It takes a village

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Purpose

In this unit students develop understanding of the financial challenges faced by superannuitants in their local community. As part of this, they research the community resources and services that are available to support the older citizens and implement a (short term) programme of help for at least one older community member.

Achievement Objectives
NA4-1: Use a range of multiplicative strategies when operating on whole numbers.
NA4-2: Understand addition and subtraction of fractions, decimals, and integers.
NA4-3: Find fractions, decimals, and percentages of amounts expressed as whole numbers, simple fractions, and decimals.
NA4-5: Know the equivalent decimal and percentage forms for everyday fractions.
S4-1: Plan and conduct investigations using the statistical enquiry cycle: determining appropriate variables and data collection methods; gathering, sorting, and displaying multivariate category, measurement, and time-series data to detect patterns, variations, relationships, and trends; comparing distributions visually; communicating findings, using appropriate displays.
Specific Learning Outcomes
  • Apply number knowledge and strategies to bank statements and budget problems.
  • Consider and apply protocols around the manageability of data collection and data safety.
  • Use research information to inform an investigation.
  • Determine appropriate variables and data collection methods.
  • Design a survey format and survey questions. 
  • Gather multivariate data to answer an investigative question.
  • Sort multivariate data to answer investigative questions.
  • Identify patterns and relationships within and between variables.
  • Choose and use appropriate data displays to present information, identify patterns in data, and communicate findings.
  • Answer an investigative question using evidence from analysis.
  • Recognise the limitations of using a group to make decisions about a wider population.
  • Suggest implications of their findings and consider who else their findings might apply to.
Description of Mathematics

In exploring matters of financial literacy, particularly balance sheets and budgets, students apply a range of additive and multiplicative strategies. Financial calculations require them to apply decimal and place value understanding. As they work with negative balances, they apply their integer knowledge.

At this level students should be able to pose investigative questions that they want to explore, consider the appropriate data they need to collect, and gather and sort the data in order to develop an answer to their question. They need to be able to identify the variables that are relevant to their investigative question and recognise the importance of developing survey questions that will answer this.

As they sort their multivariate data, students may ask additional investigative questions of the data, for example; what are the ages of the group of super annuitants, what community services are used by the super annuitant group, are men more likely to use the Meals-on-Wheels service than women, and are younger ‘pensioners’ better informed about the services that are available to them than those who are older? Students should recognise that when variables are considered together, a more complex and interesting picture, related to the investigation and its group, can be revealed.

In designing their investigation, the data collection method, and the sorting and display of data, students should consider matters such as purpose, practical implementation, manageability, surveying, data safety including ethics, and how technology can be used effectively in their investigation. Students should be supported to use the most appropriate display to use for a particular purpose, to use technology to create displays, and to find patterns and relationships in the data, including differences and similarities between distributions.

The Level 4 Statistics units Travel to school and How much bullying? provide supporting ideas for developing investigative questions, ethics and developing survey questions. 

Associated Achievement Objectives

Health and Physical Education
Healthy Communities and Environments

  • Investigate and/or access a range of community resources that support well-being, and evaluate the contribution made by each to the well-being of community members.
  • Specify individual responsibilities and take collective action for the care and safety of other people in their school and in the wider community.
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:

  • varying the type of data collected; categorical data can be easier to manage than numerical data
  • varying the type of analysis – and the support given to do the analysis
  • providing survey questions to use
  • providing prompts for writing descriptive statements
  • providing opportunities for students to work in groups and pairs with students with different levels of mathematical knowledge and confidence, in order to encourage tuakana-teina (peer learning) and scaffolding
  • providing teacher support, modelling, explicit teaching, and questioning at all stages of the investigation.

This integrated unit makes connections to health and physical education and is an example of a topic of interest. However, this context can be adapted to suit the interests and experiences of your students. Other topics of interest related to health and physical education could be used in a similar manner, for example, gender equity. This unit could also be reframed in relation to other specific groups of people that are relevant to your students. Members of your local community might also be able to visit your class and influence the unit with valuable knowledge and perspective.

