Patterns in Numbers 1
Y5
Multiples
1).
a).On a 1-100 Number Grid colour in the 2 timestable.
What do you notice?
b).On two different 1-100 Number Grids, colour in the 3 and 4 timestables.
What do you notice about the 4 timestable and the 2 timestable patterns?
c).On two more 1-100 Number Grids, colour in the 5 and 6 timestables.
What do you notice about the 6 timestable, the 3 timestable and the 2 timestable
patterns?
d).On four more 1-100 Number Grids, colour in the 7, 8, 9 and 10 timestable.
Which patterns do these belong to, if any?
2).Draw Pascal’s Triangle or use a grid given to you.
Repeat all of Question 1 on the Pascal’s Triangle grid.
3).
List the first 6 multiples of
a). 3
b). 7
f). 8
g). 12
k). 22
l). 17
c). 5
h). 15
m). 27
d).
i).
n).
9
20
34 e). 6
j). 50
o). 46
Factors
1).
To find the factors of 80 we can find the factors in pairs like this,
1 × 80 = 80 2 × 40 = 80 4 × 20 = 80 5 × 16 = 80 So factors of 80 are
8 × 10 = 80. 1, 2, 4, 5, 8, 10, 16, 20, 40 and 80.
Using this method find all the factors of
a). 8
b). 6
c).
f). 16
g). 9
h).
k). 25
l). 30
m).
p). 48
q). 34
r).
u). 100
v). 120
w).
10
15
44
60
125
d).
i).
n).
s).
x).
12
18
50
75
128
e).
j).
o).
t).
y). 20
22
64
90
150.
2).A perfect number is one where all the factors (apart from itself) add up to that number.
e.g. 6. Factors are 6, 3, 2 and 1. 3 + 2 + 1 = 6. Therefore 6 is a perfect number.
Find the next perfect number. If you find the third one you are doing very well!
3).Start with any number and list all the factors.
Add these up, apart from the number itself.
8.
e.g. 10 factors are 1 + 2 + 5 (10) = 8.
Therefore 10
8 factors are 1 + 2 + 4 (8) = 7
Therefore 10
8
Build up this chain. Now do this for other numbers. Do any 'loop'?
7.
4).12 has factors 1, 2, 3, 4, 6 and 12.
Four of these are even numbers (2, 4, 6 and 12) and 2 are odd (1 and 3).
a). Find some numbers that have factors which are all even numbers (excluding the
factor 1 of course).
b). What do you notice about these numbers?
c). Find some numbers which have half the factors even numbers and half odd numbers
(include the factor 1 this time).
d). What do you notice about these numbers?
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Y5
Square and Triangular Numbers
1).
The number of small squares it takes to make each big square is called a square number.
1
4
9
16
25
These are all square numbers.
a). Write the first 10 square numbers.
b). Find a way to make square numbers without having to draw out the diagrams.
c). Which of these numbers is not a square number?
18 16 100 1
99
81
25 50 48.
2).
The number of squares it takes to make each big triangle is called a triangular number.
a).
b).
c).
1
3
6
10 15
These are all triangular numbers.
Write the first 10 triangular numbers.
Find a way to make triangular numbers without having to draw out the diagrams.
Which of these numbers is not a triangular number?
78 19
45 1
66
50
28 40 36.
(Hint: Looking at the Pascal’s Triangle sheet may help).
Palindromes
A Palindrome is something that reads the same forwards as it does backwards.
The longest English Palindrome is 'tattarrattat'. The world’s longest is
'Salppuakivikaupplas' - which is handy if you want a caustic soda dealer in Finland!
1).
Find as many palindromes as you can. What is the biggest you could find?
Here are some sentences that are palindromes.
'Able was I, ere I saw Elba' ; 'Norma is as selfless as i am Ron' ; 'No it is opposition'
and the longest sentence,
'Doc, note, I dissent. A fast never prevents a fatness. I diet on cod.'
A number that can be read backwards, as well as forwards is a palindromic number.
2).
Which of these numbers, are or are not palindromic numbers?
a). 323
b). 57675
c). 4242
d).
3).
Which will the next palindromic date be?
6060
e). 6554655 ?
4).Choose a 2 digit number and write it down.
Change the digits round and write this number under the previous one.
Add them.
With the answer repeat the process.
Continue until you get a palindrome.
a). Some 2 digit numbers get to the palindrome quicker. Explain which ones.
b). Try it with 3 and 4 digit numbers.
c). Choose a 4 digit palindromic number. Divide it by 11.
How can you predict the answer?
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