Holy Saviour Family Maths Night July 30th 2014

7:00 – 8:30pm

Challenging all children in the mathematics classroom

30 minute presentation

Danny and TomTom 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?

  

Special offer

THREE PAIRS FOR THE PRICE

OF TWO

The free pair is the cheapest one

  

Special offerTHREE PAIRS FOR THE

PRICE OF TWOThe 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.

Option 1 split the bill - they pay $135 eachOption 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

Holy Saviour Family Maths Night July 30th 2014

7:00 – 8:30pm

Challenging all children in the mathematics classroom

Encouraging Persistence Maintaining Challenge

What characteristics would you expect for a successful mathematics lesson?

What characteristics would you expect for a successful mathematics lesson?

• 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

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

• 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

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

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:

What do our students say?

How much do you like doing maths at school?

Great

OK

Not so good

Terrible

Don’t know

How much do you like doing maths at school?

Great

OK

Not so good

Terrible

Don’t know

35%

40%

20%

5%

0%

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

Which type of lessons do you like?

Which type of lessons help you learn?

Average score

• practice 7 8• investigations 7 7• games 8 7• challenges 8 8.5

I am prepared to have a go to work things out even when I am not sure.

Always

Mostly

Occasionally

Never

Don’t know

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%

Challenging Tasks

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?

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?

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 = 146 + 6 + 6 + 2 = 206 + 6 + 6 + 6 + 2 = 26

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 = 146 + 6 + 6 + 2 = 206 + 6 + 6 + 6 + 2 = 26

Challenging Tasks

Launch

ExploreSummarise

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)

A ‘Challenging Task’ example lesson

Gr 3/4s on the topic of difference.

The students were set to work with limited explanation of the task, and they were not

shown how to do it.

The learning taskThe 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

For some students, a sheet was provided that prompted particular methods

2:45 Tenpast 4

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?

Extension was in-built

The requirement to use two methods provided challenge, and some were asked to find a third

method.

Also prepared was the following extension task in case it was needed

Work out how many days it is from June 29th to September 7th without using a calendar.

Discussion/Share Time

An important part of the lesson was the opportunity for students to share their

thinking with the class.

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?

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)

Launch

ExploreSummarise

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

FABLE FOR SCHOOLOnce upon a time the animals decided they mustdo something heroic to meet the problems of thenew world. So they organized a school.

They adopted an activity curriculum consisting ofrunning, climbing, flying and swimming. To make

it easier to administer the curriculum, ALL theanimals took ALL the subjects.

The duck was excellent at swimming, in fact better thanhis instructor, but he only just passed flying and hisrunning skills were very poor. Since he was slow atrunning he had to do extra practice after school andalso had to drop swimming and take extra classes in

running. This was continued until his poor webbed feetwere badly worn and he was only average at swimming.

But as average was acceptable at the school nobodyworried about this except the duck.

The rabbit started at the top ofhis class in running, but became a

school refuser because of thestress caused by so much extrawork in swimming.

The squirrel was excellent in climbingbut he developed behaviour problemsin the flying class, where the teacher

insisted on him starting from theground up instead of the treetop

down. He became so unfocused thathe scored a C in climbing and a D inrunning. His doctor has diagnosedADHD.

The eagle was a problem childand was disciplined severely. In

the climbing class he beat all theothers to the top of the tree, butinsisted on using his own way toget there. The school counsellorthinks he probably hasOppositional Defiant Disorder.

At the end of the year an abnormal eelthat could swim exceedingly well andalso run, climb and fly a little had thehigher average and was dux of theschool

MESSAGE:The differences in students makes a

major impact on what students need tolearn, the pace at which they need tolearn it and the support they need from

teachers and others to learn it.

Challenging Tasks Examples

Pen and Pencil

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

Our goal

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

Explain how you worked this out

• A pen costs $2 more than a pencil. If the pen costs $8, how much is the pencil?

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.

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

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?

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?

And this

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

Our goal

Remember our goal?• We can represent solutions to problems in

different ways, and see the connections between those representations.