Numeracy
Policy
Contents
3:
Welcome
4:
Simple addition and subtraction
22:
Ratio
5:
Multiplication - Grid Method
23:
Percentages, fractions and decimals
6:
Column Method
24:
Finding percentages
7:
Division
25:
Averages
8:
Long Division
26:
Triangles
9:
Place Value
27:
Perimeter and Area
Simple Number Terms
10:
Fractions of a shape
28-29:
11:
Equivalent Fractions
30:
Coordinates
12:
Simplfying Fractions
31:
Two - Way Tables
13:
Negative numbers
32:
Bar Charts
Rounding, Decimal places and
33:
Real life graphs
Significant figures
34:
Units of Measure
17:
Estimation
35:
Venn Diagrams
18:
Ordering Decimals
36:
Tention Graph
19:
Factors
14-16:
2
20-21:
Area
Welcome
Aim:
For pupils, parents and staff to apply numeracy
skills in a variety of situations and value the
life-long importance of numeracy.
The majority of the United Kingdom (UK) has a
negative attitude towards numeracy and there is
a philosophy that it is ok to be bad at numeracy.
Generally speaking, this is different to literacywhere people seldom admit to being less
competent readers and writers.
Undeniably, this attitude permeates down to
children and is reflected in their attitude to
learning numeracy and the value they place on
the subject. This is commonly referred to as
“numeracy anxiety” and is evident within
Winifred Holtby Academy. Maths anxiety is
related to people having negative connotations
towards numeracy; this can be because they
feel inadequate at numeracy or pressurised in
mathematical situations, leading them to avoid
mathematical processes wherever possible.
Applying numeracy in all subjects is vital so that
pupils can seethe functionality of maths and the
relevance that numeracy has in real-life
situations.
Using a mathematical skill isn’t the same as
applying it. For example, in simplistic terms, a
student may know how to add 2 and 3, but
would they know when to use this skill outside
the numeracy classroom? If they have £2 and
£3 and want to know how much they have in
total, do they know that addition is the
mathematical skill that they need to apply?The
numeracydepartment has now implemented a
new ‘use’, ‘apply’ and ‘extend’ focus to ensure
pupils apply all skills that they learn in real-life
Area
situations. It is the responsibility of the Maths
department to primarily teach pupils how to ‘use’
mathematical skills and ‘apply’ and ‘extend’
them to real-life situations. It is the responsibility
of the whole Academy to give pupils the chance
to ‘apply’ thenumeracy skills that they learn in all
subject areas. For this reason a numeracy
policy for the Academy has been created.
Objectives:
• For staff to become accustomed to the
calculation strategies used within the Maths
department
• To support pupils, parents and staff members
to develop their‘use’ of mathematical skills and
how to ‘apply’ and ‘extend’ them to other
subject areas
• Increase awareness,in other subject areas, of
misconceptions seen in mathematics lessons
Implementation:
The policy is a working document and provides
guidance to pupils, parents and staff on key
areas identified as requiring development
through whole-Academy audits.All staff are
asked to support the development of numeracy
skills by maximising opportunities for
numeracy-related activities within their schemes
of work and are asked to use the methods
outlined in this document to provide
consistency. If pupils have their own methods
and come to the correct answer with thorough
working out, these methods are allowed. If staff
should require any support within their
classrooms, please contact Miss S Warhurst.
Aspiration | Achievement | Respect
3
Simple addition and subtraction
864 2
+ 7 53
93 95
1
Carrying
24 1 0
- 4 82
1 928
1
Borrowing
13
10
1
Misconceptions: The main misconceptions occur in subtraction if pupils do
not realise the place value of numbers. Therefore it is vital that they show the
actual values of the numbers.
Pupils do not always realise that they cannot subtract 2 from 0, they
sometimes think they can swap the number around and calculate 2—0.
4
Multiplication - Grid Method
20
4
Work out 24 x 16
10 200 40
6 120 24
2 00
1 20
40
+ 24
384
Waboll 1
x
4
5
2
8
10
Waboll 2
x
40
5
20
800
100
Wagoll
The grid method is the
method most commonly
used within this Academy.
s o 24 x 16 = 384
Work out 24 x 16
3
12
15
08
12
10
+ 15
45
so
23 x 45 = 4 5
Pupils have not understood the
place value of each number.
Work out 23 x 45
3
120
15
800
120
100
15
20
40
5
+ 3
1035
1103
so
23 x 45 = 4 5
Pupils have also included the
calculation values into the sum.
