below Sea Level

Develop an understanding of operations of all rational numbers and solving linear equations

Benchmarks

» MA.7.A.3.1: Use and justify the rules for adding, subtracting, multiplying, dividing, and finding the absolute value of integers.

Depth of Knowledge: Moderate Date Adopted or Revised: 09/07

» MA.7.A.3.2: Add, subtract, multiply, and divide integers, fractions, and terminating decimals, and perform exponential operations with rational bases and whole number exponents including solving problems in everyday contexts.

Depth of Knowledge: Moderate Date Adopted or Revised: 09/07

» MA.7.A.3.3: Formulate and use different strategies to solve one-step and two-step linear equations, including equations with rational coefficients.

Depth of Knowledge: Moderate Date Adopted or Revised: 09/07

» MA.7.A.3.4: Use the properties of equality to represent an equation in a different way and to show that two equations are equivalent in a given context.

Depth of Knowledge: Moderate Date Adopted or Revised: 09/07

Thesis Statement

http://www.neirtec.org/activities/applets/numberline.htm

- The purpose of this lesson is to work on Big Idea #3 from the 7th grade Next Generation Sunshine State Standards (NGSSS).
- It says,
- MA.7.A.3.1: Use and justify the rules for adding, subtracting, multiplying, dividing, and finding the absolute value of integers.
- This lesson will be divided into 3 parts
- How we’ve been taught and How we are teaching. (2 Hours)
- Hands-on Math and the CRA Sequence of Instruction (2 Hours)
- A Process Does not Always Tell Us Why. (2 Hours)

http://www.labsafety.com/images/xl/Weather-Thermometer-40-to-LSS_i_LBM37561Z.jpg

In Chemistry

.

For example:

electrons – negative charge

Protons – positive charge

neutrons – neutral charge

The World’s Tallest Building

H

http://img.dailymail.co.uk/i/pix/2007/07_02/WorldsTallestDM_468x525.jpg

Mariana Trent

-10,916

Mount Everest

29,035

http://www.thetravelpeach.com/asia-vacations/everest-mount.jpg

http://www.treehugger.com/mariana%20trench.jpg

The U.S. National Debt

U.S. NATIONALDEBTCLOCK

The Outstanding Public Debt as of 09 Jan 2010 at 01:30:59 PM GMT is:

http://www.brillig.com/debt_clock/

Floors on Elevators

An elevator panel with NEGATIVE numbers.

Addends, Sum, Minuend, Subtrahend, Difference, Factors, Products, Divisor, Dividend, Quotient, Mixed/Multiple Signs

Adding Using Mixed/Multple

Signs

Mixed/Multiple Signs

Mixed/Multiple Signs exist when two signs are together.

An addition and a positive ++

An addition and a negative +-

A subtraction and a positive - +

A subtraction and a negative - -

These problems are not difficult, they just need to be solved a little differently.

When adding two integers and the signs are alike, you add and keep the sign.

2. When adding two integers and the signs are not alike, you subtract and take the largest numbers absolute value.

Subtracting Using Mixed/Multple

Signs

When subtracting two integers, you keep the minuend, change the subtraction symbol to an addition symbol, and change the sign of the subtrahend to its opposite.

Keep

Change

Change

Keep -2

Take the opposite of -7

What is -2 + +7?

Start Here

7

The Answer is 5.

Keep 5

Take the opposite of 7

What is 5 + -7?

Principle: When adding two integers, and the signs are not alike, you subtract and take the sign of the largest numbers absolute value.

The Answer is -2.

addition

Keep 3

Take the opposite of -9

What is 3 + 9 ?

Principle: When adding two integers, and the signs are the same, you add and keep the sign.

The Answer is 12.

Keep -5

Take the opposite of -4

What is -5 + 4?

Principle: When adding two integers, and the signs are not alike, you subtract and take the sign of the largest numbers absolute value.

The Answer is -1.

When multiplying two integers and the signs are alike, the product is positive.

(+)(+) = (+)

(-)(-) = (+)

When multiplying two integers and the signs are not alike, the product is negative.

(+)(-) = (-)

(-)(+) = (-)

The Answer is -4.

So a positive times a negative is a negative.

Look at the pattern

4 • 3 = 12

4 • 2 = 8

4 • 1 = 4

4 • 0 = 0

4 • -1 = ?

Well, knowing a positive times a negative is a negative, also means that a negative times a positive is a negative, so again…

The Answer is 4.

So a negative times a negative is a positive.

-4 • 3 = -12

-4 • 2 = -8

-4 • 1 = -4

-4 • 0 = 0

-4 • -1 = ?

Look at the pattern

Dividing Integers

When multiplying two integers and the signs are alike, the product is positive.

(+)/(+) = (+)

(-)/(-) = (+)

When multiplying two integers and the signs are not alike, the product is negative.

(+)/(-) = (-)

(-)/(+) = (-)

Floors on Elevators

This is an elevator panel with NEGATIVE numbers.

How far many floors have you gone up if you start at the lowest floor and go to the highest floor?

Set up the expression

Explain your reasoning

Solve the problem

Answer: 17-(-2) =

19 floors

The World’s Tallest Building

How much taller is The Burj Dubai compared to The Empire State Building?

Answer: 512 – 381 = 131 meters

http://img.dailymail.co.uk/i/pix/2007/07_02/WorldsTallestDM_468x525.jpg

The U.S. National Debt

U.S. NATIONALDEBTCLOCK

The Outstanding Public Debt as of 09 Jan 2010 at 01:30:59 PM GMT is:

http://www.brillig.com/debt_clock/

If the government taxed each American $40, 068.00, approximately how many Americans would it require to pay to off our National Debt?

Answer: -12,287,322,881,897 ÷ -40,068.00 ≈ 306,666,778 Americans

What is the difference between the lowest and the highest temperature reading on the thermometer?

Answer: 120 – (-40) = 160°F

http://www.labsafety.com/images/xl/Weather-Thermometer-40-to-LSS_i_LBM37561Z.jpg

What is the difference between the highest point above sea level and the lowest point below sea level?

Mount Everest

29,035

http://www.thetravelpeach.com/asia-vacations/everest-mount.jpg

Mariana Trent

-10,916

Answer: 29,035 – (-10,916) = 39,951

http://www.treehugger.com/mariana%20trench.jpg

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