Line them up at one end
Which is longer, a ribbon or a piece of string? You can tell without measuring either one. Lay them side by side, and push them until both start at the same line. Then look at the other end, where each one stops.
The ribbon and the string lie side by side, and both start at the same line on the left.
The one that reaches further
The ribbon keeps going after the string has stopped. It reaches further, so the ribbon is longer and the string is shorter. Both sentences say the same thing, seen from each side.
If both stopped at the same place, they would be the same length.
The ribbon reaches further than the string, so the ribbon is longer.
Why the start must line up
Slide the string along so that it starts further to the right, and its end can reach as far as the ribbon's end, or further. The string has not grown. Only its place has changed, so comparing the ends now says where the string sits, not how long it is.
That is why both must start at the same line. With the starts lined up, the end that reaches further belongs to the longer one.
the string starts 3 steps further along, so its end does too: 3 + 4 = 7 compares where the ends are, not the lengths
Line up the starts
The string starts 3 steps further along, so its end sticks out past the ribbon's even though the string is shorter. With both starts on the dashed line, the ribbon reaches 2 steps further.
How much longer
To say how much longer, mark both lengths in steps of the same size, such as blocks. The ribbon is 6 steps long and the string is 4 steps long.
The ribbon's first 4 steps sit beside the string. Count only the steps that go past the end of the string: 1, 2. The ribbon is 2 steps longer. It is not 6 steps longer, because 6 is the whole ribbon, and 4 of those steps are matched by the string.
The ribbon is 6 steps and the string is 4 steps. The last 2 steps of the ribbon go past the end of the string.
Worked example: A Ribbon and a Pencil Measured in Blocks
Question A ribbon is 6 blocks long. A pencil is 4 blocks long. (a) Which is longer, the ribbon or the pencil? (b) How many blocks longer is it?
1.Draw a row of 6 blocks for the ribbon.
The ribbon is a row of 6 blocks. 2.Draw a row of 4 blocks below for the pencil. Both rows start at the same line.
The pencil is a row of 4 blocks. Both rows start at the same line. 3.(a) The row of 6 blocks goes further than the row of 4 blocks. The ribbon is longer.
(a) The row of 6 blocks goes further than the row of 4 blocks. The ribbon is longer. 4.(b) Count the ribbon's blocks that go past the pencil: 1, 2. The ribbon is 2 blocks longer.
(b) Count the blocks that go past the pencil: 1, 2. The ribbon is 2 blocks longer.
Answer: (a) The ribbon is longer. (b) 2 blocks longer
Common mistakes
- Starting the pencil's row further along, so that both rows end at the same place. Then the two look the same length. Both rows must start at the same line.
- Saying the ribbon is 6 blocks longer. The ribbon is 6 blocks long. Only the 2 blocks that go past the pencil are extra.