Unit 4 Linear Equations, Inequalities and...
Transcript of Unit 4 Linear Equations, Inequalities and...
![Page 1: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/1.jpg)
Unit 4 – Linear Equations, Inequalities and Functions
Standards addressed in this unit:
1. Solve equations and inequalities arising from a context2. Solve equations and inequalities using algebraic manipulations
(More to come!)
![Page 2: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/2.jpg)
General MathUnit 4 – Day 1
Learning Targets
I can solve equations arising from a context by first drawing a model and then writing an equation to represent the context.
Mathematical Practices
Make sense of problems and persevere in solving themModel with mathematics
![Page 3: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/3.jpg)
Warm UpU4D1
32
4
3
y
xSimplify
![Page 4: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/4.jpg)
Concept Review U4D1
![Page 5: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/5.jpg)
Concept Review U4D1
![Page 6: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/6.jpg)
Concept Review U4D1
![Page 7: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/7.jpg)
Draw a model and solve
Stella has $11 more than Roland. Together they have $159. How much money does Stella have? How much money does Roland have?
ModelingU4D1
![Page 8: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/8.jpg)
Draw a model and solve
Modeling
Jared has twice as many DVDs as Eric. Together they have 51 DVDs. How many DVDs does Jared have? How many DVDs does Eric have?
U4D1
![Page 9: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/9.jpg)
Draw a model and solve
Modeling
The sum of three consecutive integers is 405. What are the three numbers?
U4D1
![Page 10: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/10.jpg)
Draw a model and solve
Modeling
For your birthday you received ten collectable Unicorns from a set of 100. If you use your allowance you can buy 2 more Unicorns every week.
How many weeks until you have collected all 100?
U4D1
![Page 11: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/11.jpg)
YOU TRY!Draw a model and solve
Modeling
A corn plant was 4 inches tall. It grew 1.5 inches a day and is now 22 inches tall. How many days did it take?
U4D1
![Page 12: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/12.jpg)
U4D1 – ICP
Do all BASIC PRACTICE
The odd problems in FURTHER PRACTICE
Pick two from MATH WORK
Pick one from BRAIN WORKS
Independent PracticeU4D1
![Page 13: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/13.jpg)
General MathUnit 4 – Day 2
Learning Targets
I can solve equations using algebraic manipulation
Mathematical Practices
Make sense of problems and persevere in solving themModel with mathematics
U4D2
![Page 14: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/14.jpg)
Bell Work
Get out U4D1 – ICP, make sure it is complete. Circle any problems you want to go over.
U4D2
![Page 15: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/15.jpg)
Warm Up
Kylie is addressing invitations to her party. She has already addressed 17 of them. She finishes the rest of them in 4
hours. If she addressed a total of 81 invitations, how many invitations did she address per hour?
U4D2
![Page 16: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/16.jpg)
Warm UpU4D2
![Page 17: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/17.jpg)
Solving Equations Using Algebra
When we solve an equation using algebra, we want to undo the
operations on the unknown in order to find out what it is.
Remember! Keep the equation balanced by doing the same thing on both sides!!!
Example:
Solve
U4D2
483 x
Explain the opposite of multiplication is division, etc…
![Page 18: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/18.jpg)
Solving Equations Using Algebra
Solve each equation
1.
2.
3.
U4D2
682 y
2039 w
232
p
Do first problem with class, have students do 2 & 3.
![Page 19: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/19.jpg)
Solving Two-Step Equations
What’s the first step in solving this equation? Why?
How about this one? Why?
U4D2
102
8
p
![Page 20: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/20.jpg)
Solving Two-Step Equations
Solve each equation
1.
2.
3.
U4D2
33096 y
863
p
43
10
a
Do first problem with class, have students do 2 & 3.
![Page 21: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/21.jpg)
Solving Multi-Step Equations
Let’s discuss the Distributive Property for a moment…
The Distributive Property says
Simplify
U4D2
)( cba
)3(2 x
![Page 22: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/22.jpg)
Solving Equations with the Distributive Property
What should we do first to solve this equation? Why?
