This project represents a substantive educational undertaking and will improve our understanding of the capabilities of children aged nine and 13 in mathematics and problem solving

Paul Kimmleman

The tests, which are designed to be independent of the school curriculum in any given country, will be accessible via the internet from September.

But interested parties will have to pay a registration fee, which will cover the cost of marking the tests and of giving feedback.

Sample tests, currently available on the QCA's website, include problem solving exercises such as:

Tom compares the weight of apples, bananas and pears. He finds that seven pears weigh the same as four bananas and five bananas weigh the same as six apples.

Which single piece of fruit weighs most? Which single piece of fruit weighs least?

Global research

Chief executive of the QCA, David Hargreaves, said the world class tests could be used to measure performance on a global basis.

"Consequently, they have generated great international interest and the belief that taking part in them will help to raise pupils' attainment.

"The problem solving tests have a particular appeal because there are few assessment resources available in this area in any country," he said.

The trials in Chicago will be co-ordinated by Paul Kimmleman, former president of First in the world consortium, which aims to raise standards in suburban schools so that they may be ranked first in the world.

"This project represents a substantive educational undertaking and will improve our understanding of the capabilities of children aged nine and 13 in mathematics and problem solving," he said.

Tests for nine year olds

1. After going to a small cinema, three children describe where they sat. The cinema seats are all in rows. The front row is called row A. The second row is called row B, and so on. There are the same number of seats in each row.

Amy:"I sat in the front row in seat A9. There were eight seats to the left of me."
Chris:"I sat exactly in the middle of the front row. There were seven seats between me and Amy."
Sanjay:"I sat in the back row, in seat W10."

Draw a diagram to show where Amy and Chris sat. How many seats were there in the cinema altogether? Show your working.

2. Tom compares the weight of apples, bananas and pears. He finds that seven pears weigh the same as four bananas and five bananas weigh the same as six apples.

Which single piece of fruit weighs most? Which single piece of fruit weighs least?

3. Nicola has �2 more than Mike. Mike has 50p more than Jenny. Altogether Nicola, Mike and Jenny have �6.60. How much has each person got? Show your working.

4. Write the missing + and - signs to make this correct. 10 * 20 * 30 * 40 = 0. Show your working.

Tests for 13 year olds

1. This number sequence follows the rule "double then subtract five". Write in the missing numbers. * 0.75 -3.5 -12 * . Show your working.

2. A shop has a sale of computers. There is 10% off the original price. On the last day of the sale there is a "final offer". There is 20% off the sale price.

Sheila paid �540 for the computer in the final offer. What was the original price of the computer?

3. Choose a 2-digit number. Add the digits together and subtract the total from the 2-digit number. The answer is a multiple of 9. This happens with all 2-digit numbers. Explain why.

Answers for nine year old tests

1. Diagram should show Amy in seat 9 and Chris in seat 17. The cinema has 759 seats.

2.A single banana weighs most and a single pear weighs least. Answers should show that 35 pears = 20 bananas = 24 apples.

3. Nicola �3.70, Mike �1.70 and Jenny �1.20.

4. 10 - 20 - 30 + 40 = 0.

Answers for 13 year old tests

1. 2.875 and -29

2. �750

3. Answers must show that is a 2-digit number is written as 10x+y, 10x+y-(x+y) = 9x must be a multiple of 9. E.g. "any number in the 20s gives 18, any number in the 30s gives 27" and generalise beyond this.

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