Lecture notes
Maths Multiplication, Division and Place Value Notes
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- University Of Cumbria
These notes cover Multiplication, Division and Place Value.
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MATC4402 NotesMATC4402 – Place Value (Session 4):
Maths National Curriculum:
In Year 2, children must be able to recognise the place value of each digit in a two-digit number
Principles which underpin place value:
All numbers can be represented by a finite set of digits (0,1,2,3,4,5,6,7,8,9)
Initial groups Base-10
Base-10 number system:
It is a number that counts in groups of 10 and uses the digits (0,1,2,3,4,5,6,7,8,9) to represent
any other numbers
It is also known as the decimal system number
You can count in tens until you reach groups of 10 (10,20,30,40...90) when you add another
group of 10, you get 100, which means that there is 1 group of 100, zero (0) groups of ten and
zero (0) units
H T U
1 0 0 (1 x 100) (0 x 10) (0 x 0)
Successive groupings of numbers larger than 9 are made using powers of the base
Ten (10 = 10) Hundred (10 x 10) Thousand (10 x 10 x 10)
Exchange is the correct match term, not borrow or steal
Exchange 10 for one of those
5 key principles:
10 digits
The position of a digit in a number determines its value. For example, in 59 (5 represents 50) but
in 95 (the 5 represents 5)
Year 2 – must know 2-digit numbers
Year 3 – must know 3-digit numbers
Year 4 – must know 4-digit numbers
Year 4 students must be able to recognise the place value of each digit in a two-digit number (tens and
ones)
Zero (0) represents an empty column (a place holder)
Grouping and exchanging
Pictorial representation of place value:
Children must look at numbers and see different combinations that can be made using the numbers
Ways to make the number 27:
, MATC4402 Notes
20 + 7
27 units (ones)
2 tens and 7 units (ones)
Exchange:
When you have accumulated 10 in one place, this can be exchanged for one in the place to the
left
Being able to exchange 10 of those for 10 or 10 of those for 1
Exchanging is important in understanding how we count
It is fundamental to do calculations. For example, ‘carrying one’ in addition decomposition in
subtraction
Relationship between the groupings are important and children need time and varies in
experiences to ensure they fully understand how the groupings can interchange
You can play games such as multilink man, to help children develop an understanding of
exchanging
Tens Units / ones
1 x tens 3 x units
10 3
1 3
Using base-10 apparatus (Dienes Apparatus):
Using combinations of singles, sticks and flats can create numbers
These are usually used as concrete resources
Number made using base-10 / (dienes) apparatus = 1111
Big numbers:
7 digit number → 6, 4 5 2, 3 4 1
6 represents = 6,000,000 (452 = 400 + 50 + 2) (341 = 300 + 40 + 1)
Year 6 students should be taught to:
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