professional development using online support, utilising rich mathematical tasks liz woodham mark...
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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]
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The Project
Every teacher from 3 primary schoolsInitial trainingIn-class supportWeekly teachingINSET dayWikiCPD materials
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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
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Use ITP Number Grid to find multiples and prime numbers
Click here
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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
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Can you make square numbers by adding 2 prime numbers together?
22
=
2
1694
2 11753
=
==
+++
++
13
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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
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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
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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
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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
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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
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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
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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
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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
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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