1. Zone 1 Session 3 2010 PLT conversations – place value

2. Homework from last session Please bring an example of the evidence presented by one teacher and the documentation that arose from one Numeracy PLT meeting. Be ready to describe the PLT discussion

3. PROGRAM Session 1: The Role of a Numeracy PLT Session 2: PLT Conversations - Fractions Session 3: PLT Conversations – Place value

4. The purpose of this session is for participants to: explore the stages for understanding place value experience some activities for teaching place value participate in some Numeracy PLT conversations based on evidence from AiZ classrooms

5. AGENDA 9 -9.30 Intro and Warm Up 9.30 - 11 Explore the pathway for understanding place value 11.00 – 11.30 MT 11.30 -12.30PLT discussions based on evidence What did we learn? 12.30 – 1.00 Plenary

6. Warm Up NUMBER HANGMAN

7. PLACE VALUE ONLY refers to the written form of number Material that show groupings of 10 and highlight the nature of 10 as a new unit are crucial to building the knowledge of place value For numbers > 10 there are no new symbols. Instead, there is a set of rules that generate the new numbers from those already learned

8. What are the big ideas for understanding place value? A number is a representation that can be substituted for - materials that show a quantity - a word that describes the quantity - symbols that record the number succinctly Ten is significant in our number system (10 ones makes 1 ten)

9. Stages of understanding place value Counting (0-9) as the basis for all other numbers in the base10 system Thinking in 10s. 10 ones = 1 ten, 10 tens = 1 hundred Two digit place value 20-99 first, then 11-19 Extend pattern to 3 digit numbers continue with larger numbers (10 hundreds = 1000, etc) Exponents for when very large numbers are involved (10 6 )

10. Early maths foundations Conservation: the number of items remains constant regardless of their arrangement Classify: Items can be classified according to specific criteria (eg colour, shape size) Comparison: establishing a relationship between items (shorter than, fatter than, etc) Ordering (builds on comparison) arrange items in line based on a rule Patterning: able to see, describe, extend and repeat patterns

11. The layers of understanding Materials are used to develop an understanding of counting Ten forms a new unit – bundles are introduced As numbers become larger, bundling gives way to the more abstract material - MAB

12. The layers of understanding After 3 digit numbers the use of material is no longer practical. Instead the digits are group to show thousands, millions, etc As numbers become even larger they are expressed using exponential notation 1 724 345 1,724,345 5 trillion = 5 12 rather than 5,000,000,000,000

13. Make the most of it Some place value activities

14. Number expanders 5203 5 thousands 2 hundreds 0 tens 3 ones 520 tens 3 ones

15. Montessori cards 50 thou 0 san 0 ds 20 hund 0 reds 70 tens 3 ones 5273 ones

16. SNAP

17. Place Value Bingo Create a version of Bingo that could be used to consolidate Place Value understandings. (Consider using the three representations of materials, words and symbols) Can you make a version that involves 2 and 3 digit numbers also?

18. Relationships drawings

19. Calculator wipe-out 1 574 293 What would the number be if there was a zero in the thousands place? How can you ‘wipe out’ the 4 without changing the other digits? What number do we subtract to make the calculator display 500 000? What number do we add to make the calculator display 2 000 000?

20. DOT PLATES find all the people with the same number as you how else could you use these dot plates?

21. Discussions FIFTEEN PENCILS

22. A Numeracy PLT is NOT about ‘sharing’ what I did in class today or describing an engaging activity that I came across is a collaborative, professional discussion focused on identifying a starting point for student learning and designing effective learning opportunities to move students along the learning continuum

23. Role of PLT Team Leader Keep the PLT focus PD the team Mentor Ensure challenge not ‘share’ Accountability Link data to classroom practice Team build

24. A Numeracy PLT model 1.Review the (triangulated) data Seek evidence (What did the student make, say, do or write) What do we know and how do we know it? 2. Plan the next step Where does the student need to go next? (progress/consolidate?) 3. Identify the strategies and resources needed How will the student get there? 4. Stipulate the evidence required How will we know when the student is there?

25. Team member Teacher Team Leader Team member Triangulated Data EVIDENCE Evidence: What can the student make, say, do or write? Review data Plan next step Strategies/resources New evidence

26. Some challenging questions: What makes you say that? How do we know that? What is he demonstrating that he can do well? What are his misconceptions? Is he ready for that? How does the work from day to day relate? Was the jump to addition too fast? Is that what you expected from the student? What will you do to manage the student’s leaning if he’s the only one in class at this level?

27. Some challenging questions: How did the work relate to the evidence in the Rocket report? What resources do we use to move him on? Would you consider this a valuable piece of data? Do we agree that he’s operating at Level C? Is he applying a rule to equivalence? Does he demonstrate an understanding of mixed numbers? Were activities organised to develop knowledge and understanding or just ‘tricks’?

28. Using evidence from your own school 1.Review the (triangulated) data Seek evidence (What did the student make, say, do or write) What do we know and how do we know it? 2. Plan the next step Where does the student need to go next? (progress/consolidate?) 3. Identify the strategies and resources needed How will the student get there? 4. Stipulate the evidence required How will we know when the student is there?

29. Our journey Skills AND Thinking & Reasoning Whole school planning for numeracy Guiding principles for all maths lessons What to teach? - VELS Focus statements How can we use NAPLAN data? Different models for unit planning The Role of a Numeracy PLT PLT Conversations about fractions PLT Conversations about place value