 # Solving Number Problems: Odd Numbers and Doubling

In this worksheet, students express an odd number as 2n+1 and then asking whether n is odd or even. Key stage:  KS 2

Curriculum topic:   Algebra

Curriculum subtopic:   Express Problems Algebraically

Difficulty level:   ### QUESTION 1 of 10

In this worksheet, we will learn how to express an odd number as "double a number plus one" and then identify whether the result is an odd or even number.

For Example:

Question:
Write this odd number as "double a number plus one". Then say whether the answer is odd or even.

209   =   2  x    ______   +  1

If we take one away from 209, we get 208. Then halve this number and get 104.

209   =   2  x  104  +  1, which is the same as "double 104 plus one".

The number 104 is an even number, since it is divisible by 2.

Write this odd number as double a number plus one.  Then say whether the answer is odd or even.

207   =   2  x    ______   +  1

103 (Odd)

103 (Even)

206 (Odd)

206 (Even)

Write this odd number as double a number plus one.  Then say whether the answer is odd or even.

401   =   2  x    ______   +  1

200 (Odd)

200 (Even)

100 (Odd)

100 (Even)

Write this odd number as double a number plus one.  Then say whether the answer is odd or even.

685   =   2  x    ______   +  1

342 (Even)

342 (Odd)

321 (Odd)

321 (Even)

Write this odd number as double a number plus one.  Then say whether the answer is odd or even.

161   =   2  x    ______   +  1

90 (Even)

90 (Odd)

80 (Even)

80 (Odd)

Write this odd number as double a number plus one.  Then say whether the answer is odd or even.

15   =   2  x    ______   +  1

4 (Odd)

4 (Even)

7 (Odd)

7 (Even)

Write this odd number as double a number plus one.  Then say whether the answer is odd or even.

345   =   2  x    ______   +  1

172 (Even)

172 (Odd)

152(Even)

152 (Odd)

Write this odd number as double a number plus one.  Then say whether the answer is odd or even.

967  =   2  x    ______   +  1

483 (Odd)

483 (Even)

485 (Odd)

485 (Even)

Write this odd number as double a number plus one.  Then say whether the answer is odd or even.

835   =   2  x    ______   +  1

419(Even)

419 (Odd)

417 (Even)

417 (Odd)

Write this odd number as double a number plus one.  Then say whether the answer is odd or even.

969   =   2  x    ______   +  1

484 (Even)

484 (Odd)

592 (Even)

592 (Odd)

Write this odd number as double a number plus one.  Then say whether the answer is odd or even.

877   =   2  x    ______   +  1

438 (Odd)

438 (Even)

219 (Odd)

219 (Even)

• Question 1

Write this odd number as double a number plus one.  Then say whether the answer is odd or even.

207   =   2  x    ______   +  1

103 (Odd)
EDDIE SAYS
207 = 2 x ______ + 1 207 - 1 = 2 x ______ 206 = 2 x 206/2 = x 103 = x This is an odd number.
• Question 2

Write this odd number as double a number plus one.  Then say whether the answer is odd or even.

401   =   2  x    ______   +  1

200 (Even)
EDDIE SAYS
401 = 2 x ______ + 1 401 - 1 = 2 x ______ 400 = 2 x 400/2 = x 200 = x This is an even number.
• Question 3

Write this odd number as double a number plus one.  Then say whether the answer is odd or even.

685   =   2  x    ______   +  1

342 (Even)
EDDIE SAYS
685 = 2 x ______ + 1 685 - 1 = 2 x ______ 684 = 2x 684/2 = x 342 = x This is an even number.
• Question 4

Write this odd number as double a number plus one.  Then say whether the answer is odd or even.

161   =   2  x    ______   +  1

80 (Even)
EDDIE SAYS
161 = 2 x ______ + 1 161 - 1 = 2 x ______ 160 = 2x 160/2 = x 80 = x This is an even number.
• Question 5

Write this odd number as double a number plus one.  Then say whether the answer is odd or even.

15   =   2  x    ______   +  1

7 (Odd)
EDDIE SAYS
15 = 2 x ______ + 1 15 - 1 = 2x ______ 14 = 2x 14/2 = x 7 = x This is an odd number.
• Question 6

Write this odd number as double a number plus one.  Then say whether the answer is odd or even.

345   =   2  x    ______   +  1

172 (Even)
EDDIE SAYS
345 = 2 x ______ + 1 345 - 1 = 2 x ______ 344 = 2x 344/2 = x 172 = x This is an even number.
• Question 7

Write this odd number as double a number plus one.  Then say whether the answer is odd or even.

967  =   2  x    ______   +  1

483 (Odd)
EDDIE SAYS
967 = 2 x ______ + 1 967 - 1 = 2 x ______ 966 = 2x 966/2 = x 483 = x This is an odd number.
• Question 8

Write this odd number as double a number plus one.  Then say whether the answer is odd or even.

835   =   2  x    ______   +  1

417 (Odd)
EDDIE SAYS
835 = 2 x ______ + 1 835 -1 = 2 x ______ 834 = 2x 834/2 = x 417 = x This is an odd number.
• Question 9

Write this odd number as double a number plus one.  Then say whether the answer is odd or even.

969   =   2  x    ______   +  1

484 (Even)
EDDIE SAYS
969 = 2 x ______ + 1 969 - 1 = 2 x ______ 968 = 2x 968/2 = x 484 = x This is an even number.
• Question 10

Write this odd number as double a number plus one.  Then say whether the answer is odd or even.

877   =   2  x    ______   +  1

438 (Even)
EDDIE SAYS
877 = 2 x ______ + 1 877 - 1 = 2 x ______ 876 = 2x 876/2 = x 438 = x This is an even number.
---- OR ----

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