Numeracy PassportsMrs Claire Searle Maths and Key Stage 1 Leader23.10.13

What are Numeracy Passports?

•A way of putting mental maths at the heart of maths teaching and learning. •Competitive and enjoyable way of promoting children’s understanding of their mathematical learning. •Children progress through basic number skills which are linked to particular continents. •Once one continent is completed, the child’s progress is celebrated and they travel to the next continent to work on targets with greater challenge. •Children are competing against themselves and their learning and understanding, not against other children. •The challenge for each child is to constantly improve and become faster at mental maths.

Why have Numeracy Passports?In reading, the whole point of being able to do the basics – read the words - is to understand what you have read. You can’t say you can read unless you understand the words you have read as a whole text.

In maths, the important part is to be able to use the basic skills – number bonds, multiplication tables, halving, doubling -- in problem solving and real life applications. If you want to know what is the best value in the supermarket, you need to be able to work out the price per 100g of a product when it comes in different sizes.

Or you want to buy 4 plane tickets at £160 each. Do we really want our children to have to get out a calculator or use paper and pencil for a simple calculation?

How would you work this out?

What is the cost of 4 plane tickets at £160 each?

Method 1 Use times tables

4 x 100 = 400 4 x 6 = 24 so 4 x 60 is 240

400 + 240 = £640.

Method 2 Use doubling

Double 16 is 32, double 32 is 64.So double 160 is 320, double 320 is £640.

It doesn’t matter which way you work it out, as long as you know what to do and can work it out quickly.

Key Stage 1 SATs – Year 2SATs for Year 2 seem to be here to stay. The new revised National Curriculum has raised the standards to a certain extent. If a child can do all the skills on Africa, they will find it easier to get a good level 2.

If they can do all the skills on Australasia, they will find it easier to achieve level 3.

SATs include other aspects of maths; shape and space, measure, data handling and problem solving. But knowing these key skills instantly will give your child a head start in being able to apply them.

Year 6 SATs also seem to be here to stay.

• 2 written papers – new for 2014, neither paper will allow the use of a calculator. Emphasis is on written and mental methods. Children will need to be able to do quite complex calculations with several steps under timed conditions.

• mental maths paper – need almost instant recall of basic maths skills. 5 seconds, 10 seconds and 15 second questions.

Testing in school. How would you do?

Copy down the numbers on the screen onto your grid.

We are going to do the 7 times table. You have 30 seconds.

Where it says eg 3, you write the answer to 3 x 7. Don’t write the calculation.

If you finish all 10 within 30 seconds, write down how many seconds you have left.

Passports are based on the continents of the world.

There are currently 7 – we may add another for those that finish all 7.

1.Europe2.Asia3.Africa4.Australasia5.North America6.South America7.Globetrotter

Europe Date achieved Date achieved Date achieved

Count up to 10 objects.Select the correct numeral to represent a group of objects up to 10.Say the numbers up to 20 accurately.Order numbers 1-20.Say which number is one more than any number up to 20.Say which number is one less than any number up to 20.

•Europe

Stage 1 Europe Examples Can your child answer these questions?

Count up to 10 objects. How many cakes on the plate?Can you put out the spoons for 5 people?

Select the correct numeral to represent a group of objects up to 10.

What number is this?How many cars do we need to go with it?How many pennies are here? What number do you need to show all these pennies?

Say the numbers up to 20 accurately.

Forwards and backwards, starting on any number from 0 to 20.

Start at 6 and count on until you get to 14.Start at 11 and count on to 20.Can you count backwards from 18 to 8?

Order numbers 1-20. Put these 5 numbers in order 18 5 12 9 15

Look at these numbers 1-20. Which number(s) is (are) missing?

Say which number is one more than any number up to 20.

1 more than 4 is 5.1 more than 17 is 18.

There are seven beads in this pot. If I put one more in the pot how many will there be?

Say which number is one less than any number up to 20.

1 less than 12 is 11.1 less than 6 is 5.

There are twelve pennies in my purse. If I spend one, how many will there be?

Asia Date achieved Date achieved Date achieved

Count in 2s up to 20.Count in 5s up to 50.Count in 10s up to 100.Know by heart all number bonds for 10.

Know by heart all additionand subtractionfacts for each numberup to 5.Recall the doubles ofall numbers to at leastten.

Recognise odd and even numbers up to 30.

2. Asia

Stage 2 Asia Examples Can your child answer these questions?

