Transcript 6th_MA_AF_1.1_ONE_STEP_EQUATION_DW

Name _____________________
Learning Objective
Today, we will solve1 one-step equations.
1
find the answer
CFU
What are we going to do today?
What does solve mean? Solve means to ______.
Inverse Operations
Activate (or provide) Prior Knowledge

Inverse operations are operations that undo each other.
● and
and

÷
What operation would undo the change in value?
1.)
3.)
628
8  26
4  3  12
12 ÷ 3  4
2.)
4.)
10  3  7
7  3  10
15  5 = 3
3 × 5  15
CFU
Students, you already know how to use inverse operations to undo a change in value.
Today, we will solve one-step equations using inverse operations.
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
6th Grade Algebra and Functions 1.1 (6Q)
Write and solve one-step linear equations in one variable.
Lesson to be used by EDI-trained teachers only.
Concept Development
A one-step equation contains2 one operation.
2
has within it
x23
Inverse Operations
x
 1
4
addition
division

and
● and

÷
requires3
A one-step equation
one inverse operation to solve for the variable.
• To keep an equation balanced, inverse operations must be done on both sides of the equation.
3
needs
Solving One-Step Equations
x  2  3
Inverse Operation − 2 − 2
x  1
Inverse Operation
Balance
Clarification and CFU:
Solving One-Step Equations
x
 1●4
4●
4
x  1
Go to Skill
Dev. #1
Balance
Go to Skill
Dev. #2
The solution is the value of the variable that makes the equation true.
Checking a Solution
x23
Solution
x1
x23
?
(1)  2  3
3  3 True
CFU #1
Which inverse operations would be used to solve the one-step
equation x − 4  6? How do you know?
A Addition
What is the difference between the solution (x  1) and non-solution (x  4)?
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
x4
x23
?
(4)  2  3
6  3 False
CFU #2
Which inverse operations would be used to solve the one-step
equation 4x  8? How do you know?
B Subtraction
DataWORKS Educational Research
NOT a Solution
A Multiplication
B Division
Flashcards:
Inverse Operations
6th Grade Algebra and Functions 1.1 (6Q)
Write and solve one-step linear equations in one variable.
Lesson to be used by EDI-trained teachers only.
Concept Development (Clarification and CFU)
A one-step equation requires one inverse operation to solve for the variable.
• To keep an equation balanced, inverse operations must be done on both sides of the equation.
The solution is the value of the variable that makes the equation true.
x 2
2
x
3 2



Inverse Operations

and
● and

÷
5
2
3
5
x
CFU
Why is 2 subtracted on both sides of the equation?
Why is 1 the solution to the equation x + 2 = 3?
Return to
Concept
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
6th Grade Algebra and Functions 1.1 (6Q)
Write and solve one-step linear equations in one variable.
Lesson to be used by EDI-trained teachers only.
Skill Development/Guided Practice #1
A one-step equation requires one inverse operation to solve for the variable.
• To keep an equation balanced, inverse operations must be done on both sides of the equation.
The solution is the value of the variable that makes the equation true.
Inverse Operations

Solve one-step equations.
and
● and
Step #1: Read the problem and connect it to the equation.
Step #2: Solve for the variable. Hint: Use the inverse operation.
Step #3: Check and interpret the solution. (Answer the question.)
1. Isabella is baking muffins. The recipe calls for 8
cups of sugar. Isabella has already added 3 cups of
sugar. How many more cups of sugar does she
need to add?
c 3 8
c+3=8
3 3
5+3=8
c5
8=8

÷
2. Yesterday, Samuel had $7. He was given more
money today and now has $10. How much money
was Samuel given today?
m + 7 = 10
m  7  10
3 + 7 = 10
7 7
10 = 10
m3
5 cups of sugar
Isabella needs to add ______________________.
Samuel was given ___________________
today.
$3
3. Shannon had some money in her pocket. She spent
$4 of it on school supplies. She now has $11. How
much money did she start with?
4. Jessie had a handful of marbles. He gave 5 of them
away and now has 8. How many marbles did Jessie
start with?
m  4  11
4 4
m  15
m  4 = 11
15  4 = 11
11 = 11
$15
Shannon started with ______________________.
CFU
(#1) How did I/you connect the problem to the equation?
(#2) How did I/you solve for the variable?
(#3) How did I/you interpret the solution?
m 5  8
55
m  13
m5=8
13  5 = 8
8= 8
13 marbles
Jessie started with ______________________.
Return to
Concept
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
6th Grade Algebra and Functions 1.1 (6Q)
Write and solve one-step linear equations in one variable.
Lesson to be used by EDI-trained teachers only.
Skill Development/Guided Practice #2
A one-step equation requires one inverse operation to solve for the variable.
• To keep an equation balanced, inverse operations must be done on both sides of the equation.
The solution is the value of the variable that makes the equation true.
Inverse Operations

