Year 6



Year 6

Using and applying mathematics

• Solve multi-step problems, and problems involving fractions, decimals and percentages;

choose and use appropriate calculation strategies at each stage, including calculator use

Jemma thinks of a number. She says,

'Add 3 to my number and then multiply the result by

5. The answer is 35'.

What is Jemma's number?

Riaz thinks of a number. He says,

Sapna and Robbie have some biscuits. Altogether

they have 14 biscuits.

Sapna has 2 more biscuits than Robbie. How many biscuits do Sapna and Robbie each have?

KS2 2005 Paper B level 4

'Halve my number and then add 17. The answer is

23.'

What is Riaz's number?

KS2 2002 Paper B level 4

In a supermarket storeroom there are

7 boxes of tomato soup

5 boxes of pea soup

4 boxes of chicken soup

There are 24 tins in every box. How many tins of soup are there altogether?

KS2 2004 Paper B level 4

Kim has some rectangular tiles. Each one is 4

centimetres by 9 centimetres.

4cm

9cm

She makes a design with them.

Parveen has the same number of 20p and 50p

coins. She has £7.00.

How many of each coin has she?

Y4 optional test 2003 Paper B level 4

185 people go to the school concert. They pay £1.35 each.

How much ticket money is collected?

Programmes cost 15p each.

Selling programmes raises £12.30. How many programmes are sold?

KS2 2002 Paper B level 4

Some children do a sponsored walk.

Jason is sponsored for £3.45 for each lap.

He does 23 laps. How much money does he raise?

Lynne wants to raise £100.

She is sponsored for £6.50 for each lap. What is the least number of whole laps she must do?

KS2 1997 Paper B level 4

height

This fence has three posts, equally spaced.

Not to scale

width

Calculate the width and height of her design.

KS2 2000 Paper A level 4

gap gap

15cm

15cm 15cm

153cm

Each post is 15 centimetres wide. The length of the fence is 153 centimetres. Calculate the length of

one gap between two posts.

KS2 2003 Paper B level 5

• Tabulate systematically the information in a problem or puzzle; identify and record the steps

or calculations needed to solve it, using symbols where appropriate; interpret solutions in the

original context and check their accuracy

χ represents the number of books that Alice reads

each week. Which of these represents the total number of books that Alice reads in 5 weeks?

A 5 + χ B 5 × χ C χ ÷ 5

D 5 ÷ χ

How many triangles can you see in this diagram?

[pic]

How can you make sure that you have counted them all?

χ and ? each stand for a different number.

χ = 34

χ + χ = ? + ? + χ

What is the value of ??

Y4 optional test 2003 Paper B level 4

Each shape stands for a number.

The numbers shown are the totals of the line of four numbers in the row or column.

[pic]

Find the remaining totals.

Imagine you have 25 beads. You have to make a three-digit number on an abacus. You must use all

25 beads for each number you make.

[pic]

How many different three-digit numbers can you make? Write them in order.

Two boys and two girls can play tennis.

[pic]

Ali said: ‘I will only play if Holly plays.’ Holly said: ‘I won’t play if Ben is playing.’

Ben said: ‘I won’t play if Luke or Laura plays.’ Luke said: ‘I will only play if Zoe plays.’

Zoe said: ‘I don’t mind who I play with.’

Which two boys and which two girls play tennis?

• Suggest, plan and develop lines of enquiry; collect, organise and represent information,

interpret results and review methods; identify and answer related questions

Here are some digit cards.

[pic]

Write all the three-digit numbers, greater than 500, that can be made using these cards.

KS2 2005 Paper A level 4

The graph shows how the price of a chocolate bar

has changed.

30p

20p

Jason threw some darts at this board.

Every dart landed on the board.

Price

10p

1972 1977 1982 1987 1992 1997 2002

Year

Jason scored exactly 100.

How many darts did he throw? Which numbers did they land on?

Write three more questions you cold ask about the

numbers on the dartboard.

This pie chart shows how the children in Class 6

best like their potatoes cooked.

[pic]

32 children took part in the survey.

Look at the four statements below. For each statement put a tick (⎫) if it is correct. Put a cross (⎦) if it is not correct.

10 children like chips best. χ

25% of the children like χ

mashed potatoes best.

1⁄5 of the children like roast χ

potatoes best.

12 children like jacket χ

potatoes best.

Write down two different ways in which you could extend this survey.

KS2 2005 Paper A level 5 [adapted]

Fill in the gaps below. Between 1992 and 2002,

the price of the chocolate bar increased by … p

In 1992, the price of the chocolate bar was 6 times as much as in …

The smallest increase in price was in the five years between … and …

Write down two more statements you could make about the information shown in the graph.

Y7 progress test Paper B level 4 [adapted]

Class 6 count how many seeds they find under two trees. They show the data in a graph.

[pic]

How many seeds did they find in week 3

altogether?

In how many weeks did they find more than 40

chestnut seeds?

Write down two more questions you could ask about the information shown in the graph.

KS2 2005 Paper A level 4 [adapted]

• Represent and interpret sequences, patterns and relationships involving numbers and

shapes; suggest and test hypotheses; construct and use simple expressions and formulae in

words then symbols, e.g. the cost of c pens at 15 pence each is 15c pence

In this sequence each number is double the

previous number. Write in the missing numbers.

