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Region 11: Math & Science Teacher Center Solving Equations

Region 11: Math & Science Teacher Center Solving Equations. Equality. Ratio & Proportion. Pattern Generalization. Where we’ve been…. Patterns Review - Justify It!. 3rd Grade MCA Practice Problem. 1 4 7 10. Patterns Review - Justify It!. 3rd Grade MCA Practice Problem.

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Region 11: Math & Science Teacher Center Solving Equations

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  1. Region 11: Math & Science Teacher CenterSolving Equations

  2. Equality Ratio & Proportion Pattern Generalization Where we’ve been…

  3. Patterns Review - Justify It! 3rd Grade MCA Practice Problem 1 4 7 10

  4. Patterns Review - Justify It! 3rd Grade MCA Practice Problem 1 4 7 10

  5. With a partner, talk about how a third grader would talk about this problem: • Draw the next figure in the pattern • How many dots will be in the next figure? • Describe how make the pattern Patterns Review Adult Challenge: How many dots would be in the nth figure?

  6. Patterns Review Share in Grade Level Groups: • What strategies did you see kids use? • What did the students find most challenging? • What growth did you see? • What surprised you?

  7. Patterns Review Watch video and record: Good questions Not-so-good questions

  8. Patterns Review Discuss video at your tables: • What questions helped most to get your students to explain the explicit rule for different patterns? • What did you learn about scaffolding questions? •How do you know when you are done asking questions?

  9. Goals: • Identify a developmental sequence for solving equations • Structure “math talk “about expressions & equations • Emphasize equivalence and how we communicate this with students • Discuss properties of equations Solving Equations Work with a partner to solve problems on page 1

  10. Solve. Find all values that make the statement true.

  11. Solve. Find all values that make the statement true.

  12. Solve. Find all values that make the statement true.

  13. Solve. Find all values that make the statement true.

  14. Solve. Find all values that make the statement true.

  15. Solve. Find all values that make the statement true.

  16. What does solve mean?

  17. Break

  18. Think/Pair/Share… • Define expression • Define equation

  19. Big Idea! • We solve equations because we can make them true or false. • We don’t solve expressions because we can’t make them either true or false.

  20. Expression vs. Equation Share and discuss in your group as you work on page 2: • How would you write the directions? • How would you want/expect students to show their work?…What would you write on the board?

  21. Expression vs. Equation

  22. Expression vs. Equation

  23. Expression vs. Equation

  24. Expression vs. Equation

  25. Expression vs. Equation

  26. Expression vs. Equation

  27. Expression vs. Equation • Directions make a big difference! • Directions depend on context and where you are in the curriculum • Expressions are not equations • No one “right way” to show work • Most middle school textbook authors have thought carefully about what strategies to use to solve equations

  28. CGI Algebra Video Clips

  29. Benchmarks in Student ThinkingAbout The Equal Sign Note: These benchmarks are a guide, not a firm sequence

  30. CGI Algebra Video Clips Solving the Equation (4th grader, 2 minutes, 42 seconds)

  31. CGI Algebra Video Clips Solving the Equation (4th grader, 1 minutes, 51 seconds)

  32. CGI Algebra Video Clips Solving the Equation (4th grader, 39 seconds)

  33. CGI Algebra Video Clips Solving the Equation (4th grader, 51 seconds)

  34. Benchmarks in Student ThinkingAbout The Equal Sign Note: These benchmarks are a guide, not a firm sequence

  35. Lunch

  36. Methods for solving linear equations of the form ax ± b = cx ± d Traditional Approach vs. Functions Approach

  37. Traditional approach for solving linear equations of the form ax ± b = cx ± d • Use of number facts (solve mentally) Example: 3 + x = 7 Not-so-good for: 3x + 7 = 5x – 14

  38. Traditional approach for solving linear equations of the form ax ± b = cx ± d 2)Generate and evaluate (“guess and check” or “trial and error substitution”) Example: 2x + 3 = 4x – 7 Not-so-good for: 3x – 7 = 10 – 4x

  39. Traditional approach for solving linear equations of the form ax ± b = cx ± d 3) a.Undoing (or working backwards) Example: 20 = 3x – 4 24 = 3 • x 8 = x Not-so-good for: 3x + 7 = 5x – 14

  40. Traditional approach for solving linear equations of the form ax ± b = cx ± d x 3 - 1 p 3p 3p – 1 6 18 17 + 1 ÷ 3 3) b.Undoing 17 = 3p – 1

  41. Traditional approach for solving linear equations of the form ax ± b = cx ± d 4) Cover-up Example: k + k + 13 = k + 20 k + k + 13 = k + 13 + 7 k = 7 Not-so-good for: 3x + 7 = 25 – 5x

  42. Traditional approach for solving linear equations of the form ax ± b = cx ± d 5) Transposing (change side-change sign) Example: 3x = 8 5x = 15 x = 3 Not-so-good for: – 7 + 2x 7 + – 2x

  43. Traditional approach for solving linear equations of the form ax ± b = cx ± d 6)Equivalent equations (performing the same operation on both sides) Example: 17 = 3x – 7 17 + 7 = 3x – 7 + 7 24 = 3x 24/3 = 3x/3 8 = x

  44. Traditional approach for solving linear equations of the form ax ± b = cx ± d Group Task #1 • Break into six table groups • Write one or two good problems for each method on the table • When the bell rings, move to the next table

  45. Traditional approach for solving linear equations of the form ax ± b = cx ± d Group Task #2 • Move to the table where you started • Work the problems using that particular method • Star any problems that can’t be solved easily with the method • Determine the minimum benchmark level needed to solve these problems • Be ready to report out

  46. Functions approach for solving linear equations of the form ax ± b = cx ± d 1)Table using graphing calculator(similar to guess and check) Example: 3x – 4 = x + 6 x = 5 Y1 Y2

  47. Functions approach for solving linear equations of the form ax ± b = cx ± d 2)Graphing Example: 3x – 4 = x + 6 x = 5 Y1 Y2

  48. “By viewing algebra as a strand in the curriculum from prekindergarten on, teachers can help students build a solid foundation of understanding and experience as a preparation for more-sophisticated work in algebra in the middle grades and high school.” - NCTM, 2000, p.37 Why standards?

  49. True or False Your textbook determines the algebra concepts and skills that you should cover at a particular grade level. TRUE FALSE  don’t know False: In a standards-based system, the focus is shifted from what is TAUGHT to what is LEARNED. The standards tell us what students should know and be able to do.

  50. True or False Algebra content has been shifted down and now starts in the middle grades. TRUE FALSE  don’t know False:Algebra and algebraic thinking are integrated across K-11 in the state standards. Every teacher has to do his/her part to give students the opportunity to learn the grade-level content.

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