Juggling A Business

Purpose

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.
A PDF of the student activity is included.

Achievement Objectives
NA4-1: Use a range of multiplicative strategies when operating on whole numbers.
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.
Student Activity

  

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Specific Learning Outcomes

use multiplicative strategies to solve money problems

use addition and subtraction to solve money problems

Description of Mathematics

Number Framework Links
These problem-solving activities involve addition, subtraction, multiplication, and division of whole numbers and decimal amounts. They are appropriate for students who are at stages 7 and 8, but with teacher scaffolding, they can also be accessed by students who are at stage 6. (See the table of NDP material on page 4.)

Required Resource Materials
A calculator

FIO, Level 3-4, Financial Literacy: Granny’s Gift, Juggling a Business, pages 12-13

A classmate

Activity

Activity One

Financial understanding
In this activity, Anna identifies and calculates the start-up costs of the business she wants to start with Granny’s money. This is a vital part of her financial planning to ensure that her business is a success. She also needs to match her personal goals and capabilities to the business she is starting up.
(Note: Juggling balls can be made by tying a supermarket bag around half a cup of rice then encasing in a balloon with the neck cut off. Three more balloons are placed around the ball. The balloons have holes snipped out of them so that the colour of the balloons underneath will be partially revealed for a multi-coloured effect.)
Mathematics and statistics
This activity involves solving multiplicative problems based on the data given.
The adding of the costs for question 1a is straightforward. Encourage the students to estimate their answer first. $1.99 + $6.90 + $1.50 can be approximated as $2 + $7 + $1.50 = $10.50, which is very close to the actual answer of $10.40.
In question 1b, Anna needs to make 15 juggling balls (5 sets containing 3 balls each). This involves 7 cups of rice (15 x 1/2), 60 balloons (5 x 12 or 15 x 4, depending on whether calculated as sets or individual balls), and 15 supermarket plastic bags.
For question 1c, Anna has enough balloons to make 25 balls (that is, if 12 are needed for one set of 3, then 4 balloons are needed for each ball because 12 ÷ 3 = 4 and 100 balloons in a packet ÷ 4 is 25). She has enough supermarket bags to make 30 balls and enough rice to make 24 juggling balls because there are 24 halves in 12.
(You may need to teach your students that dividing by 1/2 is the same as multiplying by 2.) Therefore, Anna can make 24 balls before needing to buy more rice. Her juggling balls are sold in sets of 3, so the problem  x 3 = 24 must be solved to answer the question.
For question 2, Anna will sell 8 sets of juggling balls for $96 (as 8 x $12 = 96). Her start-up costs were $10.40 (from question 1). Profit = sales – expenses (the students may need elaboration on this equation), that is, $96.00 – $10.40 = $85.60.
For question 3, 30 minutes x 8 can be calculated as 240 minutes then divided by 60 (240 ÷ 60 = 24 ÷ 6) to get 4 hours. A quicker method is to calculate (an hour) x 8 = 4 hours of labour. To find how much money Anna makes per hour, the students need to take their answer from question 3 ($85.60) and divide by 4 to get $21.40.
Advanced multiplicative students may notice that the problem:  x 4 = 84 (because 84 is the nearest multiple of 4 to 85.60) will give an estimate of $21, which is very close to the actual answer.
In question 4, Anna decides to pay herself $16 an hour, so $16 x 4 = $64 is an expense (wages) that needs to be subtracted from her profit of $85.60. This leaves her $21.60 to reinvest in her business.
As an extension question, ask What should Anna do with this leftover money? (She could use it to buy 2 more bags of rice, 200 balloons, and 60 supermarket bags, costing $20.78 [rounded to $20.80], that is, double the original purchase.)