χ χ 3 6 12 24 48 χ

KS2 2003 Paper B level 4

17 multiplied by itself gives a 3-digit answer.

[pic]

What is the smallest 2-digit number that can be multiplied by itself to give a 4-digit answer?

[pic]

KS2 2005 Paper B level 4

The first two numbers in this sequence are 2.1 and

2.2. The sequence then follows the rule ‘to get the next number, add the two previous numbers‘.

Write in the next two numbers in the sequence.

2.1 2.2 4.3 6.5 χ χ

KS2 2003 Paper A level 4

11

10

9

8

7

6

5

4

3

Here is a repeating pattern of shapes. Each shape is numbered.

2

1

0

0 1 2 3 4

5 6 7

8 9 10 11 12 13

1 2 3 4 5 6

7 8 9 10

Write the co-ordinates of the next triangle in the sequence.

The pattern continues in the same way. Write the

numbers of the next two stars in the pattern. Complete this sentence.

Shape number 35 will be a circle because ...

KS2 2003 Paper A level 4

What is the value of 4x + 7 when x = 5?

Y5 optional test 1998 Paper B level 4

Y4 optional test Paper B level 4

Halid makes a sequence of 5 numbers. The first number is 2. The last number is 18. His rule is to add the same amount each time.

Write in the missing numbers.

2 χ χ χ 18

KS2 1999 Paper B level 5

Take three shapes like this.

Use the three shapes to make a symmetrical shape. How many different symmetrical shapes can you

make using the three shapes?

How many of the shapes have only one line of symmetry? How many have two lines of symmetry?

Sam says: ‘In a triangle, each angle must be 90

degrees or less, because the three angles add up to

270 degrees.’

Is Sam correct? Ring YES or NO. Explain how you know.

The rule for this sequence of numbers is ‘add 3

each time’.

1......4......7......10......13......16......…

The sequence continues in the same way. Mary says, ‘No matter how far you go there will never be

a multiple of 3 in the sequence.’

Is she correct? Circle Yes or No. Explain how you know.

KS2 2001 Paper B level 5

• Explain reasoning and conclusions, using words, symbols or diagrams as appropriate

Nadia is working with whole numbers. She says, 'If

you add a two-digit number to a two-digit number

The spinner is divided into nine equal sections.

1

you cannot get a four-digit number.’ 4 2

Is she correct? Circle Yes or No. 2 3

Explain why. 1 2

KS2 2000 Paper B level 4 2 2

Mr Singh buys paving slabs to go around his pond.

PAVING SLABS

Which two different numbers on the spinner are equally likely to come up?

Meera says, ‘2 has a greater than even chance of coming up’. Explain why she is correct.

£1.95 each

£3.50 each

Square slabs

50cm by 50cm

Rectangular slabs

100cm by 50cm

50cm

100cm

KS2 2000 Paper A level 4

The diagram shows a square.

He buys 4 rectangular slabs and 4 square slabs.

What is the total cost of the slabs he buys?

'It would cost more to use square slabs all the way round.' Explain why he is correct.

KS2 2002 Paper A level 4

How many degrees is angle a? Explain how you know.

Y7 progress test 2005 Paper B [adapted]

Counting and understanding number

• Find the difference between a positive and a negative integer, or two negative integers, in

context

The temperature starts at four degrees and goes

down by ten degrees. What is the temperature now?

Y5 optional test 1998 Mental test level 4

The temperatures were:

|inside |outside |

|–1°C |–8°C |

What is the difference between these two temperatures?

KS2 2002 Paper B level 4

The temperature inside an aeroplane is 20 °C. The temperature outside the aeroplane is –30 °C. What is the difference between these temperatures?

KS2 2003 Paper B level 4

The temperature in York is 4°C. Rome is 7 degrees colder than York. What is the temperature in Rome?

KS2 2000 Paper A level 4

What temperature is twenty degrees lower than six

degrees Celsius?

KS2 2004 Mental test level 5

Megan makes a sequence of numbers starting with

100. She subtracts 45 each time.

Write the next two numbers in the sequence.

100 55 10 χ χ

KS2 1999 Paper A level 5

A sequence starts at 500 and 80 is subtracted each time.

500 420 340 ...

The sequence continues in the same way. Write the first two numbers in the sequence which are less

than zero.

KS2 2002 Paper A level 5

Circle two numbers which have a difference of 2.

–1 –0.5 0 0.5 1 1.5

KS2 2001 Paper B level 4

• Use decimal notation for tenths, hundredths and thousandths, partition, round and order

decimals with up to three places, and position them on the number line

Write a number in the box to make this correct.

0.627 = 0.6 + 0.02 + χ

In the number 5.375, what does the digit 7

represent?

A 7

1000

B 7

100

C 7

10

D 7

What number is exactly halfway between one point one and one point two?

KS2 2005 Mental test level 4

Write the number that is exactly halfway between

Write these numbers in order.

One has been done for you.

[pic]

Y5 optional test 2003 Paper A level 5

Put a ring around the smallest number.