Aspiration | Achievement | Respect
5
Column Method
391 x 39 =
3
9
1
3
9
5
1
9
7
3
0
x
3
8
First we multiply each
of the digits 3,9,1 by 9.
9x1=9
9 x 9 = 81 (put the 1
down; carry the 8)
9 x 3 = 27
27 + (carried) 8 = 35
2
1
1
1
5
Last of all, we add the
results of our calculations
to get the answer.
2
4
9
Now we multiply each of the
digits 3,9,1 by 3. Because it is
actually 30, not 3, we put a
zero down first.
3x1=3
3 x 9 = 27 (put the 7 down and
carry the 2)
3 x 3 = 9 (plus the 2 which
makes 11)
2519 + 11730 = 15249
Misconceptions: Pupils don’t always realise the value of the numbers, i.e. in
the example above it is 30 that they are multiplying by, not 3 and so
30 x 1 = 30 and not 3.
6
Division
Bus Stop Method
196 ÷ 5
The bus stop method for division is the only method we all find reliable, whatever the numbers
are. It is helpful to start by writing out the times table of the number you are dividing by.
1x5=5
2 x 5 = 10
3 x 5 = 15
0
5 196
03
5 196
Next, how many 5s in 46. 9 x 5 = 45 so the answer is 9
with 1 left over – we have run out of numbers to carry
the 1 on so we move into decimals.
4
039
5 1 9 6 .0
4
0
5 196
1
03
5 196
Now, how many 5s in 19. 3 x 5 = 15 so the answer is 3
with 4 left over.
1
1
7 x 5 = 35
8 x 5 = 40
9 x 5 = 45
Again, we start at the far left and ask how many 5s there
are in 1. The answer is 0, with 1 left over.
5 196
1
4 x 5 = 20
5 x 5 = 25
6 x 5 = 39
1
Finally, how many 5s in 10. This goes exactly
2 times so we can finish the bus stop,
remembering to put a decimal in out answer.
1
4
039
5 1 9 6 .0
1
4
1
0392
5 1 9 6 .0
1
4
1
So 196 ÷ 5 = 39.2
Aspiration | Achievement | Respect
7
Long Division
This is the division process that examiners are looking for:
Have a look at the calculation: 8,640 ÷ 15
15 8 6 4 0
5
15 8 6 4 0
- 75
11
57
15 8 6 4 0
75
114
- 105
9
576
15 8 6 4 0
75
114
- 105
90
8
15 into 8 doesn’t go, so look at the next digit.
15 goes into 86 five times, so put a 5 above the 6.
15 x 5 = 75
Take that 75 away from the 86 to get your remainder
86 - 75 = 11
Next, carry the 4 down to make 114.
15 goes into 114 seven times, so put a 7 above the 4.
15 x 7 = 105
Take 105 from the 114 to get your remainder
114 - 105 = 9
Carry the 0 down to make 90
15 goes into 90 exactly 60 times, so put a 6 above the 0.
15 x 6 = 90
8,640 ÷ 15 = 576
Place Value
•
The value of a digit depends on its position or place in the number
•
The place value depends on the column heading above the digit
•
The first four column headings are thousands, hundreds, tens and units
The number 4528 has 4 thousands, 5 hundreds, 2 tens and 8 units.
Thousands
4
•
Hundreds
Tens
5
Units
2
8
To make them easier to read, the digits in numbers greater than 9999 are
grouped in blocks of three
Read 3 456 210 as ‘three million, four hundred and fifty-six thousand, two hundred
and ten’
Aspiration | Achievement | Respect
millionths
hundred-thousandths
ten-thousandths
thousandths
hundredths
tenths
and
units
tens
hundreds
ten thousands
hundred thousands
Misconceptions:
1. Pupils do not use the place
value table.
2. Pupils don’t always line up
the decimals.
3. Pupils sometimes miss out
the zeros, for example they
mistake 1.5 and 1.05 as
meaning the same amount.
millions
Wagoll
thousands
Place value and decimals
9
Fractions of a shape
•
A fraction is part of a whole
•
The number of equal-sized parts of the shape is divided into the
denominator (bottom of the fraction)
The number of parts required is called the numerator (top of the fraction)
•
This shape is divided into eight parts and
five of them are shaded.
