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 # 4 May 22 nd, 2010 Objective: Pattern Recognition

3. Slide 3 CA Standards 6 AF 3.0 Students investigate geometric patterns and describe them algebraically. 7 AF 3.4 Plot the values of quantities whose ratios are always the same (e.g., cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of the line equals the ratio of the quantities.

4. Slide 4 Pattern Block Trains # of Shapes Perimeter 15 2 1 1 1

5. Slide 5 Pattern Block Trains # of Shapes Perimeter 15 28 2 1 1 1 1 2

6. Slide 6 Pattern Block Trains # of Shapes Perimeter 15 28 311 2 1 1 112 2 1

7. Slide 7 Pattern Block Trains # of Shapes Perimeter 15 28 311 414 2 1 1 112 2 1 1 2

8. Slide 8 Pattern Block Trains # of Shapes Perimeter 0 15 28 311 414 +3 +1 Constant Change 2 1 1 112 2 1 1 2

9. Slide 9 Pattern Block Trains # of Shapes Perimeter 02 15 28 311 414 +3 +1 Constant Change 2 1 1 112 2 1 1 2

10. Slide 10 Graph of Pattern 1 Number of Shapes PERIMETERPERIMETER 1

11. Slide 11 What is the general rule? # of Shapes Perimeter 02 15 28 311 414 n? Number of Shapes PERIMETERPERIMETER 1 1

12. Slide 12 The general rule is P = _______n + ______. (Constant Change) ( P for figure #0) # of Shapes Perimeter 02 15 28 311 414 n? Number of Shapes PERIMETERPERIMETER 1 1

13. Slide 13 Pattern Block Trains Find the perimeter of trains as each block is added Get into groups of 4 and choose a pattern

14. Slide 14 Collaborative Poster Template Copy your shape trains Create each of the 4 shapes Find the perimeter of each shape and fill out the table Create the graph using the perimeter and figure # Complete the sentence frame

15. Slide 15 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.

16. Slide 16 Debrief use of Pattern Recognition through the use of Collaborative Posters What structures are necessary in order to ensure a successful lesson when working with this strategy? What skills and knowledge do students need to be successful in creating the table, graph, sentence frame What classroom management procedures need to be in place? How does this strategy evoke the use of language? How did this strategy provide access to the mathematical concept?

17. Slide 17 Evaluation Please give feedback in the box labeled, “Comments about Pedagogy Session” in your Follow Up #4 Evaluation form.

18. Slide 18 Thank You!! Esmeralda Orozco – Esmeralda.orozco @suhsd.k12.ca.us Nury Arrivillaga – Nury.Arrivillaga @lausd.net

19. Slide 19 Teacher Instructions: All students independently complete both mathematical tasks or problems. Student pairs are formed. Target vocabulary words are written on the MS chart in the left column. For lower grades, the teacher can fill in the words. The two students write their names across the top. One student explains half of the completed task or a 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. The other student then takes a turn doing the same. Mathematically Speaking Activity

20. Slide 20 Appointment Book Teacher Instructions: Students make appointments with different classmates. Teacher signals and announces first appointment. The students pair up (find their appointment classmate) and together they solve the problem on the board/overhead/document camera. The teacher signals and announces next appointment. Cycle continues until all/most appointments are filled. Closure: Students complete sentence frames at the bottom of their handout.

21. Slide 21 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

22. Slide 22 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

23. Slide 23 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.

24. Slide 24 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.

25. Slide 25 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

26. Slide 26 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!!!!

27. Slide 27 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.