Activity Two

Financial understanding
In this activity, Anna knows that, for her business to be successful, it needs to cover all the costs of the initial start-up expenses. By taking this into account, she is planning for financial success.
Anna uses initiative and drive to advertise and market her products. She also uses the skills of others around her, paying them to do particular services.
Students may respond to question 1 more fully in a large group discussion. Question 2 is ideally linked to students’ knowledge of visual language, that is, static images.
To help with question 3, ask Why does it cost less per copy for more copies? (The reason for the lower price on larger quantities may be to entice the buyer to purchase a larger number or perhaps because the photocopying centre buys its paper in bulk and passes on this saving to those who want larger orders; running off a few copies
is also more labour-intensive than setting up the copier for a big run.)
Answers for question 3c should consider the percentage of orders expected from a leaflet drop, whether Anna has the time to fulfil these orders, whether the profit made on the orders is worth the expense of the leaflet drop, and whether a colour leaflet might generate more orders than a black and white one (enough to justify the extra
cost).
For question 4, ask:
Is this a good deal for Anna? (Anna only needs to sell two sets of juggling balls to earn the profit to cover the $20 delivery expense.)
Is it a good deal for her cousin Tavita? (It depends on how long it takes to deliver 1 000 leaflets. Some students in the class may have experience with doing paper routes and could therefore calculate the time to deliver 1 000 leaflets and an hourly rate [$20 divided by time]. The time taken would depend on how populated the delivery
area is.)
For question 5, students may need to be reminded of all the costs incurred (including design and delivery), after which this problem is simply an addition problem using previous answers. Ask Which option should Anna choose?
Answers may depend on discussion generated in question 3c.
Extension
Financial understanding
Anna’s experiences with her own business could motivate students to engage in establishing an enterprising business for themselves. The issues Anna faces, such as start-up costs, expenses, time and advertising, will provide scaffolding for students as they consider these same important aspects in relation to their business.


Social Sciences Links
Achievement objective:
• Understand how producers and consumers exercise their rights and meet their responsibilities (Social Studies, level 4)
The students could consider what rights and responsibilities Anna has to herself as a business owner and to her customers.
Other Cross-curricular Links
English achievement objective:
• Purposes and audiences: Show a developing/increasing understanding of how to shape texts for different purposes and audiences (Speaking, Writing, and Presenting, levels 3–4)
Students could design their own leaflet either for Anna’s business or a similar business of their own.
Technology achievement objectives:
• Technological products:
– Understand the relationship between the materials used and their performance properties in technological products (Technological Knowledge, level 3)
– Understand that materials can be formed, manipulated, and/or transformed to enhance the fitness for purpose of a technological product (Technological Knowledge, level 4)
Students could try making their own juggling balls or other craft items and estimate the costs involved.

Answers to Activities

Activity One
1. a. $10.40. ($1.99 rice + $6.90 balloons + $1.50 plastic bags)
b. 7.5 cups of rice, 60 balloons, 15 plastic bags. (Remember that each set has 3 balls in it.)
c. 8 sets. (8 sets uses 12 cups of rice [2 kg], 96 balloons, and 24 plastic bags.)
2. $85.60. (Profit = sales – cost: $96 – $10.40 = $85.60)
3. $21.40. (Time to make 8 sets = 4 hours. $85.60 ÷ 4 = $21.40 per hour)
4. $21.60. ($16 x 4 = $64 wages. $85.60 – $64.00 = $21.60)
Activity Two
1. Answers will vary. Some ideas could include: school newsletter, local paper, pamphlet drop, posters in local shops.
2. Answers will vary. The poster should include the three products (juggling balls, hacky sacks, and bungy balls), their prices, information on how to purchase or order them, and a picture or photo of the products, as well as stating that the juggling balls are sold in sets of 3.
3. a. Black and white: $9; colour: $149
b. Black and white: $60; colour: $790
c. Answers will vary. 1 000 colour ones would be a big outlay at the start of Anna’s
business (it would use almost half of Granny’s gift). If 50–75% of people ordered
from the leaflet, Anna probably wouldn’t have time to fill the orders. However, she
is unlikely to get that many orders from a leaflet drop, although she should have more
chance of getting orders from 1 000 leaflets than from 100. The design cost of $75 is
the same for 100 as for 1 000.
4. $20
5. a. $155 for black and white. ($75 + $20 + $60)
b. $885 for colour. ($75 + $20 + $790)
Reflective question
Answers will vary. For example, the business would need to get a loan, issue more shares, or abandon the business venture.

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