U4D2
15)12(5 x
Explain we need both sides of equation as simplified as possible to make solving easier…
![Page 23: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/23.jpg)
Solving Equations with the Distributive Property
Solve each equation
1.
2.
3.
U4D2
21)4(7 x
15)4(3 x
10)42(55 xx
![Page 24: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/24.jpg)
Independent Practice
U4D2 - ICP
U4D2
![Page 25: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/25.jpg)
General MathU4D3
• Learning Targets: Solve Equations arising from a context.
Solve equations using algebraic manipulation.
![Page 26: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/26.jpg)
Warm Up
Do these problems on your participation page:
1. Simplify 2𝑥3 − 4𝑥𝑦2 + 17𝑥2 − 2𝑥2𝑦
2. Simplify −2𝑝4
−8𝑞2
2
3. Draw a model and solve: You and your friend have $29 for movies and snacks this weekend. You have $7 less than your friend. How much money do you each have?
U4D3
![Page 27: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/27.jpg)
Solving Equations
Follow these steps:
Step 1: Simplify both sides of the equation
This means getting rid of parentheses and combining like terms
Step 2: Get your variable “alone” using the reverse of PEMDAS
U4D3
![Page 28: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/28.jpg)
U4D3
![Page 29: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/29.jpg)
U4D3
![Page 30: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/30.jpg)
Solving Equations
Follow these steps:
Step 1: Simplify both sides of the equation.
This means getting rid of parentheses and combining like terms
IF YOU HAVE VARIABLES ON BOTH SIDES, NEXT:
Step 2: Get all variables to one side of equation.
Step 3: Get your variable alone.
U4D3
![Page 31: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/31.jpg)
U4D3
![Page 32: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/32.jpg)
U4D3
![Page 33: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/33.jpg)
Next Up!
• Writing equations arising from a context!
• Whoopee!
U4D3
![Page 34: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/34.jpg)
WORDS THAT MEAN ADDITION
SUMMORE THAN
PLUSADDED TO
INCREASED BY IN ALLTOTAL
U4D3
![Page 35: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/35.jpg)
WORDS THAT MEAN
SUBTRACTION
MINUS LESS THAN
DECREASED BYDIFFERENCE BETWEEN
HOW MANY FEWER
U4D3
![Page 36: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/36.jpg)
WORDS THAT MEAN MULTIPLICATION
TIMESOF
TWICEPRODUCT OF
IN EACHFOR EVERY
U4D3
![Page 37: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/37.jpg)
WORDS THAT MEAN
DIVISION
QUOTIENTRATIO OF
HOW MANY TIMESINTO HOW MANY
HOW MUCH DID EACH
U4D3
![Page 38: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/38.jpg)
WORDS THAT MEAN
EQUAL
ISTHE SAME ASEQUIVALENT
U4D3
![Page 39: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/39.jpg)
Write an equation and solve. Draw a model if necessary.
Two more than twice a number is 77.
Find the number.
U4D3
![Page 40: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/40.jpg)
Write an equation and solve. Draw a model if necessary.
The length of a rectangle is 50 meters. This is 6 meters more than twice the width. Find the
width of the rectangle.
U4D3
![Page 41: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/41.jpg)
Write an equation and solve. Draw a model if necessary.
Nine less than one-fourth of a number is 6. Find the number
U4D3
![Page 42: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/42.jpg)
You Try!
Write an equation and solve. Draw a model if necessary.
Twelve decreased by 8 times a number is 36. Find the number.
U4D3
![Page 43: Unit 4 Linear Equations, Inequalities and Functionsmiddleschoolatsage.weebly.com/.../u4d01-03_-_lesson.pdf · 2019-11-11 · Unit 4 –Linear Equations, Inequalities and Functions](https://reader034.fdocuments.us/reader034/viewer/2022042622/5f8c5d00b8b59b59cd0f4c47/html5/thumbnails/43.jpg)
Independent Practice
U4D3 – ICP
U4D3