1 Algebra Problem Solving with the new Common Core Standards Join Bill as he uses the Common Core Standards and builds excitement, enthusiasm, and problem-solving skills with FREE easily customized activities. Complete Ready-for-Monday handout available. ************* An Online Resource Manual for Math Teachers Incorporating the Common Core Standards

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5 Standards for Mathematical Practices Describe habits of mind of a mathematically expert student 1. Make sense of problems and persevere in solving them. Algebra Problem Solving with the new Common Core Standards

6 Standards for Mathematical Practices Describe habits of mind of a mathematically expert student 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. Algebra Problem Solving with the new Common Core Standards

7 Standards for Mathematical Practices Describe habits of mind of a mathematically expert student 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. Algebra Problem Solving with the new Common Core Standards

8 Standards for Mathematical Practices Describe habits of mind of a mathematically expert student 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. Algebra Problem Solving with the new Common Core Standards

9 Standards for Mathematical Practices Describe habits of mind of a mathematically expert student 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. Algebra Problem Solving with the new Common Core Standards

10 Standards for Mathematical Practices Describe habits of mind of a mathematically expert student 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. Algebra Problem Solving with the new Common Core Standards

11 Standards for Mathematical Practices Describe habits of mind of a mathematically expert student 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. Algebra Problem Solving with the new Common Core Standards

12 Standards for Mathematical Practices Describe habits of mind of a mathematically expert student 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Algebra Problem Solving with the new Common Core Standards

13 Design and Organization Balance of concepts and skills Algebra Problem Solving with the new Common Core Standards

14 Design and Organization Balance of concepts and skills Focal points at each grade level Algebra Problem Solving with the new Common Core Standards

15 Design and Organization Balance of concepts and skills Focal points at each grade level Graded ramp up to Algebra in Grade 8 Algebra Problem Solving with the new Common Core Standards

16 Design and Organization Balance of concepts and skills Focal points at each grade level Graded ramp up to Algebra in Grade 8 Apply and extend previous understandings of... Algebra Problem Solving with the new Common Core Standards

17 Design and Organization Balance of concepts and skills Focal points at each grade level Graded ramp up to Algebra in Grade 8 Apply and extend previous understandings of... Focus on linear equations and functions in Grade 8 Algebra Problem Solving with the new Common Core Standards

18 Design and Organization Balance of concepts and skills Focal points at each grade level Graded ramp up to Algebra in Grade 8 Apply and extend previous understandings of... Focus on linear equations and functions in Grade 8 Organized into domains that progress over several grades Algebra Problem Solving with the new Common Core Standards

19 Standards from Operations, Algebraic Thinking, Expressions, Functions, and Equations Sample standards taken from Several grade levels with Supporting activities that can be Easily modified Algebra Problem Solving with the new Common Core Standards

20 Standards  Supporting Activity  Menu Math Reason about and solve one-variable equations and inequalities. Write, read, and evaluate expressions in which letters stand for numbers. Menu Math does the trick ! Algebra Problem Solving with the new Common Core Standards

21 Standards  Supporting Activity  Menu Math Algebra Problem Solving with the new Common Core Standards Hamburger$1.85 Cheeseburger$2.15 Fries$1.05 Sodas: Small$0.95 Medium$1.25 Large$1.55 Extra Large$2.05

22 Standards  Supporting Activity  Menu Math Algebra Problem Solving with the new Common Core Standards Hamburger$1.85 Cheeseburger$2.15 Fries$1.05 Sodas: Small$0.95 Medium$1.25 Large$1.55 Extra Large$ h + f =

23 Standards  Supporting Activity  Menu Math Algebra Problem Solving with the new Common Core Standards Hamburger$1.85 Cheeseburger$2.15 Fries$1.05 Sodas: Small$0.95 Medium$1.25 Large$1.55 Extra Large$ h + f = 2. c + f + s =

24 Standards  Supporting Activity  Menu Math Algebra Problem Solving with the new Common Core Standards Hamburger$1.85 Cheeseburger$2.15 Fries$1.05 Sodas: Small$0.95 Medium$1.25 Large$1.55 Extra Large$ h + f = 2. c + f + s = 3. 7f =

25 Standards  Supporting Activity  Menu Math Algebra Problem Solving with the new Common Core Standards Hamburger$1.85 Cheeseburger$2.15 Fries$1.05 Sodas: Small$0.95 Medium$1.25 Large$1.55 Extra Large$ h + f = 2. c + f + s = 3. 7f = 4. 3h + c + f + 3x =

26 Standards  Supporting Activity  Menu Math Algebra Problem Solving with the new Common Core Standards Hamburger$1.85 Cheeseburger$2.15 Fries$1.05 Sodas: Small$0.95 Medium$1.25 Large$1.55 Extra Large$ h + f = 2. c + f + s = 3. 7f = 4. 3h + c + f + 3x = 5. 4c + 3f + s + m + l =

27 Standards  Supporting Activity  Menu Math Algebra Problem Solving with the new Common Core Standards Hamburger$1.85 Cheeseburger$2.15 Fries$1.05 Sodas: Small$0.95 Medium$1.25 Large$1.55 Extra Large$ h + f = 2. c + f + s = 3. 7f = 4. 3h + c + f + 3x = 5. 4c + 3f + s + m + l = 6. 3c + 3d = $11.10 What does d = ?