0.27 0.207 0.027 2.07 2.7

KS2 2001 Mental test level 4

Here are three supermarket bills.

eight point six and eight point seven.

9999

qqff eggggg 1 87

9999

qffeeggggggg 11 87

99

qffeegggggg 1 87

efffewfffwee

5544

efffeewfffwee

554

efffeewfffwee

554

weefffdf 1995

weefffdf 1995

weefffddff

1995

eefffeddgggg

1100 00

efffedggg

11000

efffedggg

11000

Y5 optional test 1998 Mental test level 4

sshagggg

000

shhaagggg 000

shhaaggg

0000

eewfffew

5555

ewfffeew

555

eewfffeew

555

fffmkdf 1887

ssdd 1 98

fffmkkkddff

sdd

11887

1198

fffmkkddfff

sdd

1887

1198

eurrooee

665

eeuurrooee 65

eeuurrooee 65

Write a number that is bigger than nought point

pooohw 1 99

ppoooohhw

11999

ppoooohhw

119999

three but smaller than nought point four.

KS3 2003 Mental test level 4

Write each of these numbers to the nearest whole number.

13.7 is nearest to ...............

8 3⁄8 is nearest to ...............

3.38 is nearest to ...............

Y5 Optional test Paper B level 3

Round each decimal to the nearest whole number.

6.01 → χ

9.51 → χ

7.75 → χ

Y5 optional test 2003 Paper B level 4 [adapted]

Total £74.68 Total £65.90 Total £59.05

Tom rounds each bill to the nearest £10 and adds them up. What is the total amount that Tom gets?

Mary adds up the three bills exactly. What is the total difference between her total and Tom’s total?

KS2 2004 Paper B level 4

Circle the number closest in value to 0.1.

0.01 0.05 0.11 0.2 0.9

KS2 2002 Paper B level 5

Round two point six nine four to one decimal place.

KS3 2005 Mental test level 6

• Express a larger whole number as a fraction of a smaller one e.g. recognise that 8 slices of a

5-slice pizza represents 8⁄

or 1 3⁄

pizzas; simplify fractions by cancelling common factors;

order a set of fractions by converting them to fractions with a common denominator

Draw one line to join two fractions which have the

same value.

4

Look at these fractions.

1 1 5

2 3 6

7

1 2

2 8

Mark each fraction on the number line. The first one is done for you.

2 1

5 3

1

4

KS2 1998 Paper A level 4

Karen makes a fraction using two number cards.

0 1

1

2

KS3 2001 level 4

Write a fraction that is larger than 4⁄5. Write a fraction that is smaller than 1⁄5.

Write a fraction that lies between 1⁄4 and 3⁄8.

She says, 1 2

‘My fraction is equivalent to 1⁄2. One of the number cards is 6’

What could Karen’s fraction be? Give both possible answers.

Which is larger, or ?

3 5

Explain how you know.

KS2 2002 Paper A level 5

Here are some number cards.

or

KS2 2003 Paper B level 4

9

Use two of the cards to make a fraction which is

less than 1⁄2.

Complete these fractions to make each equivalent to 3 .

5

10 15

12

KS2 2001 Paper A level 5

How much less than 1 is your fraction?

KS2 1996 Paper B level 5

• Express one quantity as a percentage of another, e.g. express £400 as a percentage of

£1000; find equivalent percentages, decimals and fractions

Write these decimals as percentages.

0.25 → …%

0.6 → …%

Put a ring around the fraction which is equivalent to

forty per cent.

Write these percentages as decimals.

42% → …

5% → …

What is seven-tenths as a percentage?

KS2 2005 Mental test level 4

Write 80% as a fraction in its simplest form.

KS2 1999 Mental test level 4

Circle the two fractions that are equivalent to 0.6.

6 1 60 1

10 60 100 6

Y5 optional test 2003 Paper B level 4

Put a ring around the decimal which is equal to one-

fifth.

What is twenty out of forty as a percentage?

0.1 0.2 0.3 0.4 0.5

KS2 2004 Mental test level 4

KS2 2003 Mental test level 5

A class is collecting money for charity. They want a

total of £1000. By the end of April, they have collected £400.

What percentage of their total have they collected by the end of April?

Y7 progress test Paper A level 4

Some of the statements below are correct.

Tick (⎫) the correct ones.

Tick ( ) if correct

1 = 0.5

9 3

30 10

0.75 = 3

1

2 is equivalent to 10%

1

5 is equivalent to 5%

Y7 optional test Paper A level 4

• Solve simple problems involving direct proportion by scaling quantities up or down

On a school trip each teacher can take no more

than 20 pupils. Three teachers go on a school trip. What is the greatest number of pupils they can take with them?

Complete the table to show the least number of teachers that must go with each school trip.

Two letters have a total weight of 120 grams

[pic]

One letter weighs twice as much as the other. Write the weight of the heavier letter.

Y4 optional test 2003 Paper B level 4

KS3 2002 Paper A level 3

Jenny is going to make some cordial. The finished drink should be 1⁄3 cordial and 2⁄3 water.

Jenny puts 100 ml of cordial in a glass.

How much water should she put with it?

KS3 2004 Paper A level 4

Four biscuits cost twenty pence altogether. How much do twelve biscuits cost?

