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Consecutive Task
Task 1
Task 2
Task 3
Task 4
Task 5
Task 6
Task 7
Task 8
Task 9
Task 10
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).
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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?
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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
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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?
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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.
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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?
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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 first and last numbers together.
Multiply the second and fourth numbers together.
Choose different sets of five consecutive whole numbers and
do the same. What do you notice now?
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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?
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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?
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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.
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