Welcome to Day Three

1. Welcome to Day Three

2. Agenda • 5 Practices for Mathematical Discourse • Ratios to Proportions: An Introduction • Problem Solving with Ratios, Proportions, and Percent • Lesson and Reflection

3. The Standards for Mathematical PracticeStudent Reasoning and Sense Making about Mathematics • Make sense of problems and persevere in solving them • Reason abstractly and quantitatively. • Construct viable arguments and critique the reasoning of others. • Model with mathematics. • Use appropriate tools strategically. • Attend to precision. • Look for and make use of structure. • Look for and express regularity in repeated reasoning.

4. Bring your ideas… • As a group of professionals we have made a commitment to helping children attain success in life and a voice in the world. • Many times the best part of these kinds of professional development is simply the chance to share ideas, raise questions, and work with other practitioners to improve our own understandings and practice. • Please bring your stories of children’s learning with you.

5. Our Socio-mathematical Norms • Listen intently when someone else is talking avoiding distractions • Persevere in problem solving; mathematical and pedagogical • Solve the problem in more than one way • Make your connections explicit - Presentation Ready • Contribute by being active and offering ideas and making sense • Limit cell phone and technology use to the breaks and lunch unless its part of the task. • Be mindful not to steal someone else’s “ice cream” • Respect others ideas and perspectives while offering nurturing challenges to ideas that do not make sense to you or create dissonance. • Limit non-mathematical and non-pedagogical discussions

6. Presentation Norms • Presenters should find a way to show mathematical thinking, not just say it • Presenters should indicate the end of their explanation by stating something like “Are there any questions, discussion, or comments?” • Others should listen and make sense of presenters’ ideas. • Give feedback to presenters, extend their ideas, connect with other ideas, and ask questions to clarify understandings

7. BREAK

8. Ratios to Proportions: An Introduction

9. Counting Activity On the next slide, count the total number of vowels that you see – you will have 30 seconds.

10. Cat LivesBowling PinsFootball TeamDozen EggsUnlucky FridayValentine’s DayQuarter Hour Dollar BillDice TricycleFour Leaf CloverHandSix-PackSeven-Up Octopus

12. Words Write down any words you remember from the previous slide

13. Look for Patterns

14. Look for Patterns Dollar BillDice TricycleFour Leaf CloverHandSix-PackSeven-Up Octopus Cat LivesBowling PinsFootball TeamDozen EggsUnlucky FridayValentine’s DayQuarter Hour

15. Looking Again • How many words do you remember this time? • Are you “smarter” than you were the first time you were asked to list words? What changed? You can significantly increase your performance on a learning task if they: • Are very clear about what you will be required to do • Have a strategy for “noticing” things so you can link and relate to the information

16. Chances The chances of finding “it” are greatly increased if you are asked to look for “it”!

17. What Fraction of the Picture is Blue?

18. Division Problem Consider the problem What does the ½ in the answer represent? • ½ of ¾ • ½ of ½ • ½ of 1 • None of these

19. Ratios and Proportions Perhaps the most important issue to “notice” when working with ratios and proportions is thinking about what represents the “whole”

20. What Number Do You See?

21. Hummingbird Feeder Nectar for the feeder is to include ¼ cup of sugar for every cup of water. What ingredients will I need to make 30 cups of nectar for the feeder?

22. Hummingbird Feeder I just bought a 12-fluid-ounce hummingbird feeder. If I want to make enough nectar to fill the feeder twice, approximately how much sugar and how much water will I need?

23. Mixing Paint Jessica gets her favorite shade of purple paint by mixing 2 cups of blue paint with 3 cups of red paint. How many cups of blue and red paint does Jessica need to make 20 cups of her favorite purple paint? Use snap cubes to model this.

24. Mixing Paint Let’s see how an actual Grade 6 class handled this task on the first day of their Ratios Unit: VIDEO

25. Mixing Paint Questions • What misconceptions did the children appear to have? • How did the teacher attempt to resolve those misconceptions? • What suggestions would you have for changing the lesson and for where she should go next with the lesson?

26. Mixing Paint Questions • How can we use Cuisenaire Rods to model this problem? • What other approaches can be used to model and solve this problem?

27. Mixing Paint Let’s look at a download from the Illustrative Mathematics website that poses the problem and six different solution methods …

28. LUNCH

30. Equivalent Fractions and Equivalent Ratios 2/3 is equivalent to 6/9 2 : 3 is equivalent to 6 : 9 Make a representation of each. How are they the same and how are they different?

31. Analyzing Change At the zoo, there are two long-term resident crocodiles that have affectionately been named Prickles and Tiny. When they arrived at the zoo, Prickles was 4 m long and Tiny was 5 m long. Five years later, both crocodiles are now fully grown. Prickles is 7 m long and Tiny is 8 m long. Have Prickles and Tiny grown by the same amount?

32. Comparing Mixtures Abby’s orange paint is made by mixing 1 cup of red paint for every 3 cups of yellow paint. Zack’s orange paint is made by mixing 3 cups of red paint for every 5 cups of yellow paint. How do the shades of their orange paints compare?

33. Problem Solving with Ratios, Proportions, and Percent

34. BREAK

35. Math Content for our Classrooms • Each day we will spend time with grade level teams making lesson plans. • Each of us will make one plan that is part of a unit of plans the grade level team is working on. • Each plan must have the following: • Connected mathematics content focus from Ohio’s Mathematics Learning Standards • A focus SMP • Designed to Orchestrate Productive Mathematics Discussions (The 5 Practices)

36. Math Content for our Classrooms Three checks must be made for the completion of lesson plans: Check 1) Consult with Sandy and/or Mary about the mathematics content of the lesson and explain to her its mathematical appropriateness. When the lesson is complete Sandy, our resident mathematician, will sign off on its content (SMC’s). Check 2) Consult with Sherry about the design of the lesson to promote mathematical discourse (5 Practices). Sherry must sign off on the lessons discourse elements. Check 3) Consult with Dr. Matney about the design of the lesson having a focus Standard for Mathematical Practice. Dr. Matney must sign off on the lessons mathematics proficiency elements (SMP’s) ?Questions about COMP Lesson Plans?

37. Time of Reflection • On a sticky note tell us one thing you learned today. • Tell us one think you liked or one thing you are still struggling with.

38. Stay Safe • Please help us put the room in proper order. • Please leave your name tents for next time.