KS2 2005 Mental test level 4

Two rulers cost eighty pence. How much do three rulers cost?

KS3 2005 Mental test level 4

Six cakes cost one pound eighty. How much do ten cakes cost?

KS2 2002 Mental test level 5

Here is a recipe for pasta sauce.

[pic]

Josh makes the pasta sauce using 900g of tomatoes. What weight of onions should he use?

Y5 optional test 2003 Paper B level 5

Peanuts cost 60p for 100 grams.

What is the cost of 350 grams of peanuts?

Raisins cost 80p for 100 grams. Jack pays £2 for a bag of raisins.

How many grams of raisins does he get?

KS2 2000 Paper A level 4

Here is part of a number line. Write the two missing numbers in the boxes.

[pic]

KS2 2005 Paper A level 4

Here is part of a number line. Write the missing numbers in the boxes.

[pic]

Y5 optional test 2003 Paper A level 4

In a country dance there are 3 boys and 2 girls in every line.

[pic]

42 boys take part in the dance. How many girls take part?

KS2 1996 Paper B level 5

Knowing and using number facts

| |

|• Use knowledge of place value and multiplication facts to 10 × 10 to derive related |

|multiplication and division facts involving decimals, e.g. 0.8 × 7, 4.8 ÷ 6 |

|What is nought point four multiplied by nine? |Divide four point eight by eight. |

|KS2 2005 Mental test level 4 [adapted] |KS2 2004 Mental test level 4 [adapted] |

| | |

|What is nought point three multiplied by four? |Divide four point two by six. |

|KS2 2004 Mental test level 5 [adapted] |Y4 optional test 1998 Mental test level 4 [adapted] |

| | |

|What is four multiplied by nought point nine? |What number multiplied by eight equals four point eight? |

|KS2 2005 Mental test level 4 [adapted] |KS3 2005 Mental test level 4 [adapted] |

| | |

|Multiply seven by nought point six. |Divide four point two by seven. |

|KS2 2003 Mental test level 4 [adapted] |KS3 2004 Mental test level 4 [adapted] |

| | |

|What is nought point eight multiplied by six? | |

|Y3 optional test 2003 Mental test level 3 [adapted] | |

| | |

|Multiply nought point seven by nine. | |

|KS2 1999 Mental test level 4 [adapted] | |

| |

|• Use knowledge of multiplication facts to derive quickly squares of numbers to 12 × 12 and |

|the corresponding squares of multiples of 10 |

|What is five squared? |What is the next square number after thirty-six? |

|KS3 2001 Mental test level 4 |Y7 progress test 2005 Mental test level 4 |

| | |

|Explain why 16 is a square number. |What is the next number in the sequence of square numbers? |

|Y5 optional test 1998 Paper B level 3 |One, four, nine, sixteen ... |

| |KS3 2004 Mental test level 5 |

| | |

| |Find two square numbers that total 45 |

|Here is a sorting diagram for numbers. Write a number less than|χ + χ = 45 |

|100 in each space. |KS2 2005 Paper A level 5 |

| | |

| |What is thirty multiplied by thirty? |

| |[oral question] |

| | |

| | |

| | |

| | |

| | |

|KS2 2004 Paper A level 4 | |

| |

|• Recognise that prime numbers have only two factors and identify prime numbers less than |

|100; find the prime factors of two-digit whole numbers |

|Millie and Ryan play a number game. Is it under 20? No |Write the three prime numbers which multiply to make 231. |

|Is it under 25? Yes |χ× χ × χ = 231 |

|Is it odd? Yes |KS2 2001 Paper B level 5 |

|Is it a prime number? Yes | |

|What is the number? |The three numbers missing from these boxes are all prime |

|KS2 1999 Paper B level 3 |numbers greater than 3. Write in the missing prime numbers. |

| |χ × χ × χ = 1001 |

| |KS2 1996 Paper C level 6 |

• Use approximations, inverse operations and tests of divisibility to estimate and check results

A car park has 76 rows for parking. There are 52

car spaces in each row. Which of these is the BEST

way to estimate how many cars can park altogether?

A 100 × 50 = 5000

B 90 × 60 = 5400

C 80 × 60 = 4800

D 80 × 50 = 4000

E 70 × 60 = 4200

Julie says, ‘I added three odd numbers and my

answer was 50.’

Explain why Julie cannot be correct.

KS2 2004 Paper A level 5

This sequence of numbers goes up by 40 each time.

40 80 120 160 200 … This sequence continues.

Will the number 2140 be in the sequence?

Circle Yes or No. Explain how you know.

KS2 2000 Paper A level 5

Estimate the value of nine point two multiplied by

two point nine.

KS3 2005 Mental test level 5

Circle the best estimate of the answer to

72.34 ÷ 8.91

6 7 8 9 10 11

KS3 2002 Paper A level 5

Calculating

• Calculate mentally with integers and decimals: U.t ± U.t, TU × U, TU ÷ U, U.t × U, U.t ÷ U

What is the sum of eight point five and eight point

six?

KS2 2002 Mental test level 4

Add three point five to four point eight.

KS2 1999 Mental test level 4

Subtract one point nine from two point seven.

