In this unit students complete a number of practical measuring investigations, with an emphasis on accuracy of measuring and communication of their findings.

- plan a mathematical investigation in a group.
- take measurements to make calculations to complete an investigation
- interpret the accuracy of the investigation

Measuring is about making a comparison between what is being measured and a suitable measurement unit. Central to the development of measuring skills is lots of practical measuring experience. Also important is the reality that measurement is never exact. As measurement involves continuous quantities even the most careful measurements are only approximations.

An analysis of the process of measuring suggests that there are five successive stages. Students learn to measure by first becoming aware of the physical attributes of objects and therefore perceiving what is to be measured. When students have perceived a property to be measured they then compare object by matching, without the use of other tools of measurement. This comparison leads to the need for a measurement unit. Initially the unit may be chosen by the student from everyday objects. The use of informal or non-standard measuring units leads to the need for standard units for better precision and unambiguous communication.

This sequence is quite general and can apply to the measurement of any attribute. In fact, we believe that one of the broad aims of teaching about measurement is to help students develop an overall picture for coping with any measurement situation.

The investigations in this unit of work require the students to both use and apply standard metric measures. The students are also required to justify the level of accuracy appropriate for each investigation.

Long measuring tapes

#### Session 1

*Investigation 1*

The principal wants to use the mathematics classroom for an assembly for the school or the year 10 students or a house group (Choose a group of about 300 – 400 students). Investigate whether all the students and staff would fit in the room. This is a good activity to begin with as students can line up in both dimensions and count the number that would fit.

- Allow the students time to think about and plan ways to investigate the problem
- Discussion of strategies
*What measurements could you take to help complete this investigation?*

What calculations would you do to complete this investigation?

How many people fit across the room’s width?

How many people fit along the room’s length?

Could you solve the problem by calculating area or volume? - Allow students to choose a strategy to solve the problem and work in small groups or individually.
- Ask the students to write up their investigation and share their findings with other groups or with the class.
- Discuss the accuracy of their answers.
*Why are there a range of answers?*

What range of numbers would be acceptable?

Will the chosen group fit into the classroom based on the range of acceptable numbers?

#### Session 2

*Investigation 2 *

The school is installing a computer network system, and cable is to be laid for this in the mathematics classroom from the ceiling in one corner to the skirting board in the diagonally opposite corner. (Choose something appropriate for your room) The cable cannot be laid diagonally across the floor, but must be attached to the walls or ceiling. Investigate the most economical path for the cable.

- Allow the students to investigate the problem. Ensure that all students understand what is being asked of them.
- Discussion of strategies .
*What path would you choose?*

How do you know that is the shortest path?

What units are appropriate for your measurements?

What units do tradesmen use? - Allow students to carry out their strategy either individually or in small groups.
- Discuss the accuracy of their answers.
*What range of cable length would be appropriate?* - Students write up their investigation .
*Which path is the most economical for the cable?*

#### Session 3

*Investigation 3 *

Discuss with the students how many windows there are in the room. Ask them to investigate what percentage of the walls are make up of windows.

- Allow the students to investigate the problem
*What measurements do you need to take?*

Which measurements are needed for the windows?

Which measurements are needed for the walls?

What units will be most appropriate? - Students should draw diagrams of each window, wall etc showing the measurements.
- Students should show all calculations.
*What range of percentages would be acceptable?* - Students write up their investigation
- Discuss strategies for improving the accuracy of the calculations, and discuss rounding.

#### Session 4

*Investigation 4 *

Discuss with the students the size of the room. Ask them to investigate how much space each person in the class has.

- Allow the students to investigate the problem.
*What measurements do you need to take?*

What units will be the most appropriate? - Students should draw a diagram of the room, showing the measurements.
- Students should show all calculations.
*What range of answers would be acceptable?* - Students should write up their investigation.
- Discuss strategies for improving the accuracy of the calculations, and discuss rounding.

#### Session 5

*Investigation 5 *

The school is to begin some landscaping on a piece of ground outside the mathematics classroom. The area needs to be dug out to a depth of 16cm, then covered with a layer of fine gravel 3cm deep for drainage, a 5cm layer of sand and then a 10cm layer of wood chips. The school trailer will be used to shift the soil to another part of the school grounds, and to bring in the gravel, sand and woodchips. How many trailer loads of soil need to be removed, and how many trailer loads of gravel, sand and woodchips will be required? (Choose and area that would require at least 4 trailer loads of soil to be removed. Depending on the ability of the students either a simple shape or a complex shape could be chosen. You may like to send the students to the local landscape supplies to check out quantities and prices, and add a costing element to the investigation.)* *

- Allow the students to plan the investigation.
*What measurements will you need to take?*

What units will be the most appropriate? - Students should draw a diagram of the area, showing the measurements.
- Students should show all calculations.
*What range of answers would be acceptable?* - Students should write up their investigation.
- Discuss strategies for improving the accuracy of the calculations, and discuss rounding.