Download level-e-maths-upper-primary-secondary

Parents in Partnership
Innerwick Primary School
Mathematics
5-14
Level E
Working together to give your child confidence in
Maths
MATHEMATICS
Mathematics plays an important role in all our lives. It is used in
everyday activities, such as buying food, keeping time and playing
games.
In East Lothian we use the Core Programme in Maths. We work
together to share what we are learning with the children to ensure
they have a positive and confident attitude towards maths.
The Maths programme includes areas of
 number, money and measurement,
 information handling,
 shape, position and movement.
The children in our schools are encouraged to learn maths through
practical experiences, using concrete materials.
Mental calculations are vital in helping children to understand
number and use it well. Regular oral and mental work develops
children’s calculation strategies and recall skills.
Computer programmes are used to reinforce work and to develop
skills.
Your child will only be allowed to use a calculator, only under the
guidance of their teacher so please do not provide them with a
calculator unless this is suggested by the teacher.
It is hoped the contents of this booklet will give you some idea of
the work involved in Level E and some activities to try out.
Some methods may be different from your own ways of ‘doing
sums’. If in doubt speak to your child’s teacher!
Mathematics Tracking: Level E1-E3
3.
Add and subtract up to 3 numbers containing 2 digits,
including decimals (e.g. 7.3+8.2, 28+32+14, 9.1-4.7)
With a calculator add and subtract any number of digits with
at most 3 d.p.s
4.
Multiply and divide any whole number by a multiple of 10
or 100 (e.g. 73620, 48200)
With a calculator multiply and divide for any pair of
numbers but with at most 3 d.p.s in the answer
Information Handling
E1
1.
2.
3.
Multiply and divide any number, including decimals by 10,
100 and 1000.
4.
Find simple fractions and percentages of whole number
quantities (e.g. 3 quarters, 5 eighths, 25%, 60%, 10%)
5.
Equate widely used fractions and decimals and percentages.
6.
Decimals to 3 places – practical application in measurement
(e.g. 3g = 0.003kg, 24ml = 0.024 litres)
7.
Find ratios between quantities.
8.
Use simple unitary ratio.
9.
Simplify ratios
Non Calculator Work
1.
Multiplication for 4 digits with at most 2 decimal places by
a single digit in context
2.
Add and subtract 4 digits with at most 2 decimal places in
context
3.
Multiply and divide for 4 digits with at most 2 decimal
places by a single digit in context
1.
Collect information by selecting sources of information
including
practical
experiments,
surveys
using
questionnaires or sampling using a simple strategy
2.
Organise information by designing and using tables and
diagrams
3.
Display information by constructing straight line and curved
graphs for continuous data where there is a relationship,
such as direct proportion (e.g. travel, temperature, growth
graphs)
4.
Interpret by describing the main features of a graph so as to
show an awareness of the significance of the information
5.
Percent/Linking Fractions, Decimals and Percent
6.
Mentally find widely used percentages of whole number
quantities
7.
Without a calculator find a percentage of a whole number
quantity
8.
With a calculator find percentages of a quantity
Equations
1.
Simple equations with variables only on one side of the
equal sign involving very simple single or double
operations (e.g. -4=7, 2n+3=9)
Angles
2.
Introduce simple inequations (e.g. +3>5)
1.
Know that the sum of the angles of a triangle is 2 right
angles
Position and Movement
2.
Use ‘reflex’ to describe angles
4.
Round any number to one decimal place
5.
Addition and subtraction of positive and negative numbers
in applications such as rise in temperature.
1.
Use co-ordinates in all four quadrants to read and plot
position
E2
Fractions
1.
Both mentally and without a calculator find widely used
fractions of whole number quantities up to four digits
2.
Equivalence among fractions
3.
With a calculator find a fraction of a quantity
4.
5.
1.
2.
Add and subtract 2 digit numbers with decimals – 1 d.p only
(e.g. 3.7+1.2, 8.9-3.4, 8.6-2.9)
Reinforce equating fractions, decimals and percentages
3.
Find harder fractions of quantities (including decimals in the
context of money or measurement)
Find ratios between quantities
4.
Use simple unitary ratio (e.g. in a school the ratio of pupils
coming by foot is 1:5. In one class 4 came by car. How
many were likely to come by foot?)
Addition/subtraction of simple negative numbers (in
context)
5.
Solve simple equations
6.
Continue a sequence using square numbers
Decimals
7.
Continue a sequence using prime numbers
Reinforce decimals as special fractions (i.e. 1/10, 1/100 and
1/1000 columns)
8.
Continue a sequence using triangular numbers
2.
Know place value
9.
Side, angle, diagonal properties of quadrilaterals
3.
Equate fractions and decimals
4.
Read/record decimal scale with some graduations may need
to be reduced (to 2 d.p.s)
1.
Convert decimals to/from percentages (e.g. 0.45=45%,
6%=0.06)
5.
Round any number to 1 d.p
2.
Convert percentages to/from fractions (fraction
denominators should be a factor of 100)
3.
Practise finding percentages of amounts – easy examples
only (e.g. 10%, 30%, 35%, 12.5%)
1.
Add/subtract…
1.
Mentally 2 or 3 digit numbers up to 1 d.p
2.
Without a calculator up to 4 digits at most 2 d.p.s
Multiply/divide
1.
Mentally any numbers including decimals by 10, 100 and
1000
2.
