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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