1. Examining the Progression of Standards RSD Principals January 9 & 25, 2015 Sue Larson Nora Ramirez

2. Outcomes Develop an understanding of the coherence that exists in the AZCCRS by: Experiencing activities from the Fractions Domain at several grade levels Examining documents that show the progression and interrelationships of several domains Become familiar with resources for parents Increase knowledge of the resources available on the NCTM website

3. 3 rd Grade Fractions – about 20% 4 th Grade Fractions – about 31% 5 th Grade Fractions – about 33%

4. Fractions in the AZCCRS GradeK12345678HS Conceptual Categories Domains CC— Counting & Cardinality RP—Ratios & Proportional Relationships F—Functions OA—Operations & Algebraic ThinkingEE—Expressions & EquationsA—Algebra NBT—Number and Operations in Base TenNS—The Number SystemN—Number & Quantity NF— Fractions MD—Measurement & DataSP—Statistics & Probability G—Geometry MP—Standards for Mathematical Practice Fractions concepts Fraction Division Frac Dec %

5. Supporting Fractions in the AZCCRS GradeK12345678HS Conceptual Categories Domains CC— Counting & Cardinality RP—Ratios & Proportional Relationships F—Functions OA—Operations & Algebraic ThinkingEE—Expressions & EquationsA—Algebra NBT—Number and Operations in Base TenNS—The Number SystemN—Number & Quantity NF— Fractions MD—Measurement & DataSP—Statistics & Probability G—Geometry MP—Standards for Mathematical Practice Fractions concepts Fraction Division Frac Dec % + & – on number lines

6. Applying Fractions in the AZCCRS GradeK12345678HS Conceptual Categories Domains CC— Counting & Cardinality RP—Ratios & Proportional Relationships F— Functions OA—Operations & Algebraic ThinkingEE—Expressions & EquationsA—Algebra NBT—Number and Operations in Base TenNS—The Number SystemN—Number & Quantity NF— Fractions MD—Measurement & Data SP—Statistics & Probability G—Geometry MP—Standards for Mathematical Practice Fractions concepts Fraction division Frac Dec % + & – on number lines

7. Sharing Cookies

8. Partitioning Shapes

9. Fractions: Part- Whole

10. Fractions on a Number Line

11. Comparing Fractions Kara ran ⅖ of a mile. Her sister ran ⅘ of a mile. Who ran the furthest? Sonya read ⅗ of her book. Jae read ⅜ of the same book. Did Sonya or Jae read more of the book? Jerre grew ⅚ of an inch. Sam grew ¼ of an inch and Sasha grew ⅜ of an inch. Who grew the least? Who grew the most?

12. Equivalent Fractions

13. Equivalent Fractions Pictorial Phase Same wholeMore parts Smaller parts What happens to the whole? What happens to the parts?

14. Equivalent Fractions

16. Mowing a Lawn Samantha mowed ½ of her lawn. Then her brother mowed ½ of what she had not mowed. How much of the lawn still needs to be mowed? One-third of Mr. K’s birthday cake was eaten at the party. His friend, Taba, took ½ of what was left to his house. How much of the cake does Mr. K have now?

17. Fraction Division Tai needs ¼ of a yard of ribbon to make a bow. If she has 5 yards of ribbon, how many bows can she make? Adam has ⅓ of a pound of chocolate. He is going to share the chocolate with his best friend so that he and his friend each get the same amount. How much of a pound will each get?

18. Fractions in the AZCCRS GradeK12345678HS Conceptual Categories Domains CC— Counting & Cardinality RP—Ratios & Proportional Relationships F— Functions OA—Operations & Algebraic ThinkingEE—Expressions & EquationsA—Algebra NBT—Number and Operations in Base TenNS—The Number SystemN—Number & Quantity NF— Fractions MD—Measurement & Data SP—Statistics & Probability G—Geometry MP—Standards for Mathematical Practice Fractions concepts Fraction division Frac Dec % + & – on number lines

19. Fraction Progression

20. Other AZCCRS Progressions

21. NCTM K- 8 Membership nctm.org fractions # 2 Search Publications Choose Teaching Children Mathematics or Mathematics Teaching in the Middle Grades #1 Search fractions

22. Outcomes Develop an understanding of the coherence that exists in the AZCCRS by: Experiencing activities from the Fractions Domain at several grade levels Examining documents that show the progression and interrelationships of several domains Become familiar with resources for parents Increase knowledge of the resources available on the NCTM website

23. Evaluation, Feedback and Input Complete the project’s evaluation form Complete the + / Δ form.