Without a calculator up to 4 digits with at most 2 d.p.s by a
single digit
Non Calculator Work
Special Numbers, Patterns and Sequences
1.
Continue and describe sequences involving square and
triangular numbers
2.
Find a specific item in a sequence
3.
Prime numbers
Number Machines
3.
Be able to convert g to kg and kg to g
1.
Use function machines in reverse for inverse operations
4.
Be able to convert mls to litres and litres to mls
2.
Use notation to describe general relationships between 2 sets
of numbers (e.g. find a rule connecting posts and rails)
5.
Read scales on measuring devices including estimating
between graduations
3.
Use and devise simple rules e.g. find a rule connecting posts
and rails
6.
Realise that volume can be conserved when shape changes
7.
Calculate volumes of cubes and cuboids using rules
8.
Work with tonne when appropriate
9.
Measure and draw using standard units – accuracy and
device as appropriate to application
10. Add, subtract, multiply and divide length, weight and
volume in context with a calculator for any numbers with at
most 3 d.p.s in the answer
Range of Shape
1.
2D shape: define and classify quadrilaterals, square,
rectangle, rhombus, parallelogram, kite, trapezium
2.
Discuss the side, angle, diagonal properties of quadrilaterals
Symmetry
1.
Determine whether or not shapes have rotational symmetry
2.
Move a tile of a shape on a squared grid in order to translate,
reflect or rotate the shape
Time
1.
Time activities with a digital stopwatch in seconds, tenths
and hundredths
E3
1.
Rank simple fractions
2.
Addition/subtraction of negative numbers (e.g. – 4+6, -4-6)
3.
Round any number to 1 decimal place
4.
Read digital stop watches
5.
Calculate areas of squares and rectangles
6.
Calculate volumes of cubes and cuboids
7.
Estimate measurement of areas in square metres (e.g.
blackboard, wall, floor)
8.
Estimate measurement of small lengths in millimetres
9.
Estimate measurement of larger lengths (e.g. corridors,
playgrounds)
11. Add, subtract, multiply and divide length, weight and
volume in context without a calculator for 4 digits with at
most 2 d.p.s
12. Use scales such as 1cm to 1,2,5 or 10cm: or represented by a
ratio such as 1:100 to interpret or draw maps, plans,
diagrams or make models
Range of Shape
1.
3D shape: make models, solid and skeletal, including using
nets: triangular prism, pyramids and tetrahedron
2.
2D shape: relate diameter and circumference (practical work
only)
3.
Triangles: draw triangles given 3 sides, 2 sides and included
angle, two angles and one side
4. Triangles: draw triangles to scale involving height and
distance
Information Handling
1.
Collect information from a selection of sources
2.
Organise by designing and using a database or spreadsheet
with fields defined by pupils with the aid where appropriate
of a computer package
3.
Display information by constructing pie-charts of data
expressed in percentages with the aid where appropriate of
a computer package
4.
Interpret information from an extended range of displays
(diagrams, tables, graphs, pie charts) and databases,
retrieving information subject to more than one condition.
A computer package which uses the operators AND, NOT,
OR could be used
Non Calculator Work
1.
Convert decimals to fractions (up to 2 decimal places) and
simplify
2.
Add and subtract length, weight, volume and money (4
digits with at most 2 decimal places)
5.
Describe the main feature of a graph so as to show an
awareness of the significance of information
3.
Multiply and divide length, weight, volume and money (4
digits with at most 2 decimal places) by a single digit
6.
Calculate mean to compare sets of data
Money
Position and Movement
1.
Use bearings and distance to produce accurate scale
drawings of routes. Use scales such as 1cm to 1,2,5 or 10m
or represented by ratios such as 1:100 to interpret or draw
maps, plans, diagrams or make models
2.
Calculate distances along grid lines
1. Add and subtract money (4 digits with at most 2 decimal
places)
2.
Multiply and divide money (4 digits with at most 2 decimal
places by a single digit)
3.
With a calculator add, subtract, multiply and divide money,
in context
4.
Find percentages of amounts of money (both with and
without a calculator)
5.
Foreign exchange: use relationships between currencies to
do simple calculations (e.g. £5 = 47.25 Francs)
Measurement
1.
Estimate small lengths in mm, large lengths in metres
2.
Be able to convert between all length units
Area
1.
Estimate areas in square metres
2.
Work with square kilometre and hectare
3.
Calculate areas of rectangles and squares using rules
Angles
1.
Use the properties of angles formed by a line crossing
parallel lines
2.
Use the fact that vertically opposite angles are equa
Number, Money and Measurement
Range and type of numbers
At Level E your child will be using:
1. Negative numbers
What is the difference between these temperatures?
 a minimum of -15°C and a maximum of 27°C
 18°C indoors and -2°C outside
Use a thermometer to help your child.
2. Fractions and equivalent decimals
½= 0.5, 3/4= 0.75…, ¼ = 0.25, etc.
Ask your child to work out ½ of 60, then 0.5 of 60
3. Decimal measure to 3 places
0.25 litres = 250 ml,
1 kg 75 g = 1.075 kg,
331 m = 0.331 km
Money
1. Foreign exchange £1 = €1.45
=> £5.00 = €7.25
 When you go to Europe on holiday you have to
change your money to euros. A euro is divided
into 100 parts and each part is called a euro.
Ask your child to pay for items in euros.
£
€
1
1.44
300 = (300x1.44) = 432
 Ask your child to calculate any % discounts in shops.
Add and subtract

