Using Materials

Problem: “Each container has 38 beans (cubes or dollars). There are seven
containers. How many beans are there altogether?”
Set up a materials model of the problem:

Ask the students to think of a way to solve the problem. Get them to explain their
strategies. Move place value materials to model each strategy. These strategies might
include:
“Adding two to each 38 to make seven forties. That makes 280. Take the seven twos away. That makes 266.”
 

Or: “Seven thirties are 210. Seven eights are 56. Two hundred and ten and 56 is 266.”

Provide other examples using materials. Focus on the sharing of strategies and how
they relate to actions on the materials. For example: 8 x 26 might be solved as
(8 x 20) + (8 x 6) (using place value)
or (8 x 25) + 8 (using rounding and compensating [tidy numbers])
or (8 x 30) – (8 x 4) (using rounding and compensating [tidy numbers])
or 2 x 26 = 52, 2 x 52 = 104, 2 x 104 = 208 (multiplying and doubling).
3 x 27 might be solved as (3 x 20) + (3 x 7) or (3 x 30) – (3 x 3) or (3 x 25) + (3 x 2) or  9 x 9. Note that the last strategy is proportional adjustment and involves separating each set of 27 into three nines.

Using Imaging

Shielding: Pose similar problems and mask the place value materials with ice cream
containers. Write the numbers involved on stickies, for example, 6 x 49 = □ can be
modelled as:

Ask the students to image what is happening to the materials as others explain their
strategies. For example, 6 x 49 = (6 x 50) – (6 x 1) (rounding and compensating).
 

Other examples of problems might be:
5 x 68 = ?    4 x 97 = ?     9 x 44 = ?   3 x 99 = ?     7 x 26 = ?
 

Using Number Properties

Increase the size of the numbers involved, thereby requiring the students to
abandon imaging in favour of noticing number properties.
Examples might be:
8 x 179 = ?        3 x 66 = ?         4 x 348 = ?        9 x 83 = ?      6 x 78 = ?
6 x 333 = ?        486 x 5 = ?       4 x 275 = ?        7 x 306 = ?    5 x 999 = ?
 

Independent Activity

To develop their estimation strategies with multiplication, students should play
Multiplication Roundabout (Material Master 6–6(b)).

Financial understanding
This activity emphasises that people’s decisions differ because people have different preferences. Ana’s penfriends have different family situations, so they have different needs and wants, and no one pet is going to suit everybody.
The students are collecting, organising, and analysing information when they match the personal goals of Ana’s penfriends to the pet that would suit them best.
You may need to check that the students know what a penfriend is and the fact that they can be different ages and live in different cities or countries.
As this activity is at the end of the book, you could ask if anyone has recently got a new pet or if anyone has changed their mind, as a result of these inquiry learning activities, as to what kind of pet they would like to have if they could. Discuss the reasons why the students may not be able to have, short or long term, the pets they
would like to have (cost, allergies, limitations of the home environment, time to care for them properly, and so on). Have the students find photographs of people and discuss what pet the people in the story or photo might have and what their limitations might be in terms of being able to care for that pet. There are plenty of stories
and articles available in the School Journal to support this approach. Webquests that involve matching pets to people and environments are also available, for example, the students could search under “choosing a pet” or “choosing a pet + environment”.
Mathematics and statistics
For the activity itself, you need to ensure that the students are able to relate the information given by each penfriend to the table and that they can justify their choices of suitable pets. They also need to be clear on which parts of the information given they need to use to complete the “Total for first year” column.
Further tasks
The students could:
• write about the requirements of characters from a book study and have other students match an appropriate pet to that character
• contact the students in a school or class different from their own in terms of decile, location, size, or geographics and survey what pets those students own, how the pets are different, and why that would be the case
• investigate funding a child overseas or an organisation that supports needy children or adults (that is, people who not only cannot afford pets but who need help themselves to survive).

Social Sciences Links
Achievement objectives:
• Understand how people make choices to meet their needs and wants (Social Studies, level 2)
• Understand how cultural practices reflect and express peoples’ customs, traditions, and values (Social Studies, level 2)
The students could investigate what sort of pets people from other communities have or cannot have. They could then discuss what this might say about those communities, their customs, traditions, and values.

Other Cross-curricular Links
English achievement objective:
Purposes and Audiences: Show a developing understanding of how to shape texts for different purposes and audiences (Speaking, Writing, and Presenting, level 3)
The students could choose one of the characters described and write about what happens when they get their pet. This could also be done as a series of letters between themselves and Ana.
The students could write to or email a relation who doesn’t live nearby and ask them what pet they would like to own if they could, or if the relation is older, what pet they always wanted or enjoyed most when they were growing up.

Answers to Activity

1.