The shaded part is
5
8
Wagoll
REMEMBER
Remember to count
up the shaded and
unshaded parts to
find the denominator.
of the whole
10
16
Misconceptions: Pupils do not always realise that the denominator is the
total number of equal-sized boxes and the numerator is the number of
boxes shaded in.
10
Equivalent Fractions
•
A fraction can be written in many different ways. These are called equivalent
fractions
1
=
2
2
4
3
=
6
...
•
Equivalent fractions are two fractions that represent the same number
•
Any fraction has an unlimited number of equivalent fractions
5
100 ...
10
15
50
=
=
=
=
8
16
24
80 160
Wagoll
3
5
x4
=
x4
12
20
Misconceptions: Pupils sometimes do not multiply the denominator and the
numerator by the same amount.
Pupils sometimes think they can add or subtract to/from the denominator
and numerator.
Aspiration | Achievement | Respect
11
Simplfying Fractions
•
A base fraction is written in its simplest terms
•
A fraction is in its simplest terms if there is no common factor
÷4
Wagoll
12 = 3
20
5
÷4
Misconceptions: Pupils do not always multiply or divide the denominator and
the numerator by an amount.
Pupils sometimes believe you can only multiply the denominator and
numerator by 2 or halve it.
12
Negative numbers
•
Negative numbers can be represented on a number line
•
Number lines can be horizontal or vertical
-7
-6
-5
-4
-3
-2
-1
0
1
2
negative
3
4
5
6
positive
•
Negative numbers are to the left, or below, zero
•
Positive numbers are to the right, or above, zero
•
The further to the left, or the further down, the number line, the smaller the
number
Wagoll
End
Start
Adding a positive
number is a move to
the right
-2
End
Subtracting a positive
number is a move to the
left
Start
-8
-4
4
End
Start
Adding a negative number
is a move to the left
Start
Subtracting a negative
number is a move to the
right
7
-2
+
End
7
Misconceptions: Pupils do not always use the number line. They try to
remember rules.
Pupils sometimes go the incorrect way on the number line.
Pupils do not include a 0 on their number line.
Aspiration | Achievement | Respect
13
Rounding
Most numbers used in everyday life are rounded
•
People may say ‘it takes me 30 minutes to drive to work’ or ‘There were
forty-two thousand people at the match last weekend.’
Numbers can be rounded to the nearest whole number, the nearest ten, the
•
nearest hundred and so on
76 is rounded to 80 to the nearest 10,
235 is rounded to 200 to the nearest hundred
244 is rounded to 240 to the nearest ten.
The convention is that a halfway value rounds upwards
•
2.5 is rounded to 3 to the nearest whole number
Decimal Places
•
The number of decimal places in a number is just the number of digits after the
decimal point
2.34 has two decimal places (2dp), 3.068 has 3 decimal places (3dp)
•
You need to be able to round numbers to one, two or three decimal places
(1dp, 2dp, 3dp)
•
To round a number to one decimal place, look at the digit in the second decimal
place. If it is less than 5 remove the unwanted digits. If it is 5 or more add 1 on to
the digit in the first decimal place
•
Use the same method to round to two or three decimal places
3.5629 is 3.6 to 1dp,
3.56 to 2dp
3.563 to 3dp
14
Rounding - Decimal places
2.6
Wagoll
Round 2.6 to the nearest whole number
3
3
2
Draw a number line with the two possibilities at each end, put your number on the line,
which number is it closest to?
Round 1.64 to one
decimal place
1.64
1.7
1.6
1.6
Waboll
Wagoll
3469.6756
3469.6756
Rounded to 1 decimal place is
3469.6
(they haven't rounded up)
Rounded to 1 decimal place is
3469.7
3469.6756
3469.6756
Rounded to 2 decimal place is
35
(they have rounded the first 2 digits)
Rounded to 2 decimal place is
3469.68
Aspiration | Achievement | Respect
15
Rounding - Significant figures
Rounding to one significant figure
Significant figures are the digits of a number, from the first to the last non-zero
•
digit
3400 has two significant figures (2sf), 0.06 has one significant figure (1sf)
and 67.45 has four significant figures (4sf)
•
To round a number to one significant figure (1sf), just round the first two non-zero
digit, then replace the rest of the digits in the number with zeros
432 is 400 to 1sf, 0.087 is 0.09 to 1sf and 35.9 is 40 to 1sf
3 6
millionths
hundred-thousandths
ten-thousandths
thousandths
hundredths
tenths
and
units
tens
hundreds
thousands
ten thousands
hundred thousands
millions
Place value and decimals
8 2 4 9
3rd Significant figure
2nd Significant figure
1st Significant figure
•
3 6 8 2 4 9 to one significant figure is 4 0 0 0 0 0, this has been rounded up as
its closer to 4 0 0 0 0 0 then it is 3 0 0 0 0 0
300000
368249
400000
400000
16
Estimation
Estimation/approximation of calculations
•
To estimate the answer to a calculation, round the numbers in the
calculation to one significant figure, then work out the approximate answer
38.2 x 9.6 can be rounded to 40 x 10 which is 400, so 38.2 x 9.6 ≈ 400
48.3 ÷ 19.7 rounds to 50 ÷ 20 = 2.5, so 48.3 ÷ 19.7 ≈ 2.5
•
The sign ≈ means ‘approximately equal to.’