Mentally
7.3 + 8.2
43 - 28

Without a calculator
12.97 + 5.3
234.1 – 97.06

Negative numbers
-5 + 7
14 - 23
Multiply and divide

Mentally
6 × 70
90 × 300
800 ÷ 40
20000 ÷ 500

Mentally
6.41 × 10
4.5 × 100
92 × 1000
39.7 ÷ 10
325 ÷ 100
17.5 ÷ 1000

Without a calculator
8 × 6.7
7 × 24.83
5.6 ÷ 4
52.32 ÷ 8
Round Numbers

To one decimal place
4.72 => 4.7 to 1 decimal place
7.7538 => 7.8 to 1 decimal place
When rounding to 1 decimal place
=>
Look at the 2nd decimal figure
If it is a 5,6,7,8,or 9 => round your digit up by 1.
If it is a 0,1,2,3, or 4 => level your digit as it is.
Fractions, percentages and ratio


Mentally
3/4 of 24
10% of £7.50
⅝ of 72
40% of 360
Use simple ratios The ratio of buses to cars is 1:5. How many cars if there are 7
buses?
Write these ratios in simplest form 300:200, 24:16.
A class of 30 pupils has 18 boys. Write the ratio of boys to girls.
Patterns and sequences


Continue and describe sequences involving
Square numbers
1, 4, 9, 16, 25, 36, …
Triangular numbers
1, 3, 6, 10, 15, 21, …
Prime numbers
2, 3, 5, 7, 11, 13, 17, …
Finding specific terms in a sequence:
What is the seventh term in the sequence 1, 4, 7, 10, …?
Functions and equations
1. Use a function machine in reverse
q
×5
+7
52
=>
(52 – 7) ÷ 5 = q
2. Solve simple equations
x–4=7
4y + 3 = 23
3. Solve simple inequalities
z + 7 > 11
4. Use and devise simple rules
Measure and estimate
Estimate measurements
Areas in square metres
Small lengths in millimetres
Larger lengths in metres
Work with square kilometre, hectare, tonne
1 hectare = 10,000 sq. m
1 tonne = 1,000 kg
Read scales on measuring devices including estimating between
graduations
Time



