# How far is a km?

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Purpose

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

Achievement Objectives
GM3-1: Use linear scales and whole numbers of metric units for length, area, volume and capacity, weight (mass), angle, temperature, and time.
Specific Learning Outcomes
• Develop an understanding of the length of one kilometre.
• Measure a distance of one kilometre and the time taken to cover it.
Description of Mathematics

The metre is the Standard International (SI) unit of length. When measuring lengths much longer or much shorter than one metre, prefixes are added to the unit to indicate multiples or fractional parts of a metre. For example, one kilometre is one thousand metres.

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.

The learning opportunities in this unit can be differentiated by providing or removing support to students, or by varying the task requirements. Ways to support students include:

• pairing students so that they can be supported at the tasks
• altering the expectations of the number, and complexity of the distances in the local area that students are asked to find.

The activities in this unit can be easily adapted to draw on the interests and experiences of your students. They can be encouraged to be imaginative in the development of their fitness circuit, and the distances estimated within the local area should focus on locations of interest to your students.

Required Resource Materials
• Trundle wheels or metres
Activity

#### Getting Started

Prior to this session, measure out a circuit within the school grounds which is just over a kilometre. This could be a certain number of laps of the school field or courts, or around the school buildings. Laps of a sports area are particularly good to use because you can measure its dimensions and then calculate the number of laps required rather than having to measure the full distance. Make a mental note of where 100m and 1 km are on the circuit.

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. Ensure that students have a good personal benchmark for one metre. For most students this is likely to be a very long stride.
5. Discuss how far they think 10 metres would be, then how far 100 metres would be.
6. Describe your preplanned circuit to the students. Ask them to say where they think the 1 kilometre mark will be. For example "I think 1 kilometre is 10 laps of the field". Write down their estimates.
7. Walk with the students around the circuit. Point out where the 100m mark is. Students can make a second estimate if they change where they think the 1 kilometre mark is while they are walking.
8. 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. Students can use the 1 kilometre circuit to find out:
• How long does it take you to walk 1 kilometre?
• How long does it take you to run 1 kilometre?
• How many steps do you take in 1 kilometre? (Students may need to work in pairs to count this. Marking a tally for each 100 steps will help with keeping track of the count.)
2. Using their experience with the 1 kilometre circuit, students can estimate whether local landmarks (the marae, shops, bus stops, church, own house) are more or less than a kilometre away from school.
3. Using Google Maps, or similar, students could work out distances in the local area (both those estimated above and others).
4. Students can work in pairs to measure their own 1 kilometre circuit within the school grounds, using a trundle wheel or by making it the same number of steps as the class circuit. The pairs can then design a fitness circuit based on their route.
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 you less time/steps 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?