Percentages and income

SubjectMathematics YearYear 7 CurriculumAC v8.4 Time150

Introduction

This set of resources provides opportunities for students to learn skills and solve problems involving percentages in the context of earning a commission.

Australian Curriculum or Syllabus

Achievement standard

By the end of Year 7, students solve problems involving the comparison, addition and subtraction of integers. They make the connections between whole numbers and index notation and the relationship between perfect squares and square roots. They solve problems involving percentages and all four operations with fractions and decimals. They compare the cost of items to make financial decisions. Students represent numbers using variables. They connect the laws and properties for numbers to algebra. They interpret simple linear representations and model authentic information. Students describe different views of three-dimensional objects. They represent transformations in the Cartesian plane. They solve simple numerical problems involving angles formed by a transversal crossing two lines. Students identify issues involving the collection of continuous data. They describe the relationship between the median and mean in data displays.

Students use fractions, decimals and percentages, and their equivalences. They express one quantity as a fraction or percentage of another. Students solve simple linear equations and evaluate algebraic expressions after numerical substitution. They assign ordered pairs to given points on the Cartesian plane. Students use formulas for the area and perimeter of rectangles and calculate volumes of rectangular prisms. Students classify triangles and quadrilaterals. They name the types of angles formed by a transversal crossing parallel line. Students determine the sample space for simple experiments with equally likely outcomes and assign probabilities to those outcomes. They calculate mean, mode, median and range for data sets. They construct stem-and-leaf plots and dot-plots.

Content descriptions

Find percentages of quantities and express one quantity as a percentage of another, with and without digital technologies. (ACMNA158

Investigate and calculate 'best buys', with and without digital technologies (ACMNA174).

Teacher resources

In order to see the resources you must Register or Login if you already have an account.

Visualiser

Student learning resources

In order to see the resources you must Register or Login if you already have an account.

Worksheet

Suggested activity sequence

This sequence is intended as a framework to be modified and adapted by teachers to suit the needs of a class group.

Part A: Calculating commission

1. Introduce the concept of commission.
Commission is a way of earning income based on the value of items you have sold. Salespeople, such as real estate agents and car salespeople, are often paid a commission. Real estate agents earn a commission on the value properties they have sold. Car salespeople earn a commission based on the value of cars they have sold. The amount of the commission is usually expressed as a percentage. People who earn a commission often also get a ‘retainer’, which is a smaller amount that is paid regularly like a wage or salary and is not related to how much they have sold.
1. Explicitly teach students how to calculate commission using a gradual release of responsibility model.

To calculate a commission:

𝐶𝑜𝑚𝑚𝑖𝑠𝑠𝑖𝑜𝑛 = 𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 × 𝑡𝑜𝑡𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑠𝑎𝑙𝑒𝑠

To calculate the pay of a salesperson:

𝑃𝑎𝑦 = 𝑐𝑜𝑚𝑚𝑖𝑠𝑠𝑖𝑜𝑛 + 𝑟𝑒𝑡𝑎𝑖𝑛𝑒r

Pay Calculations

Retainer

(Earnings from hours)

= hours x rate
= 120 x \$20.09
= \$2,410.80

Commission

= percentage x total value of sale
= 1% × (365 000 + 795,000)
= 1% × 1,160,000 (1% = 1/ 100 = 0.01)
= \$11,600

Total earnings

= retainer + commission
= 2,410.80 + 11,600
= \$14,010.80

2. Explain the worksheet and provide the following instructions:
• Each problem has a points value attached. The problems in the left hand column aren’t as challenging as those in the right hand column and so have a smaller point value.
• Students are to complete at least 15 points worth of problems.
3. Students may work in small groups to discuss the problems and how they might tackle them, troubleshoot and compare ideas, but each student is to write their own solution in their own notebook.
4. Provide feedback to students on their learning by marking the problems in the left hand column fairly quickly, working through the remaining 6 problems in a more detailed way, gathering student input about their approaches and their final answers. This task is suitable as an assessment item.

Part B: Crumple and shoot

This is a low tech game that gives students the opportunity to practice a maths skill collaboratively. It will take at least half an hour, up to 50 minutes if you haven’t played the game before.

1. Organise students in teams of 3 or 4 – make sure they’re mixed ability groups.
2. Use the visualiser to explain the game and the rules to students.
3. Give each team a stack of half A4 size scrap paper. Each team appoints one scribe.
4. Read out the question from the visualiser. Each team works out and agrees on their answer before the scribe writes it (legibly) on their piece of paper.
5. When you think they’ve had enough time call out ‘Answers up’, and one member of each team holds their answer in the air.
6. Quickly go around and check the answers. If the answer is wrong –take the group’s paper. If the answer is right, the group gets to keep their paper and send a team member to the spot where they’re going to crumple it and shoot it into the wastepaper basket to get a point.
Note the answers are included on the visualiser
7. To get a point teams have to answer the question correctly and shoot their paper into the bin.
8. Crumple and shooters line up and take their turn to crumple their answer sheet and shoot it into the bin (put a line of tape on the floor for shooters, and a tape X marking the spot where the bin should be).
9. Keep a tally on the board.

Some tips

• Do a practice question before you start if you haven’t played this game previously.
• You can accept answers to the nearest whole dollar or tens if you like.
• Some questions are worth 2 points, so will need to be written on 2 pieces of paper. Think about your willingness to consider carry through errors ahead of time and be ready to defend your policy.
• You could make it compulsory to rotate shooters amongst the team or make the rule that everyone must shoot at least once if you need to level the playing field.
• Add a 2 point shooters line if a leader emerges too soon and other teams need to catch up.
• You might like to add prizes for winning teams.