Solve one-step equations.
and
● and
Step #1: Read the problem and connect it to the equation.
Step #2: Solve for the variable. Hint: Use the inverse operation.
Step #3: Check and interpret the solution. (Answer the question.)
1. Binders cost $2 each. If Miguel has $12, how many
binders can he buy?
2b  12
2
2
b6
3. Isabella gave out muffins to her 6 friends. If each
friend was given 4 muffins, how many muffins did
Isabella give out?
m
m
4 ● 6 ● 4
4
m  24
2. A box of pencils has 6 pencils inside. If Rosalina has
24 pencils, how many pencils are in each box?
6b  24
2b = 12
2(6) = 12
12 = 12
6 binders
Miguel can buy ______________________.
6
4
24
6
4
6=6
24 muffins
Isabella gave out ______________________.

÷
6
6
b4
6b = 24
6(4) = 24
24 = 24
4 pencils in each box
There are ______________________.
4. Ricky and his two friends earned money doing
chores for his neighbor. After splitting the money,
they each got $7, how much money did they earn
m
together?
7
m
3
3 ● 7 ● 3
3
m  21
21
7
3
7=7
$21
Ricky and his friends earned ___________________.
CFU
(#1) How did I/you connect the problem to the equation?
(#2) How did I/you solve for the variable?
(#3) How did I/you interpret the solution?
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
6th Grade Algebra and Functions 1.1 (6Q)
Write and solve one-step linear equations in one variable.
Lesson to be used by EDI-trained teachers only.
Relevance
A one-step equation requires one inverse operation to solve for the variable.
• To keep an equation balanced, inverse operations must be done on both sides of the equation.
The solution is the value of the variable that makes the equation true.
1. Solving one-step equations will help you solve more complex equations.
5x – 6 = 4
+6+6
5x = 10
5 5
x=2
2. Solving one-step equations will help you do well on tests.
CFU
Does anyone else have another reason why it is relevant to solve one-step equations? (pair-share) Why is it relevant to solve one-step
equations? You may give me one of my reasons or one of your own. Which reason is more relevant to you? Why?
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
6th Grade Algebra and Functions 1.1 (6Q)
Write and solve one-step linear equations in one variable.
Lesson to be used by EDI-trained teachers only.
A one-step equation requires one inverse operation to solve for the variable.
• To keep an equation balanced, inverse operations must be done on both sides of the equation.
The solution is the value of the variable that makes the equation true.
Skill Closure
Inverse Operations

and
● and
Solve one-step equations.

÷
Step #1: Read the problem and connect it to the equation.
Step #2: Solve for the variable. Hint: Use the inverse operation.
Step #3: Check and interpret the solution. (Answer the question.)
1. Angelina needs to save $20. She has already saved
$9. How much more money does Angelina need to
save?
m  9  20
9 9
m  11
m + 9 = 20
11 + 9 = 20
20 = 20
2. A can of tennis balls has 3 tennis balls inside. If
Frank has 18 tennis balls, how many cans of tennis
balls does he have?
3c = 18
3c  18
3(6) = 18
3
3
18 = 18
b6
$11
Angelina needs to save ______________________.
6 cans of tennis balls
Frank has ______________________.
Constructed Response Closure
m2=6
Sam’s solution
m 8
Sam is trying to solve the equation on the left. After applying one inverse operation, his
solution was m = 8. Explain why his solution is incorrect and what possible error he
may have made.
______________________________________________________________________
______________________________________________________________________
Summary Closure
What did you learn today about solving one-step equations?
Day 1 ______________________________________________________________________
Day 2 ______________________________________________________________________
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
6th Grade Algebra and Functions 1.1 (6Q)
Write and solve one-step linear equations in one variable.
Lesson to be used by EDI-trained teachers only.
Independent Practice
Name _________________________
A one-step equation requires one inverse operation to solve for the variable.
• To keep an equation balanced, inverse operations must be done on both sides of the equation.
The solution is the value of the variable that makes the equation true.
Inverse Operations

Solve one-step equations.
Step #1: Read the problem and connect it to the equation.
Step #2: Solve for the variable. Hint: Use the inverse operation.
Step #3: Check and interpret the solution. (Answer the question.)
1. Gabriel is baking cookies. The recipe calls for 6
cups of flour. If Gabriel has already added 2 cups
of flour, how much more flour does he need to
add?
c 26
2 2
c4
3. Books cost $5 each. If Mathew has $35, how many
books can he buy?
5b  35
5
5
b7
● and
5b = 35
5(7) = 35
35 = 35
7 books
Mathew can buy ______________________.

