Consecutive Task Task 1 Task 2 Task 3 Task 4 Task 5 Task 6 Task 7 NC Level 4 to 8+

Consecutive Task 1 Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line. (Consecutive means numbers next to each other when counting, like 3 and 4). http://nrich.maths.org/1987 Home

The ages of the youngest three add up to 42 years. Consecutive Task 2 The Seven Dwarfs were born on the same day, in seven consecutive years. The ages of the youngest three add up to 42 years. What do the ages of the oldest three add up to? http://nrich.maths.org/6770 Home

Try to prove your statements Consecutive Task 3 Many numbers can be expressed as the sum of two or more consecutive integers. For example, the number 15 can be written as the sum of consecutive integers in three different ways: 15=7+8 15=4+5+6 15=1+2+3+4+5 Look at numbers other than 15 and find out all you can about writing them as sums of consecutive whole numbers. Try to prove your statements http://nrich.maths.org/507 Home

Consecutive Task 4 The sum of 9 consecutive positive whole numbers is 2007. What is the difference between the largest and smallest of these numbers? http://nrich.maths.org/5752 Home

Start with the set of the twenty-one numbers 0 - 20. Consecutive Task 5 Start with the set of the twenty-one numbers 0 - 20. Can you arrange these numbers into seven subsets each of three numbers so that when the numbers in each are added together, they make seven consecutive numbers? For example one subset might be: {2, 7, 16} 2+7+16 = 25 and another {4, 5, 17} 4+5+17=26 25 and 26 are consecutive and so could form the start of a solution. http://nrich.maths.org/2661 Home

Choose any four consecutive even numbers. (For example: 6, 8, 10, 12). Consecutive Task 6 Choose any four consecutive even numbers. (For example: 6, 8, 10, 12). Multiply the two middle numbers together. (e.g. 8 x 10 = 80) Multiply the first and last numbers. (e.g. 6 x 12 = 72) Now subtract your second answer from the first. (e.g. 80 - 72 = 8) Try it with your own numbers. Why is the answer always 8? http://nrich.maths.org/944 Home

Choose four consecutive whole numbers, for example, 4, 5, 6 and 7. Consecutive Task 7 Choose four consecutive whole numbers, for example, 4, 5, 6 and 7. Multiply the first and last numbers together. Multiply the middle pair together. Choose different sets of four consecutive whole numbers and do the same. What do you notice? Choose five consecutive whole numbers, for example, 3, 4, 5, 6 and 7. Multiply the second and fourth numbers together. Choose different sets of five consecutive whole numbers and do the same. What do you notice now? http://nrich.maths.org/2278 Home

Consecutive Task 8 Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers? Take, for example, four consecutive negative numbers, say −7, −6, −5, −4 Place + or – signs between the numbers and work out the solutions to the various calculations. Try to find them all. e.g. −7+−6+−5+−4=−22 −7−−6+−5−−4=−2  Start with a different set of four consecutive negative numbers and take a look at both sets of solutions. Notice anything? Can you explain any similarities or predict other results? http://nrich.maths.org/5868 Home

Consecutive Task 9 The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True or false? http://nrich.maths.org/519 Home

Consecutive Task 10 2 x 3 x 4 x 5 + 1= 112 21 x 22 x 23 x 24 + 1=5052 Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square. http://nrich.maths.org/2034 Home