KS2 2003 Mental test level 4

Subtract nought point seven five from six.

KS3 2003 Mental test level 4

What number is halfway between thirty and eighty?

KS2 2004 Mental test level 4

Tick (⎫) the two numbers which have a total of 10.

[pic]

KS2 2005 Paper A level 4

Add together nought point two, nought point four

and nought point six.

KS2 2005 Mental test level 4

What is four multiplied by three point five?

KS2 2000 Mental test level 4

In a café I buy two cups of coffee and a sandwich. Altogether I pay three pounds.

The sandwich costs one pound sixty. What is the cost of one cup of coffee?

Y7 progress test 2003 Mental test level 3

A packet of crisps costs thirty-two pence.

Josh buys three packets. How much change does he get from one pound?

KS2 2005 Mental test level 4

Circle two numbers which add to make 0.12.

0.1 0.5 0.05 0.7 0.07 0.2

KS2 2000 Paper A level 4

Circle the two numbers which add up to 1.

0.1 0.65 0.99 0.45 0.35

KS2 1999 Paper A level 5

The first two numbers in this sequence are 2.1 and

2.2. The sequence then follows the rule ‘to get the next number, add the two previous numbers‘.

Write in the next two numbers in the sequence.

2.1 2.2 4.3 6.5 χ χ

KS2 2003 Paper A level 4

A magazine costs one pound forty pence.

I buy two of them and pay with a five pound note. How much change should I get?

KS3 2003 Mental test level 4

Two rulers cost eighty pence.

How much do three rulers cost?

KS3 2005 Mental test level 4

A bag of four oranges costs thirty seven pence.

How much do twelve oranges cost?

KS2 2000 Mental test level 5

• Use efficient written methods to add and subtract integers and decimals, to multiply

and divide integers and decimals by a one-digit integer, and to multiply two-digit and

three-digit integers by a two-digit integer

Calculate 2307 × 8.

KS2 2003 Paper A level 4

Calculate 15.05 – 14.84.

KS2 2002 Paper A level 5

Write in the missing digits.

4 χ 4 + 38 χ = 851

KS2 2004 Paper A level 4

Write in the missing digit.

χ 7 × 9 = 333

KS2 1996 Paper A level 4

Calculate 8.6 – 3.75.

KS2 2000 paper A level 5

In the chart any three numbers in a line, across or down, have a total of 18.45. Write the missing number.

2.46 8.61 7.38

Write in the missing digit.

5 χ × 8 = 456

11.07

1.23

KS2 1995 Paper A level 4

Write in the missing number.

χ ÷ 5 = 22

KS2 1995 Paper A level 4

4.92 3.69 9.84

KS2 1997 Paper A level 4

Calculate 31.6 × 7.

KS2 2004 Paper A level 5

Eggs are put in trays of 12.

The trays are packed in boxes. Each box contains 180 eggs.

How many trays are in each box?

KS2 1999 Paper A level 4

Calculate 123 ÷ 5.

Calculate 16.5 ÷ 3.

Calculate 27.6 ÷ 8.

Some children go camping.

It costs £2.20 for each child to camp each night.

They go for 6 nights. How much will each child have to pay for the 6 nights?

There are 70 children.

Each tent takes up to 6 children.

What is the least number of tents they will need?

KS2 1998 Paper A level 4

Shenaz buys a pack of 24 cans of cola for £6.00.

[pic]

What is the cost of each can?

KS2 1998 Paper A level 5

• Relate fractions to multiplication and division, e.g. 6 ÷ 2 = 1⁄

of 6 = 6 × 1⁄ ; express a quotient

as a fraction or decimal, e.g. 67 ÷ 5 = 13.4 or 132⁄ ; find fractions and percentages of whole-

number quantities, e.g. 5⁄

of 96, 65% of £260

One third of a number is twelve. What is the

number?

KS2 1997 Mental test level 4

What is three-quarters of two hundred?

KS2 2000 Mental test level 4

What is three-fifths of forty pounds?

KS3 2003 Mental test level 5

Calculate 60% of 765.

KS2 2000 Paper B level 4

In a sale, there is fifty per cent off all prices. A chair costs forty-five pounds in the sale. How much was it before the sale?

KS2 1999 Mental test level 4

John had £5. He gave 25% of it to charity. How

much did he give?

Joe has some pocket money. He spends three- quarters of it. He has fifty pence left. How much pocket money did he have?

Y5 optional test 2003 Mental test level 4

Y4 optional test Paper B level 4

Sophie poured some water out of a litre jug. Look how much is left in the jug. Estimate how many

millilitres of water are left.

Calculate 3⁄4 of 840.

KS2 2000 Paper A level 4

Fill in the missing numbers.

1 1

of 20 =

2 4

3 1

of 100 =

4 2

1 2

of 60 =

3 3

of …

of …

of …

Y5 optional test 2003 Paper A level 4

KS3 2003 Paper 1 level 5

• Use a calculator to solve problems involving multi-step calculations

Three pupils answered different questions. This is

what each pupil’s calculator showed:

[pic]

Asim’s question was about money. Complete the sentence:

3.5 means £3 and ……pence.

Ben’s question was about time. Complete the sentence:

3.5 means 3 hours and …… minutes.