2. a.–b. Answers will vary.
c. Answers will vary. You would need to make sure unexpected costs can be covered. If there is no extra money to spare, then there is no money to save for these possible costs. Also, if all your money goes on your pet, you may grow to resent this.
d. Answers will vary. You will have to come to terms with not getting the pet you’d
really like to get and either get a different pet that you can afford or possibly look
for ways to earn the extra income needed. You might look for ways of helping people who do have the pets you like (this may or may not be paid time).
Reflective questions
• Answers will vary. You need to be aware that pets can suffer in this situation, and if this involves them not getting enough food or time spent on them, this can be very bad for their health or well-being. There are times when the SPCA takes away people’s pets because the pets have been badly neglected.
• You might have to give away your pet; it is not fair to expect your parents or other adults to take over the responsibility for your pets if you get bored.
Final Class Discussion
1. Discussion will vary. People choose to spend their money on pets because they are interested in watching them grow, they like watching them play, they enjoy interacting with them, they value the love, affection, friendship, and company they may get from the animal, and it’s also a way of meeting and talking to other
animal lovers. Remember, too, that most hobbies cost money and many of them have no return other than pleasure.
2. Discussion will vary. It may have given you a better understanding of the costs involved in playing sport, for example, especially at representative level, or in developing another interest or hobby. It may make you spend your money more wisely when buying equipment; you might look at earning some income from
your hobby, or you might decide that the enjoyment and challenges you get are worth the money you spend.
 

Mathematics and statistics
For this activity, the students will need to know that there are about 52 weeks in a year and about 26 fortnights.
Encourage your students to think of the problems in question 1 multiplicatively by asking them for a number sentence that describes each one, for example, earning $5 a week sweeping leaves for 6 weeks can be written as 6 lots of $5 is  or symbolically as 6 x $5 =  .
Students could design a record-keeping notebook or spreadsheet or graph that Oscar (or they) could use to keep track of their income and progress towards their savings goal.
Financial understanding
In this activity, Oscar realises that he has to put in a great deal of effort if he is going to meet his financial goal (Dad’s challenge). This hard work will have many benefits and also some opportunity costs (trade-offs).

Students will realise that personal goals influence financial success or otherwise.
Oscar matches his personal goals and capabilities to his small “odd-jobs” business in order to raise money for the family holiday. This enterprising attribute is very important if people are to manage themselves and reach their potential.
In this activity, students calculate what Oscar could earn if he does odd jobs and they compare what he earns with his savings goal. They also gain an understanding of the importance of planning for personal and financial success.
Question 2 involves trade-offs (also called opportunity costs), that is, what we give up in order to get something else. This concept was developed in The Great Trade-off Game on pages 12–13 of the students’ book.
For question 3, talk about why Oscar has to do some unpaid chores because he’s a part of the family and what those chores might be. Ask: Do you have jobs that you’re expected to do, that you don’t get paid for, but which you do to help make your household function because you’re a member of the family? What are they? Why are those jobs sometimes described as “chores”?
Students may be interested in creating their own odd-jobs business. They could design a flier for their extended family and friends advertising their services. As a class, have them brainstorm a list of the sorts of things students at their age level could do to earn money.
Social Sciences Links
Achievement objective:
• Understanding how people make decisions about access to and use of resources (Social Studies, level 3)
The students could discuss:
– how Oscar will decide if the jobs are worth the effort
– what he will have to know or organise before he makes a decision to take on a particular job (for example, will Uncle Rob provide the car wash equipment?)
– what the different costs and trade-offs are that Oscar must think about (for example, work versus play, work versus homework).
Other Cross-curricular Links
Technology achievement objective:
• Outcome development and evaluation: Investigate a context to develop ideas for potential outcomes. Trial and evaluate these against key attributes to select and develop an outcome to address the need or opportunity. Evaluate this outcome against the key attributes and how it addresses the need or opportunity (Technological Practice, level 3)
Students could develop a local odd-jobs business for themselves by exploring what jobs they could offer to do and whether there would be a market for them.

Answers to Activity

1. a. $30. (6 weeks x $5)
b. $65. (26 x $2.50)
c. $48. (12 weeks x [2 sessions a week x $2] = 12 x $4 = $48)
d. $60. (12 hours x $5)
e. $203. ($30 + $65 + $48 + $60)
2. Answers will vary. Ideas may include loss of time to do other activities, such as playing with his friends.
3. a. $78. (52 weeks x $1.50)
b. Answers will vary. For example, he wouldn’t have that $1.50 to save towards
going to the movies sometime or to buy a snack.

4a.

b. No, he is still $79 short. ($360 – $281 = $79)
c. Suggestions will vary, for example, finding extra odd jobs to do, selling toys he has
grown out of, or saving a bit more of his pocket money.
5. a. $416. ($281 + $135)
b. $56. ($416 – $360)
c. Answers will vary. Ideas may include: practise swimming when he goes to the
pool with his family, ask his dad or another relative to teach him, practise harder during school swimming lessons, or ask Auntie Alison if he can use her pool to practise.
Reflective question
People have different ideas about the balance between work and leisure time. Oscar has to decide whether it is worth spending time and effort during the year earning money to go on a special holiday and have some extra spending money then. He
needs to weigh up the consequences of his decisions and decide what will work for him.

This is a relatively simple game using multiplication facts and rounding and addition skills. Students will need to know that five is commonly rounded to the next 10. They will also need to count by tens to move around the board.

Answers to Activity

A game of multiplication and rounding.

Loopy is a competitive game, so it is important that students of similar proficiency play together. One way to alleviate the competitive element is to deal out the cards so that each student has their own set of cards. For this alternative, a starter card needs to be created that will look something like this example:

The player getting the Start card reads out the fact and turns the card over. Other players search for the answer in their cards, and the first player to call out the answer (provided they have it!) is the next caller, for example:

Then they will read out the fact at the bottom of the card and turn that card over. The first player to turn over all their cards is the winner or, alternatively, play can continue until all players have finished using their cards.
Sets of Loopy cards can easily be made for any particular collection of basic facts. Follow these steps:

Answers to Activity

A game of multiplication