trial - firefly education · this trial provides you with everything you need to complete an imaths...

How to do Investigations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Teacher Book pages

Trial

Chris Linthorne | Carolyn Smales | Wayne Lightbourne | Jane Rheeder

06/15

iMaths 4 Trial

Copyright © Firefl y Education 2015 2

The iMaths PackageiMaths is an investigation-based numeracy program written for the Australian Curriculum. The iMaths 4 program has four major components – Student Book, Teacher Book, Tracker Book and iMaths Online.

Student Book• 12 Investigations with easy instructions

• 55 Topics that cover the three content strands

• Challenges to cater for fast fi nishes

• Problem Solving Strategies and Tasks

• Mental Computation Strategies and practice

• Data and Tear-out pages for the Investigations

Teacher Book• Notes, solutions and strategies for each Investigation

• An A–E rubric for each Investigation

• Answers to Student Book Topics and Problem Solving Tasks

• Answers to Tracker Book assessment items

• Access to the iPlanner electronic planning tool

Tracker Book• A readiness test to assess prior maths knowledge

• Assessment items for each Topic in the Student Book

• Working pages for Problem Solving Tasks

• A Student Assessment Profi le

iMaths OnlineiMaths Online can be found at imathsonline.com.au and provides all the digital resources needed to teach, plan and assess the iMaths program.

• iPlanner electronic planning tool

• Differentiation tasks – 3 levels

• Interactive maths games for students

• Interactive teaching tools

• Projectable Student Book pages and answers

• Projectable Tracker Book answers

• Tear-outs, Data pages, BLMs and Rubrics

• Access for students to imathskids.com.au

iMaths Online

iMaths 4 Trial


Getting started with your iMaths TrialThis trial provides you with everything you need to complete an iMaths Investigation.

In this pack you will fi nd excerpts from the iMaths Teacher, Tracker and Student Books and these will need to be used in conjunction with iMaths Online. At iMaths Online you will fi nd a range of projectable, printable and interactive tools.

Have fun discovering iMaths Investigations with

your students!

Trial tips:To get the most out of your iMaths Trial, follow these simple steps:

1. Watch the short tutorials at fi refl yeducation.com.au/pd, especially iMaths Investigations, iMaths Differentiation and iMaths Assessment. Also check out the iMaths Online Virtual Tour. You will fi nd these under the program tab when you log in.

2. Read the ‘Using the program’ pages at the beginning of this Trial Pack. These pages tell you all you need to know about conducting an iMaths Investigation with your class.

3. Print the Investigation pages from the Student Book and the Tracker Book pages for each student as needed. Log in to iMaths Online to explore all your Investigation resources

5. Students can access imathskids.com.au with the Student Access Code found in your Firefl y Account at iMaths Online.

iMaths 4 Trial


Teacher Book Pages Page

Using the programHow to do Investigations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5

Assessing the Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7

Assessing the Investigations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8

Differentiation Tasks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

iMaths Teacher Book pagesInvestigation Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Topic Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Challenge Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Problem Solving Task Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Tracker Book Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Want More? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Student Book and Tracker Book pages Page

iMaths Student Book pages Investigation 1 Ripper rides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2

iMaths Tracker Book pagesNA23 Equivalent fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4

NA33 Investigating patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5

MG12 Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6

MG13 Area of irregular shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7

MG14 Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8

MG16 Tessellation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9

Contents

iMaths 4 Trial Using the program – How to do Investigations

© Chris Linthorne, Carolyn Smales, Wayne Lightbourne and Jane Rheeder, Firefl y Education 2013 56 iMaths 4 Teacher Book ISBN 978 1 74135 172 9

Introduction to iMaths

6 iMaths 4 Teacher Book ISBN 978 1 74135 243 6

8 iMaths 4 Student Book ISBN 978 1 74135 179 8

Understanding the Investigation1 Read and plan.

Make sure you understand the meanings of: Australian market, company, range, geometric, colour scheme, deck designs, regular, guidelines, patterned, enlarge, overlapped, represent, design elements and solid colour.

Read and discuss the rubric.

Download your Investigation plan. This will help you with the organisation and understanding of the Investigation.