Charlie’s question was about length. Complete the sentence:

3.5 means 3 metres and …… centimetres.

Y7 progress test Paper B level 4

Here is a picture of three people.

[pic]

Lisa’s height is half-way between Julie’s height and

Tom’s height. Calculate Lisa’s height.

KS2 1998 Paper B level 4

Emma saves £3.50 each week. How much has she

saved after 16 weeks?

Y5 optional test Paper B level 4

Sima thinks of a number.

She divides it by 12. Her answer is 26. What is the number Sima thinks of?

KS2 1998 Paper B level 5

Nicola has £50. She buys 3 flowerpots at £12.75 each and a spade at £9.65. How much money does she have left?

Seeds are £1.45 for a packet. Steffan has £10 to spend on seeds. What is the greatest number of packets he can buy?

KS2 1999 Paper B level 5

Mrs Jones prints books.

[pic]

Jon pays £4.35 for his book, including the cover. How many pages are in his book?

KS2 1996 Paper B level 5

Understanding shape

• Describe, identify and visualise parallel and perpendicular edges or faces; use these

properties to classify 2-D shapes and 3-D solids

These two shaded triangles are each inside a

regular hexagon. Under each hexagon, put a ring around the correct name of the shaded triangle.

Imagine a triangular prism.

How many faces does it have?

KS2 1999 Mental test level 4

Imagine a cube. How many vertices does it have?

KS2 2000 Mental test level 4

equilateral equilateral isosceles isosceles scalene scalene

KS2 2001 Paper B level 4

Here are six triangles. One of them is an equilateral triangle. Put a tick (⎫) in the equilateral triangle.

Here are five shapes on a square grid.

A

B

C

D

E

Write one property which makes equilateral triangles different from all other triangles.

KS2 1998 Paper A level 4

Write in the missing letters.

Shape χ has two pairs of parallel sides. Shape χ is a pentagon.

Shape χ has reflective symmetry.

KS2 1999 Paper B level 4

Here is a shape on a square grid.

These diagrams show the diagonals of three

quadrilaterals. Write the names of the quadrilaterals in the boxes.

For each sentence, put a tick (⎫) if it is true. Put a cross (⎦) if it is not true.

Angle C is an obtuse angle. Angle D is an acute angle. Line AD is parallel to line BC.

Line AB is perpendicular to line AD.

KS2 2000 Paper B level 5

KS2 2003 Paper A level 4

• Make and draw shapes with increasing accuracy and apply knowledge of their properties

Draw two straight lines from point A to divide the

shaded shape into a square and two triangles.

Here is the net of a cube with no top. The shaded

square shows the bottom of the cube. Draw an

extra square to make the net of a cube which does have a top.

KS2 2003 Paper B level 4

Here are five shapes on a square grid.

KS2 2003 Paper B level 4

A cube has shaded triangles on three of its faces.

B

A

C

E Here is the net of the cube. Draw in the two missing

D

Which two shapes fit together to make a square?

KS2 2001 Paper B level 4

Here are some shaded shapes on a grid.

KS2 2002 Paper B level 5

On the grid below, use a ruler to draw a pentagon

that has three right angles.

Which three shapes have reflective symmetry?

KS2 2000 Paper A level 4

KS2 1998 Paper B level 5

• Visualise and draw on grids of different types where a shape will be after reflection,

after translations, or after rotation through 90° or 180° about its centre or one of its

vertices

Kyle has drawn triangle ABC on this grid.

[pic]

Holly has started to draw an identical triangle DEF. What will be the coordinates of point F?

Y5 optional test 2003 Paper B level 4

Here is a shaded shape on a grid. The shape is

rotated 90° clockwise about point A. Draw the shape in its new position on the grid. You may use tracing paper.

A

KS2 2000 Paper B level 4

The rectangle is rotated 90° clockwise about point A. Draw the rectangle in its new position. You may use tracing paper.

Draw the reflection of this shape.

[pic]

Y3 optional test 2003 Paper B level 4

A

Y5 optional test 1998 Paper B level 4

This pattern is made by turning a shape clockwise through 90° each time.

Draw the two missing triangles on the last shape.

[pic]

KS2 2005 Paper B level 4

• Use coordinates in the first quadrant to draw, locate and complete shapes that meet given

properties

The diagram shows two identical squares.

Here is a graph.

y

A

(4,2)

B

(6,3)

A is the point (10,10).

What are the coordinates of B and C?

KS2 2005 Paper B level 4

0 x

The dots on the line are equally spaced. What are the coordinates of the point A?

Megan says, ‘The point B has coordinates (11,5).’

Use the graph to explain why she cannot be correct.

KS2 1997 Paper B level 4

Here is a pentagon drawn on a coordinate grid. The pentagon is symmetrical.

y

A

(4,9)

B (7,10)

C

A, B and C are three corners of a rectangle. What

are the coordinates of the fourth corner?

Y4 optional test 2003 Paper B level 4

E (2,0) (12,0) D

0 x

What are the coordinates of point C?

KS2 2003 Paper A level 5

• Estimate angles, and use a protractor to measure and draw them, on their own and in

shapes; calculate angles in a triangle or around a point

x Look at the triangle. Angle x is fifty-five degrees.