Te reo Māori kupu such as kauwhata (graph), the names for specific types of graphs, mahere pūtea (budget), moni whiwhi (income), taurangi (variable), tirohanga tauanga (statistical survey, survey), raraunga matatini (multivariate data), raraunga matatahi (univariate data), kohikohi raraunga (data collection), and whakaari raraunga (data display) could be introduced in this unit and used throughout other mathematical learning.

Required Resource Materials
Activity

Learning activities 
Whilst this unit is presented as sequence of five sessions, more sessions than this may be required. It is also expected that any session may extend beyond one teaching period.

Session 1

This session focuses on developing students’ understanding of superannuation and the financial challenges faced by some older members in their community.

SLO:

  • Apply number knowledge and strategies to complete a bank statement.

Activity 1

  1. Write on the class chart: It takes a village…” Ask students if they can complete the African proverb. (‘It takes a village to raise a child.’). 
  2. Brainstorm together what this means.
    For example: children are young, dependent and vulnerable so all members of the community must look out for their wellbeing and safety.
  3. Identify other ‘vulnerable’ people in the community. Highlight the needs of many older people who, over time, become increasingly dependent on others, and whose wellbeing and safety should also be a focus of community care.
    (“It takes a village to care for our elderly citizens”.)
  4. Ask students to share appropriate information about relatives or friends of the family who are ‘pensioners’. Discuss some of the generic challenges that many older citizens face.
    For example: limited means, ill health/disability, the loss of life partner, loss of purpose, loss of independence, loneliness, a sense of isolation.
  5. Identify the nearest group of older community residents to the school.
    For example: residents of ‘pensioner flats’/community housing for the elderly. Ask if students know any of the residents.

Activity 2

Make available to student pairs a copy of Copymaster 1.
Note: the values provided in the resource were up-to-date at the time of creation. Since then, incomes and expenses will have changed. You should decide whether you will work with the provided data, as an example of how to budget, acknowledging that the costs and incomes have changed, or if you want to create new data that reflects current costs and incomes.

  1. Have students read about Pita and Nancy and make a Venn diagram showing the differences and similarities in their circumstances.
    A blank Venn Diagram for Pita, Nancy, and Mr X.
  2. Have students add a third familiar older person (super annuitant) to the diagram.
    Support students to recognise that an older member of a community has usually made a full contribution to the community during their lives, has in their working life paid taxes which partially fund superannuation, has a unique and interesting life story, and that their health, social and economic circumstances may differ from others. Your students might have stories of relatives, family friends, or community members to share as part of this discussion. Be sensitive to your students’ backgrounds and lived experiences.

Activity 3

  1. Recognise that Pita, Nancy and Mr X are all super annuitants.
    Write on the class chart: New Zealand Superannuation
    Brainstorm together what students know about this.
     
  2. Allow time for student pairs to research superannuation. You may need to suggest some websites that are useful.
     
  3. Have students find out and record:
    • At least five interesting facts about NZ superannuation.
    • The amount of ‘pension’ that Pita will probably receive.

Activity 4

Make available to each student a copy of Copymaster 2 (Pita’s bank statement).

  1. Briefly discuss together the contents of his monthly statement.
    Recognise that this statement does not show charges for being overdrawn. Point out that this would apply and would accrue.
     
  2. Allow time for students to work in pairs to complete the calculations and questions.
     
  3. Have students share their observations about Pita’s situation.

Session 2

This session is about developing student understanding of the impact of financial constraints on the day-to-day life of a super annuitant. It involves planning to visit a local older resident.

SLO:

  • Apply number skills to a budget problem.

