Oranges L4

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In this unit we focus on selecting appropriate units for measurement in practical situations. Students are required to justify the instrument they have used in relation to the degree of accuracy required in their measurements.

Achievement Objectives
GM4-1: Use appropriate scales, devices, and metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time.
Specific Learning Outcomes
  • Recognise that objects have many measurable attributes.
  • Identify and accurately measure attributes of common objects.
  • Make decisions based on measurements.
Description of Mathematics

Measuring is about quantifying a feature, or attribute, of an object. Examples of these attributes include length, mass, and temperature. Measurement involves making a comparison between the size of the attribute being measured and a suitable measurement unit. For example, if the peel of an orange is measured for length, a measure of 34cm means that 34 units of 1 centimetre fit into the orange peel with no gaps or overlaps.

Central to the development of students’ measurement skills and processes is ample 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. For example, the length of the orange peel might be measured as 34cm or 338mm, depending on the precision needed for the measurement purpose. This unit gives students the opportunity to carry out practical measuring tasks and emphasises the fact that there are many attributes of objects that can be measured.

Opportunities for Adaptation and Differentiation

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:

  • making measurement tools available for practical use
  • directly modeling the correct usage measurement tools, including scales and rulers
  • providing students with opportunities to copy, demonstrate, and identify the correct use of measurement tools
  • clarifying the language of measurement units, such as “metre square” as an area that is 1m x 1m
  • clarifying the meaning of symbols, e.g. 45cm as 45 centimetres, and 45m2 as 45 square metres; 45g as 45 grams, and 45mL as 45 millilitres
  • modelling ways to collect, and organise, measurement data, such as tables
  • creating a poster or presentation, that highlights the key learning around the correct use of measurement tools, which students can refer to throughout whilst measuring different attributes
  • easing the calculation demands by providing calculators where appropriate.

Task can be varied in many ways including:

  • reducing the complexity of the numbers involved, e.g., whole number versus fraction dimensions. The choice of measurement units influences the difficulty of calculation as well as the level of precision
  • allowing physical solutions with manipulatives before requiring abstract (in the head) anticipation of measures
  • creating or using models of standard units, e.g. 1 litre of water for the mass of 1 kilogram, the width of a nail on an index finger for 1cm, so students get ‘a feel’ for the size of units
  • providing tables for students to use when recording measurement data
  • reducing the demands for a product, e.g. less calculations and words, and more diagrams and models.

The context for this unit can be adapted to suit the interests and cultural backgrounds of your students. If use of fruit, or any food, is a cultural issue for your students, then choose an item that is more appropriate. Note that in this unity no food is wasted. You might integrate the investigation of The Orange with a unit on healthy eating or food production. Students may be curious about the amount of vitamin C in an orange (about 70mg). Students might explore the concept of a milligram, in connection with their learning around a millimetre.

Students might explore fruits and vegetables in relation to diet. How many of each fruit or vegetable do they eat in one year?

The same types of activities used with an orange might be adapted for another consumable product, such as a tube of toothpaste or a roll of paper towels. Consider how this learning could reflect the cultural diversity of your students. For example, could you compare food items from different countries?

Te reo Māori vocabulary terms such as mehua (measure), karamumano (milligram), karamu (gram), mitarau (centimetre), mitamano (millimetre), rūri (ruler), āwhata (scale of a measuring instrument) and ine-taumaha (scale for measuring weight) could be introduced in this unit and used throughout other mathematical learning.

Required Resource Materials
  • Oranges
  • Measuring equipment including; rulers, scales, measuring jugs, and any others you think might be useful

Session 1

In this session we discuss the attributes of an orange that could be measured.

  1. Present the class with an orange.
  2. Ask: How can you measure an orange?
  3. Focus the discussion on the attributes of an orange that could be measured.  List the possibilities on the board. For example:
    • Amount of juice
    • Length or area of the skin of the orange
    • Circumference or diameter of the orange
    • Mass of whole orange, skin, and flesh
    • Number of pips or segments
    • Angles of segments
    • Volume
    • Time it takes to peel or eat
    • Temperature of an orange (Peel, flesh, centre)
    • Rolling distance - time to stop
    • Acidity and sweetness of the juice (might be measured on a scale or using tools like litmus paper)
    • Fraction of the orange that is water
    • Density of an orange (Does it float?)
    • Colour of an orange (Look up spectrophotometer)

You might go online to look up “fascinating facts about oranges” that might yield interesting attributes to measure.

