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
• Know the relative sizes of , , , and
• Know that converting to a smaller unit gives a larger number
• Know that converting to a larger unit gives a smaller number
• Know that
• Know that
• Know that
• Know that ruler markings show equal intervals
• Know that a ruler can begin at 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) to

b) to

c) to

Worked Example 3

Convert the following lengths.

a) to

b) to

c) to

Worked Example 4

A ribbon is 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 mark on a ruler and ends at the mark. Solve 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) to

b) to

c) to

Problem 3

Convert the following lengths.

a) to

b) to

c) to

Problem 4

A rope is 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 mark on a ruler and ends at the mark. Find its length.

Exercises

Understanding and Fluency

Exercise 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

Exercise 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

Exercise 3.

Convert the following.

a) to

b) to

c) to

Exercise 4.

Convert the following.

a) to

b) to

c) to

Exercise 5.

Convert the following.

a) to

b) to

c) to

Exercise 6.

Convert the following.

a) to

b) to

c) to

Exercise 7.

Read the indicated length on a ruler or tape measure.

a) A line ends at the mark

b) A line ends at the mark

c) A line ends at the mark

Exercise 8.

Find the length of each object from the ruler readings.

a) Starts at and ends at

b) Starts at and ends at

c) Starts at and ends at

Reasoning

Exercise 9.

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

Exercise 10.

A student says and another student says . Determine who is correct and explain why.

Exercise 11.

Explain why the length of an object measured from the mark to the mark is not .

Exercise 12.

A student converts to metres and gets . Describe the mistake.

Problem-solving

Exercise 13.

A hiking trail is long. Write this distance in metres.

Exercise 14.

A ribbon is long. How many metres is this?

Exercise 15.

A craft stick is long. Write its length in centimetres.

Exercise 16.

A builder measures a plank as . Write this in centimetres and in millimetres.

Exercise 17.

A toy car begins at the mark on a ruler and ends at the mark. What is its length?

Exercise 18.

A map shows two towns are apart. If on the map represents 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 and
• A student may confuse the facts and
• 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 mark on a ruler
• A student may write answers without appropriate units

Next: 085. Perimeter of 2D Shapes