Activity 1

Write Budget on the class chart. Ask who has managed a budget of their own.
Together, brainstorm and record what the students already know about budgets. Key ideas to elicit from the students:

  • Many people of all ages find that developing a budget helps them to better manage their finances.
  • A budget is a plan for the money a person expects to receive (income) and how they expect to spend it (expenses).
  • A budget needs accurate and complete information to be useful.
  • A budget helps a person to see where they might be spending too much.
  • A budget can help a person to see any savings that they can make.
  • For people who have a limited income, a budget can help them avoid spending more than they earn or getting into debt (owing money to other people).
  • A budget can help a person reach a savings goal.

 Activity 2

  1. Pose the situation to student pairs.
    Imagine you are Pita. What might you do about your financial situation? 
    (Recognise that currently Pita, like many other super annuitants, is not living extravagantly. Recognise the limitations that are already placed on Pita’s lifestyle as he strives to live within his means).
    Make available copies of Copymaster 3 to each student. Have students work in pairs to:
    • Suggest changes they may make to their expenditure if they were Pita.
    • Prepare a budget that includes a contingency (emergency) fund.
    • List the practical ways in which their new budget may affect Pita.
  2. Have students work with a different partner to share their budget and ideas.
     
  3. As a class, list the advantages and challenges of NZ superannuation.

Activity 3

  1. Ask students to refer to their Venn diagrams from Session 1 and recognise the different circumstances of Pita, Nancy and Mr X.
    Refer to understanding developed in Session 1: “It takes a village to care for our elderly citizens”.
  2. Brainstorm together and record student ideas about community resources and services that are available for older citizens. Ask how they can find out more information.
    Agree on 2 courses of action:
  • Ask the older persons in their community.
  • Research support organisations and services.

Activity 4

  1. Develop Action 1 (Ask the older persons in their community).
  2. Have student pairs discuss protocols and develop an action plan for contacting an older resident in their community (eg. in local ‘pensioner flats’, council housing, retirement village).
    Have them understand that the purpose of a visit is for each student pair to visit and to ‘get to know’ one older person, to find out information about support services that are available and how useful they are, and to offer help with practical tasks, if appropriate.
    Allow time for students to consider an approach that is practical and manageable.
  3. As a class, share plans, ensuring respectful and appropriate protocols are maintained and emphasised. Have students write introductory contact letters that specify a visit date, time and duration and contact number/details should the recipient be unavailable or choose not to participate.

Session 3

This session is about planning an investigation and the data gathering process.

Prior to this session, deliver introductory information to older citizens.

SLOs:

  • Research information to inform an investigation.
  • Determining appropriate variables and data collection methods.
  • Consider manageability and data safety/ethics.
  • Design survey format and survey questions.

Activity 1

  1. Explain that today’s session is about preparing for each student pair to visit a local, older resident.
    Review the three purposes of the visit:
    • To get to know them and to hear (a little of) their story.
    • To find out which services and resources they most use.
    • To undertake a helpful and practical task for this person, if appropriate.
  2. Explain that the class will plan their investigation into community services and resources.
    They should consider manageability, survey format, and data safety.

Activity 2

  1. Have student pairs undertake Action 2 from Session 2, Activity 3  (i.e. refer back to their brainstorms together and find out more information about community resources and services that are available for older citizens.
  2. Allow time for student pairs to research resources and services available nationally and locally, and to record important information they learn.  Provide graphic organisers and research templates, as necessary.

Suggested sources:

  1. As a class share and list the resource and services information they have gathered.
  2. Have student pairs consider what more they would like to find out and develop an investigative question that interests them Have them list the information they need to gather to answer the question, and develop survey questions.
    See the Level 4 Statistics units Travel to school and How much bullying? for ideas on developing investigative and survey questions.

Activity 3

  1. For practical implementation reasons, pool student ideas to create one survey. Display this in a way that is visible to all students (e.g. on a PowerPoint).
  2. As a class, agree on an investigative question. For example:
    How well do current services and resources for the elderly support those in our local community?
    Do current services and resources for the elderly meet the needs of the men and women in ________________ (specify group)
     
  3. Recognise that the data gathered will need to include a number of variables. For example: age bands, gender, living arrangements (alone/partnered), level of ability/disability, specific services used/not used, rating services, frequency of use, necessary services that are not provided.
     