÷
2. Louisa had a handful of nickels. She gave 8 of them
away and now has 4. How many nickels did Louisa
start with?
n 8  4
c+2=6
4+2=6
6=6
4 cups of flour
Gabriel needs to add ______________________.
and
88
n  12
n8=4
12  8 = 4
4=4
12 nickels
Louisa started with ______________________.
4. Jenny and her 4 friends earned money selling sugar
free lemonade. After splitting the money, they each
got $9. How much money did they earn together?
5●
m
9 ● 5
5
m  45
m
9
5
45
9
5
9=9
$45
Jenny and her friends earned ___________________.
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
6th Grade Algebra and Functions 1.1 (6Q)
Write and solve one-step linear equations in one variable.
Lesson to be used by EDI-trained teachers only.
Periodic Review 1
Name _________________________
A one-step equation requires one inverse operation to solve for the variable.
• To keep an equation balanced, inverse operations must be done on both sides of the equation.
The solution is the value of the variable that makes the equation true.
Inverse Operations

Solve one-step equations.
Step #1: Read the problem and connect it to the equation.
Step #2: Solve for the variable. Hint: Use the inverse operation.
Step #3: Check and interpret the solution. (Answer the question.)
and
● and

÷
1. Carmella is baking biscuits. The recipe calls for 11
cups of flour. She has already added 6 cups. How
much does she still have to add?
2. Fernando is building a bookshelf. He has used 26
pieces. He has 12 of the pieces left. How many
pieces does the bookshelf have?
f  6  11
p  26  12
6 6
c5
c + 6 = 11
5 + 6 = 11
11 = 11
5 cups of flour
Carmella needs to add ______________________.
3. Claire made 6 batches of meatballs. She made a
total of 48 meatballs. How many meatballs does
each batch make?
6m  48
6
6
b8
6m = 48
6(8) = 48
48 = 48
8 meatballs
Claire made ______________________.
 26  26
n  38
n – 26 = 12
38  26 = 12
12 = 12
38 pieces
The bookshelf has ______________________.
4. Tyrone and his three friends are going to split a box
of crackers. They each get 14 crackers. How many
crackers were in the box?
4●
c
 14 ● 4
4
m  56
c
 14
4
56
 14
4
14 = 14
There were ______________________.
56 crackers in the box
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
6th Grade Algebra and Functions 1.1 (6Q)
Write and solve one-step linear equations in one variable.
Lesson to be used by EDI-trained teachers only.
Periodic Review 2
Name _________________________
A one-step equation requires one inverse operation to solve for the variable.
• To keep an equation balanced, inverse operations must be done on both sides of the equation.
The solution is the value of the variable that makes the equation true.
Inverse Operations

Solve one-step equations.
Step #1: Read the problem and connect it to the equation.
Step #2: Solve for the variable. Hint: Use the inverse operation.
Step #3: Check and interpret the solution. (Answer the question.)
1. Larissa has 17 dollars. She gets her allowance.
Now she has 28 dollars. How much was her
allowance?
17  a  28
 17
 17
a  11
3. Geoffrey earns $7 for mowing lawns. Last month,
he earned $42. How many lawns did he mow?
7m  42
7
7
b6
● and
7m = 42
7(6) = 42
42 = 42
6 lawns
Geoffrey mowed ______________________.

÷
2. A set of colored pencils has 45 pencils taken out.
There are currently 29 pencils left. How many
pencils were there originally?
p  45  29
17 + a = 28
17 + 11 = 28
28 = 28
$11
Larissa’s allowance is ______________________.
and
 45  45
n  74
p  45 = 29
74  45 = 29
29 = 29
pencils in the set originally.
There were 74
__________________
4. Thomas and his 5 friends made cookies. They
shared them equally and each got 13. How many
cookies did they make altogether?
6●
c
 13 ● 6
6
c  78
m
 13
6
78
 13
6
13 = 13
78 cookies
Thomas and his friends made __________________.
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
6th Grade Algebra and Functions 1.1 (6Q)
Write and solve one-step linear equations in one variable.
Lesson to be used by EDI-trained teachers only.
Periodic Review 3
Name _________________________
A one-step equation requires one inverse operation to solve for the variable.
• To keep an equation balanced, inverse operations must be done on both sides of the equation.
The solution is the value of the variable that makes the equation true.
Inverse Operations

Solve one-step equations.
Step #1: Read the problem and connect it to the equation.
Step #2: Solve for the variable. Hint: Use the inverse operation.
Step #3: Check and interpret the solution. (Answer the question.)
1. Estevan worked on his English homework for 25
minutes. He finished all his homework in 57
minutes. How long did it take him to finish the rest
of his homework?
25  h  57
 25
 25
h  32
3. Javier can make 7 paper airplanes each hour. If he
made 28 airplanes, how long did he spend making
them?
7a  28
7
7
a4
● and
7a = 28
7(4) = 28
28 = 28
4 hours making airplanes
Javier spent ______________________.