Topics Before you start the Investigation you need to know…

Investigation 1Ripper rides

MG13 Area of irregular shapes ...................... p126

MG14 Angles .................................................... p128

MG16 Tessellation ............................................ p132

NA23 Equivalent fractions .................................p76

NA33 Investigating patterns .............................p96

MG12 Area ....................................................... p124

Teacher note• Comprehensive lesson notes,

suggestions and resources are available in iMaths 4 Teacher Book.

• The BLMs and Investigation plan for this Investigation can be downloaded from imathsonline.com.au.

The iBoards Company is coming to the Australian market. iBoards is famous for making surfboards, skateboards and snowboards.

The company is looking for a talented young designer to create some exciting deck designs for its new Aussie iBoard range.

There are strict guidelines for design – each deck must have no more than 3

4 of its surface covered by design and no less than 1

4 of its surface covered by one solid colour. Investigate a way to prove that your pattern covers as close as possible to 3

4 of the board.

The designs must be geometric and consist of a specific set of lines and shapes.

Get designing!

How to do InvestigationsInvestigation notesOn the opening pages of the Investigation notes, the About the Investigation text provides you with a brief snapshot of the purpose of the Investigation. The Planning the Investigation text tells you the duration of the Investigation, the suggested group size and the resources needed.

When presenting the Investigation to the class, use the introductory text and photo in the Student Book to give students an insight into the context of the Investigation and whet their appetite. Discuss how the listed Topics fit into the Investigation. Discussing the Topics with students will give them a connection to real life problems and establish the context.

1 Introducing the Investigation

You can teach the Topics before your students start the Investigation or as the need arises throughout. However, teaching the Topics to your students before they begin will help them to successfully and more independently complete their Investigation.

2 Teaching the Topics

You can assess the Topics at any time using the relevant Tracker Book pages. However, you will get a more valid indication of students’ knowledge and understanding if you assess the Topics at the conclusion of the Investigation. While doing the Investigation, students will develop a deeper understanding and improve their knowledge of the Topics.

3 Assessing the Topics

After teaching the Topics, it’s time to return to the Investigation. At this stage, students need to form groups, read and discuss what their task is and plan how they are going to do it. The teacher should monitor this discussion and make sure the students have a clear understanding of the task.

Students should download a copy of the Investigation plan from imathskids.com.au and write up their plan. Alternatively, you can download a copy for them from imathsonline.com.au.

Discuss the meaning of the words in the vocabulary list. Students should be familiar with these maths and everyday terms in order to understand the instructions and the questions in each step of the Investigation.

5 Planning the Investigation

Download a copy of the rubric from imathsonline.com.au and print one for each student. Have students read through the rubric. Discuss the criteria in the Ability to… column, and have students match each of the criteria to the steps of the Investigation by completing the Step column.

The rubric should be revisited during and after the Using maths steps, and during the Reasoning and reporting step.

4 Discussing the Rubric

iMTB_N4 - BOOK.indb 6 21/03/14 4:11 PM

iMaths 4 Trial Using the program – How to do Investigations

© Chris Linthorne, Carolyn Smales, Wayne Lightbourne and Jane Rheeder, Firefl y Education 2013 6ISBN 978 1 74135 172 9 iMaths 4 Teacher Book 7

ISBN 978 1 74135 243 6 iMaths 4 Teacher Book 7

ISBN 978 1 74135 179 8 iMaths 4 Student Book 9

Materials

Inve

stig

atio

n 1Materials

Internet access

InquiryInvestigate and list 5 reasons why boards come in so many diff erent shapes, sizes, designs and materials.

Guidelines for board designThe board design must include:• 2 small triangles• 2 medium triangles• 2 large triangles• 6 horizontal lines• 6 vertical lines• 3 sets of parallel lines• 4 intersecting lines• an interesting shape that will

tessellate at least 8 times• an unusual shape that is fl ipped

or refl ected• an acute, right and obtuse angle.

2 Look at other board designs.Look at the size and shape of surfboards, skateboards and snowboards. Examine the deck patterns. Are there any with geometric patterns?

Choose your favourite board type and print out the appropriate template from BLMs 1.1–1.3. Keep in mind that only 3

4 of the board will be patterned. You may need to enlarge the board template toA3 so you have a bigger design space.

