1. Developing Fraction Sense
with
Pattern Blocks
Cheryl Roddick Associate Professor, San Jose State University Christina Silvas-Centeno Mathematics Curriculum Specialist, SJUSD

2. Agenda: Introducing Fractions: “The Doorbell Rang”
A) Skills Trace across NCTM and California Content Standards
for Fractional understanding.
Pattern Blocks, Fractional Parts, and Fair Trades
Arithmetic of Fractions
Providing Meaning to the Algorithms
In this workshop, pattern blocks are used as the foundation for understanding all aspects of fraction concepts as well as computations. Participants will learn how to use the blocks to: 1) develop the idea of fractional parts, 2) make fair trades with the pattern blocks to create equivalent fractions, 3) solve real world problems involving addition, subtraction, multiplication, and division of fractions, and 4) provide meaning for the algorithms for arithmetic of fractions.
Intro 5 minutes - Cheryl

3. Models of Division Sharing Model (“How many in a group?”)
There are 9 cookies and 6 children. How many cookies does each child get?
Measurement Model (Repeated Subtraction or “How many groups?”)
There are 12 cookies and you eat ½ cookies each day. How many days can you eat cookies?
Cheryl will model the equal shares and measurement (equal groups) models
5 minutes

4. Chris - quick synopsis of the trace through NCTM standards and Content standards - 5 minutes

5. Skills Trace through Content Standards for the conceptual development of fractions: Equivalency, Equal Exchanges, Solving Problems
Kindergarten: NS 1.1
1st Grade: NS 1.3

6. 2nd Grade Content StandardsNS

7. 2nd Grade Content StandardsNS NS NS NS NS

8. 3rd Grade - Content StandardsNS

9. 3rd Grade - Content StandardsNS NS NS NS

10. 3rd Grade - Content StandardsNS

11. 4th Grade Content StandardsNS NS NS

12. 4th Grade Content StandardsNS MG
SDAP

13. 5th Grade Content StandardsNS NS

14. 5th Grade Content StandardsNS NS NS NS NS
SDAP

15. 6th Grade Content StandardsNS NS NS NS NS

16. 6th Grade Content StandardsNS NS NS NS

17. 6th Grade Content StandardsNS AF AF

18. 6th Grade Content Standards
SDAP
SDAP
SDAP
SDAP

19. The Basics of Fractions
Let two yellow hexagons = 1.
1. What fraction is represented by each of the following pattern blocks?
a b.
c. d.
chris model 1 hex. Run through the fair exchanges for one hexagon.
Group does 2 hex. 10 minutes

20. Possible Extensions
How do you represent 1 1/2? Draw three different ways.
Create your own pattern block picture to represent 1, and make 1/2 of it blue. Draw both your original picture and what ½ looks like.
Chris - Don’t do, but say it is extension and why

21. Finding the Fractional Part
Let the flower = 1.
1. Draw 1/2 of this shape.
2. Draw 1/4 of this shape.
3. Draw 2/4 of this shape.
4. Draw 1/8 of this shape.
Chris model: 5 mins

22. Please do the following activity.
Let the king’s crown = 1.
Make 1/3 of this shape with pattern blocks. ____________________
Make 1/2 of this shape with pattern blocks. ____________________
Make 2/3 of this shape with pattern blocks. ____________________
Can you make 1/5 of the crown? Why? ___________________________
Chris will model flower and participants will actually work on king’s crown - 15 minutes
Students had trouble determining whether 1/5 of the crown was possible.
G2 NS 4.1, 4.2, G3 NS 3.1

24. 45 minute mark - 1/2 of presentation

25. Please do the following activity.
G NS 4.1, 4.2, G3 NS 3.1
Let the fish = 1.
Make 1/5 of this shape with pattern blocks. ____________________
Make 1/2 of this shape with pattern blocks. ____________________
Make 3/10 of this shape with pattern blocks. ____________________
Can you make draw 1/3 of the fish? Why? ___________________________
Not doing - just an example for an extension

