Download Assessment Material for OCN: Calculations, BZR870

1.1 /
Assessment Material for OCN: Calculations, BZR870
SHORT MULTIPLICATION
WITHOUT CARRYING
When we multiply any number by a number less than 10 we call this short
multiplication.
To do this we multiply the number out in stages taking each figure
separately.
EXAMPLES
(i)
43 x 2
 start here
43 x
2
86
2x4 = 8
(ii)
2x3 =6
123 x 3
123
3 x
369
 start here
As you can see we multiply
the number on the bottom
by each number on the top.
(iii)
210 x 2
2 10
2 x
420
 start here
Have a go at these.
1)
21x
2
2)
32x
2
3)
43x
2
4)
12x
4
5)
24x
2
6)
13x
3
7)
123x
2
8)
112x
4
9)
213x
3
10)
412x
2
11)
333x
3
12)
302x
2
Set these out yourself, then work out the answers.
13)
Reece buys a packet of crisps for each of her 3 children, the
crisps cost 31p each - how much is that altogether?
14)
Rhian and her 2 sisters are going on holiday together. They
each pay a deposit of £120 for the holiday. Rhian writes a
cheque for the money. How much will the cheque be for?
15)
I buy 4 new dining chairs. Each one cost £25, how much will I
spend?
16)
A box of matches contains 55 matches. How many will there
be in 3 boxes?
17)
I want to build 4 shelves, each one 122 cm long. How much
wood will I need?
1.1
SHORT MULTIPLICATION
WITH CARRYING
Carrying numbers in multiplication works exactly the same as in addition.
EXAMPLES A
(i)
(ii)
25 x 3
25
1 3 x
5
3 x 5 = 15, 5 down, carry the 1.
25
1 3 x
75
3 x 2 = 6,
42 x 3
42 x
3
126
(iii)
32 x 6
32 x
1
6
192
plus the 1 we carried makes 7
A.
Make sure you understand the examples, then have a
go at the exercise.
1)
29x
2
2)
42x
6
3)
55x
2
4)
64x
3
5)
32x
5
6)
36x
6
7)
85x
8
8)
26x
8
9)
A supersave rail ticket to Birmingham costs £18. If 4 friends
go to Birmingham how much will this cost?
10)
Evan goes shopping to buy shoes for his 3 children. If the
shoes cost £26 per pair, how much will it cost him?
1.2
MULTIPLICATION BY 10
X 10
When multiplying whole numbers by 10 we write the number then add a nought
on the end.
e.g. (i)
2 x 10 = 20
 add a nought
Have a go at the exercise below.
A.
1)
3 x 10 =
2)
4 x 10 =
3)
6 x 10 =
4)
7 x 10 =
5)
9 x 10 =
Can you see the pattern?
e.g. (ii)
21 x 10
= 210
55 x 10
= 550
60 x 10
= 600
Now have a go at these:
6)
32 x 10 =
7)
51 x 10 =
8)
19 x 10 =
9)
16 x 10 =
10)
81 x 10 =
11)
40 x 10 =
12)
30 x 10 =
13)
50 x 10 =
14)
122 x 10 =
15)
359 x 10 =
16)
428 x 10 =
17)
120 x 10 =
18)
210 x 10 =
19)
370 x 10 =
20) 560 x 10 =
21)
Toilet rolls cost 31 pence each. How much would it cost for a
pack of 10 rolls?
22) 10 friends go on holiday. The holiday costs them £220 each.
How much would that be altogether?
23) Bill collects 10 pence pieces in a jar. If he has collected 92, how
much money does he have?
24) Kitchen tiles are 10cm wide, how long would a row of 25 tiles be?
25) On average a match box holds 78 matches. How many would
there be in 10 boxes?
Have a go at x 100. Ask your tutor to demonstrate this.
X 100
B.
Work out the answers to the questions below
1)
2 x 100 =
2)
5 x 100 =
3)
6 x 100 =
4)
8 x 100 =
5)
7 x 100 =
2.1
SHORT DIVISION
Thinking in Twos
EXAMPLES
(i)
(iii)
4
2) 8
(ii)
21
2) 42
A.
