Page 30 - 01-Yr5_Front cover-ccp.indd

32
• Consecutive numbers • • • •

~=M•l&10~ 11] Find four consecutive numbers ~=M•l&10~
PAGE 54 which total: PAGE 55
a 206 b 78
c 130 d 182.
Show all your workings-out.

[D Show thot you can make 34 numbers between • Investigate. Does this always work
1 and 40 by adding consecutive numbers. with 1hree consecutive numbers?
• Trial examples using a range
W Explain the link between the 6 numbers you cannot make. of numbers.
• Write what you find out.

@:] :. • True or false? Investigate.
• Write what you find out.
CHALLENGE
• 5, 7, 9 and 11 are four consecutive alternate numbers.
• Find five consecutive alternate numbers which total:
a 45 b 90 c 180 d 125.
• Can you think of a quick way to find the five numbers without having
to add them?

[!] ~ Challenge

Possible solution: a 50 + 51 + 52 + 53 = 206 a 5 + 7 + q + 1 1 + 1 3 = 45

1 impossible 5 + 6 = 11 10 + 11= 21 15+ 16= 31 b 18 + 1 q + 20 + 22 = 78 b 14 + 16 + 18 + 20 + 22 = qo
2 impossible 3+4+5= 12 4 + 5 + 6 + 7 = 22 32 impossible
1+2= 3 6+7= 13 11+12 = 23 16 + 17 = 33 c 31 + 32 + 33 + 34 = 130 c 32 + 34 + 36 + 38 + 40 = 180
4 impossible 2+3+4+5= 14 7 + 8 + q = 24 7 + 8 + q + l 0 = 34
d 44 + 45 + 46 + 4 7 = 182 d 21 + 23 + 25 + 27 + 2q = 1 25
2+3= 5 7 + 8 = 15 12 + 13 = 25 17 + 18 = 35
1+2+3= 6 16 impossible 5 + 6 + 7 + 8 = 26 l l + 12 + l 3 = 36
3+4= 7 8+q= 11 13 + 14 = 27 18 + lq = 37 A quick way to find the five
8 impossible 5+6+7= 18 l + 2 + 3 + 4 + 5 + 6 + 7 = 28 8 + q + l 0 + 1 l = 38 consecutive alternate
4+5= q q+JO= lq 14 + 15 = 2q lq + 20 = 3q Open: investigate whether the square numbers that will make a
l +2+3+4= 10 2 + 3 + 4 + 5 + 6 = 20 q + 10 + 11 = 30 6 + 7 + 8 + q + l 0 = 40 of the centre number of three total, is to find a fifth of the
consecutive numbers is always one total and use it as the central
greater than the product of the other number of the five
two numbers. It is always true. consecutive alternate
The numbers that can't be made start with 1 and double each time. numbers.

Open: investigate whether the sum of three consecutive numbers is
a You can make odd numbers except 1 by adding two consecutive numbers. always a multiple of three. It is always true. For any three consecutive
numbers, one is always a multiple of three and the other two always total
b Four consecutive numbers added together always make an even number.
a multiple of three.