4. You will need a
calculator…or your phone!
First:
Enter a 3 digit numeral
onto your calculator where
all the digits are the same
e.g. 111
(please don’t use 000)
Then…
Divide it by the sum of its
digits. 111 for example
would be divided by 3
DON’T PRESS = YET
Finally…on the count of
three, lets all press =123
5.
6. It’s all to do with pattern, one of the big ideas at
the heart of mathematics.
111 ÷ 3 is indeed 37. But 222 ÷ 6 is also 37, since
we are dividing twice as much as before (222 is
twice 111) by twice as much as before (6 is twice
3)!
Or, putting it another way:
111 ÷ 3 = 37, which can be written as (111 x 1) ÷ (3 x 1) = 37
222 ÷ 6 = 37, which can be written as (111 x 2) ÷ (3 x 2) = 37
333 ÷ 9 = 37, which can be written as (111 x 3) ÷ (3 x 3) = 37
444 ÷ 12 = 37, which can be written as (111 x 4) ÷ (3 x 4) = 37
555 ÷ 15 = 37, which can be written as (111 x 5) ÷ (3 x 5) = 37
666 ÷ 18 = 37, which can be written as (111 x 6) ÷ (3 x 6) = 37
777 ÷ 21 = 37, which can be written as (111 x 7) ÷ (3 x 7) = 37
888 ÷ 24 = 37, which can be written as (111 x 8) ÷ (3 x 8) = 37
999 ÷ 27 = 37, which can be written as (111 x 9) ÷ (3 x 9) = 37
Beautiful!
8. So …
What is the
main purpose
of the course?
January 2019
9. • To address your subject knowledge in
mathematics
• To equip you to teach mathematics to
pupils in early years and primary
settings
10. • Workshops – you will do a lot of
mathematics!
• Subject-knowledge development,
self-study and tests
• An assignment
• Placement tasks, including …
planning, teaching, assessing
and evaluating mathematics in
schools
11. Place Value – making connections
Adapted from Haylock and Cockburn (2008)
Symbols
Concrete Experiences
PicturesLanguage
Digit
Value
Place
Worth
Tens
Ones
Equals
Excellent!! Well done!!
Right, moving on…
Oh, hang on. Does anyone want to know how that works…? Really? No-body knows?
Well, we’re running out of time so we must move on!
I’m actually only joking. But it does raise an interesting point. Mathematics can be a confusing, even baffling subject for some of our children. That was a simple magic trick designed to surprise. The maths is interesting.
Key things to consider when using this vocabulary with children:
making sure that the teen and ty numbers are said clearly.
digit - in the same way that words are made out of letters numbers are made out of digits. Children need to be encouraged to use this term to describe the parts of a number.
value and worth may need to be discussed and some understanding established with the children. These are tricky words to explain.
TASK: Discussion in pairs
How would you explain the terms ‘value’ and ‘worth’?
FEEDBACK: You may wish to use ‘stands for’ or ‘means’. It is important that you are comfortable with the vocabulary you are using as well.
36
Value of each digit is determined by it’s place
For example:
The value of 6 in 36 is 6 ones (units)
It is worth 6
The value of 3 in 36 is 3 tens
It is worth 60