Waboll
Estimate 2,342 + 637
2,342
rounds to
2,600
+ 637
rounds to
+ 637
Wagoll
2342 rounds to 2000
So 2,342 + 637 is about 2,600
2,600
637 rounds to 600
2000+600=2600
This would score 0 marks in an exam
because it has been rounded to 2 significant
figures and not 1
Misconceptions: Pupils sometimes round to the nearest tenths, hundreds
etc... not to 1 significant figure.
Aspiration | Achievement | Respect
17
Ordering Decimals
Example: Put the following decimals in ascending order:
1.506, 1.56, 0.8
• 0.8 only has 2 digits so is the smallest
Waboll
• 1.55 has digits so is the second smallest
• 1.506 has 4 digits and so is the largest
Wagoll
1. Draw out a place value table
1
1
0
5
5
8
0
6
0
6
0
0
2. Input the numbers into the correct colums
3. Input 0’s into the empty space
4. Compare using the first column (Units): Two of them are "1"s and the other is a
"0". Ascending order needs smallest first, and so "0" is the winner:
Answer so far: 0.8
5. Compare the Tenths: Now there are two numbers with the same "Tenths" value of
5, so move along to the "Hundredths" for the tie-breaker
6. Compare the Hundredths: One of those has a 6 in the hundredths, and the other
has a 0, so the 6 wins. So 1.506 is less than 1.56
Only one number left, it must be the largest:
Answer: 0.8, 1.506, 1.56
Misconceptions: Pupils sometimes don’t use the place value table,
therefore do not realise the values of each digit.
18
Factors
•
A factor is any whole number that divides into another exactly
The factors of 20 are 1, 2, 4, 5, 10, 20
•
When you find one factor there is always another that goes with it, unless you
are investigating a square number.
1 x 12 = 12, 2 x 6 = 12, 3 x 4 = 12 so the factors of 12 are 1, 2, 3, 4, 6, 12
1
Wagoll
12
12
2
6
4
3
Multiples
•
A mutiple of a number is any number in the times table
5 x 7 = 35, so 35 is a multiple of 5 and 7
5x1=5
Wagoll
5x2=10
5x3=15
5x4=20
5x5=25
5x6=30
5x7=35
Multiples of 5
Aspiration | Achievement | Respect
19
Simple Number Terms
Prime numbers
•
A prime number is a number with only two factors
17 has only the factors 1 and 17
3 has only the factors 1 and 3
•
The factors of a prime number are always 1 and itself
•
There is no rule or pattern for spotting prime numbers, pupils have to learn
them
The prime numbers up to 50 are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47
•
All prime numbers are odd, except for 2, which is the only even prime number
Remember
Wagoll
1 is not a prime
number as it only has
one factor (1).
So 12 is not a prime
number as it has more
then 2 factors.
20
Simple Number Terms
Square numbers
•
Square numbers are the result of a number been multiplied by itself
1, 4, 9, 16, 25, 36, … are all square numbers
•
The square numbers can be represented by square patterns
1x1
=1
2x2
=4
Remember
3x3
=9
Pupils are expected
to know the square
4x4
=16
5x5
= 25
numbers up to
15 x 15 (= 225).
Cube numbers
•
Cube numbers are the result of a number been multiplied by itself 3 times
1, 8, 27, 64, 125, 216, … are all square numbers
•
The square numbers can be represented by square patterns
1 is the first cube
8 is the second cube 27 is the third cube
64 is the fourth cube
number because
number because
number because
number because
1 x 1 x 1 = 10
2x2x2=8
3 x 3 x 3 = 27
4 x 4 x 4 = 64
Misconceptions: When squaring numbers pupils sometimes multiply the
number by 2, rather then by itself.