Time activities with your child using a
stopwatch in seconds, tenths & hundredths.
Ask your child to read timetables and plan journeys.
At the airport ask you child to interpret arrivals and
departure boards.
Perimeter, Formulae, Scales
1. Calculate area and volume using formulae
Areas of rectangles & squares Area = l × b
The area of a shape is the amount of space it takes up.
1 cm2
1 cm
A= 1 cm2
1 cm
Volumes of cubes and cuboids
1 cm
1 cm3
1 cm
Volume = l × b × h
V = 1 cm3
1 cm
2. Use scales to interpret or draw maps, plans and diagrams.
Scales given in the form ‘1 cm to 10m’ or ‘ 1:10 means that every
time you measure 1cm on the diagram, in real life it measures
10m.
This lorry has been drawn
using a scale:1 cm = 1.5m.
(a) Measure the height of
the lorry.
(b) Calculate the real
height of the lorry in metres.
(c) Calculate the real length of the lorry.
The Norwegian flag is drawn to a
scale of:1 cm = 40cm.
(a) Calculate the real height of the
flag.
(b) Calculate the real width of the
flag.
Shape, Position and Movement
Range of Shapes
1. Your child will be discussing properties of 2D shapes
Discuss the side, angle and diagonal properties of
quadrilaterals or four sided shapes
square
kite
rhombus
rectangle
trapezium
parallelogram
A square has
- four equal sides
- four right angles
- diagonals which bisect at
right angles.
A kite has
- two pairs of equal sides
- one pair of equal angles
- diagonals which intersect
at right angles.
2. Properties of 3D shapes
Use nets to construct 3D shapes: A net
is the shape opened out.
tetrahedron (triangular based pyramid),
triangular prism, square based
pyramid
 Draw triangles
Ask your child to draw a triangle using a ruler,
protractor and a pair of compasses.
Position and Movement
1. Discuss position and movement
Use bearings and distances to produce accurate scale
drawings
A helicopter flies 70 km south-east, then 50
km on a bearing of 055°. Make a scale drawing
of this journey. Use a scale of 1 cm to 10 km.
Use co-ordinates in all four quadrants to plot position
Y
5
4
A (2, 3)
3
B (-4, 2)
2
1
-5
-4
-3
-2
C (-5, -2)
-1 0
-1
1
2
3
-2
-3
-4
-5
D (1, -3)
4
5
X
U
s
e
a
s
c
Symmetry
a
l
1. Work with symmetry
e
Determine whether a shape has rotational symmetry
o
f
1
c
m
☼
t
Show understanding of the terms: translate,
reflect and
o
rotate
1
0
k
Angles
1. Use the term ‘reflex’ to describe angles between 180° and 360°
2. Know that the sum of the angles in a triangle is 180°
b°
a°
c°
a° + b° + c° = 180°
3. Recognise pairs of equal angles and use the given terms
correctly.
corresponding
alternate
Information Handling
Collect
1. Select sources of information
Experiments
Surveys – favourite colour, television program, soft drink,
etc.
Sampling – estimate how many vehicles pass your house in one
hour by counting how many pass in five minutes.
Organise
2. Design and use tables
Complete the work rota below to show this information.
Everyone works on Friday and Saturday.
Two people work each night from Monday to Thursday.
Rajiv works on Monday and Wednesday.
Joanna has Tuesday and Wednesday off.
Frank has Thursday and Monday off.
Sarah can work any four nights.
Joanna
Rajiv
Frank
Sarah
Mon
√
Tue
Wed
Thu
√
Fri
√
Sat
√
 Design and use databases and spreadsheets
This target is often covered in other areas of the curriculum.
Display
3. Construct graphs for continuous data
Use the information from the table below to draw a line
graph of temperature v. time.
Time
Temperature (°C)
5 am
4°C
6 am
7°C
7 am
8°C
8 am
10°C
9 am
14°C
10 am
17°C
11 am
20°C
25
Temper atur e (°C)
20
15
10
5
0
5:00 AM
6:00 AM 7:00 AM
8:00 AM
9:00 AM 10:00 AM 11:00 AM
Ti me
4. Construct pie charts
Use the information from the table below to construct a pie
chart of people’s views on the quality of food in a restaurant.
Opinion
Percentage (%)
Excellent
Good
Fair
Poor
No opinion
20%
35%
25%
15%
5%
Opinions on food
No opinion
5%
Poor
15%
Fair
25%
Excellent
20%
Good
35%
Interpret
5. Interpret an extended range of displays
Retrieve information subject to more than one condition
Number of customers in a café at different times of day
Mon
Tue
Wed
Thu
Fri
8 am
10 am
24
18
20
16
22
32
25
20
23
20
12
noon
41
30
42
32
25
2 pm
4 pm
36
20
18
25
30
18
17
12
20
20
On what day and at what time was the café busiest?
Calculate the mean (average)
To compare sets of data
Snowfall (cm)
2000
2001
December
29
15
January
39
35
February
25
28
Which year had the higher average snowfall?
6. Describe the main features of a graph
Given a graph of water level in a harbour vs.
time, identify high & low water and say when
they occur.
Children respond to activities that involve active learning in a real context.
Interacting with your child by talking about maths or playing games is very
worthwhile. Numbers are everywhere, on buses, on telephones, on money etc.
The following suggestions can involve you and your child informally in maths
activities, and make their learning enjoyable.
Some games to support
mathematics:
 Monopoly
 Dominoes
 Playing cards
 Bingo
 Connect 4
 Yahtzee
 Battleships
 Suduko
The learning process can increasingly involve the
use of computers. The following websites offer children practice and
extension in using their maths skills.
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http://www.channel4.com/learning/primary.html
www.mathsyear2000.co.uk
www.nrichmaths.org
www.bbc.co.uk/education/megamaths
www.topmaths.co.uk/mathsgames
http://www.funbrain.com
www.aaamath.com
www.mathplayground.com/games
www.actionmath.com
www.coolmath4kids.com
www.coolmath-games.com
www.dositey.com/index
www.getsmarter.org
www.homeschoolmath.net/math
www.skool.co.uk