1. A Collaboration between: Los Angeles Unified School District University of California, San Diego San Diego State University University of California, Irvine San Diego Mathematics Project Preparing for Success in Algebra English Language Learners in Mathematics

2. Slide 2 Welcome California Mathematics and Science Partnership (CaMSP) Academic Year Follow Up Session #2 February 26 th, 2011 Objective: Possible Outcomes and Probability

3. Slide 3 Probability The probability that you just read this: 1

4. Slide 4 CA Standards 6 PS 3.1 Represent all possible outcomes for compound events in an organized way (e.g., tables, grids, tree diagrams) and express the theoretical probability of each outcome. 6 PS 3.3 Represent probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability of an event, 1 - P is the probability of an event not occurring.

5. Slide 5 CST Released Items

6. Slide 6 CST Released Items

7. Slide 7 Vocabulary ProbabilityLikely RandomUnlikely Possible OutcomesTable Possible ChoicesTree Diagram FractionSet Percent

8. Slide 8 Connect to Prior Knowledge Converting fractions to percents Probability of an event is from 0 to 1 Likelihood of an event Tree Diagrams Charts Set Notation

9. Slide 9 Foldable: Little Book

10. Slide 10 New Strategy: Around the World Do not abandon your partner Talk only to your partner or consult with the pair closest to you Work together one problem at a time When you finish a problem, move on to another that is open or has the least amount of people. You don’t have to work the problems out in order. Make sure your partner understands how to do the problem.

11. Slide 11 Lesson Modification How did the strategies used (Foldable Little Book & Around the World) provide access to the mathematical concept? How can this lesson be modified, or improved, to fit your teaching style? How can the Around the World activity be managed for best results? How can you differentiate this lesson for students of different levels?

12. Slide 12 Looking Back & Moving Forward Make a list of all strategies that we have used in our trainings by placing them into three columns: Vocabulary, Practice, Review Based on this list, write down what you want to see more of? Do we need to share more strategies for vocabulary, for practice, or for review?

13. Slide 13 Evaluation Please give feedback in the box labeled, “Comments about Pedagogy Session” in your Follow Up #4 Evaluation form.

14. Slide 14 Thank You!! Esmeralda Orozco – Esmeralda.orozco@sweetwaterschools.org Edwin Moraila – epm0109@lausd.net

15. Slide 15 Strategy Stop QUICK Write Strategy: Springboard for Instructional Conversations Scaffolds: Bridging and Contextualization Language Domains: Writing and Reading Description: Students give quick reaction to prompt presented. Goal is to capture feelings or meaning to the person not linguistic correctness. Affect: Supports low-risk learning environment Interaction / Practice: Facilitation of Language Development

16. Slide 16 Strategy Stop 3 Step Interview Access Strategy: Instructional Conversations Scaffolds: Bridging, Modeling, Schema-Building Language Domains: Listening, Speaking, Reading Description: Students share to A/B partners. Then each share their partner ’ s thoughts/responses to the rest of the table/group. Affect: Supports low-risk learning environment Interaction / Practice: High accountability (peers); practice with language development

17. Slide 17 Strategy Stop Mind Mirror Strategy: Advanced Graphic Organizer Scaffolds: Bridging, Contextualization, Schema Building Language Domains: Listening, Speaking and Writing Description: Students tie ideas together in a graphic by giving simple quotes from the text to synthesis of ideas. Affect: Supports learning environment with accountability Interaction / Practice: All must participate and practice oral language.

18. Slide 18 Strategy Stop Hand Up, Stand Up, Pair Up (Kagan Strategy) Strategy: Instructional Conversations Scaffolds: Bridging, Contextualization, Schema Building Language Domains: Listening, Speaking Description: Students stand up after thinking about a question or having had a prompt to answer/think about, put their hand up and “ high 5 ” someone to pair up. Now they discuss their answer to a certain prompt or problem Affect: Supports learning environment with accountability Interaction / Practice: All must participate and practice oral language.

