Mailboxes

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Purpose

In this unit students will research, design, make, and test a cardboard letterbox, applying their knowledge and understanding of a standard measure, centimetres. They will also undertake a statistical investigation into the use of both electronic and postal mail. 

Achievement Objectives
GM2-1: Create and use appropriate units and devices to measure length, area, volume and capacity, weight (mass), turn (angle), temperature, and time.
S2-1: Conduct investigations using the statistical enquiry cycle: posing and answering questions; gathering, sorting, and displaying category and whole-number data; communicating findings based on the data.
Specific Learning Outcomes
  • Use standard measures of length to investigate the sizes of items of letter mail.
  • Use standard measures of length to design and make a letterbox.
  • Record the design process, including using appropriate symbols and abbreviations to record length measurements.
  • Pose an investigative question, plan a questionnaire, gather and sort data, display and discuss findings, and present these.
  • Explain how technology both reflects and changes society and the environment, and increases people’s capability.
Description of Mathematics

At Level 1, students learn to recognise the attribute of length, and come to understand that measurement units are countable, and can be partitioned and combined. They apply these understandings to measure length accurately with non-standard units, meaning without gaps or overlaps. 

In turn, students develop an understanding of a linear scale, recognising that it is made up of units of equal size that are known as ‘standard units’ because they are understood by everyone. Within this, students learn to align zero with the start of an item being measured, and to accurately reposition the ruler when required to measure a length longer than the ruler. Through experiences of measuring length, students become familiar with the metre and centimetre as units of measure and the abbreviations m and cm. At this stage, part measures of these units (i.e. mm - millimetres) are explored as half or ‘a little bit’.

The statistical investigation component of this unit allows students to participate in the planning and collecting of appropriate data. This is used to answer a question that has been composed with the support of the teacher. In turn, students learn to sort data, use tally marks to keep track of response numbers, present the data using a bar graph, use the data to give an appropriate answer to the investigative question, and suggest effects of their findings. Key teaching points for the bar graph data display are that the numbers on the vertical axis label points, not spaces, and that the height of the bar shows the total in the category. The columns should have spaces between them because the data are discrete.

Associated Achievement Objectives

Technology
Technological Practice

  • Develop a plan that identifies the key stages and resources required to complete an outcome.

Characteristics of technology

  • Understand that technology both reflects and changes society and the environment and increases people’s capability.
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:

  • providing graph paper with larger squares to support children in drawing different sized envelopes and bar graphs
  • allowing students to work with a buddy and create their own ruler and/or tape measure
  • challenging students to use rulers of different sizes when measuring items
  • providing opportunities for students to work in whole class, paired, and small-group settings, and as individuals. Organise these groups strategically to encourage peer learning, scaffolding, and extension
  • providing individualised support
  • having students work in pairs to create a shared letterbox.

The context for this unit can be adapted to suit the interests and experiences of your students by, for example:

  • having the children decorate their mailboxes to reflect an aspect of New Zealand's environment, culture, or their own culture, whānau, or interests
  • connecting the current mathematics with New Zealand's history. For example, how did Māori and Pacific people send messages prior to the arrival or European settlers in New Zealand? What about before they travelled to New Zealand? How did this change with the arrival of European settlers? Look into the mokihi (mogihi - raft) or waka which were used to traverse rivers. These allowed people to pass on messages and goods to relatives on the other side of the river
  • organising children into groups and assigning them different groups of people to write appropriate emails to. For example, grandparents, parents, friends, siblings, principal, coach, school teacher. This could be linked with a purpose for writing (e.g. thank you letters, persuasive texts, invitations etc.)
  • acknowledging other cultures by asking students if they have stories to share about communication before postal services.

Te reo Māori kupu such as ine (measure), rūri (ruler), and mitarau (centimetre) could be introduced in this unit and used throughout other mathematical learning. You could also encourage students, who speak a language other than English at home, to share the words related to measurement that they use at home.

Required Resource Materials
  • Letterbox picture (Copymaster 1)
  • Camera/iPad/cell phone
  • Computer with inter/intranet connections
  • Used envelopes of various sizes
  • Blank envelopes for students to write (students could also create these as an extension task)
  • 30cm rulers
  • Pencils
  • Cardboard shoe boxes
  • Stiff cardboard
  • Scissors
  • Craft knives
  • Glue
  • Parcel tape or wide cellotape
  • Paint, paintbrushes
  • Graph paper
  • The Jolly Postman, by Janet & Allan Ahlberg (available online)
Activity

Whilst this unit is presented as sequence of five sessions, it is expected that any session may extend beyond one teaching period.

Session 1

This session is about researching measurements associated with letter mail and letterboxes.