  4. Select the best survey questions developed in Activity 2, Step 3. Refine with agreement.
     
  5. Save and distribute the survey.
     
  6. Agree that when each pair visits a member of the sample group, that person will be asked their preference for an oral or written survey.

Session 4

This session is about students visiting survey participants, getting to know their stories and gathering data to answer the investigation question.

SLOs:

  • Gathering multivariate data to answer an investigative question.
  • Consider and apply protocols around the manageability of data collection and data safety.

Prior to this session, the date, visit time and specific participants will have been identified, agreed upon, and arrangements will have been made.

Activity 1

Agree on visit protocols, including considering appropriate koha, reminder about ethics and data safety for the participants.

Activity 2

Review the purposes of the survey and visit, and agree on a consistent format for each visit:

  • To get to know them and to hear (a little of) their story.
  • To find out which services and resources they most use.
  • To undertake a helpful and practical task for this person, if appropriate.

The format should be respectful and safe for the participants.

Activity 3

Remind students to make a suitable time for a return visit to spend time with the older person and undertake a/another helpful task.

Activity 4

Have students complete their visits and gather survey data.

Session 5

This session is about students sorting and displaying data, looking for patterns, variations, relationships, and trends and communicating findings.

Prior to the session make copies of all survey results for each student pair.

SLOs:

  • Sort multivariate data to answer investigative questions.
  • Identify patterns and relationships within and between variables.
  • Choose and use appropriate data displays to present information, identify patterns in data, and communicate findings.
  • Answer an investigative question using evidence from analysis
  • Recognise the limitations of using a group to make decisions about a wider population.
  • Suggest implications of their findings and consider who else their findings might apply to.
     

Activity 1

Have students work in pairs to sort their data, and record, display, and write findings. If appropriate, the recording, displaying, and writing could be done by individuals (as opposed to pairs of students). Support students to use appropriate graphing tools (e.g. a paper template, graphing software). You might choose to introduce two types of graph to the class, for all to use. Alternatively, your students might have sufficient knowledge and experience to choose their own graph types, with less support from the teacher.

  1. Have student sort, display and answer summary questions about univariate data. For example:
    Which is the most/least frequently used service?
    What is the level of disability of the participant group?
  2. Have students produce an appropriate range of graphs to display their findings. These are likely to be bar graphs, dot plots, and strip graphs.
    If students are comparing groups they will make two dot plots on the same axes for numerical data, and side-by-side bar graphs for categorical data.  
  3. As a class, discuss the graph features and why they are fit for purpose. Have students make statements about the distributions.

Activity 2

  1. Have students compare the distributions of their graphs. Have them look for patterns or relationships. For example:
    Do younger participants access and use (specified) services more frequently?
    Do men use the ‘meals on wheels’ service more than women?
    Are younger participants more informed about available services and older participants?
    Do participants with disabilities use the local bus service?
  2. Have students write about trends, patterns and relationships for which they have evidence. 
  3. In pairs, have students suggest reasons for trends and patterns and prepare to present their findings.

Activity 3

  1. As a class, answer the investigative question.
  2. Together make statements, based on the evidence collected, about the nature and level of resources and services available to support older members of the community, and the degree to which they are used by and meet the needs of the group.
    Recognise that the data are particular to the surveyed cohort and may not be representative of all NZ super annuitants.
  3. As a class, identify any needs of the group that are not being met and plan a response or advocacy plan.
  4. List further questions for investigation that have arisen.
  5. Have students evaluate the success of the investigation and also suggest ways in which it could be improved.

Activity 4

Conclude by reflecting on the statement: “It takes a village to care for our elderly citizens”.
Plan practical details of completing helpful tasks and possible ongoing contact with survey group members.

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Level Four