Aspiration | Achievement | Respect
21
Ratio
•
A ratio is a way of comparing the sizes of two or more quantities
•
A colon (:) is used to show ratios
3:4 and 6:20 are ratios
Simplfying ratio
Simplify the Ratio 16 : 12
Divide both number values by the HCF
(Highest Common Factor)
÷4
16 : 12
4
:
3
÷4
The simplified Ratio Answer
is 4 : 3
Dividing amounts in ratios
Split £10 in the ratio of 2 : 3
Wagoll
1. Split £10 into two parts
2. Split £10 into three more parts
3. Share £10 between 5 parts (10 ÷ 5)
4. Each part is worth £2 so 2 parts is worth £4
5. Three parts is worth £6
6. £4 + £6=£10 (the original value)
£4 : £6
£10
£2
£4
£2
£2
£2
£2
£6
Misconceptions: Pupils sometimes do not add the ratios together.
They sometimes just divide the amount by each ratio; for example the
question above would be answered:
•
10 ÷ 2 = 5
• 10 ÷ 3 = 3.33333
Pupils do not always add up their answers to check it gives the original value.
22
Percentages, fractions and decimals
25 squares are shaded in out of
100 squares altogther:
Fraction:
Decimal:
25
100
=
1
4
0.25
Percentage: 25%
How to convert Percentage,
These are some
Fractions and Decimals
you should memorise:
To change
Percentage
to a:
Decimal
Divide by 10
Fraction
Percentage
Put the percentage
over 100 and
55% = 0.55
simplify if possible.
11
55
55% =
=
20
100
Fraction
to a:
Divide the
Divide the
numerator by the
numerator by the
denominator.
denominator and
to a:
Decimal
1%
0.01
1
5%
0.05
1
10%
0.1
12½%
0.125
1
20%
0.2
1
25%
0.25
1
0.333...
multiply by 100.
7
= 7÷8 = 0.875
8
Decimal
Percent
7 =
7÷8 x100
8
= 87.5%
Put the decimal
Multiply by 100 (or
over 100 and
move the decimal
simplify if possible.
point two places
right).
17
68
0.68 =
=
25
100
0.68 = 68%
Fraction
1
1
1
50%
0.5
75%
0.75
80%
0.8
4
90%
0.9
9
99%
0.99
100%
1
3
99
100
20
10
8
5
4
3
25
4
5
10
100
1 out of 1
Aspiration | Achievement | Respect
23
Finding percentages
Without a calulator
The easiest percentages to find are:
25% - divide by 4
5 % - divide a 10% value by 2
50% - divide by 2
1% - divide by 100
10% - divide by 10
1%
225 ÷ 100 = 2.25
10%
225 ÷ 10 = 22.5
Find 34%
of 225
30%
22.5 x 3 = 67.5
4%
2.25 x 4 = 9
34%
67.5 + 9 = 76.5
With a calulator
Percentage Increase
Percentage Decrease
The value of Frank’s house has gone
up by 20% in the last year. If the
house was worth £150,000 1 year
ago, how much is it worth now?
Find the resut in a single calculation.
The original amount is 100%
100%
An ipod originally costing £75 is
reduced by a sale. What is the sale
price?
The original amount is 100% like this
70%
20%
Now we subtract 30%. We now have
Now we add 20%. We now have 120%
70% of the original amount.
So multiply by 1.2
So multiply by 0.7
24
30%
Averages
There are four main averages used in different circumstances.
The sum of all the values divided by how
Mean
many number they are
E.g. Find the mean of 6, 3, 1, 4
Medium
6+3+1+4
4
= 14 ÷ 4
= 3.5
The value in the middle of the data after it has been arranged in size
order. If we have an even number of numbers, then you find the
middle of the two values.
Example 1.
Find the median of 4, 6, 3, 2, 1
1, 2, 3, 4, 6
Example 2.
Median is 3
Find the median of 4, 6, 3, 2, 1, 2
1, 2, 2, 3, 4, 6
Median = the mid point of 2 and 3
Median is 2.5
Mode
The value in the data that occurs most frequently, E.g.
Find the mode of 3, 15, 0, 3, 1, 0, 4, 3
Mode = 3
If there is no number that occurs most often, then there is no mode.
There can be more than one mode.
