Transcript Algebra I - Denise Kapler

Skill Mastery
Homework
Problem Solving
Word Problems
Project Work
Collaboration
Portfolio Problems
Think about
•What you know
•Look things up
•Share ideas
•Use your imagination!
Skill Mastery
Coursework includes Homework
 Name
 Date
 Neat and Organized
Title: Homework # ; Page from Book
 Work shown as appropriate
6 Steps to
Solving a Word Problem
1.
2.
3.
4.
Draw a picture
State given
State unknown
Develop relationship
between given and unknown
5. Solve
6. Answer in a complete
sentence
1. Draw
Write
2. What do you know
-from inside problem
-from outside problem
3. What is the unknown
-what do you need to
find
4. What is the relationship
between the known and unknown
Find
5. Solve
-Substitution
-Cross Products
-GEMDAS
-Properties of Real Numbers
Property of Distribution
Property of Equality – what you do to one
side you do to another
-Collect and Combine Like Terms
-Isolate the variable
Think !!!
6. Answer
–Does answer make sense, is it reasonable?
–Check if correct (plug back in)
–Check units
–Write in a complete sentence
Project Work
1. Each student begins to solve the problem.
5
2. Join into Cooperative Groups
Minutes
3. Each student does a Problem Write-up.
Project Work
1. Each student begins to solve the problem.
2.
Write two sentences about what you tried.
Stand up when finished.
Share with group.
Join into Cooperative Groups
Minutes
3. Each student does a Problem Write-up.
Project Work
1. Each student begins to solve the problem.
2. Join into Cooperative Groups 10
a. Poster: create 3 sections Each member has a different color
marker. Work on Section 1. Then discuss and complete 2.
- Section 1 Problem Summary and Title
Group Member Names Date
- Section 2 Area for each member and group work
- Section 3 Final Answer
b. Collaboration – 1 person stays, others gather ideas.
c. As a group, determine final answer.
d. On the back of the Poster write:
Explain how your group solved the problem.
Explain how your group knows your answer is correct.
e. Sharing Circle
Each group states their answer
One group that is sure starts the discussion
3. Each student does a Problem Write-up.
Minutes
Project Work
1. Each student begins to solve the problem.
2. Join into Cooperative Groups
a. Poster with 3 sections Each member has a different color marker.
- Section 1 Problem Title Group Members Date
- Section 2 Area for each member work and group work
- Section 3 Final Answer
b. Collaboration – 1 person stays, others gather ideas 3
Example: How did you begin?
What strategy are you using to solve it?
Why did you choose this approach?
b. As a group, determine final answer.
c. On the back of the Poster write:
e. Sharing Circle
Each group states their answer
One group that is sure starts the discussion
3. Each student does a Problem Write-up.
Minutes
Project Work
1. Each student begins to solve the problem.
2. Join into Cooperative Groups
a. Poster with 3 sections Each member has a different color marker.
- Section 1 Title Group Members Date
- Section 2 Area for each member work and group work
- Section 3
Final Answer – Complete this section
b. Collaboration – 1 person stays, others gather ideas.
c. As a group, determine final answer. 5
d. Write on the back of the Poster:
Explain how your group began to solve the problem.
Explain how your group knows your answer is correct.
We started by ….
Then we .... (use this as many times as needed)
We found our answer by .....
We verified our answer by checking ….
e. Sharing Circle
3. Each student does a Problem Write-up.
Minutes
Project Work
1. Each student begins to solve the problem.
2. Join into Cooperative Groups
a. Poster with 3 sections Each member has a different color marker.
- Section 1 Title Group Members Date
- Section 2 Area for each member work and group work
- Section 3 Final Answer
b. Collaboration – 1 person stays, others gather ideas.
c. As a group, determine final answer.
d. Write on the back of the Poster:
1. Explain how your group began to solve the problem.
2. Explain how your group knows your answer is correct.
We started by ….
Then we .... (use as many times as needed)
We found our answer by .....
We verified our answer by checking ….
Minutes
e. Sharing Circle
3. Each student does a Problem Write-up.
Project Work
1. Each student begins to solve the problem.
2. Join into Cooperative Groups
a. Poster with 3 sections Each member has a different color marker.
- Section 1 Title Group Members Date
- Section 2 Area for each member work and group work
- Section 3 Final Answer
b. Collaboration – 1 person stays, others gather ideas.
c. As a group, determine final answer.
d. On the back of the Poster write:
Explain how your group solved the problem.
Explain how your group knows your answer is correct.
e. Sharing Circle
Each group states their answer
One group that is sure starts the discussion
3. Each student does a Problem Write-up.
Project Work
1. Each student begins to solve the problem.
2. Join into Cooperative Group
a. Poster with 3 sections Each member has a different color marker.
- Section 1 Title Group Members Date
- Section 2 Area for each member work and group work
- Section 3 Final Answer
b. Collaboration – 1 person stays, others gather ideas.
c. As a group, determine final answer.
d. On the back of the Poster write:
Explain how your group solved the problem.
Explain how your group knows your answer is correct.
e. Sharing Circle
Each group states their answer
One group that is sure starts the discussion
3. Individual Problem Write-up
Summary of group work and answer.
Each student writes up his or her solution to the problem.
Write up includes an explanation of why you did each step.
Portfolio Problem
On front
Upper Right: Name, Title and Design
Lower Right: Homeroom Teacher
On inside
Worksheet
Do your best work
1. Think carefully
2. Write neatly, use a ruler
3. Share ideas with others
4. Each student solves
5. Compare your solution
6. Strive for exemplary!
Show Work
Draw
Graph – 4 Steps
Solve
6 Steps to Solve a Word Problem
Solve for
x
x is the unknown number
x is the variable
Remember
You can only do four operations to a number.
1. Add
2. Subtract
are inverses
3. Multiply
4. Divide
are inverses
Addition combines numbers
Subtraction is the addition of the opposite sign
Multiplication is repeated addition
Division is repeated subtraction
Exponents are repeated multiplication x2 = x * x
The inverse of using exponential powers is to
take the radical.
x =x
2
Solve for x
1st Write the equation
2nd Think
Ask yourself: What do I do next?
3rd Begin
4th Isolate the variable
5th After each step, ask yourself:
What do I do next?
6th Check your answer by substituting
back into your equation
Steps to Solve for x.
Isolate the variable by following these 3 steps
1. Work one side, then the other. Collect and combine like terms.
2. Work across the sign. Collect and combine like terms.
3. Keep the = down the center of your work
Use the Properties of Real Numbers
Property of Equality (Substitution – replace objects of = value)
Property of Distribution
Commutative Property
Associative Property
Follow the Order of Operation: GERMDAS
G
grouping symbols
ER
exponents
radicals
MD
multiplication division
AS
addition
subtraction
Steps to Solve for x.
Work carefully
Be careful of your signs
Mind the exponential powers of your variables. x2 =x *x ; x= x1
Distribute to each term
Remember Mathematicians are Lazy!
Many things in math are not written.
Example: -x = -1 x x1 and x = 1* x1
Some concepts have many symbols
Example multiply times x *
2(x+1)
6x
Check your answer – substitute answer back in; check units
THINK. Does your answer make sense?
-x