28 Standards  Supporting Activity  Menu Math Algebra Problem Solving with the new Common Core Standards Hamburger$1.85 Cheeseburger$2.15 Fries$1.05 Sodas: Small$0.95 Medium$1.25 Large$1.55 Extra Large$2.05 Mathematical Properties A.3(h + f) B.3h + f C.3h + 3f

29 Standards  Supporting Activity  Menu Math Algebra Problem Solving with the new Common Core Standards Hamburger$1.85 Cheeseburger$2.15 Fries$1.05 Sodas: Small$0.95 Medium$1.25 Large$1.55 Extra Large$2.05 Variations on a Theme A. Donut Shop B. Board Shop C. Music Store D. Pizza Parlor

30 Standards  Supporting Activity  Menu Math Algebra Problem Solving with the new Common Core Standards Hamburger$1.85 Cheeseburger$2.15 Fries$1.05 Sodas: Small$0.95 Medium$1.25 Large$1.55 Extra Large$2.05 Extensions of a Theme A. Tax B. Shipping C. Customer Contracts D. Delivery

31 Standards  Supporting Activity  Hundreds Magic Generate and analyze patterns. Analyze patterns and relationships. Write and interpret numerical expressions. Hundreds Magic takes the cake ! Algebra Problem Solving with the new Common Core Standards

32 Standards  Supporting Activity  Hundreds Magic Algebra Problem Solving with the new Common Core Standards

33 Standards  Supporting Activity  Hundreds Magic Algebra Problem Solving with the new Common Core Standards Arithmetic Patterning

34 Standards  Supporting Activity  Hundreds Magic Algebra Problem Solving with the new Common Core Standards n-1nn+1 n n+11 n+1 n+10 Algebra Generalization

35 Standards  Supporting Activity  Hundreds Magic Algebra Problem Solving with the new Common Core Standards Algebra Reasoning using Geometry

36 Standards  Supporting Activity  Backwards Math Use the four operations with whole numbers to solve problems. Write and evaluate numerical expressions involving whole- number exponents. Backwards Math can do it all ! Algebra Problem Solving with the new Common Core Standards

37 Standards  Supporting Activity  Backwards Math Here are the answers to one hundred math problems. Use four 4’s to create problems that will give these answers. Remember to use the correct order of operations to solve your problems: Parentheses, Exponents, Multiply or Divide, Add or Subtract. Algebra Problem Solving with the new Common Core Standards

38 Standards  Supporting Activity  Backwards Math Here are the answers to one hundred math problems. Use four 4’s to create problems that will give these answers. Remember to use the correct order of operations to solve your problems: Parentheses, Exponents, 1 = Multiply or Divide, Add or Subtract. Algebra Problem Solving with the new Common Core Standards

39 Standards  Supporting Activity  Backwards Math Here are the answers to one hundred math problems. Use four 4’s to create problems that will give these answers. Remember to use the correct order of operations to solve your problems: Parentheses, Exponents, 1 = Multiply or Divide, 2 =Add or Subtract. Algebra Problem Solving with the new Common Core Standards

40 Standards  Supporting Activity  Backwards Math Here are the answers to one hundred math problems. Use four 4’s to create problems that will give these answers. Remember to use the correct order of operations to solve your problems: Parentheses, Exponents, 1 = Multiply or Divide, 2 =Add or Subtract. 3 = Algebra Problem Solving with the new Common Core Standards

41 Standards  Supporting Activity  Backwards Math Here are the answers to one hundred math problems. Use four 4’s to create problems that will give these answers. Remember to use the correct order of operations to solve your problems: Parentheses, Exponents, 1 = Multiply or Divide, 4 = 2 =Add or Subtract. 3 = Algebra Problem Solving with the new Common Core Standards

42 Standards  Supporting Activity  Backwards Math Here are the answers to one hundred math problems. Use four 4’s to create problems that will give these answers. Remember to use the correct order of operations to solve your problems: Parentheses, Exponents, 1 = Multiply or Divide, 4 = 2 =Add or Subtract. 5 = 3 = Algebra Problem Solving with the new Common Core Standards

43 Standards  Supporting Activity  Backwards Math Here are the answers to one hundred math problems. Use four 4’s to create problems that will give these answers. Remember to use the correct order of operations to solve your problems: Parentheses, Exponents, 1 = Multiply or Divide, 4 = 2 =Add or Subtract. 5 = 3 =6 = Algebra Problem Solving with the new Common Core Standards

44 Standards  Supporting Activity  Backwards Math Extension ideas for the four 4’s. Instead of using four 4’s to make expressions, use four 5’s. Algebra Problem Solving with the new Common Core Standards

45 Standards  Supporting Activity  Backwards Math Extension ideas for the four 4’s. Or use four 6’s, Or use four 2’s, Or use four 3’s,... Algebra Problem Solving with the new Common Core Standards

46 Standards  Supporting Activity  Backwards Math Extension ideas for the four 4’s. Look carefully at the expressions used to make the numbers 1 = 2 = 3 = with different “raw materials.” Do you see patterns there? Algebra Problem Solving with the new Common Core Standards

47 Standards  Supporting Activity  Backwards Math Extension ideas for the four 4’s. Using four 4’s (or other raw materials), make ten different expressions equaling: the number 1, the number 2, the number 3,... What did you learn about the number system? Algebra Problem Solving with the new Common Core Standards

48 Algebra Problem Solving with the new Common Core Standards

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