1. Lesson 1.2

2. MATH ROUTINE

3. Explain! prime number composite number prime factorization Greatest Common Factor

4. RECALLING THE PROBLEMS

5. PROBLEM A set of 36 blue checkers and 60 red checkers is to be arranged into piles. Each pile may contain only blue or only red checkers. All piles, both blue and red, must contain the same number of checkers. What is the greatest number of checkers that each pile can have?

6. Idea Generation

7. Visualization

8. 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12

9. PROBLEM Mary has a rectangular piece of of paper, 30 cm by 18 cm. She wants to cut it into square sheets of the same size. What is the largest size of square sheets can she get?

10. VISUALIZATION 30 cm 18 cm

11. VISUALIZATION 6 cm

12. PROBLEM There are 42 apples and 77 oranges to be sold as part of the family fair in school. The organizer wants the same number of items of fruit in each bag. Apples and oranges should not be mixed. What is the greatest number of of items that can be placed in a bag?

13. VISUALIZATION

15. Prime Factorization in GCF 1. 36 = 2 2 x 3 2 60 = 2 2 x 3 x 5 GCF= 12 2. 30 = 2 x 3 x 5 18 = 2 x 3 2 GCF= 6

16. Prime Factorization in GCF 3. 42 = 2 x 3 x 7 77 = 11 x 7 GCF= 7

17. Try some more! 1. 36 = 2 2 x 3 2 48 = 2 4 x 3 GCF= ?

18. Try some more! 2. 30 = 2 x 3 x 5 180 = 2 2 x 3 2 x 5 GCF= ?

19. Try some more! 3. 48 = 2 4 x 3 72 = 2 3 x 3 2 GCF= ?

20. Try some more! 2 4 x 3 x 5 2 3 x 3 2 x 5 3 GCF= ?

21. Try some more! 3 2 x 5 x 7 2 3 x 3 2 x 5 3 2 x 5 2 x 7 2 GCF= ?

22. Exploring Other Means Using the same examples

23. PROBLEM An Asian Conference is being attended by 96 students from the Philippines, 72 from Malaysia and 48 from Indonesia. What is the greatest number of discussion groups that can be formed so that the students from each country are distributed equally among all the groups?

24. VISUALIZATION 96 Filipinos

25. 72 Malaysians

26. 48 Indonesians

27. How many groups? 24 groups

28. Going further! 9 students How many students are in each group?

30. PROBLEM Tony wants to cut three pieces of ropes to pieces of equal length and as long as possible without wasting anything. The ropes are 36 meters, 48 meters and 96 meters long. How long should he cut each piece?

31. Visualization VISUALIZATION 96 m48 m36 m

32. Visualization 12 m each

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