Using maths3 Calculate 3

4 of the board.Use the appropriate blank board shape (BLMs 1.1–1.3) to investigate a method to find 1

4 of the area of your board.

Once you have 14 , it should be easy to find 3

4 . The area you find will be your design space.

4 Plan and draw your design. Read the guidelines in the box to the right. Experiment with designs that meet the guidelines. Arrange the geometric pattern to cover 3

4 of the board.

When you are happy with your design plan, carefully draw it onto the outline of your board.

Name your creation.

Reasoning and reporting5 Find the most popular, accurate design. Make a class display of all designs. Group the

boards by type.

Explain how you have included all the geometric design elements that were required.

Prove that 14 of your board has been left blank

for the solid colour.

Choose the three boards you would select to submit to iBoards.

Give reasons for your choices.

Go to imathskids.com.au – the Investigation 1 area contains the Investigation plan, websites and BLMs that you need to complete this Investigation.

BLMs 1.1–1.3ISBN 978 1 74135 179 8 iMaths 4 Black Line Masters © Carolyn Smales, Wayne Lightbourne and Jane Rheeder 2011 Firefly Education Pty Ltd

BLM 1.3 Investigation 1: Ripper rides

Board shapes: Snowboard

ISBN 978 1 74135 179 8 iMaths 4 Black Line Masters © Carolyn Smales, Wayne Lightbourne and Jane Rheeder 2011 Firefly Education Pty Ltd

Investigation 1: Ripper ridesBLM 1.2

Board shapes: Skateboard

BLM 1.1


Investigation 1: Ripper rides

Board shapes: Surfboard

Inve

stig

atio

n 1

Paints RulerColoured pencils

iSurf

Surf, skate or snowboard magazines

Many of the tasks in the Investigation will be done as a class or in small groups. However, in order to discriminate between students, the tasks in the last step should be individual tasks. Sometimes this will take the form of a written report, but sometimes it will be easier to ask each student to share their understanding orally. How students answer the Communicating and reflecting questions should be a good indicator of how well they can demonstrate their understanding and apply the higher-order thinking skills of generalising, justifying and evaluating.

10 Assessing individuals

The last step is the reasoning part of the Investigation. This is the most important step. Here students have the opportunity to reflect on their results, and describe and explain the processes, generate inferences, make generalisations and evaluate their answers. They are also required to communicate their findings and justify their results or decisions.

In the Investigation notes for each Investigation, you will see a list of questions under the heading Communicating and reflecting. You can use these questions: • when conferencing with individual students about the results

of their Investigation • as a guide to what a written response should contain.

9 Reasoning and reporting

In this part of the Investigation, students should apply their knowledge of mathematics and strategies, which they have learned by doing the Topics. This is where students enhance their fluency and understanding of the content. By applying their knowledge, students will develop a deeper understanding of the Topics. In this section, students will usually encounter a situation in which they have to apply the problem solving strategies they have learned and practised in the Student Book.

Using maths8

iMaths Online is where you will find Differentiation tasks, Black Line Masters, websites relevant to each Investigation, projectable Student Book pages and much more. To start using these teacher resources, sign up at imathsonline.com.au using the Access Code on the front inside cover of this Teacher Book.

Once you have signed up to iMaths Online you will receive another Access Code for your students to use to log in to imathskids.com.au, the dedicated student portal to iMaths Online. Ask your students to write the Access Code on the title page of their Student Book. At imathskids.com.au students can download Tear-outs, Data pages and Black Line Masters for the Investigations, access relevant websites and play interactive maths games.

Only websites that are most suitable and relevant to the Investigations are linked through iMaths Online. This avoids students wasting time searching through inappropriate websites to find simple facts.

Accessing iMaths Online7

Encourage students to discuss what they already know and explore ways to find out more.

Help them search for more information about the subject of the Investigation and explore the maths concepts and strategies needed to conduct it.

6 Getting Started


iMaths Online is where you will fi nd Differentiation tasks, Black Line Masters, websites relevant to each Investigation, projectable Student Book pages and much more. To start using these teacher resources, sign up at imathsonline.com.au.

