1. Zone 1 Session 2 2010 PLT conversations

2. Homework from last session Please bring samples of some of the planning docs your school has developed as part of your Numeracy Annual Plan

3. Warm Up LaunchExplore Summarise Domain- Mathematics Week 3 Term 1 Dimension~ Number / Measurement Monday 60 minutes Tuesday 60 minutes Wednesday 60 minutes Thursday 60 minutes Friday 60 minutes Number Fluency Activity Whole Group Octable- use yellow numbers & add 5 to each. Multiply green numbers by 2, Double all purple numbers, then add 3. 2 & 1-minute times table challenge. Octable- Write the numbers before & after the blue numbers, add 10 then take away 2 from all the red numbers. Tell me about the answer- 7x9= how many digits will it have, will it be odd or even, will it be divisible by 2, will it be a whole number……. 2 & 1-minute time table challenge. Teaching Focus Whole Group Focus- To use place value to determine the size and order of numbers to millions. Vocabulary- million, thousand, hundred, ten, one, tenths, hundredths, decimal, place value Focus- To use place value to determine the size and order of numbers to millions. Vocabulary- million, thousand, hundred, ten, one, tenths, hundredths, decimal, place value Focus- To use place value to determine the size and order of numbers to millions. Vocabulary- million, thousand, hundred, ten, one, tenths, hundredths, decimal, place value Focus- To use place value to determine the size and order of numbers to millions. Vocabulary- million, thousand, hundred, ten, one, tenths, hundredths, decimal, place value Focus- To learn how to round numbers up & down. Vocabulary- rounding up & down, higher, lower than, approximate, estimate, nearest Calculat ors Arthur, Elia, Jackie, Brittney, Miriam, Trent, Mikaela, Alrabab, Students write down vocabulary words in their maths books. Use number expanders to make and discuss numbers. e.g. 236= 2 H, 3 T & 3 O, / 2 H & 36 O, / 23 T & 6 O, / 236 Ones… Students write the given numbers in expanded form & as digits, e.g. two hundred & ninety-eight, 200+90+8, 2 hundreds, 9 tens, 8 ones, 298. Students finish work from yesterday. Look through magazines & newspapers to find and make 6 digit numbers or bigger, paste these in your maths book. Write these numbers in words Order them from smallest to largest. Look through magazines & newspapers to find and make 6 digit numbers or bigger, paste these in your maths book. Write these numbers in words Order them from smallest to largest. Make a number that has a 6 in the tens of thousands place…. Students continue with making the numbers (as written on the blackboard), writing them in words & ordering from smallest to largest. Early finishers- Play ‘What number am l? on their own or with a partner. Protracto rs Jasper, Pratap, Marnie, Ruby, Natasha, Patrick, Fatima, Mitchell Use large place value columns. Students write a single digit & stand in on of the place value columns. ‘How do we say this number? What do we need to think about to work out what the number is? What does the 2 in this number represent? What does the 6 represent? Discuss the need to count places from the right & grouping digits into threes e.g. the last three digits are always hundreds, tens, ones, the next three are always hundreds of th’s, tens of th’s and thousands…. Continue to discuss how place value can change the size of a number. Ask students to make a number with a 5 in the thousands, a 2 in the 100’s of thousands. Students complete similar tasks in their books. Write these numbers in words. Order from smallest to largest. Students write reflection in their maths books, write down what they learnt today. What did you learn that was new? What can you now do that is new? What do you know now that you didn’t know 1 or 2 lessons ago? What new things did you do that were part of how you learned? Who uses this kind of knowledge and skill in their work? Ask students to discuss what thinking they had to do when making the numbers with some numbers having to be in a specific place value column? From Irene’s school

4. PROGRAM Session 1: The Role of a Numeracy PLT Session 2: PLT Conversations Session 3: A process for studying lessons

5. The purpose of this session is for participants to: revisit the role of a Numeracy PLT explore the stages for understanding fractions experience a Numeracy PLT conversation about fractions participate in some Numeracy PLT conversations based on data from AiZ classrooms identify some worthwhile focus questions for use in a Numeracy PLT

6. AGENDA 9 - 9.30 Share any planning docs 9.30 – 9.45 Warm Up 9.45 –10.00 Recap of PLT roles 10 – 11.00 Examining the pathway for understanding fractions 11.00 – 11.30 MT 11.30 -12.00 Consider Ryan’s evidence 12 – 1.00 PLT discussions based on evidence What did we learn?

7. Warm Up 27134726 34521743 56827338 79615846 23547281 54294411 76967059 98561437 12432662 76588351

8. 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

9. Ryan has spent a fortnight learning about fractions with a focus on creating equivalent fractions

10. From the fraction & decimal interview

12. What are the big ideas for understanding fractions? EQUAL parts of a DEFINED unit Applies to continuous and discrete models Requires multi-layered understandings - part of whole - numbers - division - benchmarking - operators

13. Show one quarter in 5 different ways Show one half of a square other than a line through the middle When would the situation suit this half? Is it 1? Instead of ¾ of 20 = …… Try if ¾ of the unit is 9, what is the unit? The bottle was 3/5 full. I drank ⅓ of that. What fraction of a full bottle did I drink? Hands up for Common Denominators

14. Stages of understanding fractions Sharing (6 shared between 3 or 6 ÷ 3) Part/whole (¾ is 3 out of 4 equal parts of a set) Measure (¾ is a distance of 3 [¼ units] from 0 on a number line Benchmarking (¾ is larger than ½ and the larger the denominator smaller the piece) Operator (¾ of something.. a ‘shrinking’ action) Quotient (3 ÷ 4, ¾ is the amount each person gets) Ratio (3 parts juice, 4 parts water 3:4 ratio of juice to water) Each adds a layer of understanding

15. A reading: Knowledge skills and behaviours of students with an understanding of fractions A game: Colour in fractions 1st roll is denominator, 2nd roll is numerator Each row = one whole unit. (ie board = 6 units) A brick cannot be cut to make desired fraction If unable to use the fraction thrown, must PASS First to colour in their wall wins.

16. Ryan has spent a fortnight learning about fractions with a focus on creating equivalent fractions Use his work samples to model a PLT discussion

17. DVD Evidence: What does he say?

18. 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

19. 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?

20. Team member Teacher Team Leader Observer/recorder of questions being asked/challenges posed Team member Triangulated Data Evidence: What can the student make, say, do or write? Review data Plan next step Strategies/resources New evidence

21. Give some examples of good challenging questions that were asked What evidence seemed useful? What did the team leader do that helped the process? What resources were referred to? What timelines were set for the collection of future evidence? What type of future evidence was suggested? What else did you notice that was of interest? Observer

22. 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 Ryan? What will you do to manage Ryan’s leaning if he’s the only one in class at this level?

23. 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’?

24. For next 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

25. Using the evidence from your own classroom Give some examples of good challenging questions What evidence seemed useful? What did the team leader do that helped the process? What resources were referred to? What timelines were set for the collection of future evidence? What type of future evidence was suggested?