084r. Metric Length and Reading Rulers

Learning Intentions

• choose a suitable unit for a length within the metric system
• convert between metric lengths (km, m, cm and mm)
• read a length shown on a ruler or tape measure

Pre-requisite Summary

• Know that length measures how long, tall, or far something is
• Know that the metric system uses units based on powers of $10$
• Know the relative sizes of $1\text{ km}$, $1\text{ m}$, $1\text{ cm}$, and $1\text{ mm}$
• Know that converting to a smaller unit gives a larger number
• Know that converting to a larger unit gives a smaller number
• Know that $1\text{ km}=1000\text{ m}$
• Know that $1\text{ m}=100\text{ cm}=1000\text{ mm}$
• Know that $1\text{ cm}=10\text{ mm}$
• Know that ruler markings show equal intervals
• Know that a ruler can begin at $0$ or that an object’s length can be found by subtracting two readings

Worked Examples

Worked Example 1

Choose the most suitable metric unit for each length.
a) The length of a pencil
b) The distance between two suburbs
c) The thickness of a coin

Worked Example 2

Convert the following lengths.
a) $4\text{ m}$ to $\text{cm}$
b) $250\text{ cm}$ to $\text{m}$
c) $7\text{ cm}$ to $\text{mm}$

Worked Example 3

Convert the following lengths.
a) $3.5\text{ km}$ to $\text{m}$
b) $4200\text{ m}$ to $\text{km}$
c) $165\text{ mm}$ to $\text{cm}$

Worked Example 4

A ribbon is $2.4\text{ m}$ long. Convert this length to centimetres and millimetres.

Worked Example 5

Read the length of a line shown on a ruler marked in millimetres.

Worked Example 6

An eraser starts at the $2.3\text{ cm}$ mark on a ruler and ends at the $5.8\text{ cm}$ mark. Find its length.

Problems

Problem 1

Choose the most suitable metric unit for each length.
a) The height of a classroom door
b) The distance from Brisbane to Sydney
c) The width of a fingernail

Problem 2

Convert the following lengths.
a) $6\text{ m}$ to $\text{cm}$
b) $340\text{ cm}$ to $\text{m}$
c) $9\text{ cm}$ to $\text{mm}$

Problem 3

Convert the following lengths.
a) $2.8\text{ km}$ to $\text{m}$
b) $6500\text{ m}$ to $\text{km}$
c) $124\text{ mm}$ to $\text{cm}$

Problem 4

A rope is $1.8\text{ m}$ long. Convert this length to centimetres and millimetres.

Problem 5

Read the length of a line shown on a ruler marked in millimetres.

Problem 6

A crayon starts at the $1.7\text{ cm}$ mark on a ruler and ends at the $6.2\text{ cm}$ mark. Find its length.

Exercises

Understanding and Fluency

1. Choose the most suitable unit.
   a) The length of a bus
   b) The thickness of a sheet of cardboard
   c) The distance around an athletics track

2. Choose the most suitable unit.
   a) The length of a bookmark
   b) The distance from one town to another
   c) The width of a staple

3. Convert the following.
   a) $5\text{ m}$ to $\text{cm}$
   b) $8\text{ cm}$ to $\text{mm}$
   c) $300\text{ cm}$ to $\text{m}$

4. Convert the following.
   a) $2\text{ km}$ to $\text{m}$
   b) $4500\text{ m}$ to $\text{km}$
   c) $90\text{ mm}$ to $\text{cm}$

5. Convert the following.
   a) $1.2\text{ m}$ to $\text{cm}$
   b) $0.7\text{ km}$ to $\text{m}$
   c) $135\text{ mm}$ to $\text{cm}$

6. Convert the following.
   a) $750\text{ cm}$ to $\text{m}$
   b) $63\text{ cm}$ to $\text{mm}$
   c) $4200\text{ m}$ to $\text{km}$

7. Read the indicated length on a ruler or tape measure.
   a) A line ends at the $4.6\text{ cm}$ mark
   b) A line ends at the $37\text{ mm}$ mark
   c) A line ends at the $8.2\text{ cm}$ mark

8. Find the length of each object from the ruler readings.
   a) Starts at $0\text{ cm}$ and ends at $5.4\text{ cm}$
   b) Starts at $1.2\text{ cm}$ and ends at $6.9\text{ cm}$
   c) Starts at $24\text{ mm}$ and ends at $71\text{ mm}$

Reasoning

9. Explain why centimetres are a better unit than metres for the length of a pen.

10. A student says $3.5\text{ m}=3500\text{ mm}$ and another student says $3.5\text{ m}=350\text{ mm}$. Determine who is correct and explain why.

11. Explain why the length of an object measured from the $2\text{ cm}$ mark to the $7\text{ cm}$ mark is not $7\text{ cm}$.

12. A student converts $480\text{ cm}$ to metres and gets $48000\text{ m}$. Describe the mistake.

Problem-solving

13. A hiking trail is $6.4\text{ km}$ long. Write this distance in metres.

14. A ribbon is $325\text{ cm}$ long. How many metres is this?

15. A craft stick is $112\text{ mm}$ long. Write its length in centimetres.

16. A builder measures a plank as $2.35\text{ m}$. Write this in centimetres and in millimetres.

17. A toy car begins at the $3.4\text{ cm}$ mark on a ruler and ends at the $9.1\text{ cm}$ mark. What is its length?

18. A map shows two towns are $8\text{ cm}$ apart. If $1\text{ cm}$ on the map represents $5\text{ km}$ in real life, how far apart are the towns?

Potential Misunderstandings

• A student may choose a unit that is much too large or much too small for the object being measured
• A student may confuse when to use kilometres for long distances and when to use metres for shorter everyday lengths
• A student may think converting to a smaller unit means dividing, rather than multiplying
• A student may think converting to a larger unit means multiplying, rather than dividing
• A student may confuse the facts $1\text{ m}=100\text{ cm}$ and $1\text{ cm}=100\text{ m}$
• A student may confuse the facts $1\text{ cm}=10\text{ mm}$ and $1\text{ mm}=10\text{ cm}$
• A student may misread ruler markings by counting lines instead of intervals
• A student may read the final mark of an object on a ruler without subtracting the starting mark
• A student may assume every object starts at the $0$ mark on a ruler
• A student may write answers without appropriate units

Next: 085. Perimeter of 2D Shapes