Once you have signed up to iMaths Online you will receive another Access Code for your students to use to log in to imathskids.com.au,the dedicated student portal to iMaths Online. Ask your students to write the Access Code on the title page of their Student Book. At imathskids.com.au students can download Tear-outs, Data pages and Black Line Masters for the Investigations, access relevant websites and play interactive maths games.

Only websites that are most suitable and relevant to the Investigations are linked through iMaths Online. This avoids students wasting time searching through inappropriate websites to fi nd simple facts.

Accessing iMaths Online7

iMaths 4 Trial Using the program – Assessing iMaths

© Chris Linthorne, Carolyn Smales, Wayne Lightbourne and Jane Rheeder, Firefl y Education 2013 7

/ /Date

Know

+

Apply

=

Total

Apply

Apply

NA33 Investigating patterns

For each pattern, complete the table of values to the 5th term, describe the change using a rule, then continue the table of values to the 10th term.

a Triangle matchstick pattern (5 marks)

Term 1 2 3 4 5 6 7 8 9 10

Number of matchsticks 3

b Triangle and square matchstick pattern (5 marks)

Term 1 2 3 4 5 6 7 8 9 10

Number of matchsticks 4

Know

56 iMaths 4 Tracker Book ISBN 978 1 74135 185 9

The student’s score out

of 10 is recorded and

dated.

Topic

The Apply questions assess

higher-order thinking skills

and application of knowledge

and understanding.

The Know questions

assess recall and

basic application of

knowledge.

Assessing the TopicsThe two main ways for students to formally demonstrate their learning in iMaths are by completing –

1 all the assessment items in the Tracker Book

2 the Investigations from the Student Book.

Assessing the Topics – iMaths Tracker BookThe Tracker Book contains a set of assessment items for each Topic in the Student Book. These items assess the descriptions in the content strand and are divided into two groups – Know and Apply. The Know questions assess the student’s basic understanding of the concept, while the Apply questions assess the application of their knowledge in often novel situations.

The example page below from iMaths 4 Tracker Book is for Topic NA33 Investigating patterns.

After the questions have been marked, the scores for the Know and Apply items can be tallied and entered in the score boxes at the bottom of the page.


© Chris Linthorne, Carolyn Smales, Wayne Lightbourne and Jane Rheeder, Firefly Education 2013 8

Assessing the Investigations Investigations are the core of the iMaths program. They provide the context to which students apply their knowledge and understanding of the content. The iMaths Investigations build and develop a student’s understanding of the maths concepts, improve their mathematical fluency and problem solving skills, and provide real-life contexts in which they can develop higher-order reasoning.

The rubrics, which are provided for each Investigation, assess all of the above proficiency skills.

Each rubric lists the criteria used to evaluate student performance at each step of the Investigation. These criteria are further described in five achievement standards (A to E).

Why use a rubric?For teachers, a rubric – •clarifiesexactlywhatisbeingassessed •helpsdefinewhatisexpectedineachoftheA–Estandards •documentsthedecisionsmadewhenevaluatingstudentwork •assiststeachersinbeingobjective,fair,transparentandconsistent.

For students, a rubric – •clearlydefinesthecriteriaonwhichtheirworkwillbejudged •helpsthembecomebetterjudgesofthequalityoftheirownwork •providesfeedbackonhowtoimprovetheirperformance.

For parents, a rubric – •clearlyexplainsteacherexpectations •providesaclearerunderstandingofthetasks •providesanindicationoftheirchild’sperformance.

How to use a rubric1 The rubrics are found at the end of each Investigation in the Teacher book or can be

downloaded at imathsonline.com.au.

A copy of the rubric should be given to students at the beginning of the Investigation. Discuss the criteria in the Ability to… column and have students identify which step of the Investigation they are describing by filling in the Step column in the rubric.

2 The rubrics are best annotated during the Investigation, but can be finalised after the students submit their folios.

3 Mark or highlight the descriptor or parts of the descriptor that best indicates the student’s performance.

How to tally the results1 Criteria in the Ability to… column are not equally important. The questions in the

Communicating and reflecting section of the Investigation are generally used to assess the Reasoning step. These criteria are significantly more difficult and should have a greater weighting than the others in the rubric, as they generally involve reflecting on learning, making generalisations, justifying decisions and other higher-order thinking skills. You will get a more valid assessment of student performance if the tasks in this step are completed individually.

