Number systems

1. Maths SolveIt

Number and Place Value
Year One
Maths | Year 6 | Number and Place Value | SolveIt | Number Systems

2. Number Systems

3.

Aim
• I can compare numbers and determine the value of each digit.
Success Criteria
• I can identify patterns in the way numbers are written.
• I can organise my ideas clearly.
• I can identify the value of each digit in a number.

4.

The Big Question
Can you identify numbers from different number systems?

5.

Contents
Beginning
Preparing
Exploring
Reviewing
The Big Question

6. Beginning

7.

Our Number System
In our number system, we use certain digits to represent numbers:
1, 2, 3, 4, 5, 6, 7, 8, 9
We use 0 as a place holder.
We can combine these digits in different ways to make numbers.
3 485 994
58
3904
792

8.

Our Number System
The value of a digit depends on its position in a number.
4 865 037
What is the value of the 4?
What does the 0 represent?
4 millions
0 hundreds
What does the 5 represent?
5 thousands

9.

Our Number System
Our number system is
standard, so once someone
knows the digits and
understands place value, they
can read and understand
any number.
Work with your partner to
read the following numbers
and answer the questions to
show your understanding.

10.

Understanding Numbers
568 392
Five hundred and sixty-eight thousand, three hundred and ninety-two.
Which digit is in the
thousands place?
8

11.

Understanding Numbers
7 957 001
Seven million, nine hundred and fifty seven thousand and one.
What does the 9
represent?
Nine hundred
thousands.

12.

Understanding Numbers
43 005 830
Forty-three million, five thousand, eight hundred and thirty.
If you divide this
number by 10, what
will the answer be?
Four million, three
hundred thousand,
five hundred and
eighty-three.

13.

Different Systems
Our number system is not the only number system. There are many
other number systems used by different people and for different purposes.
Our number system is a base 10 system, which means it uses ten
symbols to represent numbers. Some number systems have different
bases, such as binary, which is a base 2 system, or hexadecimal, which
is a base 16 system. Binary uses just two symbols to represent numbers,
while hexadecimal uses 16 symbols to represent numbers.
Other number systems are base 10, like ours, but use different symbols to
represent the 10 digits.
1234567890

14.

Different Systems
Today, we are going to be looking at different number systems.
We will focus on the Arabic, Chinese and Hindu number systems,
as well as our own.
These are all base 10 number systems.

15.

Understanding Number Systems
The following chart shows six numbers written in each of
the four different number systems.
You can also see this chart on
your Number System Sorting
Activity Sheet.
Your challenge is to sort the numbers into the four
different systems and identify all six numbers in each
number system.

16.

Understanding Number Systems

17. Preparing

18.

Identifying Patterns
Our challenge is to identify all six numbers in each
of the four number systems.
We can start by looking at the numbers we
recognise from our own system, then looking for
patterns in the way the numbers are written.
Look for similarities in the way the numbers
are written. For example, it may help you to look for
numbers that are written as single symbols. You may find
it useful to look for the 'longest' numbers, or those written
with the most symbols. Some numbers might have two of
the same symbol, so this can help you to identify which
number it represents. There may be some numbers that
share the same symbols. Look for these things to help you.

19.

Identifying Patterns
You might like to start by creating a table to keep track of the
different numbers you identify.
You may be able to cut out the numbers and try to sort and match
them this way.
What ideas do you have for identifying and sorting the numbers?

20. Exploring

21.

Identifying Numbers

22. Reviewing

23.

The Big Question
Can you identify numbers from different number systems?

24.

Number System Solutions
It makes sense to start with the numbers from our own number system.

25.

Number System Solutions
We can organise the numbers we have identified in a table.
Then we can use these numbers to identify the unfamiliar ones.
Number System A
3
35
10
57
73
100
Number System B
Number System C
Number System D

26.

Number System Solutions
We can then start to look for patterns. 3 has just one symbol.
We can use this to identify it in other number systems by looking for
other numbers that are just one symbol.

27.

Number System Solutions
It looks like we have identified 3 in two of the different number systems,
while we still have two possibilities for 3 in the last number system.
Let's enter this into the table.

28.

Number System Solutions
Look at the possibilities for 3 in number system D.
Which do you think is most likely to represent 3?
Number System A
3
35
10
57
73
100
Number System B
Number System C
Number System D

29.

Number System Solutions
It would seem like
is the symbol most likely to represent 3.
We can work on this idea and see if it makes sense.
Number System A
3
35
10
57
73
100
Number System B
Number System C
Number System D

30.

Number System Solutions
Now that we have identified 3, it makes sense to look for this
symbol to identify 35.

31.

Number System Solutions
We can add these symbols to the table.
We can also use the symbols for 5 from the 35 to identify the symbols for 57.
Number System A
3
35
10
57
73
100
Number System B
Number System C
Number System D

32.

Number System Solutions
We can use the symbols for 5 from the 35 to identify
the symbols for 57.

33.

Number System Solutions
Now we can see a pattern emerging.
We can use the symbols for 7 and 3 to identify 73.
Number System A
3
35
10
57
73
100
Number System B
Number System C
Number System D

34.

Number System Solutions
We can use the symbols for 7 and 3 to identify 73.

35.

Number System Solutions
We have managed to identify all the numbers except 10 and 100.
What can we look for to help us identify these numbers?
Number System A
3
35
10
57
73
100
Number System B
Number System C
Number System D

36.

Number System Solutions
We could attempt to identify 100 first, as it may have two
matching symbols at the end of the number.
We can also identify 10 using the same symbols.

37.

Number System Solutions
So now we have identified all the numbers in number systems B and C.
Number System A
3
35
10
57
73
100
Number System B
Number System C
Number System D

38.

Number System Solutions
Looking at number system D, we can notice a pattern in all the tens numbers.
The
Number System A
3
35
10
57
73
100
symbol appears in all of them.
Number System B
Number System C
Number System D

39.

Number System Solutions
This suggests that
Number System A
3
35
10
57
73
100
signifies a tens number and is therefore the symbol for 10.
Number System B
Number System C
Number System D

40.

Number System Solutions
We can match this symbol with 10.
This just leaves 100 to identify.

41.

Number System Solutions
The only symbol left is
. This does seem to fit as 100
because it has a symbol that looks to represent 1 at the start.

42.

Number System Solutions
We have identified all the symbols in each of the number systems.
Number System A
Number System B
Number System C
Number System D
3
35
10
57
73
100
Did you manage to identify them all?
Did you use a similar approach, or did you use different reasoning?

43.

Aim
• I can compare numbers and determine the value of each digit.
Success Criteria
• I can identify patterns in the way numbers are written.
• I can organise my ideas clearly.
• I can identify the value of each digit in a number.