Download Properties of Numbers, Reasoning about Numbers

YR5 pp44-71
21/3/01 4:15 pm
Page 46
UNIT 23
Properties of
Numbers,
Reasoning about
Numbers
This week we will be working on multiples,
factors and square numbers. We are going to
count in steps and give examples of general
statements.
OBJECTIVES
• To recognise and extend more complex number
sequences.
• To recognise multiples and factors and
relationships between them.
• To recognise and generate square numbers.
L ANGUAGE
square number, multiple, factor, odd, even, sequences.
RESOURCES
PCMs 26 and 27, paper, pencils.
• Can you start at 5 and count in twenties to
205? Was that difficult?
Teaching Input 1
o
• Can you count in fives from zero to 100
and back?
Write some 2-digit numbers on the board, for
example, 18, 21, 27, 40, 70, 35, 42, 56.
• Can you count in sixes from zero to 102
and back?
• Which numbers are divisible by seven? This
is the same as saying that seven is a factor.
• Can you count in sevens from zero to 105
and back?
Repeat.
• Can you count in twenty-fives from zero to
1000 and back?
c
• Can you describe the rules and extend the
following sequences:
• Now test it. Decide for yourself how to
work and how to record your work.
40, 27, 14, …
41, 37, 32, 26, …
d
105, 125, 150, 180, …
d
PCM 26
Ask the children to complete the exercise on
PCM 26.
• Did any of the numbers not fit anywhere?
Which?
• Which box had most numbers?
Teaching Input 2
o
• Can you count in tens to 500 and back?
• Can you count in twelves to 144 and back?
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• Which numbers have an odd number of
factors?
• What do you notice about these numbers?
• Can you make up a sequence for the group
to continue? Make sure each child has a turn.
c
• Which number under 50 do you think has
the most factors?
• How did you record your work?
Teaching Input 3
o
• Can you tell me a rule about odd and even
numbers and the difference between them?
How about their sum?
• What can you tell me about them? Give
examples please. For example, the sum of
three even numbers is even – give examples
such as 4 6 8 18. Write the children’s
statements down.
• How can we recognise a number that is
divisible by 10?
YR5 pp44-71
21/3/01 4:15 pm
Page 47
PROPERTIES OF NUMBERS, REASONING ABOUT NUMBERS
• How can we recognise a number that is
divisible by 100?
UNIT 23
i
• We call a number whose factors add up to
itself (not including itself) a perfect number.
For example, 1 2 3 6.
• How can we tell if a number is divisible by
2, 4 and 5? Give examples.
• What do we mean by factors?
• Can you find another perfect number under
50? 28: 1 2 4 7 14 28
• Can you give me two numbers that are
factors of 10?
• Are there any other pairs of factors of 10?
i
d
• Can you explain what you have been
doing?
• What numbers did you find?
Teaching Input 5
o
• Did you finish?
• A multiple of 14 is also a multiple of 2 and
a multiple of 7. Can you give examples
which prove this statement?
• What number squared makes 36? 49? 81?
16? 64?
• Do you think you found them all?
Teaching Input 4
o
d
paper and pencils
• Investigate pairs of factors of numbers
between 20 and 100. For example, 20
has factor pairs 4 and 5, 2 and 10 and 1
and 20. Children should record their
work.
paper and pencils
p
PCM 27
Each child needs one set of cards from the PCM.
Explain that a square number is a number
that is made by multiplying a number by
itself. On the board draw a square divided
into four smaller squares.
• Sort the cards into 2-digit and 5-digit
numbers. Shuffle each pack and lay them
face down in front of you.
• 2 2 4.
• Pick a card from each pile.
• Four is a square number and it can be
written as:
• Add the two numbers, then subtract the
smaller from the larger.
22 = 4
• Now try dividing them. Estimate your
answer first.
2 squared = 4
Now draw a square divided into nine smaller
squares (3 by 3).
• Is there a remainder?
• Now multiply the 5-digit number by 10.
• 3 3 9.
32 = 9
• What would the answer be if you
multiplied it by 5?
3 squared = 9
• Can you tell me what 42 is?
• How could you work it out easily?
• Can you tell me what 102 is? 52? 82? 62?
Write on the board: 32, 22, 92, 72.
• Can you tell me the square numbers?
Repeat.
• Can anyone tell me another square
number?
d
• Can you explain your work?
• What numbers did you get?
• Were there remainders after division? Could
the remainders be written as fractions?
• Would it have been easier to use a calculator?
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