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Level Three > Geometry and Measurement

# How far is a km?

Keywords:
Purpose:

In this unit we explore the size of a kilometre and the time it takes to cover this distance.

Achievement Objectives:

Achievement Objective: GM3-1: Use linear scales and whole numbers of metric units for length, area, volume and capacity, weight (mass), angle, temperature, and time.
AO elaboration and other teaching resources

Specific Learning Outcomes:
• develop a concept of a km
• measure a distance of 1km and the time taken to cover it
Description of mathematics:

Knowing, understanding and having some ‘feel’ for the basic units of measurement are important skills. Similarly, knowing how to measure these units is important too. This unit concentrates on establishing knowledge of the kilometre.

As a by-product of this unit students will use maps and charts. In the process they will be practicing some of the skills from the Geometry strand. These can be found in the Position section of the Geometry web site. In particular, it might be worthwhile teaching the unit Location, Location, Level 3, before this one.

Many calculations throughout the school and university curricula require computations that involve units. These problems relate to length, area, time and so on. A knowledge of units, the relation between units, and how units are combined to produce other units are fundamental to practical problems.

Students' measurement experiences must enable them to:

1. develop an understanding of the size of the standard unit
2. estimate and measure using the unit

This unit seeks to do this for the kilometre.

Required Resource Materials:
car
pedometer (optional)
trundle wheels or metres
simple map of community
Activity:

#### Getting Started

1. Begin by questioning the students to establish the need for a unit larger than a metre:
How far do you think it would be from the school gate to the dairy?
How could we measure?
2. Discuss the impracticality of using a metre rule and the large number of units that would be required and introduce the concept of a kilometre as 1000 metres.
3. Explain to the students that you want to know how far a kilometre is, so you can get an idea of how far it is to the local shops.
4. Measure out a circuit in you car from the school gates which is just over a kilometre. Make a note of a landmark at the 100m and 1 km mark.
5. Give the students a simple map with the circuit marked on it. Ask the students to mark where they think the 1 kilometre mark will be.
6. Walk with the students around the circuit. Point out where the 100m mark is. Students can make a second mark on their map if they change where they think the 1 kilometre mark is while they are walking. Make a note while walking of how long it takes the students to reach the 1 kilometre mark. This information will be used later.
7. When you return to the class ask the students to compare their estimates with other class members. Tell the students where the 1 km mark was and see who was close with their estimate.

#### Exploring

Over the next few days the students will work in pairs to develop a sense of the length of a kilometre.

1. Using their maps with the kilometre walk marked on it students can estimate whether local landmarks (shops, bus stops, church, own house) are more or less than a kilometre away from school.
2. Tell the students how long they took to walk the kilometre in the first session. Using this information students may be able to estimate how far distances they walk from home are (to school, to a friend's house, to the shops).
3. If you have access from school to a large field or a city block then you could help the students measure it using a trundle wheel or measuring it in your car. If you have pedometers the students could measure distances using these. Students could then design a 1 kilometre circuit and design a fitness activity.
4. Using the scale on a map students could work out distances in the community.
5. During the sessions reinforce the students' developing sense of the size of a kilometre by asking the following questions.
Why do we need the unit of km?
What kinds of things are measured in kms?
How can we measure 1km? What is the easiest way?
Why does it take me less time than John to walk 1km?
How many metres in a km?
How many cm in a km?

#### Sharing

1. Have the students compare distances that they walk in the community.
2. The students could try out each other's fitness circuits and time each other.
3. Brainstorm everything the students know about 1km. For example:
How many times around the field/block is 1km?
How long it takes to walk/run a km?
How long does it take a car to go 1km?
How does a car measure 1km?
How many kilometres is it between two local destinations? How long would it take us to walk there? or drive there? What is the longest trip you've gone on? What is the farthest you've biked, or walked or run?