The Range represents the spread of data, the largest value
The Range subtract the smallest value, E.g. 7, 6, 8, 12, 9
Range = 12 – 6 = 6
Misconceptions: People assume the “average” is the mean average,
however all of the above are averages.
When finding the median, people sometimes do not order the numbers in
ascending order.
Aspiration | Achievement | Respect
25
Triangles
Scalene
Lengths of sides and
angles are
all different
Isosceles
Two lengths are the same.
Two base angles are the
same
Indicates sides of
the same length
Indicates angles are
the same size
Equilateral
All lengths are the same.
All angles are 60˚
26
Perimeter and Area
8 cm
Perimeter
•
The perimeter of this
rectangle is 22cm.
The perimeter of a shape
3 cm
is the sum of the lengths of
all it’s sides
Perimeter is measured in length E.g. centimetres (cm), square metres (m)
and square kilometres (km)
Area of irregular shapes (counting squares)
•
The basic units of area are square centimetres (cm²), square metres (m²) and
square kilometres (km²)
•
To estimate the area of an irregular shape, trace it onto a sheet of centimetre
squares, say, and then count the squares.
These shapes are drawn on a centimetre grid.
10
12
14
1
2
3
4
5
6
7
8
9
11
13
15
16
6
14
1
9
10
2
3
8
4
7
11 5 13
12
Aspiration | Achievement | Respect
27
Area
Area of a rectangle
•
The area of a rectangle can be calculated by the formula:
area = length x width A = lw
8 cm
The area of the rectangle is:
8 x 3 = 24cm²
The area of this
rectangle is 24cm²
3 cm
Area of a triangle
There are two ways to write the formula for finding the area of a triangle:
Area = base x height x
1
2
Area = base x height
2
To find the area of this triangle
8 x 6 = 48cm²
48cm² ÷ 2 = 24cm²
The area of this
triangle is 24cm²
8 cm
28
6 cm
Area
Area of a parallelogram
•
To find the area of a parallelogram, multiply the base by the perpendicular
height between the sides
•
The formula of the area of a parallelogram is usually given as:
Area = base x height A = bh
The area of the parallelogram is:
This is the
8 x 3 = 24cm²
3 cm
The area of this
perpendicular
8 cm
parallelogram is 24cm²
This is the
Area of a trapezium
perpendicular
To work out the area of a trapezium:
h
2 Multiply this by the perpendicular height (h)
The area of the trapezium is:
1. 8 + 12 = 20m²
2. 20 x 6 = 120m²
3. 120 ÷ 2 = 60m²
a
height.
1 Find the sum of the parallel sides lengths (a + b )
3 Divide by 2
height.
b
h ( a+b)
2
8m
6m
The area of this
trapezium is 60m²
12 m
Aspiration | Achievement | Respect
29
Coordinates
y
10
X
A (3,8)
X
8
6
D (-5,4)
X
4
2
Y
-7
-6
-5
-4
-3
-2
-1
X
X
(X,Y)
0
C (1,0)
X
1
2
3
4
5
6
-2
E (-2,-2)-4
F (-7,-5)
-6
-8
-10
X
B (2,-8)
Tips:
•
When drawing the four quadrants, think of it like two number lines, the negative
numbers are lower then the positive numbers
•
The x axis co ordinate are given first and the y axis co ordinate are given
last (in alphabetical order)
•
When drawing the four quadrants, make sure each number is placed at regular
intervals precisely on the guidlines
Misconceptions: Pupils sometimes mix up the x and y co ordinates (go up
the axis and then across.
30
7
x
Two - Way Tables
•
A two-way table is a table that links two variables
The table shows the languages taken by the boys and girls in form 9Q.
French
Spanish
Total
Boys
7
5
12
Girls
6
12
18
Total
13
17
30
• One of the variables is shown by the rows of the table
• Another of the variables is shown by the columns of the table
This table shows the nationalities of people on a jet plane and
the types of ticket they have.
Remember
Usually a column
and a row for the
totals are included
in the table. If they
are not, always add
up each row and
column anyway.
You almost always
need these values
to answer the
questions.
First class
Business class
American
6
8
51
65
British
3
5
73
81
French
0
4
34
38
German
1
3
12
16
10
20
170
200
Total
Waboll
There are no totals so you
cannot check if you are correct
Wagoll
Economy
Total
Like
Skateboards
Do not like
Skateboards
Totals
Like
Snowmobiles
80
25
105
Do not like
Snowmobiles
45
10
55
Totals
125
35
160
There are total columns so that answers can
be checked at the end.