Count in 2s up to 20

How far can you count in twos?What number would follow in this sequence:6,8,10,12….? How far can you continue the sequence?What about this sequence? 18,16,14,…What would come next? Can you get back to 0?What number is missing? 18 ___ 14 12

Count in 5s up to 50

How far can you count in fives?What number would follow in this sequence:25,30,35,40, ….? How far can you continuethe sequenceWhat about this sequence? 45,40,35,25,…What would come next? Can you get back to0?What number is missing? ___ 20, 25, 30

Count in 10s up to 100

How far can you count in tens?What number would follow in this sequence:40,50,60, ….? How far can you continue the sequence?What about this sequence? 90,80,70,…What would come next? Can you get back to 0?What number is missing? ___ 70 60 50

Africa Date achieved Date achieved Date achieved

Know by heart all number bondsthat total 20.Know by heart all addition andsubtraction facts for each numberup to 10.Know by heart all bonds of multiplesof 10 up to 100.Know by heart doubles of allnumbers to 20.Know by heart all halves of numbersto 20.Know by heart all multiplicationfacts for 2 up to 12 x 2.Know by heart all division factsfor 2 up to 24.Know by heart all multiplicationfacts for 5 up to 12 x 5.Know by heart all division factsfor 5 up to 60.Know by heart all multiplicationfacts for 10 up to 12 x 10.Know by heart all division factsfor 10 up to 120.

3. Africa

Stage 3 Africa

Examples Can your child answer these questions?

Know by heart all number bonds that total 20.

0 + 20 = 201 + 19 = 202 + 18 = 20Up to….19 + 1 = 2020 + 0 = 20

How many pairs of numbers which total 20 can you remember?What would you add to 8 to get a total of 20?Use number cards from 0 to 20 – can you pair the numbers which make 20?

Know by heart all addition facts for each number up to 10.

0 + 8 = 81+ 7 = 83 + 4 = 72 + 4 = 61+ 6 = 7(Adding 2 numberswhere the total is upto 10)

What numbers could you add to give a total of 8?Are there any other ways to get a total of 8?

Know by heart all subtraction facts for each number up to 10.

10 – 1 = 97 – 2 = 58 – 2 = 69 – 0 = 96 – 3 = 38 – 5 = 3

There are 10 beans on a plate – I hide some and write this to show what I have done: 10 – 3 = 7. Use the 10 beans and hide a different amount – can you write the subtraction sentence for what you have done?Look at this addition : 7 + 2 = 9Can you make a subtraction sentence using these numbers? (9 – 2 = 7, 9 – 7 = 2)

Australasia Date achieved Date achieved Date achieved

Know by heart addition and subtraction facts for each number up to 20.

Know by heart all sums and differences of multiples of 10 up to 100.

Know by heart all number bonds that total 100.

Know by heart all doubles of multiples of 5 and 10 up to 100.

Know by heart all halves of multiples of 10 up to 100.

Know by heart all multiplication facts for 3 up to 12 x 3.

Know by heart all division facts for 3 up to 36.

Know by heart all multiplication facts for up to 12 x 4.

Know by heart all division facts for 4 up to 48.

Know by heart all multiplication facts for 8 up to 12 x 8.

Know by heart all division facts for 8 up to 96.

Recognise multiples of 2, 5, 10 up to 1000.

4. Australasia

Stage 4Australasia

Examples Can your child answer these questions?

Know by heart all addition facts for each number up to 20.

0 + 19 = 193 + 15 = 187 + 4 = 1112 + 4 = 1613+ 6 = 19(Adding 2 numberswhere the total is upto 20)

What numbers could you add to give a total of 17?Are there any other ways to get a total of 17?

Know by heart all subtraction facts for each number up to 20.

20 – 1 = 1917 – 2 =1518 – 2 = 1619 – 0 = 1916 – 3 = 1318 – 5 = 1315 – 8 = 719-10 = 9

There are 16 beans on a plate – I hide some and write this to show what I have done: 16 – 4 = 12. Use the 16 beans and hide a different amount – can you write the subtraction sentence for what you have done?Look at this addition : 17 + 2 =1 9Can you make a subtraction sentence using these numbers? (19 – 2 = 17, 19 – 7 = 12)

Know by heart all sums and differences of multiples of 10 up to 100.

60 + 30 = 9070 + 80 = 15020 + 90 = 11070 – 20 = 5090 – 60 = 3040 – 30 = 10

Add 80 and 30, tell me how you did it.Tell me all the number pairs you know with multiples of 10 which make 90.What is the difference between 20 and 80? (60)Look at these multiples of 10… which pairs give a total of 100? A total of 140?0 10 20 30 40 50 60 70 80 90 100

North America Date achieved Date achieved Date achieved

Double any 2 digit number.