÷
2. Elizabeth had several colored pencils. She gave out
14 of them to her friends and how has 13. How many
pencils did she start with?
c 14  13
25 + h = 57
25 + 32 = 57
57 = 57
32 minutes
It took Estevan ______________________.
and
 14  14
c  27
c  14 = 13
27  14 = 13
13 = 13
27 pencils
Elizabeth had ______________________.
4. Adolfo and his six friends earn money doing yard
work. After splitting up the money, they each got 15
dollars. How much money did they earn together?
7●
y
 15 ● 7
7
y  105
y
 15
7
105
 15
7
15 = 15
$105
Adolfo and his friends earned ___________________.
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
6th Grade Algebra and Functions 1.1 (6Q)
Write and solve one-step linear equations in one variable.
Lesson to be used by EDI-trained teachers only.
Blank Page
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
6th Grade Algebra and Functions 1.1 (6Q)
Write and solve one-step linear equations in one variable.
Lesson to be used by EDI-trained teachers only.
Concept Development (Flashcard 1 of 6)
A one-step equation requires one inverse operation to solve for the variable.
x47
What is the operation of the equation?
Subtraction
What inverse operation would be used to
solve the equation? How do you know?
Addition
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
6th Grade Algebra and Functions 1.1 (6Q)
Write and solve one-step linear equations in one variable.
Lesson to be used by EDI-trained teachers only.
Concept Development (Flashcard 2 of 6)
Return to
Concept
A one-step equation requires one inverse operation to solve for the variable.
x63
What is the operation of the equation?
Addition
What inverse operation would be used to
solve the equation? How do you know?
Subtraction
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
6th Grade Algebra and Functions 1.1 (6Q)
Write and solve one-step linear equations in one variable.
Lesson to be used by EDI-trained teachers only.
Concept Development (Flashcard 3 of 6)
A one-step equation requires one inverse operation to solve for the variable.
5x  25
What is the operation of the equation?
Multiplication
What inverse operation would be used to
solve the equation? How do you know?
Division
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
6th Grade Algebra and Functions 1.1 (6Q)
Write and solve one-step linear equations in one variable.
Lesson to be used by EDI-trained teachers only.
Concept Development (Flashcard 4 of 6)
A one-step equation requires one inverse operation to solve for the variable.
x
2
8
What is the operation of the equation?
Division
What inverse operation would be used to
solve the equation? How do you know?
Multiplication
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
6th Grade Algebra and Functions 1.1 (6Q)
Write and solve one-step linear equations in one variable.
Lesson to be used by EDI-trained teachers only.
Concept Development (Flashcard 5 of 6)
A one-step equation requires one inverse operation to solve for the variable.
x78
What is the operation of the equation?
Addition
What inverse operation would be used to
solve the equation? How do you know?
Subtraction
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
6th Grade Algebra and Functions 1.1 (6Q)
Write and solve one-step linear equations in one variable.
Lesson to be used by EDI-trained teachers only.
Concept Development (Flashcard 6 of 6)
Return to
Concept
A one-step equation requires one inverse operation to solve for the variable.
7x  49
What is the operation of the equation?
Multiplication
What inverse operation would be used to
solve the equation? How do you know?
Division
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
6th Grade Algebra and Functions 1.1 (6Q)
Write and solve one-step linear equations in one variable.
Lesson to be used by EDI-trained teachers only.
EDI – Cognitive, Teaching and English Learners Strategies
Learning Objective : Today, we will solve one-step equations.
Cognitive Strategies
Teaching Strategies
Elaboration
Demonstration
Targeted vocabulary: solve, inverse operations, contains, requires
Language Strategies
Vocabulary Words
Academic
solve, contains, requires
Content
inverse operations
Support
Multiple-Meaning
Vocabulary
Strategy
Synonym
requires
Definition
solve, inverse operations, contains
Homophone
Internal Context Clue
Listen, Speak
Read
Similar Sounds
Tracked Reading
Decoding Rules
Write
Writing
Content Access Strategies
Comprehensible
Input
Cognates
Graphic Organizer
Contextual Clues
Contextualized
Definitions
Pictures
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
6th Grade Algebra and Functions 1.1 (6Q)
Write and solve one-step linear equations in one variable.
Lesson to be used by EDI-trained teachers only.
Blank Page
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
6th Grade Algebra and Functions 1.1 (6Q)
Write and solve one-step linear equations in one variable.
Lesson to be used by EDI-trained teachers only.