The pupils has used the totals to find missing
numbers in the table
Aspiration | Achievement | Respect
31
Bar Charts
A bar chart is made up of bars or blocks of the same width, drawn horizontally
•
or vertically on an axis
•
The heights or lengths of the bars always represent frequencies
•
The bars are seperated by small gaps to make the chart easier to read
•
Both axes should be labelled
•
The bar chart should be presented with a title
•
A dual bar chart can be used to compare two sets of data
Waboll
Wagoll
Misconceptions:Pupils can sometimes produce bar charts , but cannot read from them,
encourage them to read from it and “what does it tell us?”
32
Real life graphs
Distance Time Graphs
A distance time graph shows that time and distance that something has travelled
Misconceptions:
• Pupils sometimes can interpret a positive slope as speeding up and a
negative slope as slowing down
• Pupils can fail to mention distance or time. For example: the pupil has not
mentioned how far away or the time for each section of the journey
• Pupils can misinterpret the scale
Conversion Graphs
Tina is on holiday in Bermuda. Her travel agent gave
her this conversion graph with her currency.
She spends $6 – how much is that in pounds sterling?
1. Find $6
2. Draw a straight line until you hit the graph line
3. Draw a straight line from the graph line
4. Find the value of the point
£4.20
Aspiration | Achievement | Respect
33
Units of Measure
The metric system
•
The basic unit length is the metre (m). Other units are millimetres (mm), centimetres
(cm) and killometres (km)
•
The basic unit of weight is the kilogram (kg). Other units are the gram (g) and
the tonne (T). 1000 g = 1 kg, 1000 kg = 1 T
•
The basic unit of capacity is the litre (l). Other units are millilitres (ml) and centilitres
(cl). 1000 ml = 1 litre, 10 ml = 1 cl, 100 cl = 1 litre
The imperial system
•
The basic unit of length is the foot (ft). Other units are yards (yd), inches (in) and
miles (m). 12 in = 1 ft, 3 ft = 1 yd, 1760 yd = 1 m
•
The basic unit of weight is the pound (lb). Other units are the ounze (oz), the stone
(st) and the ton (ton). 16 oz = 1 lb, 14 lb = 1 st, 2240 lb = 1 ton
•
The basic unit of capacity is the pint (pt). Other units are gallons (gall) and quarts
(qt). 2 pt = 1 qt, 8 pt = 1 gall.
Conversions factors
•
Because many imperial units, such as miles and pounds, are still in common use
you need to be able to convert between them. To do this we use conversion factors
•
34
There are five conversion factors that you need to know:
2.2 pounds = 1 kilogram
1 foot = 30 centimeters
5 miles = 8 kilometres
1.75 pints = 1 litre
1 gallon = 4.5 litres
Venn Diagrams
A
(∩ - means intersection)
B
A ∩ B ( A and B) represents the intersection of sets
A and B.
This is all the items which appear in set A and in set
B.
A
(U - means union)
B
A U B ( A or B or both) represents the union of sets
A or B.
This is all the items which appear in set A or in set B
or in both sets.
A
B
A’ We use ' (the apostrophe) to denote the
complement of a set.
A' is all the items which are not in set A.
Means the universal set – all
elements being considered
A∩B
Example
{3,4} These are in A and they are in B
AUB
A
B
1
2
5
3
7
8
9
in set B or in both sets
A’
6
4
{1,2,3,4,5,6} These appear in set A or
{6,7,8,9,10} These are not in A
10
{1,2,3,4,5,6,7,8,9,10} These are all the
numbers in the set
Aspiration | Achievement | Respect
35
Tention Graph
A Tention Graph can be used to display tentions within a story. The key
tention points of a story are picked and are plotted on a line graph.
Example
Y
Red’s Tension Graph
Wolf attempts to
eat Red.
Woodsman kills
the wolf.
Red is safe.
Tension
Red walks towards
her Grandma’s
house.
Red encounters the
wolf.
Red pose questions
to Grandma/Wolf.
Wolf leaves and
Red continues to
walk.
Time
X
Misconceptions:
• Pupils don’t use equal spacing on the axis
• Pupils get the x and y axis mixed up
If staff should require any support within their
classrooms, please contact Miss S Warhurst.
Alternatively there is a staff maths workshop every
Monday at 3pm in 2M8.