1. Page 1 www.tie.net Building Understanding of the Fractions Through Hands-On Experiences Marcia Torgrude and Bailey Kowalski K-12 Math Specialists mtorgrude@tie.netmtorgrude@tie.net and bkowalski@tie.netbkowalski@tie.net http://bit.ly/19fRdDr

2. Page 2 Promote a deeper understanding of the progression of fractions within the Common Core. Develop hands-on strategies to build understanding of operations of fractions. Reinforce the Lesson in 3 Acts and Instructional planning. Practice the use of questioning, mathematical discourse, productive struggle, and formative assessment. Outcomes for Today

3. Page 3 I Have….. Who Has Let’s play! What does this have to do with learning math? Where does it fit the common core standards? What about the Standards of Mathematical Practice?

4. Page 4 Rich Task Reflection & Discussion Share anecdotal notes and pictures of using a rich task in your classroom. Group Discussion: After using a rich task, what was different, if anything, in your classroom – prepare student work, discussions, and any other items to share.

5. Page 5 Standards of Mathematical Practice

6. Page 6 What does it mean to “do mathematics?” What does it mean to “do mathematics?” The Standards of Mathematical Practice are descriptions of the fundamental skills needed to “do” mathematics. These are our new “basic skills”. Phil Daro’s Take on the Common Core State Standards for Mathematics

7. Page 7 What does it mean to “do mathematics?” What does it mean to “do mathematics?” Standards of Math Practice are the “how” of mathematics Content Standards are the “what” of mathematics

8. Page 8 We must get past the idea of mathematics as a collection of algorithms, steps, or procedures. Just getting answers, although important, is not “doing mathematics.” “Doing mathematics”

9. Page 9 Working with Fraction Progressions Equivalence Addition Subtraction Multiplication Division Ratio/Proportion Rate of Change

10. Page 10 4 th Grade Fraction Progressions Read pages 6- 8 Standards – 4.NF.1, 4.NF.2, 4.NF.3

11. Page 11 Fraction Equivalence, Addition and Subtraction Using Pattern Blocks http://illuminations.nctm.org

12. Page 12 Journal Reflection What is a fraction? What happens to the fraction when we increase the whole? Write 3 new ideas you learned about fractions today.

13. Page 13 5 th Grade Progressions – Addition and Subtraction Read Page 11 Coasting Along Activity

14. Page 14 Fraction Progression 4 th Grade – refer to 6-9 to decimals 5 th Grade – page 11 – 14 6 th Grade – page 5-7 Write the “must do’s” for each grade level on poster Gallery Walk

15. Page 15 Fraction Using Cuisenaire Rods Using Cuisenaire rods model: 1 + 1 2 3 1 – 1 2 3 1 x 1 2 3 1 x 1 3 2 1 ÷ 1 2 3 http://www.learner.org/courses/learningmath/num ber/session8/part_b/index.html Interactive and Video

16. Page 16 Array Model for Fractions http://www.learner.org/vod/vod_wi ndow.html?pid=1853http://www.learner.org/vod/vod_wi ndow.html?pid=1853 Modeling equivalence, adding, subtracting, multiplying, and dividing

17. Page 17 Why do we invert and multiply to divide? Show your reasoning in your journals Discuss Large Group

18. Page 18 Why do we invert and multiply to divide? 34563456

19. Page 19 Why do we invert and multiply to divide? How does this work? ¾ ÷ 5/6= B How many 5/6 are in ¾?  x 5/6 = ¾ B x 5/6 = ¾ I need to multiply 5/6 by its reciprocal to solve for B or box. B x 5/6 x 6/5 = ¾ x 6/5 B = ¾ x 6/5 ¾ ÷ 5/6 = ¾ x 6/5

20. Page 20 Do We Have to Invert?

21. Page 21 6-8 th Grade Progression – Fractions, Ratios and Proportions NS - Grade 6 – pg. 5-7 Ratio/Proportion –Overview – pg. 2-4 –Grade 6 – pg. 5-7 –Grade 7 – pg. 8-12 –Grade 8 – pg. 11-13 Create a new poster progression Develop a definition of a ratio and a definition of a fraction

22. Page 22 6-8 th Grade Progression – Ratios and Proportions

23. Page 23 Promote a deeper understanding of the progression of fractions within the Common Core. Develop hands-on strategies to build understanding of operations of fractions. Reinforce the Lesson in 3 Acts and Instructional planning Practice the use of questioning, mathematical discourse, productive struggle, and formative assessment Did We Meet Our Outcomes?

24. Page 24 Do a Rich Task Analyze the student journal for student growth Compare data from AimsWeb Complete reflection survey Final thoughts Data Collection Time

25. Page 25 Rich Task – Bubble Wrap

26. Page 26 Your Turn – Share Your Lesson and Student Work

27. Page 27 One Student’s Journey What did you notice at the beginning What was their mathematical understanding? What was their ability to communicate in writing? How confident were they? (affective journaling) What growth evidence do you find?

28. Page 28 AimsWeb Data Compare Fall/Winter/Spring or make a prediction for spring What do you notice whole group? Determine how much each of your students grew What does this tell you? What will you do with the results?

29. Page 29 Reflection Survey Please look through your binder and your journals to reflect on all the learning that has taken place this year Refer to the handout http://bit.ly/MathIRMC

30. Page 30 SD Framework for Teaching

31. Page 31 Virtual Fractions http://mtorgrude.tie.wikispaces.nethttp://mtorgrude.tie.wikispaces.net – Symbaloo link on navigation bar

32. Page 32 Your Final Thoughts https://www.youcubed.org/week-of-inspirational-math/

33. Page 33 We Made It!!!