big idea #3
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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
Protons – positive charge
neutrons – neutral charge
.
electrons – negative charge
For example:
The World’s Tallest Building
H
http://img.dailymail.co.uk/i/pix/2007/07_02/WorldsTallestDM_468x525.jpg
Above and Below Sea Level
http://www.treehugger.com/mariana%20trench.jpghttp://www.thetravelpeach.com/asia-vacations/everest-mount.jpg
Mariana Trent-10,916
Mount Everest29,035
The U.S. National Debt
U.S. NATIONAL DEBT CLOCK 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
Teaching Using Direction
What is -2 + 4?
Start Here
4
The Answer is 2.
What is -2 + 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
The Answer is 9.
…
What do you think?
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.
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
The Answer is -7.
…
What do you think?
What is +4 + +2?
Start Here
2
The Answer is 6.I bet you know this one.
Principles/Hypothesis Formed
1. 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
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.
KeepChange Change
What is -2 - -7?
Start Here
7
The Answer is 5.
Keep -2 Change to addition
Take the opposite of -7
What is -2 + +7?
What is 5 - 7?
The Answer is -2.
Keep 5 Change to addition
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.
What is 3 - -9?
The Answer is 12.
Keep 3 Change to addition
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.
What is -5 - - 4?
The Answer is -1.
Keep -5 Change to addition
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.
Multiplying Integers
Principle
1. When multiplying two integers and the signs are alike, the product is positive.
(+)(+) = (+) (-)(-) = (+)
2. When multiplying two integers and the signs are not alike, the product is negative.
(+)(-) = (-) (-)(+) = (-)
Why does a positive times a negative equal a negative?
4 • 3 = 124 • 2 = 8 4 • 1 = 44 • 0 = 0
4 • -1 = ?Look at th
e patternThe Answer is -4.
So a positive times a negative is a negative.
But why does a negative times a negative equal a positive?
-4 • 3 = -12-4 • 2 = -8 -4 • 1 = -4-4 • 0 = 0
-4 • -1 = ?Look at the pattern
The Answer is 4.
So a negative times a negative is 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…
Dividing Integers
Principle
1. When multiplying two integers and the signs are alike, the product is positive.
(+)/(+) = (+) (-)/(-) = (+)
2. When multiplying two integers and the signs are not alike, the product is negative.
(+)/(-) = (-) (-)/(+) = (-)
Bring it All Together
Floors on ElevatorsThis 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?
(1)Set up the expression(2)Explain your reasoning(3)Solve the problem
Answer: 17-(-2) = 19 floors
The World’s Tallest Building
http://img.dailymail.co.uk/i/pix/2007/07_02/WorldsTallestDM_468x525.jpg
How much taller is The Burj Dubai compared to The Empire State Building?
Answer: 512 – 381 = 131 meters
The U.S. National Debt
U.S. NATIONAL DEBT CLOCK 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)
http://www.labsafety.com/images/xl/Weather-Thermometer-40-to-LSS_i_LBM37561Z.jpg
What is the difference between the lowest and the highest temperature reading on the thermometer?
Answer: 120 – (-40) = 160°F
Above and Below Sea Level
http://www.treehugger.com/mariana%20trench.jpg
http://www.thetravelpeach.com/asia-vacations/everest-mount.jpg
Mariana Trent-10,916
Mount Everest29,035
What is the difference between the highest point above sea level and the lowest point below sea level?
Answer: 29,035 – (-10,916) = 39,951