Activity 1

  1. Begin by reading school intranet messages or having students read emails/daily notices etc. Discuss electronic mail and ask what other ways we receive mail. Write the word ‘mail’ on the class chart or in a class modelling book. Brainstorm other forms of mail and record associated words/ideas.
  2. Read The Jolly Postman, by Janet & Allan Ahlberg. Emphasise that letter mail comes in different sizes.
  3. Display the picture of a letterbox (Copymaster 1). Discuss its features and what ‘job’ it has: to receive mail of different sizes and keep it safe and dry. Notice the size of the box, the size of the letter slot and the newspaper/parcel space.
  4. Explain that the students will be making their own cardboard letterboxes.
    Ask. “What do we need to know before we make our own letterboxes?” Record student responses. Guide discussion to include ‘the size of the mail/letters’.

Activity 2

  1. Make paper, pencils, 30cm rulers, and used envelopes of assorted sizes available.
  2. Have students work together in pairs to explore how they could measure an envelope. Have one student demonstrate how to use a ruler to measure an envelope. Highlight the importance of aligning the edge of the envelope with zero, and of having the ruler aligned with a straight edge. Use the analogy that starting at zero is like standing at the beginning of a walking race. When you step out it is one step which is like the first measure of one on a ruler. Ensure that all dimensions of the letter are measured. You might record a list of instructions for "how to measure an envelope" as the student models the measuring process. 
  3. Together, practice reading the length measure, including expressing part measures. 
  4. Model how to record the measure correctly using abbreviations. Explain that students are going to measure and record various sizes of letter mail. 
  5. Distribute the used envelopes and have students measure them, following the instructions described and process modelled. Have students order a selection of envelopes from smallest to largest, draw these and record the dimension measurements. You could order all of the envelopes measured as a class.

Activity 3

  1. Review what is known about measurement (e.g. start at 0, no gaps or overlaps, we can use "half" or "part of" measures, we have measured using centimetres).
  2. As a class, discuss the measures recorded yesterday, and agree on an optimum size range for the letterbox, the letter slot, and the newspaper or parcel space, giving reasons why. Record this as a range (no smaller than x and no bigger than y) with a diagram (e.g. a number line). If a bulk supply of standard size shoeboxes is available, you might consider using these as the optimum size.
  3. Explain that if the Jolly Postman was to deliver letters in the school neighbourhood, some of the letterboxes might not be so easy for him to use because not all letterbox designers have researched letter size. Go on a class walk in the school neighbourhood to see the variation in letterbox design and to photograph some for display and discussion. Notice any that have a narrow letter slot which makes it difficult to fit larger sizes of letter mail. Alternatively, you could ask your students to bring in a few photos of letterboxes belonging to members of their whānau.

Session 2

This session is focused on students using accurate measures to design and create a cardboard letterbox. Students will use a flow diagram to explain this process.

Activity 1

  1. Start by discussing letterbox photographs taken on the walk/gathered by students, noting functional design features, and individual ‘quirky’ features which give some letterboxes character.
  2. Remind students of the agreed optimum range of letterbox measurements from Session 1. Draw attention back to the letterbox photos, and ask students to estimate and consider which letterboxes they think would fit into this range. 
  3. Make pencils and paper available. Have students draw their own letterbox design, including the measurements of the box, the slot, and any additional features, for example, an aperture for a newspaper (as shown in Copymaster 1). Model this process for students. Isometric or grid paper may be useful for some students. Students ready for extension could be challenged to create their letterbox using an interesting 3D shape as the base.
  4. Once the designs are completed, make construction materials and rulers available to the students.
  5. Review the key measurement skills discussed earlier and emphasise the importance of making accurate measurements.
  6. Give time for letterboxes to be constructed. Make paint and other construction material available as desired/needed. ‘Quirky’ features can be added once basic construction is completed. Roam and support students with the measurement and construction of their designs.
  7. The last task is for students to paint (or create) their letterbox number, choosing a favourite number. Should two students choose the same number, for example 10, have them use 10a, 10b and discuss why numbering actually works this way in building subdivisions, shared driveways etc.

Activity 2

  1. As students near the end of their letterbox construction, gather the class together to introduce the flow diagram shown below. Model recording the process of making your own letterbox (or a students' letterbox), using the first three stages of the flow diagram. Include drawings that show measurement and annotations. An easy way to do this would be to give each student an A3 piece of paper divided into four quadrants. Each of the quadrants could be used to describe one stage of the process.
  2. Have students start working on their flow diagram, before (if necessary) returning to their letterbox construction.
  3. Once all students have made some progress on the first three stages of their flow diagram, gather the class together and pose the following question:
    How can we test our designs? 
    Discuss the purpose of the letterboxes (i.e. to receive mail). Agree that students could position their boxes in a suitable classroom space, list their addresses (i.e. as name, class and letterbox number), write letters to each other, place them in envelopes and post them into the appropriate box. The width of the slit, size of the box and ease of opening can be evaluated by seeking feedback from classmate users. 
  4. Allow students to continue working on their letterboxes, flow diagrams, and to start on writing letters. You could also write letters as part of your writing programme.

