Money and Percentage

Purpose

In this unit we highlight the terms and concepts associated with money and percentages by exploring money and percentages in a variety of real life contexts. This unit is concerned with applications of percentages more than learning how to calculate percentages. For more on calculating percentages see the Level 4 unit Getting Percentible.

Achievement Objectives
NA5-3: Understand operations on fractions, decimals, percentages, and integers.
Specific Learning Outcomes
  • Explain the use of percentages in day to day living.
  • Explain concepts such as GST, commission, discount, bonus, net pay, gross pay, PAYE and use these concepts in applied problems.
Description of Mathematics

Percentages are commonly used in real life. Many of these applications involve money. In this unit, we explore  money and percentages in a variety of real life contexts.

 Prior to using this unit, students should be familiar with decimals and fractions. The Level 4 units: Getting Partial to Fractions, Getting Partial to Decimals, and Getting Partial: Fractions of sets form a good foundation for the content in this unit. 

Percentages are rates out of 100 (per hundred, per century), or a fraction with the number over 100. Students should recognise the meaning of percent as deriving from the fraction over 100, should identify that a the % symbol is made up of the / and the 00 from this fraction.

50% means at a rate of 50 out of 100, a rate that is equivalent to one half. This means that 50% of a quantity (say, 40) can be calculated by multiplying the quantity by 50/100 (say, 40 x 50/100). The answer, 20, reflects the fact that 50 out of 100 and 20 out of 40 are equivalent rates, just like the fractions 50/100 and 20/40 are equivalent. 

50% can be represented as an infinite number of equivalent fractions, such as 50/100 = 1/2 = 2/4 = 23/46, …. Percentages can be written as decimals, using the structure of the place value system. 50/100 also means 50 hundredths which is 5 tenths or 0.5 (note that 5 is in the tenths place). As a decimal, 50% can be represented as 0.5. Converting percentages to decimals can sometimes assist in calculation, such as 0.6 x 80 = 48 is an equivalent calculation to 60% x 80 = 48.

When working with percentages, students must also realise that ‘of’ means ‘multiplied by’.  20% of 50 means 20% times 50, and since from above we know that % means per 100 or a fraction over 100, 20% of 50 means 20/100 times 50, or 1000/100, which is 10.

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 differentiate include:

  • revising and working with commonly used percentages, such as 50%, 25%, 10%, to build up students’ fluency and confidence, before moving to the application of more complex percentages
  • using models for recording, especially double number lines used in the unit
  • encouraging students to use a variety of recording methods to illustrate their thinking, and encouraging them to share their representations with others
  • providing opportunities for students to work in mixed groupings and pairs, in which they can benefit from peer learning and scaffolding, and the sharing and justification of individual’s ideas
  • providing opportunities for small group and individualised instruction that addresses specific gaps in knowledge
  • providing access to calculators to allow students to confirm their estimations and experiment with more complex percentages.

The contexts for activities can be adapted to suit the interests and experiences of your students by:

  • using the members of the class to create percentage problems
  • creating scenarios with contexts (e.g. sports, shared interests, links to other current curriculum areas) that interest your students
  • involving students in financial literacy  contexts in which percentages are important, such as saving money or budgeting.

Te reo Māori kupu such as ōrau (percent) and whakahekenga ōrau (percentage discount) could be introduced in this unit and used throughout other mathematical learning

Required Resource Materials
  • Newspapers
  • Card or paper for students' questions
  • Calculators
  • Copymaster One (Percentage worksheet): This goes over skills from Level 4 and may be used to get students started.
  • Copymaster Two (Newspapers Money and Percentages)
  • Copymaster Three (Some Terms Defined): An information sheet which explains some relevant terms (could be photocopied for student work stations).
  • Copymaster Four (Shopping at the Mall): This exercise could be used as an assessment for processes.
  • Copymaster Five (Earning Money): This exercise looks at wages, and PAYE.
  • Copymaster Six (Investing Savings): An investigation looking at the effects of compound interest
  • Copymaster Seven (GST): Questions concerning GST in New Zealand
  • Copymaster Eight (Commission and Salaries): Questions and investigation, commission versus salary.

For information about GST in New Zealand click on the site below to enter the NZ GST Homepage or use the quick reference summary sheet that accompanies this unit.  Up-to date information about PAYE is also available at:  http://www.ird.govt.nz.
http://www.ird.govt.nz/gst/

Activity

Teaching sequence

Getting Started

Revision of percentages.

  1. Introduce the topic of percentages. Depending on your class this may involve a quick brainstorming session, an extended revision, or one or two directed questions.
     
  2. Give students Copymaster One. This contains a mixture of types of questions involving percentages and will give you some idea of your class’s strengths and weaknesses. You might adapt these to reflect a context that is more relevant to your students. The worksheet could be used either as an individual activity, or students could work in pairs. Students who need assistance could be paired with more knowledgeable students or could work through some examples in a group with the teacher.
     
  3. Gather the class back together and go over the answers to ensure that everyone understands how to work them out.
  4. Introduce Copymaster Two (Newspapers, Money and Percentages) and allow students to work through it in pairs or small groups (i.e. up to four). Each group/pair/individual will need access to a newspaper and a copy of the Copymaster. The aim of this activity is to revise skills and develop an awareness of the role of percentages/money in every day life. Use Copymaster Three (Some Terms Defined) as a supporting resource.

    Explain to the students that they will have the week to research the task and will be given some time to write it up but must be ready to present their findings to the class on Friday.

    Allow some time to discuss the task and provide direction and support as to the form the results are to be presented in. There is the opportunity to develop some skills of statistical data presentation (especially pie charts), or the students could just write down the percentages they find.

Exploring

Over the next 3-4 sessions, have students work on tasks involving money and percentages in daily life. These tasks aim to build on earlier skills and further develop an awareness of the role of percentages and money in every day life. Encourage students to refer back to Copymaster Three (Some Terms Defined) for information on relevant terms.

The question sheets for the five tasks have been designed so that they can be used in a variety of ways. You may wish to print and laminate them and use them in a workstation format with different groups working on different tasks. Alternatively, you may work on these in a more structured, whole-class manner, with individual students or groups of students to work with their own copy of the Copymaster..

Although the questions are fairly self explanatory you may wish to go over each with the class before they split up to work on them. You will need to be available to help with individual enquiries while students are working.

The five tasks cover different areas in which percentages and money may be used:

  • Shopping at the Mall: This exercise looks at the finances of three girls at the mall.
  • Earning Money: This exercise looks at wages, and PAYE.
  • Investing Savings: An investigation looking at the effects of compound interest
  • GST: Questions concerning GST in New Zealand
  • Commission and Salaries: Questions and investigation, commission versus salary.

Allow some time in each lesson to refer to the week’s newspaper research task. Ask students what they have found, check on their methodology, and provide support as required. Remind them that they will have to report their findings on Friday. Some time could be allocated in class to writing up.

Reflecting

This final session is to be used to tie together the previous sessions in the unit, and to report back on the class’s newspaper investigations.

  1. Provide time for groups to share their results with other groups, before choosing a few groups to share their results with the class. 
  2. Discuss any discrepancies in students' findings.
    What are possible reasons for any differences? 
    Whose method of estimating percentages is most accurate? 
    Whose is easiest?
    Did anyone use a different strategy or approach?
Attachments

Printed from https://nzmaths.co.nz/resource/money-and-percentage at 2:36am on the 29th March 2024