The last one-sixth space is filled by two one-twelfth pieces.
Other correct answers (each row makes exactly one whole):
Pieces of 1/6
Pieces of 1/12
Check
5
2
10/12 + 2/12 = 1
4
4
8/12 + 4/12 = 1
3
6
6/12 + 6/12 = 1
2
8
4/12 + 8/12 = 1
1
10
2/12 + 10/12 = 1
Why it happens: One 1/6 piece is the same size as two 1/12 pieces. So every time you remove a 1/6 piece you can put two 1/12 pieces in its place, and the whole is still full.
Q2.
Make a whole using 1/12, 1/4, and 1/2 pieces.
Answer
One 1/2 piece + one 1/4 piece + three 1/12 pieces = one whole.
Change every piece into twelfths first, because 12 works for 2, 4 and 12.
Another correct answer: two 1/4 pieces + one 1/4 piece + three 1/12 pieces will not do, because it has no 1/2. But 1/2 + two 1/12 + ... always check the total comes to exactly 12/12.
Q3.
Make a whole using any five pieces of the same size.
Answer
Use five 1/5 pieces.
1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 5/5 = 1 whole
If five equal pieces make one whole, each piece is one-fifth.
Why it happens: If all five pieces are the same size and they exactly fill the whole, then the whole has been cut into 5 equal parts. That is what 1/5 means. No other same-size piece will work — five 1/4 pieces would be too much (5/4) and five 1/6 pieces too little (5/6).
Q4.
Make a whole using any seven pieces.
Answer
One good answer: five 1/6 pieces and two 1/12 pieces — that is 7 pieces in all.
Seven pieces of two different sizes, filling one whole.
How to invent your own: Turn every piece into twelfths. Then just make seven numbers of twelfths add up to 12 — for example 6 + 2 + 1 + 1 + 1 + 1 = 12 gives 1/2 + 1/6 + four 1/12 pieces, which is also 7 pieces.
Q5.
Play in a group with this kit and find other interesting combinations to make a whole. Write or draw your findings.
Answer
Work in a group. One child lays pieces on the whole strip, another writes down the fractions, and the group checks that the total is exactly 1.
Sample answer — findings written by a group:
Combination we made
Number of pieces
Check in twelfths
1/2 + 1/3 + 1/6
3
6/12 + 4/12 + 2/12 = 12/12
1/2 + 1/4 + 1/4
3
6/12 + 3/12 + 3/12 = 12/12
1/3 + 1/3 + 1/6 + 1/6
4
4/12 + 4/12 + 2/12 + 2/12 = 12/12
1/4 + 1/4 + 1/4 + 1/6 + 1/12
5
3/12 + 3/12 + 3/12 + 2/12 + 1/12 = 12/12
1/2 + 1/6 + 1/6 + 1/12 + 1/12
5
6/12 + 2/12 + 2/12 + 1/12 + 1/12 = 12/12
Twelve 1/12 pieces
12
12/12
Two things our group noticed:
Every combination adds up to 12 twelfths. Twelfths work well because 2, 3, 4, 6 and 12 all divide 12.
The more pieces you use, the smaller the pieces have to be.
Try this at home: Make a whole using pieces that are all different sizes. 1/2 + 1/3 + 1/12 + 1/12 works: 6/12 + 4/12 + 1/12 + 1/12 = 12/12.