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# Big Idea #3 - PowerPoint PPT Presentation

Big Idea #3. 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.

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### Big Idea #3

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)

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

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

### Above and Below Sea Level

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.

### Vocabulary Words That You Need to Know

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

Start Here

4

The Answer is 2.

Start Here

2

The Answer is 0.

### What is -1 - 2?

Start Here

2

The Answer is -3.

### What is +5 + 4?

Start Here

What do you think?

The Answer is 9.

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.

### What is +2 + -4?

Start Here

4

The Answer is -2.

### What is -5 + +1?

Start Here

1

The Answer is -4.

### What is -3 + -4?

Start Here

4

What do you think?

The Answer is -7.

### What is +4 + +2?

Start Here

2

I bet you know this one.

The Answer is 6.

### Principles/Hypothesis Formed

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.

### Principle

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

Change to addition

Keep -2

Take the opposite of -7

### What is -2 - -7?

What is -2 + +7?

Start Here

7

The Answer is 5.

Change to addition

Keep 5

Take the opposite of 7

### What is 5 - 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.

Change to

addition

Keep 3

Take the opposite of -9

### What is 3 - -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.

Change to addition

Keep -5

Take the opposite of -4

### What is -5 - - 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.

### Principle

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.

(+)(-) = (-)

(-)(+) = (-)

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

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

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

### Principle

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

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

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

### Above and Below Sea Level

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