Have a go at these division sums.
1)
2) 6
2)
2) 18
3)
2) 24
4)
2) 86
5)
Two bus tickets cost 64p altogether. How much does each one
cost?
6)
Two friends each share a win of £26. How much will each cost?
How many 2’s in 9? How much is left?
4 remainder 1
2) 9
B.
These questions have a remainder.
1)
How many 2’s in 7? What is left over?
2)
How many times does 2 go into 11? What is left?
3)
Share 15p between 2 people. How much is left?
(iv)
1
1 6
2) 3 2
1
2 into 3 goes 1
with 1 left over.
2) 3 12
2 into 12
goes 6
C.
Now try some with carrying
1)
2) 72
2)
2) 36
3)
2) 54
4)
2) 92
5)
2) 78
6)
2) 30
If 2 will not go into the first number, try the first 2 numbers.
EXAMPLES
(v)
6
2) 1 2 4
2 into 1 won’t go
so say 2 into 12
goes 6
62
2) 1 2 4
2 into 4 goes 2
(vi)
7
7 6
2) 1 5 2
2) 1 5 12
2 into 1 won’t go
2 into 15 goes 7
with 1 left over
2 into 12 goes 6
1
D.
Now have a go at these.
1)
2) 128
2)
2) 140
3)
2) 164
4)
2) 110
5)
2) 136
6)
2) 152
7)
A girl is paid £54 for 2 weeks. How much can she spend each
week?
8)
A strip of ribbon is 32cm long. If I cut it into 2 equal pieces,
how long will each one be?
9)
You buy 2 cream cakes for you and a friend, and the bill is 72p.
How much should you pay each?
Short Division - No Carrying
Now that you can divide by 2, here is some practice dividing by other numbers.
The same rules apply.
EXAMPLES
(i)
1 1
3) 3 3
(ii)
2 10
4) 8 4 0
Make sure each answer goes above the corresponding number
E.
Make sure you understand the examples, then try the
exercise.
1)
5) 55
2)
3) 69
3)
4) 84
4)
6) 66
5)
3) 360
6)
8) 800
7)
3) 99
8)
4) 484
9)
7) 70
10)
5) 500
11)
3) 369
12)
4) 880
13)
Three friends go on holiday. They share a cottage that costs
£363. How much will each person pay?
14)
A second hand car costs £690. If it is paid for over 3 months,
how much will that be each month?
15)
4 friends go for a meal that cost £48. How much do they pay
each?
Check your answers, then discuss with your tutor what you need to
work on next.
Answers
Short Division
Thinking in Twos
A
B
C
D
1)
3
2)
9
3)
12
4)
43
5)
32p`
6)
£13
1)
3, remainder 1
2)
5, remainder 1
3)
7p, remainder 1p
1)
36
2)
18
3)
27
4)
46
5)
39
6)
15
1)
64
2)
70
3)
82
4)
55
5)
68
6)
76
7)
£27
8)
16cm
9)
36p
No Carrying
E
1)
11
2)
23
3)
21
4)
11
5)
120
6)
100
7)
33
8)
121
9)
10
10)
100
11)
123
12)
220
13)
£121
14)
£230
15)
£12
2.2
DIVIDING BY 10
When you divide a whole number by 10 you can take a ‘0’ off the end of the
number to make it 10 times smaller.
e.g.
20  10
Have a go at the exercise below.
1)
30  10 =
2)
40  10 =
3)
60  10 =
4)
70  10 =
5)
90  10 =
Can you see a pattern?
e.g.
230  10 = 23
450  10 = 45
700  10 = 70
Now have a go at these.
6)
320  10 =
7)
410  10 =
8)
170  10 =
9)
610  10 =
= 2
10)
830  10 =
11)
600  10 =
12)
400  10 =
13)
900  10 =
14)
3620  10 =
15)
2190  10 =
16)
1300  10 =
17)
4200  10 =
18)
2700  10 =
19)
710  10 =
20) 2100  10 =
21)
My council tax is £700. If I pay it in 10 monthly instalments,
how much would each one be?