2 After marking or highlighting the rubric, you will need to make a judgment on the student’s overall performance for that Investigation. In the example on the opposite page, the criteria in the Reasoning rows have been given extra weight and the teacher has decided that the overall result is more appropriately a B.

The teacher reasoned that the previous criteria were assessing tasks that have been done in a group, and the student submitted work that may have had the benefit of peer tutoring. A B standard is a true indication of the student’s real understanding.


© Chris Linthorne, Carolyn Smales, Wayne Lightbourne and Jane Rheeder, Firefl y Education 2013 9

ISBN 978 1 74135 172 9

iMaths 4 Teacher Book 27

Investigation 1

ISBN 978 1 74135 243 6


Rubric

Overall rating

Teacher comments

Name: Due date:

Step Ability to... A B C D E

Profi

cien

cy s

tran

ds

Und

erst

andi

ng, F

luen

cy a

nd P

robl

em S

olvi

ng

Calculate 34 of the

area of the board.Independently found and used an efficient method to identify 3

4 of the board.Accurately counted both whole and part squares.

Needed prompting to find the most efficient way to find 3

4 of the board.Made very few errors when counting the whole and part squares.

Used a simple method to divide the board into 4 equal parts.Counted the whole squares but needed help to accurately count the part squares and find 3

4 .

Needed teacher guidance to find a way to divide the board into 4 equal parts.Counted the whole squares but was unable to include the part squares to find 3

4 .

Could not find a way to divide the board into equal parts.Counted an estimated number of whole squares only.Did not count any part squares.

Plan a board design using all of the required geometric elements.

Independently used all the geometric elements accurately to draw a plan of the design.Formed a complex and visually appealing pattern.

Needed prompting to use all the geometric elements to draw a plan of the design.The elements formed a clearly defined pattern.

Needed some help to use all the geometric elements to draw a plan of the design.The elements formed a simple, uncomplicated pattern.

Needed teacher guidance to use all the geometric elements in the design plan.The elements formed a very basic pattern.

Did not understand what the geometric elements looked like.The design was random with no clear pattern.

Transfer the design onto a template of a board.

Transferred the design plan neatly and accurately onto the template.

Was able to fix any problems identified when transferring the design plan onto the template.

Made some errors when transferring the design plan onto the template.

Had difficulty transferring the design plan accurately onto the template.

The final result was untidy and did not contain the geometric elements.

Reas

onin

g

Explain the design. Used clear, concise and appropriate mathematical terms to explain the elements of the board design.

Described the elements of the design clearly. Made only minor errors when using mathematical terms to describe the pattern.

Gave a simple description of the elements of the design.Made some errors when using mathematical terms to describe the pattern.

Described some of the elements of the design, but did not always use the correct mathematical terms when describing the pattern.

Did not understand what the geometric elements looked like and was therefore unable to describe the design elements.

Prove that 14 of the

board has been left blank for a solid colour.

Gave a clear and detailed description of an efficient method used to calculate 1

4 of the board.

Described a reasonable method for calculating 1

4 of the board.Gave a simple description of the method used to calculate 14 of the board.

Had difficulty describing the method used to calculate 1

4 of the board.

Was unable to describe the method used to calculate 1

4 of the board.

Justify the choice of the best three board designs. Explain how the elements combined to form an appealing and well balanced design.

Gave well reasoned and detailed arguments for their choice of the best three designs.

Briefly described why the elements on the three boards chosen combined to form an appealing and well balanced design.

Gave a simple explanation of the elements which helped them choose the best three designs.

Reasons for choosing the best three designs did not always relate to the elements.

The reasons for choosing the three best designs were confused and unrelated to the design elements.

Investigation 1 Ripper rides

iMTB_N

4 - BOO

K.indb 2721/03/14 4:12 PM

Harry Grey

B

The highlighted areas on this rubric show

the result of the student’s performance

in the Understanding, Fluency, Problem

Solving and Reasoning components of the

Profi ciency strands.