  1. Invite the students to select one of the attributes to measure in small groups.  Try to ensure that a variety of attributes are being investigated.  More than one group could measure each attribute. Consider the knowledge make-up of these groups. Is there a mix of more mathematically-confident students and less mathematically-confident students?
  2. Send the groups away to discuss how they are going to measure their selected attribute.  If multiple groups are measuring the same attribute encourage them to devise different approaches.  Instruct them to write up a proposal for their investigation, including details on:
    • attribute being measured
    • equipment required
    • method (step by step)
    • recording and presenting their results
  3. Discuss the idea of precision.
    How can we make our measurement as precise as possible?
    Students might mention that oranges vary a bit so multiple oranges might be needed. An average might be used.
    How can we make sure we are consistent in the way we measure?

Session 2

In small groups we attempt to measure one of the attributes of an orange identified in Session 1.  Our measurements will be compiled into a class report on The Orange.

  1. Share the groups' proposals with the class.
  2. Discuss whether proposals are reasonable to carry out, or what improvements need to be made. You might put teams together to peer review proposals, and encourage tuakana-teina.
  3. Emphasise the importance of accuracy.
    What units will you use? (cubic centimetres (cm3) or millilitres (mL) for volume, centimetres or millimetres for length, grams for mass)
    How will you ensure that your measurements are accurate?  (repeat where possible, double check when reading scales, read the scale correctly, take three different measurements then average, etc.)
  4. Once proposals have been checked by the teacher, students have the rest of the session to carry out their measurements and begin writing them up. Distinguish the measurements that damage the orange from those that do not. Discuss why measurements that do not damage the orange would be preferable. For example, measuring the circumference and diameter does not damage the orange, but measuring the skin does (unless students look up and use the rule for surface area of a sphere). Limit damaging measures but encourage groups that are not damaging the orange to measure many different oranges. Volume can be found by formula or by immersing the orange in water to see the volume it displaces. Comparing the accuracy of volumes from formula and measurement is interesting (opens up the idea of measurement error).

Session 3

In this session students complete the write up of their Orange investigations, that are then compiled into a class report on The Orange.  Students then select a different attribute which they will investigate as a group over the next two sessions.

  1. Students are given time to complete their group reports on their orange or oranges as required.
  2. When students measure many oranges, they sort the data and display that data in a suitable way, e.g. stem and leaf graph for masses, volumes, areas, and lengths.
  3. Bring all groups together and discuss findings.
    What are each group’s results?
    What could each group have done differently?
    How accurate are each group’s results?
    How could they have been more accurate?
    What attributes were easiest/hardest to measure?
    What were successful/unsuccessful approaches to measuring each attribute?
    Why were the approaches successful or unsuccessful?
  4. Compile the class results into a report on The Orange.
  5. Explain that students will have the next two days in small groups to investigate a different attribute.

Session 4

This session is given to students to work in their groups measuring their oranges.

  1. Circulate and provide assistance to students, where required, and ensure that students are using good measurement techniques. Can your students?

    • Read the scales on measurement tools to the nearest unit
    • Round appropriately where needed
    • Record the measurement with correct numbers and units

    Where necessary provide mini-tutorials for groups of students about using measurement tools.

  2. Emphasise accuracy:
    What can you do to get your results to be at a sensible level of accuracy?
  3. Tell groups that they should have finished most of their measurements by the end of the session.  There will be some time next session to finish off, but they will need to leave time for writing up their results.
  4. Teams of students might compare their results to those of other teams.

    Why might results be different? (Different oranges, different choice of tools and units, measurement error, etc.

Session 5

In this session students complete their measurements of their oranges, and write up their results to share with the class.

  1. Allow time as required for students to complete their investigations and write up results.
  2. Bring groups together to share results.
  3. Class discussion – What have you learned?
    What have you learned about your orange?
    Were any of the results surprising?
    What have you learned about measurement?
    Were there attributes that you measured that you didn’t previously know how to?
    What was the most interesting thing that anyone in the class measured? What made it interesting?
    Who might be interested in our results? Why would they be interested? (e.g., Marmalade makers might be interested in mass of oranges)
    What other objects could we measure?
  4. Ask for suggestions on what other objects around the classroom, or school, that could be measured. Try to create a list of objects which could be measured in a variety of ways.  Consider how these objects could reflect the cultural diversity, and/or current learning interests of your students (e.g. culturally significant items of clothing, culturally significant buildings, native plants). This learning could be linked to the idea of ko wai au? (Who am I?) and be used to develop connections between students. It could also be used as a context to look at how different items have changed over time. Some examples include:
    • Pieces of clothing, such as hats, shoes, jerseys
    • A school feature such as pool, shed or hall
    • A plant, tree, flower, or other living object
    • A piece of furniture, or another inanimate object
    • Cars in the carpark or street
    • Small objects such as raisins, seeds, or acorns.
  5. Allow groups some time to choose an object which they want to investigate.
  6. Instruct groups to write up a proposal of all the attributes they intend to measure and how they will measure them.  Encourage groups to find at least three distinct attributes to measure.  If they cannot, suggest that maybe they should choose a different object.
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Level Four