26. Multiplication of Fractions
Amber’s friend Jessica pulls out 12 candies from the bag, and divides them into four equal groups.
a. How many candies are in each group?
b. What fraction is one of the groups?
Cheryl - Sharing problem and then connect to second slide for fractions
5 minutes

27. Multiplication
Amber has 12 starburst candies and she eats 1/4 of them. How many candies has she eaten?
Amber has 12 starburst candies and she eats 3/4 of them. How many candies has she eaten?
Cheryl will have participants do this problem - 5 minutes. Students do not make the connection that the equal sharing problem is the same as the fraction problem. Not understanding the relationship between denominator and numerator.
Students could find 1/3 of three objects but had difficulty finding 1/3 of 12 objects (in the sunburst problem).

28. Addition and Subtraction of Fractions (Estimation)
José and Minh went to the store together and bought some candy. José bought 2/3 lb. of gummy worms and he gave 1/2 lb. of the candy to Minh. How much candy (in lbs.) does José have left?
Cheryl - Participants try this problem. REMEMBER - to ask participants to estimate before solving - walk them through it.
10 minutes - we are at 65 minutes

29. The Doorbell Rang Revisited
Recall the story The Doorbell Rang, where cookies were being shared among friends. If you have more friends than cookies, then each friend can only have a fraction of a cookie. (Let’s say these are big cookies!) Using pattern blocks, solve the different scenarios below to determine how many friends you can give cookies to.
Cheryl - talk set up the table 10 minutes

30. Fraction of whole cookie to give to each friend
Number of cookies
Fraction of whole cookie to give to each friend
Number of friends you can give a portion to 3 6 5
75 minutes

31. Why Invert and Multiply?
Use patterns blocks to model the solution to
5 ÷ 5/6.
You need to divide each hexagon into 6 equal pieces this is 5 x 6 = 30.
Then take the pieces 5 at a time. How many groups do you have? 30 ÷ 5 = 6. Thus the answer to 5 ÷ 5/6 is 5 x (6/5) = 30/5 = 6.
5 minutes

32. Where do we go from here?
After developing a foundation for fractional understanding, students should be allowed to use these methods to solve fraction word problems.

33. In the 4th grade, of the students are boys
In the 4th grade, of the students are boys. If there are 36 girls in 4th grade, how many students are there altogether?
G4 NS 1.7, SDAP G NS 2.1, NS 2.3, NS 2.4, NS 2.5, SDAP 1.3

34. In the 4th grade, of the students are boys
In the 4th grade, of the students are boys. If there are 36 girls in 4th grade, how many students are there altogether?
The group, set, or whole are
divided into
7 equal parts.
Girls: 36 =
Boys: X =
Do not forget that the parts are equal pieces!
36 = 4 units
36  4 = 9 students
Therefore:
1 unit = 9 students
= 3  9 = 27
= 63 students
There are 63 students in the 4th grade.

35. Kiley has 1,200 markers. of them were red, of them were green, and of them remaining amount was blue. The rest of the remaining markers were purple. How many purple markers were there?
G4 NS 1.7, SDAP G NS 2.1, NS 2.3, NS 2.4, NS 2.5, SDAP 1.3
G NS 1.2, NS 1.3, NS 2.1, AF 2.1, AF 2.2

36. Kiley has 1,200 markers. of them were red, of them were green, and of them remaining amount was blue. The rest of the remaining markers were purple. How many purple markers were there?
Are red
Are green
Equal Parts
= 1200 markers
= 200 markers

37. Kiley has 1,200 markers. of them were red, of them were green, and of them remaining amount was blue. The rest of the remaining markers were purple. How many purple markers were there?
Are red
Are green
6 units = 1200 markers
1 unit = 200 markers
Equal Parts
5 units = 200 markers
1 unit = 40 marks
4 units = 160 markers
= 200
200
= 5 equal parts
160 markers are purple