22) In a warehouse, crates can be stacked in piles of 10. If you have
340 crates, how many piles would that be?
23) A Spanish villa costs £2130 to rent for 2 weeks. If 10 friends
share the rent how much would they each pay?
24) If 10 francs are worth £1, how many pounds would you get for
920 francs?
Check your answers, then discuss with your tutor what you need to
work on next.
4.1 Use a calculator to perform calculations with whole numbers up to
100.
It cost me 95p to get to college during peak time but only 73p
to get home. How much is that altogether?
During break I buy myself a cup of tea for 65p and a biscuit
for 22p. How much does this cost?
Shona is arranging a night out. She sells 193 tickets in
advance. On the night 79 people pay on the door. How many
people go altogether?
For a college summer trip Jamie hires 3 coaches. 48 students
travel on the first coach, 27 on the second and 42 on the third.
How many students go on the trip?
A CD player costs £97. In a sale it is reduced to £68 pounds.
How much is it reduced by?
Bahrit is 58 years old. His sister Suni is 7 years younger,
how old is she?
Marion has 936 calories in one day. If she eats 232 for her
breakfast, how many does she have during the rest of the day
A box of matches contains 180 matches. How many will
there be in 3 boxes?
I want to build 4 shelves, each one 136 cm long. How much
wood will I need?
A jumper costs £15.45. The customer gives £20 – what
change does he get?
How much change will you get from £15.00 if you buy a book
costing £12.99?
If I buy a bike costing £44.50 and give the assistant five
£10 notes, how much change should I get?
A box of chocolates costs £5.65. The customer pays with a
£10 note what change should she get?
Tutor as observed student working out the answers to the sums by calculator or
calculating the answers manually and checking afterwards with a calculator.
Name of student: ---------------------------Tutor: -------------------------------------------Date: -----------------------------------
Place Value Of Decimals
We use the decimal point to separate whole numbers from parts of numbers (the decimal
numbers)
This happens when we use money
decimal point

£2.57


2 whole pounds
the pence are parts
of a whole pound.
£0.57 is 57 parts of 100.
and it happens when we use other decimal numbers
decimal point

12.77


The whole number
the decimal number
is before the point
is after the decimal point
You would write this in words as Twelve point seven seven
A
Have a go at writing these in numbers. The first 2 are done for you.
Seven point three
=
7.3
Twenty two point eight five
=
22.85
1)
Five point five
2)
Twelve point one
3)
Twenty point six two
4)
Nine point three nine
5)
Eleven point one seven five
6)
Fifty point five
B
Now have a go at writing these in words. The first 2 are examples.
7.4
=
Seven point four
6.35
=
Six point three five
1)
9.1
2)
23.84
3)
30.4
4)
3.04
5)
2.99
6)
1.04
3.1 Write decimal numbers involving tenths and hundredths.
Write each amount in £ using a decimal point in the
appropriate place.
214p , 506p , 938p , 600p , 109p , 20p , 76p ,
834p , 47p , 532p , 104p , 97p
214p, 639p
You see several pairs of shoes in a shop window with different
prices on them. Your job is to put the prices in order from the
most expensive to the cheapest.
£52.36 ,
£35.65 ,
£97.21 , £102.97, £ 15.89
The shop assistant has priced the goods up in pence rather
than pounds. Please re-price all the goods.
569p , 1025p , 369p
145p , 697p , 546p ,
, 958p , 259p , 638p
428p , 145p
751p
Look for patterns in numbers.
5.1 Extend simple number sequences involving one operation.
ODD AND EVEN
Start from the number one and add two to it. What do you notice about
the number sequence? ( Even or odd?)
1, 3, 5
Start from the number two and add two to it. What do you notice about
the number sequence? ( Even or odd?)
2, 4, 6
Put the sums in order – smallest first to highest last.
Example:
A) 5X6=
30
B) 3X4=
12
So correct sequence is:
C) 8X7=
56
12, 30, 56 = B, A, C
1.
