Penstripe Student Planner Catalogue 24-25 - Flipbook - Page 133
6
CHOOSE YOUR PENSTRIPE PAGES
MATHEMATICS – NUMBER
MATHEMATICS – ALGEBRA
Mathematics - algebra
Mathematics - number
1
2
2
4
3
6
4
8
5
10
6
12
7
14
8
16
9
18
10
20
11
22
12
24
Split the numbers you are
multiplying into units, tens,
hundreds… and multiply each
part separately. E.g. 243 x 17
x
200
40
3
10
2000
400
30
7
1400
280
21
3
4
5
6
7
8
6
8
10
12
14
16
9
12
15
18
21
24
12
16
20
24
28
32
15
20
25
30
35
40
18
24
30
36
42
48
21
28
35
42
49
56
24
32
40
48
56
64
27
36
45
54
63
72
30
40
50
60
70
80
33
44
55
66
77
88
36
48
60
72
84
96
9
Then add together all the products. 10
2000+1400+400+280+30+21
11
=4131
12
18
20
22
24
27
30
33
36
36
40
44
48
45
50
55
60
54
60
66
72
63
70
77
84
72 81 90 99 108
80 90 100 110 120
88 99 110 121 132
96 108 120 132 144
Directed numbers
Adding a negative number is the same
as subtracting the positive.
Multiplying and dividing
negative numbers
Subtracting a negative is the same as
adding the positive.
When the signs are different (i.e. positive
and negative) the answer is negative.
Types of number
When the signs are the same (i.e. positive
and positive or negative and negative) the
answer is positive.
Odd numbers: 1, 3, 5, 7, 9, 11 …
Even numbers: 2, 4, 6, 8, 10 …
Square numbers (formed by multiplying a
number by itself): 1, 4, 9, 16, 25, 36, 49, 64,
81, 100, 121, 144, 169, 196, 225
Multiples of a number are numbers that
belong to its multiplication table.
E.g. the multiples of 4 are 4, 8, 12 …
Prime factors of a number are its factors
that are prime. Use a prime factor tree!
Factors of a number are numbers that divide
exactly into a number. FACTORS FIT!!!
E.g. the factors of 20 are 1, 2, 4, 5, 10, 20.
Prime numbers are numbers that have TWO
factors only. E.g. 2, 3, 5, 7, 11, 13, 17, 19 …
Design Right and Copyright © 1997, 2016 Penstripe Y1
Percentages/ decimals/ fractions
50%
25%
75%
10%
20%
30%
60%
12.5%
331/3%
etc.
0.5
0.25
0.75
0.1
0.2
0.3
0.6
0.125
.
0.3
1/2
1/4
3/4
1/ 10
2/10 = 1/5
3/10
6/10 = 3/5
1/8
1/3
Description
Mathematics – Number
133
Design Right and Copyright © 2024 Penstripe
48
2
Circle the prime
number and stop.
Indices (powers)
Rules of indices
a – 5 means “take 5 from a”
or “5 less than a”
p2 means p x p
ax x ay = ax+y
4b
means p x p x p
ax ÷ ay = ax-y
pn means p x p x … x p
(n times)
(ax)y = axy
3
p
means “4 multiplied
by b” or “4 lots of b”
k/2
means “k divided by 2”
v2
means “v x v”
or “v squared”
p1 = p
1/n
p
Circle the first type of like
terms. Collect them together.
= 3a + 4b -2a + b -3c
n
means √p
E.g. 271/3 = 3√27 = 3
E.g. 6a2b x 3ab3
= 6x3 x a2x a x b x b3
= 18 x a(2+1) x b(1+3)
Remember
– common mistake!
= 3a -2a +4b +b -3c
Underline the next set of like
terms. Collect them together.
= 3a -2a +4b +b -3c
a
DEAL WITH THE DIGITS AND
THEN WITH THE INDICES!!!
p-n means 1/pn
E.g. 3-2 = 1/32 = 1/9
E.g. 3a + 4b - 2a + b - 3c
=
Simplifying expressions
p0 = 1
Simplifying by collecting
like terms
= 18a3b4
a2 = a x a and 2a = 2 x a
E.g. 6a2b ÷ 3ab3
so
= 6÷3 x a2 ÷ a x b ÷ b3
a2 + 2a cannot be simplified
further as a2 is not LIKE 2a !!!
+ 5b -3c
= 2
Continue and tidy up!
Prime factors
Cubed numbers (formed by multiplying a
number by itself 3 times): 1, 8, 27, 64, 125,
216, 343, 512, 729, 1000
3 + s means “3 plus s”
or “s more than 3”
2
Multiplying brackets grid method
Multiplying brackets
grid method
a(b+c)
24
Multiplying brackets
grid method
a(b-c)
An example of
multiplying to get a
quadratic equation
(a+2)(a-3)
Multiplying double
brackets
(a+b)(a+c)
12
2
=2 x 2 x 2 x 2 x 3
4
=2 x3
6
2
3
x
b
c
a
ab
ac
= ab + ac
x
b
-c
x
a
b
a
-3
a
ab
-ac
a
a2
ab
a
a2
-3a
c
ac
cb
2
2a
-6
= ab - ac
x
= a - 3a + 2a - 6
= a2 - a - 6
2
= a2 + ab + ac + bc
Time
To find the difference between two times
1. Draw a time line
2. Count in minutes to the next hour
3. Count in hours until you can’t count a
whole hour
4. Count in minutes to the given time
E.g. How long is a journey starting at 11:30
and ending at 14:15?
x a(2-1) x b(1-3)
= 2ab-2
= a +5b -3c
Quadratic formula
For solving ax +bx+c = 0
2
x = –b+
– b2–4ac
2a
Other useful websites:
11.30 >>>>> 12.00 >>>>> 14.00 >>>>> 14.15
30mins
2hrs
15mins
Useful web addresses
www.mathsnet.net
www.countonus.org.uk
www.nrich.maths.org
www.bbc.co.uk/bitesize/subjects
www.emaths.co.uk
www.mathsisfun.com
= 2 hours and 45 minutes
Page Ref.
Y1-7
Description
Mathematics – Algebra
Page Ref.
Y1-8
Design Right and Copyright © 1997, 2016 Penstripe Y1
Grid method for
multiplication
