1. ‘Engaging students in dynamic and collaborative maths & statistics’
A workshop of activities and ideas, for a differentiated teaching approach, that develops the statistical confidence of Year 9 & Year 10 students. A scheme will be presented that provides for individual and group learning at different curriculum levels within one class.

2. The world our students will work in relies on teams of people developing ideas, communication and collaboration. As a Maths teacher we can offer them that experience.

4. Student engagement Stats 1 ‘Investigate the throwing of a paper dart’
PPDAC cycle process complete, relaxed overview
Use of a summative question.
Based on ‘Harrier dart ‘ from Peter Newell workshop AMA Sat morning

5. WORKSHOP PARTICIPANTS
Form groups of about 4. All make some darts.
Harrier dart instruction sheets available.
Go fly them in your groups – trials
Back into room and develop up your dart investigation using PPDAC enquiry cycle. Discussion – notes on A3 sheet

9. CLASS of STUDENTS: Teaching process
Pose a question; How high can a paper dart fly? How far can a paper dart go? How long can a paper dart stay in the air? Into groups decide on question, start planning – groups decide and plan what their data collection and recording will be.
Plan: Teacher adds in aspects on board to help groups who are a bit stuck. Metres – rough estimates - tape measure – nearest half metre - (removes reading scale as an issue) If sky ward, use trees/buildings as guide. Stop watches - phones.
Data collected by groups
Analysis: Make a Dot plot on A3 & ‘I notice’ thoughts.
Conclusion: Discussion in groups
Groups present to class.
[Formal option: Presentation by Poster, members of group allocate the PPDAC parts to write up. Have examples of different investigation statements, graphs on other posters for them to check against.]

10. Low entry – high ceiling
Check out our mind-set about ourselves as teachers. We can ask ourselves when looking at a problem, situation or an investigation - ask ‘who is doing the maths’? The structure within a classroom in routines, seating norms, group work set ups, Do Now’s and Exit cards etc. are essential but when we structure the problem we are taking the maths out of it. Maths and stats knowledge and methods are both extremely important. BUT our classrooms need to be places where people actually do Maths. Problem solve, plan, find the question to ask, explore, give it a go, get it wrong, alter, decide what knowledge is needed, what method would be useful, discuss ideas with each other, explain their methods, hear other ideas and methods. Just as in music if we practice writing the notes and never play or hear an instrument, where is the joy and wonder in that?

11. Harrier Dart specs & performance
Write a report for the leader of a ‘dart throwing’ competition
Do a draft of every part you are responsible for in your exercise books – sketches of the dart and writing, headings for the poster
Present paper & dart diagrams, specifications and written methods as a poster (three or fours)
Summarise your findings verbally to the rest of the class –all members need to be familiar with all aspects, in order to answer questions

12. INVESTIGATION PROCESS (Measurement focus)
STAGE 1
Draw a diagram with dimensions and area of the paper required to produce the harrier dart
Make the harrier darts – one each. Fly them in the classroom to check out which one to use
Draw diagrams that show the side view and the plan view of the chosen dart
Provide dimensions of the dart on the diagrams and include the wing span and the length of the dart’s fuselage
Find and show working for the area of the wings and the area of the body of the dart

13. INVESTIGATION PROCESS
STAGE 2
Discuss what you want to find out about your dart in flight, what your dart does
Think how you will do this - organise yourselves - equipment – recording – trials – tasks – responsibilities - …………..
Collect your information
Ponder the connections between Harrier dart shape, dimensions and flight – provide jottings & diagrams of your ideas – what could you change & what do you think will be different in the flight
Complete your A3 poster and check all group members are up to speed with all findings
Prepare as a group for your class presentation

14. INVESTIGATION PROCESS
STAGE 3
Make a new dart of a different size or type, note some differences – shape, dimensions, area …..
Fly the darts outside and take note of their different aspects and performance - flight paths, distance travelled, height reached ….
Ponder and explore the connections between dart shape, dimensions and differences in flight – provide jottings & diagrams of your ideas
Complete your A3 poster and check all group members are up to speed with all findings
Prepare as a group for your class presentation

15. FURTHER EXPLORATION

17. Student understanding - probability Stats 2 Exploring probability through a game. Saving the whales as part of the Probability matrix of TASKS. A pod of whales has stranded on sandbanks at Farewell Spit. Save them as quickly as you can

19. Based on ‘Wallowing Whales’ Figure it Out booklets Statistics Book 1 Level 4. Adapted by Barb Wallis
Task 4: Wallowing Whales’ – initial strategy written
- game played for 3 rounds
Task 5: Experimental change of strategy, as game was played, written up. Homework.
Day 6
[7 marks]
Task 1: Wallowing Whales’ – further rounds, best strategy – collected from whole class
Task 2: Wallowing Whales’ – theoretical probabilities – array of values
- class discussion of connection
Task 3: Theoretical strategy written. Homework.

20. Student engagement Stats 3
‘Investigate the effect of rotor blade length on helicopter flight by ….’
PPDAC cycle process to replicate the design process in a real student context. Use of a comparative question.
Plan – sources of variation, number of trials decided, prediction. Calculator for stats measures. Box & Whisker graphs. Full conclusion.
Based on ‘Helicopter rotor blades – long & short‘ from Gillian Frankcom & Alan Santos

21. A statistical investigation
Helicopters
A statistical investigation

22. ‘Helicopter rotor blade length’
The structured worksheet is adapted to a PPDAC investigation in a similar way to the ‘paper dart’ and ‘reaction time by ruler’ activities. It is a more advanced use of the PPDAC cycle, planning aspect expanded -sources of variation sorted in planning, number of trials, method of release, timing method, expanded to whole class data collection and leads to source of ‘box & whisker’ plots -including graphics calculators if available - use of statistical measures for ‘I notice…’ and conclusions.
Also can be used as a basis of discussion of sample results; – same scale boxes placed on the wall & then can look at the median variation by forming lines as a border (also upper and lower quartiles). Compare to combining the samples for stats information.

23. Helicopter Rotor blade length investigation
Workshop participants make their rotors and fly them in pairs
Discuss sources of variation – begin the planning stage of a full investigation. How it could be organised.
Worksheet & power point resource.

25. Structured assignments for the reinforcement of aspects of the statistical enquiry cycle.
Fundraising : Selling chocolates or Doing odd jobs
All Blacks Team: 2015 Men’s Rugby World cup winners
Contributed by Jen Triggs, Barb Wallis & Christine Massey High School

27. Collecting Data in the Classroom Simple activities to engage students
Amy Cornelisen
Garin College

28. I wonder how far an origami frog can jump.
Does the type of paper matter?
Does the size of the paper square matter?
Will a party favour frog jump farther?
How will I measure? From the “nose” or the “tail”?
What accuracy will I use?

29. Done by: Sally Zaatiti

30. Creating a Frog Origami
In this presentation you are given step by step instructions to make a frog origami and if it is made correctly it acts like it is really jumping.

31. POWERPOINTS Harrier Dart Investigations
Barb Wallis (based on Peter Newell workshop)
Helicopter investigation
Alan Santos/Gillian Frankcom
All Blacks investigation/ Fundraising
Jen Triggs, Christine Kiernan, Barb Wallis
Origami leap frog
Amy Cornelisen (construction by Sally Zaatiti)
Contact facilitator: