1. Holy Saviour Family Maths Night July 30 th 2014 7:00 – 8:30pm Challenging all children in the mathematics classroom 30 minute presentation

2. Danny and Tom Tom and Danny travelled from school to the shops on foot. Danny walked half the distance and ran half the distance. Tom walked half the time and ran half the time. They started at the same time, and walked at the same speed as each other and ran at the same speed as each other. Who arrived first, or was it a tie?

4. Special offer THREE PAIRS FOR THE PRICE OF TWO The free pair is the cheapest one Special offer THREE PAIRS FOR THE PRICE OF TWO The free pair is the cheapest one Virginia and Samantha go shopping for shoes. Virginia chooses one pair for $110 and another for $100. Samantha chooses a pair that cost $160. When they go to pay, the assistant says that there is a sale on, and they get 3 pairs of shoes for the price of 2 pairs. Give two options for how much Virginia and Samantha should each pay? Explain which option is fairer.

5. Option 1 split the bill - they pay $135 each Option 2 split the saving – Virginia pays $160 and Samantha pays $110 Virginia $110 + $100 Samantha $160 When they go to pay, the assistant says that there is a sale on, and they get 3 pairs of shoes for the price of 2 pairs. (cheapest pair is the free pair) Now the total spend is $270

6. Holy Saviour Family Maths Night July 30 th 2014 7:00 – 8:30pm Challenging all children in the mathematics classroom Encouraging Persistence Maintaining Challenge

7. What characteristics would you expect for a successful mathematics lesson?

8. All participants actively engaged in learning Collaboration The talk is about the maths Students know the focus and purpose The learning objective is met Enabling and extending Challenging struggle All students aware of success criteria Feedback and self reflection Problem solving Effective, efficient and diverse strategies Students using various approaches building on what they know Relevant, real life connections Opportunity for transfer Deep and good questioning Using the language of mathematics Success

9. We know that many students: forget what they have learnt from one year to the next, are unwilling to engage with challenging tasks, develop negative attitudes to mathematics early. The current context in Victoria

10. Understanding – (connecting, representing, identifying, describing, interpreting, sorting, …) Fluency – (calculating, recognising, choosing, recalling, manipulating, …) Problem solving – (applying, designing, planning, checking, imagining, …) Reasoning – (explaining, justifying, comparing and contrasting, inferring, deducing, proving, …) In the Australian Curriculum

11. Choosing tasks and structuring lessons If we are seeking fluency, then clear explanations followed by practice will work If we are seeking understanding, then very clear and interactive communication between teacher and students and between students will be necessary If we want to foster problem solving and reasoning, then we need to use tasks with which students can engage, which require them to make decisions and explain their thinking

12. for students to: know that they can learn know that they can learn mathematics know that they can get smarter by trying hard enjoy the mathematics they are learning see the usefulness of mathematics to them be able to interpret the world mathematically see the connection between mathematics learning and their future study and career options We believe that it is important:

13. What do our students say?

14. How much do you like doing maths at school? Great OK Not so good Terrible Don’t know

15. How much do you like doing maths at school? Great OK Not so good Terrible Don’t know 35% 40% 20% 5% 0%

16. Which type of lessons do you like? Give each a score out of 10 Which type of lessons help you learn? Give each a score out of 10 practice investigations games challenges

17. Which type of lessons do you like? Which type of lessons help you learn? Average score practice 78 investigations 77 games 87 challenges 88.5

18. I am prepared to have a go to work things out even when I am not sure. Always Mostly Occasionally Never Don’t know

19. I am prepared to have a go to work things out even when I am not sure. Always Mostly Occasionally Never Don’t know 48% 36% 8% 5% 3%

20. Challenging Tasks

21. I know I have between 15 and 25 apples. When they are put into groups of 6 there are 2 apples left over. How many apples do I have?

23. 6 + 6 + 2 = 14 6 + 6 + 6 + 2 = 20 6 + 6 + 6 + 6 + 2 = 26

24. I know I have between 15 and 25 apples. When they are put into groups of 6 there are 2 apples left over. How many apples do I have? 6 + 6 + 2 = 14 6 + 6 + 6 + 2 = 20 6 + 6 + 6 + 6 + 2 = 26

25. Challenging Tasks LaunchExploreSummarise

26. What ‘Challenging Tasks’ are NOT! Asking questions that are so easy that everyone can do them Lessons that are so hard that the students feel overwhelmed Setting up groups that might allow some students to hide Excessive repetition (although, some is needed)

27. A ‘Challenging Task’ example lesson Gr 3/4s on the topic of difference.

28. The students were set to work with limited explanation of the task, and they were not shown how to do it.

29. The learning task The time is now 2:45. The bus leaves at 10 past 4. How long is it until the bus leaves? This layout was intended to communicate the need for two different methods

30. For some students, a sheet was provided that prompted particular methods 2:45 Ten past 4

31. And some slight variations on the task were prepared (enabling prompts) The time is now 2:45. The bus leaves at 5 to 3. How long is it until the bus leaves?

32. Extension was in-built The requirement to use two methods provided challenge, and some were asked to find a third method.

33. Also prepared was the following extension task in case it was needed Work out how many days it is from June 29 th to September 7 th without using a calendar.

37. Discussion/Share Time An important part of the lesson was the opportunity for students to share their thinking with the class.

38. The consolidating task Sammy goes to bed at quarter past 8 in the evening. He gets up at ten to 7 in the morning. How long has he been in bed?

39. Thinking about the lesson structure In this view, the sequence – Launch (without telling) – Explore (for themselves) – Summarise (drawing on the learning of the students) … is cyclical and might happen more than once in a lesson (or learning sequence) LaunchExploreSummarise

40. Post-assessment This lesson was taught at Holy Saviour on the last day of term 2 in 2012 Near the start of term 3, the students were asked to complete a similar item under test conditions 96% of the students who were present for both the learning task and the test answered the test item correctly with a clear explanation

41. FABLE FOR SCHOOL Once upon a time the animals decided they must do something heroic to meet the problems of the new world. So they organized a school. They adopted an activity curriculum consisting of running, climbing, flying and swimming. To make it easier to administer the curriculum, ALL the animals took ALL the subjects.

42. The duck was excellent at swimming, in fact better than his instructor, but he only just passed flying and his running skills were very poor. Since he was slow at running he had to do extra practice after school and also had to drop swimming and take extra classes in running. This was continued until his poor webbed feet were badly worn and he was only average at swimming. But as average was acceptable at the school nobody worried about this except the duck.

43. The rabbit started at the top of his class in running, but became a school refuser because of the stress caused by so much extra work in swimming. The squirrel was excellent in climbing but he developed behaviour problems in the flying class, where the teacher insisted on him starting from the ground up instead of the treetop down. He became so unfocused that he scored a C in climbing and a D in running. His doctor has diagnosed ADHD.

44. The eagle was a problem child and was disciplined severely. In the climbing class he beat all the others to the top of the tree, but insisted on using his own way to get there. The school counsellor thinks he probably has Oppositional Defiant Disorder. At the end of the year an abnormal eel that could swim exceedingly well and also run, climb and fly a little had the higher average and was dux of the school

45. MESSAGE: The differences in students makes a major impact on what students need to learn, the pace at which they need to learn it and the support they need from teachers and others to learn it.

46. Challenging Tasks Examples

47. Pen and Pencil

48. In this lesson, I need you to show how you get your answers keep trying even if it is difficult (it is meant to be) explain your thinking listen to other students

49. Our goal We can represent solutions to problems in different ways, and see the connections between those representations.

50. Explain how you worked this out A pen costs $2 more than a pencil. If the pen costs $8, how much is the pencil?

51. The Learning task A pen and a pencil cost $7. The pen costs $6 more than the pencil. How much does the pencil cost? Represent your solution using two DIFFERENT methods.

52. If you are stuck A drink and a snack costs $10. The drink costs $2 more than the snack. How much does the drink cost? Ask the students to show their solution in two different ways

53. If you are finished A book and a ruler and an eraser costs $20. The book costs more than the ruler. The book and the ruler costs $16, the ruler and the eraser costs $12. How much might the book, the ruler and the eraser each cost?

54. Now try this A hat and a pair of sunglasses cost $110. The sunglasses cost $100 more than the hat. How much does the hat cost?

55. And this At a party there are 230 people. There are 100 more adults than children. How many adults are there at the party?

56. Our goal Remember our goal? We can represent solutions to problems in different ways, and see the connections between those representations.