Teaching to the Next Generation SSS (2007)

1. Teaching to the Next Generation SSS(2007) Elementary Pre-School Inservice August 17, 2010

2. Next Generation Sunshine State Standards • Eliminates: • Mile wide, inch deep curriculum • Constant repetition • Emphasizes: • Automatic Recall of basic facts • Computational fluency • Knowledge and skills with understanding

3. Comparison of Standards

5. Coding Scheme for SSSK - 8 MA.3.A.2.1

8. Topics not Chapters

10. Resources with enVisionMATH Daily Review WB Problem of the Day Interactive Learning Quick Check WB Center Activities Reteaching WB Practice WB Enrichment Interactive Stories (K-2) Letters Home Interactive Recording Sheets Vocabulary Cards Assessments

11. Four-Part Lesson Daily Spiral Review: Problem of Day Interactive Learning: Purpose, Prior Knowledge Visual Learning: Vocabulary, Instruction, Practice Close, Assess, Differentiate: Centers, HW

12. Conceptual Understanding

13. Conceptual Understanding

14. Conceptual Understanding

15. Old Instruction vs New Instruction

16. Old Instruction vs New Instruction

17. Algebraic Thinking NGSSS Grades 3 - 5

18. Participants will explore: • Students’ progression from arithmetic to algebraic thinking • Algebraic thinking “thread” in Grades 3 through 5. • Introducing algebraic thinking through patterns

19. Algebra Thread • MA.3.A.4.1Create, analyze, and represent patterns and relationships using words, variables, tables and graphs. (Moderate Complexity) • MA.4.A.4.1Generate algebraic rules and use all four operations to describe patterns, including non-numeric growing or repeating patterns. (High Complexity) • MA.5.A.4.1 Use the properties of equality to solve numerical and real world situations.(Moderate Complexity)

20. ArithmeticAlgebra 7 + 3 = _____ vs. _____ = 7 + 3 The language of arithmetic focuses on ANSWERS The language of algebra focuses on RELATIONSHIPS

21. Students begin describing mathematics inpictures, words, variables, equations, charts, and graphs. k X How Does Algebraic Thinking Start? m y

22. Repeating Patterns • Begins in Kindergarten • Creating and Extending Patterns • Naming the Pattern . . . A B C …

23. Repeating Patterns . . . • What is the core of the pattern? • To get at the predictive nature, you need to have terms specified: 1, 2, 3, 4, 5, 6, 7, …. 1 2 3 4 5 6 7 8 9

24. Repeating Patterns . . . • What is the next figure? How do you know? • What is the 32nd figure? How do you know? • What is the 58th figure? How do you know? • Write how you know what numbers are hexagons. • Write how you know what numbers are squares. • Write how you know what numbers are triangles. 1 2 3 4 5 6 7 8 9

25. PATTERNPATTERNPAT…1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 • What’s the core? • What’s the 70th letter? How do you know? • What’s the 75th letter? The 76th? The 77th? • Write how you can determine the letter in position n, where n can be any whole number?

26. Growing Patterns • Describe in words, mathematically • Why is it difficult to describe the nth term? …

27. Dragon Math Make a series of pattern block dragons that look like this: … Year 1 Year 2 Year 3 In words, how do you describe the pattern?

28. Finding the Rule

29. Finding the Rule

30. Finding the Rule

31. Finding the Rule

32. Finding the Rule Let nstand for age, finish the chart.

33. Finding the Rule Can you explain each rule above, from the the dragons? Can you visualize the rule?

34. What Did We Do? • Took an “interesting to kids” situation • Made a chart to organize the data • Described the data and made a generalization in words • Described the data and generalization with a variable • Tied in a visual aspect—justify the rule

35. Letter Patterns Objectives • Describe the growth pattern • Record data on T-chart • Describe the rule for growth in words • Represent the rule with an expression • Graph the function table

36. Growing the Letter “T” • Create the letter “T” using 5 color tiles. Year 0 Year 1 Year 2

37. Growing the Letter “T” # of Years # of Tiles 0 5 1 6 2 7 T - Chart ● ● ● 15 10 ___ n + 5 n ___

38. Growing the Letter “I” • Create the letter “I” using 7 color tiles. Year 0 Year 1 Year 2

39. Growing the Letter “I” # of Years # of Tiles 0 7 1 8 2 9 T - Chart ● ● ● 10 ___ 17 n ___ n + 7

40. Making a Chart • Make the H’s below on your graph paper. • Make a chart of the term numbers and number of tiles. • Predict, before drawing, how many tiles for the next H. Draw it to check.

41. Growing the Letter “H” # of Years # of Tiles 1 7 2 12 3 17 T - Chart 4 22 ● ● ● ● ● ● n ___ 5n + 2

42. How many tiles are needed to make the nth term? • Can you explain why the nth term has that rule? • What would this look like if you graphed it? 1st 2nd 3rd (5n + 2)

43. Graphing a Function . . . x y

44. What Have We Done? • Considered a sample of the types of patterns that students will encounter • Described the patterns in words • Used charts to see the patterns • Generalized to a rule with a variable in order to predict

45. Equality Principles If you have an equation, you can +, -, ×, or ÷ both sides by the same number (except dividing by zero), and keep things “balanced.” 45

46. Equality Principles If you have an equation, you can +, -, ×, or ÷ both sides by the same number (except dividing by zero), and keep things “balanced.” If two things are equal, one can be substituted for the other. 46

47. Equality Principles = Does not mean “find the answer” Represents a balanced situation 47

48. Grade 3 48

49. Grade 3

50. Verbal & Algebraic Equations • Three times a number , increased by 1 is 25. • If 3 is added to twice a number, the result is 17 • When a number is increased by 8, the result is 13. • Three times a number, increased by 7, gives the same result as four times the number increased by 5. FIND THE NUMBER!