Parents in Partnership

Innerwick Primary School

Mathematics

5-14

Level E

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

E1

  1. 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)
  2. Multiply and divide any whole number by a multiple of 10 or 100 (e.g. 73620, 48200)
  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
  4. Round any number to one decimal place
  5. Addition and subtraction of positive and negative numbers in applications such as rise in temperature.

Angles

  1. Know that the sum of the angles of a triangle is 2 right angles
  2. Use ‘reflex’ to describe angles

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. Find ratios between quantities
  5. 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?)

Decimals

  1. Reinforce decimals as special fractions (i.e. 1/10, 1/100 and 1/1000 columns)
  2. Know place value
  3. Equate fractions and decimals
  4. Read/record decimal scale with some graduations may need to be reduced (to 2 d.p.s)
  5. Round any number to 1 d.p

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
  3. With a calculator add and subtract any number of digits with at most 3 d.p.s
  4. With a calculator multiply and divide for any pair of numbers but with at most 3 d.p.s in the answer

Information Handling

  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)
  2. Introduce simple inequations (e.g. +3>5)

Position and Movement

  1. Use co-ordinates in all four quadrants to read and plot position

E2

  1. 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)
  2. Reinforce equating fractions, decimals and percentages
  3. Find harder fractions of quantities (including decimals in the context of money or measurement)
  4. Addition/subtraction of simple negative numbers (in context)
  5. Solve simple equations
  6. Continue a sequence using square numbers
  7. Continue a sequence using prime numbers
  8. Continue a sequence using triangular numbers
  9. Side, angle, diagonal properties of quadrilaterals

Non Calculator Work

  1. Convert decimals to/from percentages (e.g. 0.45=45%, 6%=0.06)
  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%)

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

  1. Use function machines in reverse for inverse operations
  2. Use notation to describe general relationships between 2 sets of numbers (e.g. find a rule connecting posts and rails)
  3. Use and devise simple rules e.g. find a rule connecting posts and rails

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)

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)
  3. Multiply and divide length, weight, volume and money (4 digits with at most 2 decimal places) by a single digit

Money

  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
  3. Be able to convert g to kg and kg to g
  4. Be able to convert mls to litres and litres to mls
  5. Read scales on measuring devices including estimating between graduations
  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
  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
  5. Describe the main feature of a graph so as to show an awareness of the significance of information
  6. Calculate mean to compare sets of data

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

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.

  1. 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
  1. 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

Mentally7.3 + 8.243 - 28

Without a calculator 12.97 + 5.3234.1 – 97.06

Negative numbers-5 + 714 - 23

Multiply and divide

Mentally6 × 70800 ÷ 40

90 × 30020000 ÷ 500

Mentally6.41× 1039.7 ÷ 10 4.5 × 100 325 ÷ 100 92 × 1000 17.5 ÷ 1000

Without a calculator8 × 6.75.6 ÷ 4

7 × 24.8352.32 ÷ 8

Round Numbers

To one decimal place4.72 => 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

Mentally3/4 of 2410% of £7.50

⅝ of 7240% 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 numbers1, 4, 9, 16, 25, 36, …

Triangular numbers1, 3, 6, 10, 15, 21, …

Prime numbers2, 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

q52=>(52 – 7) ÷ 5 = q

  1. Solve simple equations

x – 4 = 74y + 3 = 23

  1. Solve simple inequalities

z + 7 > 11

  1. 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 planjourneys.

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 & squaresArea = l × b

The area of a shape is the amount of space it takes up.

Volumes of cubes and cuboidsVolume = l × b × h

  1. Use scales to interpret or draw maps, plans and diagrams. Scales given in the form ‘1 cm to 10m’ or ‘ 1:10means 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

  1. 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

Symmetry

  1. Work with symmetry

Determine whether a shape has rotational symmetry

☼

Show understanding of the terms: translate, reflect and rotate

Angles

  1. Use the term ‘reflex’ to describe angles between 180° and 360°
  1. Know that the sum of the angles in a triangle is 180°

a° + b° + c° = 180°

  1. Recognise pairs of equal angles and use the given terms correctly.

correspondingalternate

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

  1. 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.

Mon / Tue / Wed / Thu / Fri / Sat
Joanna / √ / √ / √ / √
Rajiv
Frank
Sarah

Design and use databases and spreadsheets

This target is often covered in other areas of the curriculum.

Display

  1. Construct graphs for continuous data

Use the information from the table below to draw a line graph of temperature v. time.

Time / 5 am / 6 am / 7 am / 8 am / 9 am / 10 am / 11 am
Temperature (°C) / 4°C / 7°C / 8°C / 10°C / 14°C / 17°C / 20°C

  1. 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 / Excellent / Good / Fair / Poor / No opinion
Percentage (%) / 20% / 35% / 25% / 15% / 5%

Interpret

  1. 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

8 am / 10 am / 12 noon / 2 pm / 4 pm
Mon / 24 / 32 / 41 / 36 / 18
Tue / 18 / 25 / 30 / 20 / 17
Wed / 20 / 20 / 42 / 18 / 12
Thu / 16 / 23 / 32 / 25 / 20
Fri / 22 / 20 / 25 / 30 / 20

On what day and at what time was the café busiest?

Calculate the mean (average)

To compare sets of data

Snowfall (cm)

December / January / February
2000 / 29 / 39 / 25
2001 / 15 / 35 / 28

Which year had the higher average snowfall?

  1. 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.