Calculate the size of angle y.

x

y

KS2 2001 Mental test level 5

Measure angle x accurately. Use a protractor (angle measurer).

KS2 2004 Paper B level 5

Two of the angles in a triangle are sixty degrees

and seventy degrees. What is the size of the third angle?

KS3 2005 Mental test level 5

Complete the drawing below to show an angle of

157°. Label the angle 157°.

KS3 2000 Paper A level 5

Look at these angles.

A pupil measured the angles in a triangle.

She said: ‘The angles are 30°, 60° and 100°.’ Could she be correct? Tick (⎫) Yes or No.

Explain your answer.

KS3 2004 Paper A level 5

What is the angle between the hands of a clock at four o ’clock?

KS2 2003 Mental test level 5

This diagram is not drawn accurately. Calculate the

size of angle m

angle P angle Q angle R angle S angle T

One of the angles measures 30°. Write its letter.

KS3 2000 Paper A level 5

Look at the angle.

Put a ring around the number which is the approximate size of the angle.

60° 90° 110° 135° 240°

KS2 2000 Mental test level 5

70º

m

KS3 2004 Paper A level 5

70º

Measuring

• Select and use standard metric units of measure and convert between units using

decimals to two places, e.g. change 2.75 litres to 2750 ml, or vice versa

How many millilitres are there in three-quarters of a

litre?

Look at the diagram. It shows how to change

metres into centimetres and millimetres.

Y4 optional test 2003 Mental test level 4

×100

×10

Change sixty millimetres to centimetres.

KS3 2001 Mental test level 4

number of metres

number of centimetres

number of millimetres

A table is two hundred centimetres long. How many metres is that?

KS3 1999 Mental test level 4

This table shows the weight of some fruits and vegetables. Complete the table.

×1000

Change 5 metres into centimetres. Change 9 centimetres into millimetres. Change 8000 millimetres into metres. Y7 progress test 2003 level 4

A bottle holds 1 litre of lemonade. Rachel fills 5 glasses with lemonade. She puts 150 millilitres in each glass.

How much lemonade is left in the bottle?

KS2 2003 Paper A level 4

Put a ring round the number which is the approximate weight of a thirty-centimetre plastic ruler.

KS2 2002 Paper A level 4 [adapted]

2 g 20 g 200 g 2 kg 20 kg

KS2 2001 Mental test level 5

• Read and interpret scales on a range of measuring instruments, recognising that the

measurement made is approximate and recording results to a required degree of accuracy;

compare readings on different scales, for example when using different instruments

The diagrams in this question are not drawn

accurately. The diagram shows Jo’s key.

[pic]

Use the scale to find the length of Jo’s key. This time you cannot see all of Jo’s key.

One end is at 2.8cm on the scale. Where is the other end on the scale?

Y7 progress test 2005 level 4

Here are a pencil sharpener, a key and a rubber.

Actual size

0 1 2 3 4 5 6 7 8 9 cm

What is the length of all three things together? Give your answer in millimetres.

What is the length of the key? Give your answer in millimetres.

KS2 2002 Paper A level 4

This scale shows the weight of Fred’s cat.

All the water in these two containers is to be poured

into the empty container below.

4kg 5kg

500 ml

400 ml

300 ml

200 ml

100 ml

500 ml

400 ml

300 ml

200 ml

100 ml

What is the weight of Fred’s cat?

This scale shows the weight of Fred’s dog.

5kg 6kg

Draw where the water level will be in the container.

1 litre

1/2 litre

Y4 optional test Paper B level 4

How much more does Fred’s dog weigh than his cat?

KS2 2004 Paper B level 4

On this scale, the arrow (↑) shows the weight of a pineapple.

0 1 2

kg

The diagram shows the volume of water in two

measuring jugs.

Here is a different scale.

500

400

Mark with an arrow (↑) the weight of the same pineapple.

1000

500

0

300

200

100

ml ml

0

0 1 2 3 4

kg

KS2 2001 Paper B level 4

Jug A Jug B

Which jug contains more water? Tick (⎫) A or B. How much more does it contain?

2003 Y7 progress test Paper B level 4

• Calculate the perimeter and area of rectilinear shapes; estimate the area of an irregular

shape by counting squares

Calculate the perimeter of a rectangle which is

eleven metres long and four metres wide.

KS2 2003 Mental test level4

Millie has some star-shaped tiles. Each edge of a

tile is 5 centimetres long.

5 cm

The area of a rectangle is 16 cm2. One of the sides is 2 cm long.

What is the perimeter of the rectangle?

Y4 optional test 1999 Paper B level 4

Not actual size

She puts two tiles together to make this shape.

Here are some shapes drawn on a grid.

[pic]

Write the letters of the two shapes that are equal in area.

Y4 optional test 2003 Paper B level 4

Here is a 1cm square grid. Some of the grid is shaded.

Work out the perimeter of Millie’s shape.

KS2 2004 Paper A level 4

Lauren has three small equilateral triangles and one large equilateral triangle. The small triangles have sides of 7 centimetres. Lauren makes this shape.

7 cm

Not actual size

Calculate the perimeter of the shape.

KS2 2001 Paper B level 4

Liam has two rectangular tiles like this.

