In this unit students complete a number of practical measuring investigations, with an emphasis on accuracy of measuring and communication of their findings.
Measuring is about making a comparison between what is being measured and a suitable measurement unit. Central to the development of measuring skills is engaging in 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.
The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to support students include:
Tasks can be varied in many ways including:
Although each of the sessions are presented in a successive order, you could present them as measurement 'stations' for students to explore throughout a single (or several) lesson(s). If you choose to do this, ensure that you have explained each session, and modelled the processes involved, to enable student's successful and productive participation.
The contexts presented in this unit can be adapted to suit the interests and cultural backgrounds of your students, and to make links with other curriculum areas. The investigations can be framed using story shells, such as constructing boxes to hold fudge for a fundraiser, measuring the tennis court to get fit for the cross country, or working out how many flyers will fit in a delivery bag. Students might pose their own measurement challenges that are significant to them.
Te reo Māori kupu such as ine (measure, measurement), mitarau (centimetre), mitamano (millimetre), and manomita (kilometre) could be introduced in this unit and used throughout other mathematical learning.
For each session, present the problem and have the students work in pairs or small groups to decide what strategies would be best to complete the investigation. Scaffolding questions are provided within each session. If necessary, review and model appropriate strategies. After students have decided on their strategies, give them time to investigate the problem. Roam and support students as necessary. After a suitable period of time, gather the class together and have groups of students share their ideas. You might get groups to share with other groups, before choosing one group to share with the whole class.
Consider providing a graphic organiser, such as a Think Mat, to encourage students to contribute and reflect on their ideas as a group. After groups have presented their groups, reflect and review as a class (e.g. What range of answers would be acceptable?), and confirm and discuss the accuracy of the answers presented. You might use any gaps demonstrated in knowledge as the focus of a subsequent teaching session.
Investigation 1: How many times would you have to walk around the tennis courts to cover a distance of 2 kilometres? (If a court is not available choose an appropriate area close to the mathematics classroom.)
Investigation 2: Calculate the thickness of a page in your textbook.
Investigation 3: The class set of mathematics textbooks are to be covered with plastic film. The film comes in rolls that are 600mm wide. Determine how many 10m rolls of film will need to be bought.
Investigation 4: Construct a box with a volume of 60cm3. The dimensions of the box should be whole numbers of centimetres. Calculate the surface area of the box. Which dimension would give the minimum surface area?
Investigation 5: Two vans are selling hot chips at the local A&P Show. Both vans use the same size scoop to serve a measure of chips. Mr Grease twists his paper to make a cone for his chips, and Mrs Crisp uses cylindrical containers. Why do customers think that Mr Grease is more generous?
Dear families and whānau,
Recently, we have been investigating different measurement problems. Ask your child to share some of their learning with you. Perhaps you could make up some measurement problems for each other, using measurements from around your house or local area.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/measurement-investigations-1 at 8:45pm on the 26th February 2024