A) 5X4=
B) 3X7=
C) 2X7=
Answer = ------
2.
A) 5X6=
B) 3X4=
C) 8X7=
Answer = ------
3.
A) 2X6=
B) 2X9=
C) 7X7=
Answer = ------
4.
A) 9X5=
B) 8X4=
C) 7X5=
Answer = ------
5.
A) 10X6=
B) 3X5=
C) 9X3=
Answer = ------
Multiplication Patterns E3 Calculations
Complete the list and describe the pattern!
1, 6, 36, 216,
,
, ...
What is the pattern?
9, 27, 81, 243,
,
, ...
What is the pattern?
4, 16, 64, 256,
,
, ...
What is the pattern?
5, 20, 80, 320,
,
, ...
What is the pattern?
3, 9, 27, 81,
,
, ...
What is the pattern?
2, 4, 8, 16,
,
, ...
What is the pattern?
8, 24, 72, 216,
,
, ...
What is the pattern?
1, 4, 9, 16, 25,
,
,
,
,
, …..
BZR870 Calculations
E3
End of Assessment Project
Student name:………………………………………………….
You work for a large company employed as a PA. Your
manager has give you a series of maths problems to find the
answers to.
A supersave rail ticket to Birmingham costs £19. If 4
friends go to Birmingham how much will this cost?
Mark goes shopping to buy shoes for his 3 children. If the
shoes cost £27 per pair, how much will it cost him?
Toilet rolls cost 52 pence each. How much would it cost for
a pack of 10 rolls?
10 friends go on holiday. The holiday costs them £320
each. How much would that be altogether?
Sanjay collects 10 pence pieces in a jar. If he has collected
75, how much money does he have?
A prize of £54 has to be shared by 3 people. How much will
they each get?
4 friends win a total of £832 on the lottery. How much will
each person receive?
My council tax is £900. If I pay it in 10 monthly
instalments, how much would each one be?
In a warehouse, crates can be stacked in piles of 10. If you
have 440 crates, how many piles would that be?
You need to write cheques to the following people/ organisations.
Make sure the cheques are written correctly and the amount is put in
the right place.
12. Write cheques to pay for the following items:
When?
What did you buy? Where did you
buy it?
21/3/12
28th February
2012
1/4/10
How much did
it cost?
A microwave
Had a haircut
Argos
Clinton James
£65.00
£22.00
Lunch for 2
Wetherspoons
£16.00
Please check the following bills with a calculator and work out the
exact total for each. Try estimating first.
1)
Cosy Corner Café
Egg +Chips
£1.50
Burger
£1.95
2)
Cheese Sandwich £1.05
TOTAL
3)
Bangles Jewellery
Necklace
£5.60
Bracelet
£2.75
Hairgrip
£1.99
TOTAL
_____
____
McGuigan’s Linens
Double fitted sheet
£8.99
Double sheet
£7.99
Duvet Cover
(Double)
4)
£12.50
Rug (reduced)
£5.67
TOTAL
_____
Freshco Veg
Potatoes (2.5kg)
99p
Onions
40p
Carrots
52p
Peas (frozen)
89p
Lettuce
32p
Tomatoes
76p
Cauliflower
57p
TOTAL
College Shop
5)
Folder
Pen
Pad (A4) blank
Pad (A4) lined
Notebook
TOTAL
150p
17p
98p
99p
75p
_____
Below is a set of numbers, some are missing. Your task is to
identify correctly the missing numbers in order that all the
numbers are in sequence.
1)
3,
6,
2)
6, …..
3)
9, 18,
9,
12,
, 18, 24,
….,
15, …..
, 21, ………
30, 36
36, 45, 54,
…….
4)
2, 4, 6, 8, 10, …., 14, 16, …….
5)
8, 16, ….. , 32, 40, 48, 56, …….
Look at the decimal numbers below. Your job is to decide whether
the value of the number underlined is either a tenth or hundredth.
116.74 ……………………………
78.26
……………………………
58.36
……………………………
96.12 ……………………………
0.25 ……………………………
51.84
……………………………