11cm

What is the area that is shaded?

KS2 2005 Paper B level 4

He makes this L shape.

5cm

Here is a map of an island.

Cave

Wood

Church

Lighthouse

What is the perimeter of Liam’s L shape?

KS2 2000 Paper A level 5

What is the area of this shape?

4cm

Not to scale

Estimate the area of the Wood.

KS2 1995 Paper B level 4

10cm

7cm

10cm

KS2 2002 Paper B level 5

Handling data

• Describe and predict outcomes from data using the language of chance or likelihood

Shade this spinner so that there is a 50% chance

that the arrow will land on shaded.

Here are two spinners, A and B. Each one is a

regular hexagon.

1 2

3 2

1

1 1

3

2

Y7 progress test Paper A level 4

Here is a spinner which is a regular octagon. Write

1, 2 or 3 in each section of the spinner so that 1 and

2 are equally likely to come up and 3 is the least likely to come up.

[pic]

KS2 2005 Paper B level 4

A B

For each statement, put a tick (⎫) if it is true. Put a cross (⎦) if it is not true.

Scoring ‘1’ is more likely on A than on B. Scoring ‘2’ is more likely on A than on B. Scoring ‘3’ is as equally likely on A as on B.

Zara spins both spinners. The score on A is added to the score on B. She says, ’The sum of the scores

on both spinners is certain to be less than 7’ .

Is she correct? Circle Yes or No. Explain how you know.

KS2 2001 Paper A level 4

• Solve problems by collecting, selecting, processing, presenting and interpreting data,

using ICT where appropriate; draw conclusions and identify further questions to ask

Table and pie chart of favourite boy bands

[pic]

esources/mathematics/nns_itps/data_handling/

Table, dual bar chart and stacked bar chart showing favourite colours of two Year 6 classes, produced in MicrosoftExcel

Table and pie chart of favourite sport of Year 6 girls,

produced in Microsoft Excel

[pic]

Table and conversion graph for euros to pounds, produced in Microsoft Excel

[pic]

[pic]

| |

|• Construct and interpret frequency tables, bar charts with grouped discrete data, and line |

|graphs; interpret pie charts |

|A school has a quiz each year. There are two teams. Here are |The pie chart shows information about children who go to a |

|their results. |nursery school. |

| | |

| | |

|North South | |

|300 |two |

| |four years old |

|250 |years old |

| | |

|200 |three |

|Points |years old |

| | |

|150 | |

| | |

|100 |Altogether, 80 children go to the nursery school. How many of |

| |the 80 children are two years old? |

|50 |How many of the 80 children are four years old? |

| |Y7 progress test Paper A level 4 |

|0 | |

|1999 2000 2001 2002 2003 | |

|Year | |

|In which year did North beat South by 100 points? In which year|This graph shows the cost of phone calls in the daytime and in |

|did South beat North by the greatest |the evening. |

|amount? | |

|KS2 2004 Paper B level 4 |60p |

| | |

|Some children do a sponsored walk. The graph shows their |50p |

|results. | |

|[pic] |40p |

|How many children walked 21 laps or more? |Cost 30p |

|Y5 optional test 2003 Paper A level 4 |of call |

| | |

| |20p |

| | |

| |10p |

| | |

| |0p |

| |0 2 4 6 8 10 12 |

| |Length of call in minutes |

| | |

| |How much does it cost to make a 9 minute call in the daytime? |

| |How much more does it cost to make a 6 minute call in the |

| |daytime than in the evening? |

| |KS2 2002 Paper A level 4 |

| |

|• Describe and interpret results and solutions to problems using the mode, range, median and |

|mean |

|These are the marks from a spelling test. |Rob runs 100 metres ten times. These are his times in seconds. |

| | |

|Jay 16 |13.4 13.0 13.9 13.7 13.3 |

|Karen 13 |13.5 14.0 14.4 13.8 14.0 |

|Dominic 18 | |

|Tariq 13 |What is his mean (average) time? |

|Lara 12 |KS2 1995 level 5 |

|Oliver 14 | |

|Gemma 19 |Write a different number in each of these boxes so that the |

|What is the median number of marks? |mean of the three numbers is 9. |

|Y5 optional test Paper B level 4 | |

| | |

| | |

| |Write a number in each of these boxes so that the mode of the |

| |five numbers is 11. |

| | |

| | |

| | |

| |KS2 1997 Paper A level 5 |

© Qualifications and Curriculum Authority. Used with kind permission.

If you wish to find your own QCA test questions and mark schemes linked to the PNS please go to testbase.co.uk.

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5

|1 |40 |4 |1 |1 |

|40 |60 |10 |4 |400 |

2

=

4

| | |

|Number of pupils |Number |

| |of teachers |

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|100 | |

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|104 | |

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|199 | |

| |even |not even |

|a square | | |

|number | | |

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|number | | |

2

2

5

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| |3500 |3.5 |

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|apples | |1.2 |

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|grapes |250 | |

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|ginger | |0.03 |

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Helping children to achieve age-related expectations: 27 00028-2007CDO-EN

securing Level 4 by the end of Key Stage 2 © Crown copyright 2007

Primary National Strategy

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