Comparing Length

1Summary 重點摘要

Objects have lengths. Align one end first, then compare.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Step 1: Align one endTo compare the lengths of two things, first lay them flat on the same desk with one end of each on the same starting line; this is the first step of a fair comparison. Example: after lining up the ends of two pens, the one whose tip reaches farther is the longer one. Why align? Because if one pen is placed a little forward and the other a little back, the reaching distance cannot be trusted. A common mistake is laying them slantwise or comparing without aligning the starting ends, which easily gives a wrong result.
2. Step 2: Compare by eyeAfter one end is aligned, look carefully first; often the eye can already tell which is longer. Example: the red pen reaches 2 cm farther than the blue pen, so the red pen is longer; if the two tips are almost level and the eye cannot decide, switch to measuring with a ruler. When comparing by eye, look from directly above, because from a slanted side the lengths look different from the truth. A common mistake is forcing a conclusion when the view is unclear; remember, if you cannot see clearly, measure, for numbers are reliable.
3. Step 3: Measure with a rulerWhen measuring with a ruler, line one end of the object up with the 0 mark, lay it flat against the ruler, and see which number the other end reaches. Example: if the end of a pen starts at 0 and the tip stops at 12, the pen is 12 cm long. Why must we start at 0? Because the numbers on a ruler grow step by step from 0, and a wrong starting point makes the reading different from the true length. A common mistake is lining the object up with the ruler's edge or the mark 1, which turns 12 cm into a reading of 11 cm; always check the starting point before measuring.
4. Step 4: Read the scaleOn a ruler, the space between two neighbouring numbers is one big step, and each small step is 1 cm; reading the scale means reading how many steps the object reaches from 0. Example: an eraser starts at 0 and reaches the mark 5, so it is 5 cm long. Read with your eyes right above the mark, because a slanted view shifts the number and makes it inexact. A common mistake is miscounting the steps; simply remember: once the start is at 0, the number the other end points to is the length in centimetres, and checking step by step keeps it right.
5. Step 5: Compare the numbersOnce both lengths are measured in centimetres, comparing lengths becomes comparing numbers: with the same unit, the bigger number is always the longer one. Example: a pencil is 12 cm and a ruler is 20 cm; 20 is greater than 12, so the ruler is longer, and 20 - 12 = 8 tells us it is longer by 8 cm. Before comparing, check that both lengths use the same unit, for one in centimetres and one in metres cannot be compared directly. A common mistake is adding the two numbers, but comparing lengths calls for comparing sizes or finding the difference.
6. Step 6: Tall or longFor standing people or upright things we ask which is taller; for things lying flat we ask which is longer, yet both comparisons follow the same rule. Example: a standing brother is taller than a standing sister because the top of his head reaches higher; a long rope laid on the desk beside a short rope is longer. Whether comparing height or length, align the starting points on one line first, for example both people standing on the same floor line. A common mistake is comparing two people when one stands a little forward; such a height comparison cannot be trusted.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Align one end before comparing.
• Line up 0 on the ruler with the object's end.
• 20 > 12: bigger number means longer (same unit).
• Tall for upright; long for lying down.
• Difference = longer minus shorter.