SPIRAL PROGRESSION in the K + 12 MATHEMATICS CURRICULUM

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1 SPIRAL PROGRESSION in the K + 12 MATHEMATICS CURRICULUM Soledad A. Ulep University of the Philippines National Institute for Science and Mathematics Education Development (UP NISMED)

2 Objective of the Presentation To enable the participants to understand the underlying principles and nuances of the spiral progression model in teaching Mathematics

3 Coverage of the Presentation K + 12 Mathematics Curriculum Framework Spiral Progression Approach and its Benefits Example of a Lesson that Teaches Mathematics through Problem Solving Examples of Using the Spiral Progression Approach

4 The K + 12 Mathematics Curriculum Framework

5 Goals of Mathematics in K to 12 Critical thinking Problem solving

6 How to Achieve these Goals Content Skills and process Values and attitudes Tools Context

7 Content Numbers and Number Sense Measurement Geometry Patterns and Algebra Statistics and Probability

8 Skills and Processes Knowing and Understanding Estimating Computing and Solving Visualizing and Modeling Representing and Communicating Conjecturing, Reasoning, Proving and Decision-Making Applying and Connecting

9 Values and Attitudes Accuracy Creativity Objectivity Perseverance Productivity

10 Tools Manipulative objects Measuring devices Calculators and Computers Smartphones and Tablet PCs Internet

11 Contexts Beliefs Environment Language Culture Learner s prior knowledge and experiences

12 Underlying Learning Principles and Theories Experiential and Situated Learning Reflective Learning Constructivism Cooperative Learning Discovery and Inquiry-based Learning

13 Spiral Curriculum Builds upon previously learned knowledge Deepens understanding of topics

14 Features Learners revisit a topic. The complexity of the topic increases with each revisit. New knowledge being developed in each revisit has a relationship with previously learned knowledge.

15 Benefits of Using Spiral Progression It helps reinforce learning. It allows a logical progression from simple to complex ideas. It encourages students to apply their previous learning to later topics and new situations. It helps learners appreciate the connections among the different content strands.

16 Problem Solving Problem solving should not only be a goal of learning mathematics. Problem solving should also be a means of learning mathematics.

17 Problem (Grade 1) Karen has a piece of square paper. She wants to share one-half of the paper to Jun. If you were Karen, how would you divide the paper?

18 Different solutions: Solution 1 Solution 2 Solution 3 Solution 4

19 Verification of Solution 4

20 Other ways : Start with folding a sheet of square paper this way.

21 Example:

22 Area Measurement in the K +12 Curriculum

23 Grade 2 Area Measurement

24 Area Measurement

25

26 1 unit 1 unit 3 units 5 units Area = 3 x 5 = 15 square units Grade 3

27 width length Area of rectangle = length x width = l x w

28 3 cm 5 cm Area of rectangle = length x width = l x w = 3 x 5 = 15 square cm

29 3 cm 3 cm 2 cm 6 cm Grade 4

30 3 cm 3 cm 2 cm 6 cm

31 3 cm 3 cm 2 cm 6 cm

32 3 cm 3 cm 2 cm 6 cm

33 5 cm 3 cm

34 5 cm 3 cm

35 5 cm height 3 cm base Area of parallelogram = base x height = bh

36 4 cm 5 cm

37 4 cm 5 cm

38 4 cm 5 cm Area = bh 2

39 4 cm 5 cm

40 Area = bh 2

41

42 h b

43 10 cm 17 cm 25 cm

44 b 1 T1 h T2 b 2 Area of Trapezoid = Area of T1 + Area of T2 = + = = b 1 h b 2 2 2h h( b + b ) ( b1 + b2)h 2

45 b 1 b 2 h b 2 b 1 Area of Parallelogram = bh Area of Trapezoid = = (b 1 + b 2 ) h 1 2 (b1 + b2) h

46 b 1 h h 2 b 2 b 1 Area of Parallelogram = bh h = (b 1 + b 2 ) 2 1 ( b + b )h Area of Trapezoid = 1 2 2

47 Grade 5

48

49 Area of the Circle = Area of the Parallelogram

50 Area of the Circle = Area of the Parallelogram Area of Parallelogram = bh Area of Circle = 1 2 Cr b = 1 2 C 1 C 2 1 = (2 r) r 2 = r 2 h = r C = 2 r h b

51 Grade 6

52

53 Patterns and Algebra in the K + 12 Curriculum

54 Draw the next two figures: Figure 1 Figure 2 Figure 3 Figure 4 How many sticks are used in each of Figure 1 to Figure 6? How many sticks will there be for Figure 10?

55 Problem How many sticks were used in the figure below? Count systematically.

56 6 + (5 1) x5 (5 x 6) (5 1) 1 + (5 x 5)

57 n s s = 1 + 5n

58 Problem What is the sum of the measures of the interior angles of the pentagon shown?

59 Solution 1: Using GeoGebra

60 Solution 2 Solution 3 Solution 4 a = 180(5-2) a = 180(5 1) a = 180(5) - 360

61 Solution 2 Solution 3 Solution 4 a = 180(n-2) a = 180(n 1) a = 180n - 360

62 n a a = 180 (n-2)

63 Problem In a small gathering, there are 5 guests. If each guest shakes hands with the other guests only once, how many handshakes are there in all?

64 A B C D Solution 1 A B C D E AA A B A C A D AE AB BB BC BD BE AC B C AD B D C C C D C D D D CE E AE BE CE DE E E DE (½)[(5 x 5) 5]

65 (½)(5 x 4)

66

67 Thank you!

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