1. Develop understanding of fractions as numbers. 1. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. 2. Understand a fraction as a number on the number line; represent fractions on a number line diagram. 3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. (Source: www.corestandards.org)

2. Definition: Fraction A fraction is the comparison of two numbers through the mathematical operation of division. A fraction is the comparison of two numbers through the mathematical operation of division. The number on the top of the fraction is called the numerator. The number on the top of the fraction is called the numerator. The number in the bottom of the fraction is called the denominator. The number in the bottom of the fraction is called the denominator.

3. Examples of Fractions numerator denominator

4. Concept Exploration = 1 package = 12 candies

5. Divide the package into 12 groups with the same number of candies Observe 1/12 package = 1 candy.

6. Divide the package into 6 groups with the same number of candies Observe 1/6 package = 2 candies.

7. Divide the package into 4 groups with the same number of candies Observe 1/4 package = 3 candies.

8. Divide the package into 3 groups with the same number of candies Observe 1/3 package = 4 candies.

9. Divide the package into 2 groups with the same number of candies Observe 1/2 package = 6 candies.

10. Divide the package into 1 group with the same number of candies Observe 1/1 package = 12 candies.

11. Summarize Observations

12. Observations in a Table Fraction of a Whole PackNumber of Candies 1/121 1/62 1/43 1/34 1/26 1/112

13. Stop and Reflect What fraction concepts have we discovered? What fraction concepts have we discovered?

14. Unit Fractions A fraction with a 1 in the numerator and a positive whole number in the denominator is called a unit fraction. All of the following are unit fractions. A fraction with a 1 in the numerator and a positive whole number in the denominator is called a unit fraction. All of the following are unit fractions.

15. Multiples of Unit Fractions Recallof a package. How many are shown below?

16. Multiples of Unit Fractions How many are shown below?

17. Number Line Activity Draw a horizontal line across the upper half of sheet of 8.5 ” by 11 ” paper. Draw a horizontal line across the upper half of sheet of 8.5 ” by 11 ” paper. Line up 12 candies side-by-side along the line Line up 12 candies side-by-side along the line Mark a tick mark at the edge of each candy Mark a tick mark at the edge of each candy

18. Number Line Activity At each tick mark, count how many 1/12 packs are to the left of the tick mark. Then label the tick mark At each tick mark, count how many 1/12 packs are to the left of the tick mark. Then label the tick mark

19. Which number is bigger? Use the number line.

20. Stop and Reflect When two fractions have a common denominator, how can you tell which fraction is the larger number? When two fractions have a common denominator, how can you tell which fraction is the larger number?

21. Multiples of Unit Fractions Recallof a package. How many candies are in of a package? 4 candies, 6 candies, 8 candies, 10 candies, and 12 candies

22. Update the number line.

23. Multiples of Unit Fractions Recallof a package. How many candies are in and of a package? 6 candies, 9 candies, and 12 candies

24. Update the number line.

25. Multiples of Unit Fractions Recallof a package. How many candies are in and of a package? 8 candies and 12 candies

26. Update the number line.

27. Multiples of Unit Fractions Recallof a package. How many candies are in of a package? 12 candies

28. Update the number line.

29. Stop and Reflect Look at the completed number line. What patterns or relationships do you see? Look at the completed number line. What patterns or relationships do you see?

30. Which number is bigger? Use the number line.

31. Equivalent Fractions Represent with four fractions. Represent with four fractions. Observe

32. Equivalent Fractions Represent with three fractions. Represent with three fractions. Observe

33. Equivalent Fractions Write four fractions that are equivalent to. Write four fractions that are equivalent to.

34. Stop and Reflect How can you tell if a fraction is equivalent to a unit fraction? How can you tell if a fraction is equivalent to a unit fraction?