Penstripe Student Planner Catalogue 24-25 - Flipbook - Page 121
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MATHEMATICS – NUMBER
MATHEMATICS – ALGEBRA
Mathematics - algebra
Mathematics - number
1
2
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
2
3
4
5
6
7
8
9
10
11
12
4
6
8
10
12
14
16
18
20
22
24
3
4
6
8
9
12
12
16
15
20
18
24
21
28
24
32
27
36
30
40
33
44
36
48
5
10
15
20
25
30
35
40
45
50
55
60
6
12
18
24
30
36
42
48
54
60
66
72
7
8
14
16
21
24
28
32
35
40
42
48
49
56
56
64
63
72
70
80
77
88
84
96
9
Then add together all the products. 10
2000+1400+400+280+30+21
11
=4131
12
18
27
36
45
54
63
72
81
90
99 108
20
22
30
33
40
44
50
55
60
66
70
77
80
88
90 100 110 120
99 110 121 132
24
36
48
60
72
84
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 …
p2 means p x p
4b
means “k divided by 2”
v2
means “v x v”
or “v squared”
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 …
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
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Simplifying expressions
p0 = 1
Circle the first type of like
terms. Collect them together.
= 3a + 4b -2a + b -3c
DEAL WITH THE DIGITS AND
THEN WITH THE INDICES!!!
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
(ax)y = axy
p1 = p
p1/n means n√p
E.g. 271/3 = 3√27 = 3
= 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
= a +5b -3c
2
ax ÷ ay = ax-y
E.g. 3a + 4b - 2a + b - 3c
Prime factors of a number are its factors
that are prime. Use a prime factor tree!
Circle the prime
number and stop.
ax x ay = ax+y
means p x p x p
pn means p x p x … x p
(n times)
p-n means 1/pn
E.g. 3-2 = 1/32 = 1/9
Prime factors
= 2
Multiplying brackets
grid method
a(b-c)
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
x
b
-c
x
a
b
a
ab
ac
a
ab
-ac
a
a2
ab
c
ac
cb
= ab + ac
= ab - ac
= 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
Multiplying brackets grid method
Multiplying brackets
grid method
a(b+c)
24
Rules of indices
Simplifying by collecting
like terms
Continue and tidy up!
48
p
k/2
Square numbers (formed by multiplying a
number by itself): 1, 4, 9, 16, 25, 36, 49, 64,
81, 100, 121, 144, 169, 196, 225
2
3
means “4 multiplied
by b” or “4 lots of b”
=
Multiples of a number are numbers that
belong to its multiplication table.
E.g. the multiples of 4 are 4, 8, 12 …
Design Right and Copyright © 1997, 2016 Penstripe Y1
Indices (powers)
a – 5 means “take 5 from a”
or “5 less than a”
Even numbers: 2, 4, 6, 8, 10 …
Cubed numbers (formed by multiplying a
number by itself 3 times): 1, 8, 27, 64, 125,
216, 343, 512, 729, 1000
121
3 + s means “3 plus s”
or “s more than 3”
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
An example of
multiplying to get a
quadratic equation
(a+2)(a-3)
a
-3
a
a2
-3a
2
x
2a
-6
= a2 - 3a + 2a - 6
= a2 - a - 6
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
