Question

Materials: string, pair of scissors
1) Prepare five (5) strings with equal lengths.
2) Cut the first string once.
(a)How many pieces are there?
Cut the second string twice. (b) How many pieces are there?
Cut the third string thrice. (c) How many pieces are there?
Cut the fourth string four times. (d) How many pieces are there?
Cut the fifth string five times. (c) How many pieces are there?
3) Based from your answers, complete the table below.
Number of cuts (x)
1
2 3 4
Number of pieces (y)
5
4) Without cutting a string 6 times, how many pieces are there?
5) Have you seen a pattern? If yes, describe the pattern and state your
conjecture. Use a formula or equation in your conjecture, where y is
the number of pieces and x is the number of cuts.
6) Using your conjecture, how many pieces of strings can be made from
(a)12 cuts? (b) 24 cuts? (c) 35 cuts? and (d) 42 cuts? Show your
solutions.​

Answer 1

a) 6

b)8

c)11

d)15

e)20

Total 20 strings

Answer 2

Sequence

Explanation:

1) An image is attached showing the strings.

2) a) On cutting 1st string once,

There are 2 pieces.

b) On cutting the 2nd string twice ,

there are 3 pieces.

c) On cutting the 3rd string thrice,

there are 4 pieces.

d) On cutting the 4th string four times,

there are 5 pieces.

e) On cutting the 5th string 5 times,

there are 6 pieces.

3) In the figure, the required table is shown.

4) Without cutting the string 6 times, there were total (for all string 1 to 5 ) 20 pieces.

5) A pattern was seen as number of pieces was one more than the number of cuts.

So, the equation that will satisfy this relationship is,

$x=y-1$

6) Using this equation following number of pieces  will be made, x is given , we need to find y

$a) 12 \ cuts\\12=y-1\\\implies13=y\\\\b) 24 \ cuts\\24=y-1\\\implies25=y\\\\c) 35 \ cuts\\35=y-1\\\implies36=y\\\\\\d) 42 \ cuts\\42=y-1\\\implies43=y$

Hence, 13 pieces, 25 pieces, 36 pieces, 43 pieces will be the required number of pieces after given number of cuts.