Reasoning in Numbers
‘Reasoning in Numbers’ is a resource book for predominately Years 5 and 6.
It gives the Year 5 and 6 teachers several hundred questions to use with their
pupils to develop reasoning skills and problem solving. There is a quick
reference guide at the back to help teachers to find questions appropriate to the
area they are teaching. The book has been trialled at St Fidelis, Erith and their
teachers said:
“
It encouraged children to justify in a more
exciting way than just asking them to explain
their answer or method.
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606298 Reasoning in Numbers_Layout.indd 1
Five
13/11/2015 16:28
What other numbers also have the all the
factors of 6?
Five is a Fibonacci number. 1, 1, 2, 3, 5, 8,
13, what will the next two numbers in the
sequence be? Explain how you worked out the
next two numbers in the sequence.
12, 18, 24, 30 etc
True or false? Another name for a cube is a
hexahedron?
Penta- means five. Find different words that
start with penta.
True – hexa means six and hedron means …
A) octahedron b) tetrahedron
Pentagram
Seven
Seven is a prime number. True or false? Prime
numbers are always odd numbers?
False, 2 is also a prime number. It has two
factors 1 and 2
True or false? There are 10 prime numbers
between the numbers 1 and 30.
What is similar? What is different about these
two shapes?
True, they are 2, 3, 5, 7, 11, 13, 17,
19, 23, 27
Pentominoes are shapes made from five
squares. How many of these are possible?
(Only count shapes which cannot be made by
flipping them over or rotating them)
12 answers
Three
Zero
solid
turns from a
t that water
0°C is the poin
zero,
to a liquid
a number by
Can
en I multiply
she correct?
Sara says, “Wh
ys zero.” Is
alwa
is
er
the answ
why?
ain
expl
you
nothing
use if you have
d.
beca
iplie
ect
She is corr
e to be mult
nothing ther
then there is
Six
Six is a triangular number. 1, 3, 6
The factors of 6 (1, 2 and 3) add up to six, This
makes it a ‘perfect’ number.
Roger says, “All the factors of six, (1, 2, 3 and
6) will also be found as the factors of 36.”
Explain why he is correct.
Thirty-six is a multiple of six
606298 Reasoning in Numbers_Layout.indd 5
nal means
Three dimensio has length,
something that Name
h.
width and dept in dark
ed
shad
the shape
blue.
Square
shape that has
Name a 3D
.
a square face
mid
re based pyra
en
Cuboid, squa
Peter says, “Wh to
three sides.
angles need
A triangle has
gle two of the
drawing a trian correct?
ce.
One
surfa
Is he
and one
be obtuse”.
has one edge g it a twist and
angles of a
strip
the
ius
of
e
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the sum
r, givin
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an obtuse angl
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r says, “I can
degrees and
Take a long
180
together. Pete
but less than
triangle is 180
r side
90 degrees
join the ends strip blue and the othe
es is
is greater than
the
obtuse angl
one side of
sum of two
correct?
degrees. The
green.” Is he
180 degrees.
ssible
than
impo
is
ter
it
grea
because
He is incorrect
one side
strip only has
because the
ber.”
a prime num
“One is not
Four
Linda says,
with four
Why?
of pyramid
e
Is she correct?
prim
on is a type
and
r
facto
A tetrahedr
s.
it only has one one and its own
Because
triangular face
REASONING
IN rs,
NUMBERS
5
two facto
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13.
3D shape that
r
and
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Nam
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has a triangula
13/11/2015 16:29
Triangular prism
Two
?
True or False
even prime
two is the only g.
The number
onin
ain your reas
one
number. Expl
two factors,
ber only has
A prime num
cycle
and itself.
a bicycle is a
. For example,
numbers are
code
Bi means two
ry
s:
els. In bina
with two whe two. It uses just two digit
10, the
written to base
2 becomes
ber
num
4
the number
0 and 1. If the
mes 11 and
6?
number 5 and
number 3 beco
. What is the
100
mes
beco
.
Explain why
re
2 = 4. All squa
number: 2 x
a 9.
1, 4, 5, 6 or
4 is a square
in either a 0,
numbers end
?
next
True or false
the
ber from
a square num
ber?
If I subtract
an odd num
ber you get
square num
numbers 3,
get the odd
True, you will
their
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True or fals
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16 ounces
in a pound.
True
True or fals
14 is a pyr
e?
amidal num
The sum
pyramida
ber or squ
of
l number
are
equals 16. the first four odd
numbers
The sum
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True 1 +
1 + 4 + 9. the first three squ
3+5+7
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sConvince
Other pyr
me that 4
amidal num
2 = 16
91, 140,
2x2x2
204, 285 bers are 1, 5, 14,
x 2 = 16
…
30, 55,
– A fourth
True or fals
power
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54 is a pyr
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False, 55
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606298
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Convince
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ber.
3+4+5
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E.g. 30 +
= 15 also
diagram)
.
40 + 50
shown as
+ 60
a
By Emma Blackman
Good for inspiration for starters and for ‘Points for
development’ as it encourages children to justify.
16:29
REASONING
IN NUMBERS
It helps to tease out ideas and get children to justify.
Mr Hanna - Year 6 teacher.
“
Pentagon
REASONING
IN NUMBERS
PR
O
MissCosshall - Year 5 teacher.
Name a shape that has: a) six vertices and b) a
shape that has six edges.
For example: pentathlon, pentagon,
pentagram, pentasyllabic
“
“
“
By Emma Blackman
O
F
Mrs Atherton – Maths Subject Leader
“
“
“
It gave good ideas which teachers could use as a
platform to create their own reasoning questions
for example: True or false and convince me.
REASONING
IN NUMBERS
By Emma Blackman
It encourages an investigative approach to maths.
Mrs Tylee – Year 6 teacher.
REASONING
IN NUMBERS
It is available as a hard copy but with each purchase the images
will be sent to the school for the teachers to use within their lessons.
8
606298
Reasoning
Nineteen
REASONIN
19 is a hex
agonal num
which can
be arrange ber. These are num
hexagons.
d
bers
Other hex into a pattern of
nested
numbers
Formula
are 7, 19,
:
37.
3n(n-1)
+1
G IN NU
MBERS
1
7
19
37
in Numb
ers_Layout.in
dd 8
By Emma Blackman
13/11/2015
The costListening
of the book is
you wouldfor
likeyou
a copy sent to your school,
to£20.00.
you, If
working
then please email [email protected] with your school’s details
606298 address,
Reasoning in Numbers_Layout.indd
1
(name,
telephone number
and who to send the invoice to).
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REASONING
IN NUMBERS
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