19. Slide 19 Strategy Stop A-Z Review Access Strategy: Cooperative learning Scaffold: Metacognition Language Domains: Writing &Listening and Speaking Description: It is a review strategy. Students think of a word related to a certain topic, one or more for each letter of the alphabet. Affect: Supports low-risk learning environment Interaction / Practice: Facilitation of Language Development, practice writing, and orally presenting

20. Slide 20 Strategy Stop Mathematically Speaking: Access Strategy: Instructional Conversations Scaffold: Schema-Building,Meta-Cognition Language Domains: Listening and Speaking Description: Students solve 2 different problems or half of a task. They take turns explaining their half of the completed task or given problem to the other student as he or she tallies on the chart each time a target word is used in the explanation. Students keep talking until all target words have been used. Affect: Supports low-risk learning environment Interaction / Practice: Facilitation of Language Development, practice speaking and listening, and orally presenting MATH!!!!

21. Slide 21 Strategy Stop 3 x 3 Sentence Builders Access Strategy: Academic Language Scaffold: Contextualization, Text Representation Language Domains: Writing Description: Picking 4(2 x2) or 9 (3x3) words from vocabulary list students put them in boxes and create sentences with words that go across horizontally, vertically and diagonally. Affect: Supports low-risk learning environment Interaction / Practice: Facilitation of Language Development, practice writing, and understanding interrelation between concepts and terms.

22. Slide 22 Strategy Stop Collaborative Poster Access Strategy: Cooperative Learning Scaffold: Bridging, Text Re-presentation, Schema Building Language Domains: Writing and Listening& Speaking Description: Students work in groups of four, each with a different colored marker. Students work together to strike a balance in solving the task while learning from each other and discussing the content. Affect: Supports low-risk learning environment Interaction / Practice: Facilitation of Language Development, practice writing, and deepens understanding concepts and procedures.

23. Slide 23 Foldables - Little Book Teacher Instructions: Keep the printing on the outside during all folds. Fold the sheet into fourths using the shorter side (hamburger folds). Open the sheet and fold in half using the longer side (hotdog fold). Open the sheet and fold in half using the shorter side. Cut from the center to the next fold. Open the sheet and fold in half using the longer side (hotdog fold). Fan out the cut sides and form the little book. Fill in your book with the information. Handout: Fraction Book

24. Slide 24 Analysis Pizza Teacher Instructions: This organizer can be used to organize parts into a whole or to take a whole topic and examine its respective parts. Slice the pizza into the number of slices needed to cover the topic. Have the students write sentences, draw pictures, or cut out and glue pictures onto the pizza to communicate knowledge and ideas about the topic. Handout: Fraction Analysis Pizza

25. Slide 25 Multiple Representations Learners acquire and store knowledge in two primary ways: linguistic (by reading or hearing lectures), and nonlinguistic (through visual imagery, kinesthetic or whole-body modes, and so forth). The more students use both systems of representing knowledge, the better they are able to think about and recall what they have learned. Marzano, R.J., Pickering, D.J., & Pollock, J.E. (2001). Classroom instruction that works: Research-based strategies for increasing student achievement. Alexandria, VA: Association for Supervision and Curriculum Development

26. Slide 26 Multiple Representations Teacher Instructions: Xerox and have students cut apart the pages(s) of cards. When cutting, tell students to trim extra off of edges as edges will not match. Place one complete set in an envelope, one envelope per group (group size: 2 – 4). Provide each group with blank copy or construction paper and glue sticks (or tape) Students are to match the 4 representations and glue them under the column headings. Variations: Leave out 2 or 3 pieces. Students are required to generate the missing pieces. If students are working on a particular skill leave out all of the pieces related to it and require students to generate them. Handout: Fraction Mix and Match Bag

27. Slide 27 Collaborative Posters Instructions Part 1: Have the materials person get a poster paper and problems handout. Fold the poster paper into three sections by turning the shorter edges to meet in middle without overlapping. Each group member should use a different colored marker and write his or her name in the top right corner. Write your assigned problem in the top section. Handout: Textbook Problems

28. Slide 28 Collaborative Posters Instructions Part 2: Show your work in the middle section. Remember that each person should write using only his or her colored marker. Your group may show more than one way to solve the problem Use the third section of your paper to copy and complete the sentence frames provided. The two co-reporter will explain their group solution to the class. The co-reporters should assist each other as they present.

29. Slide 29 3x3 Sentence Builder Fold a piece of paper into 9 squares. Pick 9 words from the target vocabulary list. Place a word into each of the 9 squares. Create a sentence using the 3 words on each vertical column, each horizontal row, and both diagonals for a total of 8 sentences