This image shows a flow diagram of a four step process: Research, Design, Build, Test and Improve.

Session 3

This session has a statistical investigation focus. We investigate the effect of email on the volume of postal mail over time.

Activity 1

  1. Reread the mail brainstorm from Session 1. Explain that people haven’t always had computers and email, but that they used to rely on letter mail for their messages. (‘email’ was introduced internationally c. 1993.)
    Ask: “Does anyone have an “I wonder” about email and letter mail.” 
    Encourage students to share their knowledge, and/or conduct research, around mail in different cultures, countries, and throughout time. This could be done as part of your literacy or inquiry programme.
  2. Agree on a worthwhile investigation. For example: investigating whether the increase in the use of electronic mail means that people are now getting less letter mail than they did x years ago (suggest 5 to 10 years ago: a time period that is meaningful to the students.)
  3. Have students suggest an investigative question. For example: "Has the amount of postal mail our parents/families/whānau receive in their letterboxes changed in the last 5 years?"
  4. Have students discuss in pairs, and then share with the whole class, how they think the data could be collected. 
  5. Agree to a simple class data gathering process such as:
  • Each student in the class will ask at least one parent/caregiver and one extended family member/family friend/wider whānau member to complete a questionnaire (paper or digital) asking:

    This image shows a questionnaire. The first question is "do you use email". The possible answers are "yes" and "no". The second question is "is the amount of letter mail you receive in your letterbox: the same as 5 years ago, less than 5 years ago, or more than 5 years ago?" Participants are asked to suggest a reason for this change (optional).
  1. Have students complete preparations for gathering the data, including setting a realistic response time for participants.
  2. Have students carry out the data collection.

Session 4

This session is focused on students sorting data, and using it to create an effective data display. They will use this display to answer the investigative question.

Activity 1

  1. Explain that the questionnaires are ready for analysis. As a class, discuss what this means. Emphasise the process and purpose of analysing and presenting information (e.g. analysis allows us to see patterns and answer the investigative question). Agree that one way to present information is to use a bar graph. Review the features of a bar graph, highlighting the key teaching points (see the Description of Mathematics at the start of this unit).
  2. Make a copy of each questionnaire response, one copy of the blank questionnaire for each student to record results, graph paper and pencils available.
  3. Explain that each of the questionnaire responses will be read aloud. Each student should listen and record the results on the blank form, using tally marks.
    Have a student model this and discuss. For example:

    This image shows a blank questionnaire form with tally marks recorded.

Alternatively, you could display the questionnaire responses around the room and have students visit each response and record their tally marks.

  1. When all students have completed their tally charts, together, discuss the data values, the label and the scale for each axis on the graph, and possible titles for the display.

Activity 2

  1. Explain to students that they are now going to create their own data display (graph) for these data.
  2. Scaffold each student to create their own graph. You might let some students work on this independently or in pairs, whilst working in a group with students in need of greater support. Provide plenty of opportunities to students to share and reflect on their work.
  3. Once students have completed their graphs, have them write their own answer to the investigative question, and consider how this change might affect people (e.g. "Has the amount of postal mail our parents/families/whānau receive in their letterboxes changed in the last 5 years?"). Draw links back to the Jolly Postman to support students' thinking. Encourage students to think about postal workers, the reduction in the volume of Christmas cards sent, the increase of online shopping and courier deliveries, and other factors that affect the amount of postal mail sent. You might find a relevant article or video online that could be shared with the class.

Session 5

This session is focused on presenting findings and reflecting on the investigative process.

Activity 1

  1. Have students present their completed display and findings to a partner. Have students explain their partner’s work and ideas to the class.
  2. Refer back to the questionnaires that gave a reason for the change in the amount of mail received. Show these reasons to the class (perhaps on a list or memo cards). Discuss these, identifying any connections students can make to the data, surprises and common messages.

Activity 2

  1. Support students to evaluate their investigation by posing the following questions in an appropriate manner:
  • How effective was our questionnaire? (Did we ask the right questions? Should we have asked them in another way?)
  • Can we say that what we have found out is true for all of our city or our country? (No, we haven’t asked enough people.)
  • Is there another investigative question you want to ask now?
  • Do you think your family will have a letterbox in 10 years? Why do you think this?
  1. Have students reflect on the amount of use the letterboxes have had to this point in time, consider any improvements, and complete the final section of their flow diagram (test and improve). Display these diagrams alongside the letterboxes.
  2. You could also have students write a short presentation in an appropriate format (e.g. pictures with captions, list, story) to reflect on the measurement and statistics skills that have been developed and applied throughout the unit, and to reflect on the different stages of the technology design process.
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Level Two