Halve any 2 digit number.Know by heart all multiplication facts for 6 up to 12 x 6.Know by heart all division facts for 6 up to 72.Know by heart all multiplication facts for 7 up to 12 x 7.Know by heart all division facts for 7 up to 84.Know by heart all multiplication facts for 9 up to 12 x 9.Know by heart all division facts for 9 up to 108.Know by heart all multiplication facts for 11 up to 12 x 11.Know by heart all division facts for 11 up to 132.Know by heart all multiplication facts for 12 up to 12 x 12.Know by heart all division facts for 12 up to 144.

5. North America

Stage 5North America

Examples Can your child answer these questions?

Double any 2 digit number.

Double 26 = 52Double 97 = 194

Which numbers are missing in this sequence?17 34 ? 136 ?I think of a number and halve it – the answer is 55.Which number was I thinking of? How do you know?

Halve any 2 digit number.

(EVEN numbersonly)Half 48 = 24Half 86 = 43Half 96 = 48

Which numbers are missing in this sequence?96 ? 24 ? ?Use the number 86 to explain what doubling andhalving mean.

Know by heart all multiplication facts for 6 up to 12 x 6.

0 x 6 = 01 x 6 = 6…Up to12 x 6 = 72

Which is the number before 36 in the 6x table?What is the answer to 6 x 6? 8 x 6?What are 6 8s?

Know by heart all division facts for 6 up to 72.

72 ÷ 6 = 1266 ÷ 6 =11…Down to0 ÷ 6 = 0

What is the answer to 36 ÷ 6? 48 ÷ 6?Which is the missing number: ? x 6 = 24? Howdo you know?How many groups of 6 in 48?

South America Date achieved Date achieved Date achieved

Double any number withup to 1 decimal place.Halve any number with upto 1 decimal place.Recall quickly multiplicationfacts up to 12 x 10and use them to multiplypairs of multiples of 10and 100 e.g. 30 x 70, 40 x 200.

Recall quickly divisionfacts of all tables up to12 x 10 and use them todivide pairs of multiples of10 and 100 e.g. 240 ÷ 40 = 6.

Identify pairs of factors forall 2 digit whole numbers.

6. South America

Stage 6South America

Examples Can your child answer these questions?

Double any number with up to 1 decimal place.

Double 5.7Double 12.6

Which number did you double to get the answer3.8? How do you know?

Halve any number with up to 1 decimal place.

Halving anynumber with aneven digit decimal.Halve 7.2Halve 9

If I halve 2.6 litres of juice into two jugs, howmuch juice in each jug?

Recall quickly multiplication facts up to 12 x 12.

3x86x79x4

Which is the missing number? 6x ? = 42The answer is 36 – which multiplication sumcould it be?

Use multiplication facts up to 12 x 12 to multiply pairs of multiples of 10 and 100 eg 30 x 70, 40 x 200, 8 x 120.

30x7040x200500x600

Which two numbers multiply together to give4800?

Globetrotter Date achieved

Date achieved

Date achieved

Know by heart all thesquares of numbers between 12 x 12.

Recognise and recallfactors of numbers up to100 and correspondingmultiples of 100.

Use knowledge of placevalue and X facts to 10 x 10to derive related x / ÷ factsinvolving decimals(e.g. 0.8 x 7 = 5.6).

Know by heart tests ofdivisibility for multiples of2, 3, 4, 5, 6, 9 and 10.

7. Globetrotter

Stage 7 Globetrotter

Examples Can your child answer these questions?

Know by heart all the squares of numbers between 12 x 12 (1 and 12).

1 squared is 1 62 = 36 11 squared is 121

Can you tell me all the square numbers between 50 and 100? A number squared is 49, what is the number?

Recognise and recall factors of numbers up to 100 and corresponding multiples of 100.

The factors of 24 are 1,24,2,12,3,8,4,6

Which is the missing number? 6x ? = 42 The answer is 36 – which multiplication calculation could it be?

Remember

First stage is to learn what each skill needs. Tables can be learned by rote or sung to start with.

Then build up speed. The aim is to get faster. When you think your child is ready to be tested on a part of the passport then initial that section and send the passport into school for the class teacher to see.

When tested in school:

Answers need to be instant. They all need to be correct.

No fingers, no counting or chanting through the tables.

Practise little and often.

Use websites to help.

Mathletics www.mathletics.co.uk http://www.st-pauls.wilts.sch.uk/math.html