The Lumenary · K–2

Measuring length and time

Name: ______________________

Date: ______________________

You will learn to

Compare and order objects by length, side by side and by using a third object such as a string
Measure a length by laying copies of a unit end to end, with no gaps and no overlaps
Explain why a smaller unit gives a bigger number
Measure with a ruler, starting from 0, and explain what to do when an object does not start at 0
Tell and write the time to the hour and half hour on analogue and digital clocks

1.
Wei and Lucía want to know whose pencil is longer. What is the fair way to compare them?
- A.Put them side by side, with their ends lined up at the same starting line
- B.Put them side by side anywhere and see which end is further to the right
- C.The brighter pencil is longer
2.
A leaf lies along a ruler. Its stem is at 0 and its tip is at 7. How many centimetres long is the leaf?
3.
A crayon does not start at 0. One end is at 3 and the other end is at 12. How many centimetres long is the crayon?
4.
Amara measures the same table twice: once with paper clips and once with her hand spans. Which measurement gives the bigger number?
- A.Paper clips
- B.Hand spans
- C.Both give the same number
5.
A pencil is really 5 paper clips long. Jomo lays clips along it, but leaves gaps between them. What happens to his count?
- A.He counts too few clips
- B.He counts too many clips
- C.He still gets exactly 5
6.
Gideon's game: is this statement true or false? "When I bend a string into a wiggly shape, it becomes shorter."
- A.True
- B.False
7.
The rope is longer than the stick. The stick is longer than the pencil. Which statement must be true?
- A.The rope is longer than the pencil
- B.The pencil is longer than the rope
- C.We can't tell until we put the rope next to the pencil
8.
On a clock, the long hand points to 6, and the short hand is halfway between 9 and 10. What time is it?
- A.Half past 9 (9:30)
- B.Half past 10 (10:30)
- C.9 o'clock (9:00)
- D.Half past 6 (6:30)
9.
It is 2 o'clock. Counting on in half hours like Margaret (2:30, 3:00, …), how many half hours is it until 4 o'clock?

Answer key — Measuring length and time

1.
Put the pencils side by side with their ends lined up at the same starting line. Then the one that sticks out further at the other end is the longer one. If they don't start together, the comparison can trick you.
2.
The leaf starts at 0, so the number at its tip is its length: 7 centimetres. (There are 8 marks from 0 to 7, but only 7 spaces, and the spaces are the centimetres.)
3.
The number 12 counts 12 centimetres from 0. The first 3 of them, from 0 to 3, are not under the crayon. So the crayon is $12 - 3 = 9$ centimetres long. You can also count on from 3: 4, 5, 6, …, 12 is 9 steps.
4.
Paper clips. A paper clip is much smaller than a hand span, so many more clips than hand spans fit along the table. The smaller the unit, the bigger the number. (In the lesson: 24 clips but only 6 hand spans.)
5.
The gaps cover part of the pencil but are not counted, so the clips reach the end too soon. Jomo counts too few clips — maybe only 4. Overlapping clips do the opposite and give too many.
6.
False. Bending changes where the ends of the string are, but not how long the string is. Straighten it and it reaches exactly as far as before. In the Lean file this is the theorem bend_keeps_length.
7.
In order from longest to shortest: rope, stick, pencil. So the rope is longer than the pencil. This rule — if A is longer than B and B is longer than C, then A is longer than C — always works.
8.
The long hand pointing to 6 means it has gone halfway round: half past. The short hand has passed 9 and is halfway to 10. So it is half past 9, written 9:30.
9.
Counting on: 2:00 → 2:30 → 3:00 → 3:30 → 4:00. That is 4 jumps of half an hour. It makes sense: 2 hours, and 2 half hours in each hour, gives 4 half hours.