Transcript A number is divisible by

NCETM workshop - 12th March 2008
Professional Development
Using Online Support,
Utilising Rich Mathematical Tasks
Liz Woodham
Mark Dawes
Jenny Maguire
[This is a PowerPoint version of the original SMART notebook]
The Project
Every teacher from 3 primary schools
Initial training
In-class support
Weekly teaching
INSET day
Wiki
CPD materials
How many different 3 digit numbers can you
make from the digits 1, 3 and 5?
How many of these are prime numbers?
1
3 5
Use ITP Number Grid to find
multiples and prime numbers
Click here
Divisibility Rules
A number is divisible by:
it is an even number
2 if
3 if
4 if
5 if
the last digit is 0 or 5
6 if
it is even and the digits add to a multiple of 3
7 if
use a calculator
8 if
you can halve it three times
9 if
10 if
the digits add to 9
the digits add to a multiple of 3
you can halve it and halve it again
the last digit is 0
Can you make square numbers by
adding 2 prime numbers together?
+
+
+
=4
=9
= 16
2 3 5 7 11 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
Daniel and Milan
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!
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 odd
therefore you would get an even number, which wouldn't be prime
Other strategies which children used
Genevieve, Tayler and Abi
First 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 bonds
or asked for advice
Jessie and Hannah
For 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.
Rebecca
If 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 and
sharing 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