Professional Development Using Online Support,

Utilising Rich Mathematical Tasks

Liz WoodhamMark Dawes Jenny Maguire

NCETM workshop - 12th March 2008

[This is a PowerPoint version of the original SMART notebook]

The Project

Every teacher from 3 primary schoolsInitial trainingIn-class supportWeekly teachingINSET dayWikiCPD materials

1 3 51

How many different 3 digit numbers can you make from the digits 1, 3 and 5?

3

How many of these are prime numbers?

1 5531 533 51 531 31 51

Use ITP Number Grid to find multiples and prime numbers

Click here

Divisibility Rules

2 if it is an even number

A number is divisible by:

5 if

3 if

6 if

4 if

9 if

8 if

10 if

7 if

the digits add to a multiple of 3

you can halve it and halve it again

you can halve it three times

it is even and the digits add to a multiple of 3

the last digit is 0 or 5

the last digit is 0

the digits add to 9

use a calculator

Can you make square numbers by adding 2 prime numbers together?

22

=

2

1694

2 11753

=

==

+++

++

13

Try with the squares of numbers between 4 and 20

Do you discover any square numbers which cannot be made by adding 2 prime numbers together?

If you do can you think why these numbers cannot be made?

Explain how you tackled the investigation

Tips: make a list of square numbers

We noticed that you had to add 2, 3 or 5 to most of the numbers

So we tried each of these numbers and worked out if the answer was a prime number and it worked!

Daniel and Milan

If a square number is odd,then if you take 2 away from it,if that number isn't a prime number,you can't add 2 numbers to make a square

When asked why, Oliver replied that if it didn't work taking 2 away, the other prime numbers were oddtherefore you would get an even number, which wouldn't be prime

Other strategies which children used

Genevieve, Tayler and AbiFirst we tried random numbers which fitted the rules.Then we found prime numbers close to the square and used littler prime numbers to fill the gaps.When we got stuck we started thinking of number bondsor asked for advice

Jessie and HannahFor numbers over 100 we got a close odd number and found a prime number to go with it.Then we checked to see if the first number was a prime number.

RebeccaIf the square number is odd you have to take away 2 and if that number is prime, it can be done.If the square number is even it has to be odd + odd or even +even

Improving investigative and problem solving skills was identified on our School Development Plan.

We felt we needed to focus on:

Engaging reluctant mathematicians

Developing children's explanation of their strategies

What we have gained from the project:

focus on and development of Nrich ideas to match the needs of our children / designing Smartboard pages

opportunity to watch Mark deliver lessons and to observe our children closely

discussion with Mark and feedback on our lessons

increase in children's confidence to begin work

increase in teachers' confidence to deliver

opportunity for peer observations/discussions andsharing practice/resources with other schools

involvement of parents/ successful Education Evening

Engaging reluctant mathematicians

Importance of selecting an investigation at a level they can access but can be developed by more able

Emphasising that in investigations you don't get the solution first time/ it's OK to get it wrong and try again

Stopping regularly for "mini plenaries" after they have been given a time to explore

Grouping of children to work with more confident children when appropriate

How we develop children's explanations:

Asking children to think about what they would tell others to do in order to begin the investigation

Encouraging children to explain why they got the solution

Exploring and describing patterns

More able children working with and encouraging less confident without telling them the answer (a challenge for the more able!)

Giving children the task of planning an investigation for a group of younger children

Where next?

Maintain profile of the work by reporting on it regularly in staff meetings and governors

Embed the Nrich materials in our planning

Include investigations in all the units of work

Aim to teach more through investigations

Continue to give opportunity for peer observations