Teachers look at the highlighted sections and use their judgment to decide on an overall level of achievement. (A–E)

an efficient method to identify 4of the board.Accurately counted both whole and part squares.

Independently found and used an efficient method to identify 3

4


Transferred the design plan

elements on the three boards chosen combined to form an appealing and well balanced design.

Briefly described why the elements on the three

The elements formed a clearly defined pattern.

Gave a clear and detailed description of an efficient method used to calculate 1

4of the board.

Independently used all the geometric elements accurately to draw a plan of the design.

Used clear, concise and appropriate mathematical terms to explain the elements of the board design.



Teachers look at the highlighted sections and use their judgment to decide on an overall level of achievement. (A–E)

Investigation 1

ISBN 978 1 74135 243 6


Rubric

Overall rating

Teacher comments

Name: Due date:

Step Ability to... A B C D E

Profi

cie

ncy

stra

nds

Und

erst

andi

ng, F

luen

cy a

nd P

robl

em S

olvi

ng

Calculate 34 of the

area of the board.Independently found and used an effi cient method to identify 3

4 of the board.Accurately counted both whole and part squares.

Needed prompting to fi nd the most effi cient way to fi nd 3

4 of the board.Made very few errors when counting the whole and part squares.

Used a simple method to divide the board into 4 equal parts.Counted the whole squares but needed help to accurately count the part squares and fi nd 3

4 .

Needed teacher guidance to fi nd a way to divide the board into 4 equal parts.Counted the whole squares but was unable to include the part squares to fi nd 3

4 .

Could not fi nd a way to divide the board into equal parts.Counted an estimated number of whole squares only.Did not count any part squares.

Plan a board design using all of the required geometric elements.

Independently used all the geometric elements accurately to draw a plan of the design.Formed a complex and visually appealing pattern.

Needed prompting to use all the geometric elements to draw a plan of the design.The elements formed a clearly defi ned pattern.

Needed some help to use all the geometric elements to draw a plan of the design.The elements formed a simple, uncomplicated pattern.

Needed teacher guidance to use all the geometric elements in the design plan.The elements formed a very basic pattern.

Did not understand what the geometric elements looked like.The design was random with no clear pattern.

Transfer the design onto a template of a board.


Was able to fi x any problems identifi ed when transferring the design plan onto the template.

Made some errors when transferring the design plan onto the template.

Had diffi culty transferring the design plan accurately onto the template.

The fi nal result was untidy and did not contain the geometric elements.

Reas

onin

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Explain the design. Used clear, concise and appropriate mathematical terms to explain the elements of the board design.

Described the elements of the design clearly. Made only minor errors when using mathematical terms to describe the pattern.

Gave a simple description of the elements of the design.Made some errors when using mathematical terms to describe the pattern.

Described some of theelements of the design, but did not always use the correct mathematical terms when describing the pattern.

Did not understand what the geometric elements looked like and was therefore unable to describe the design elements.

Prove that 14 of the

board has been left blank for a solid colour.

Gave a clear and detailed description of an effi cient method used to calculate 1

4 of the board.

Described a reasonable method for calculating 1

4 of the board.Gave a simple description of the method used to calculate 14 of the board.

Had diffi culty describing the method used to calculate 1

4 of the board.

Was unable to describe the method used to calculate 1

4 of the board.

Justify the choice of the best three board designs. Explain how the elements combined to form an appealing and well balanced design.

Gave well reasoned and detailed arguments for their choice of the best three designs.

Briefl y described why the elements on the three boards chosen combined to form an appealing and well balanced design.

Gave a simple explanation of the elements which helped them choose the best three designs.

Reasons for choosing the best three designs did not always relate to the elements.

The reasons for choosing the three best designs were confused and unrelated to the design elements.

Investigation 1 Ripper rides Harry Grey

B

How to read the rubrics It is important that you and your students know what is expected for each standard.

An A student will not only submit work that is totally error free, but will have used a method that was quick and efficient. It is entirely possible that a B or C student submits work that is error free, but they will have used a more time consuming and less efficient method. Students who are at an A standard will show flair and creativity in the ways they approach a problem. Look out for that.

A students will also complete tasks independently, without any help at all from their teacher or peers.

B students will generally use a workable method, but will need prompting to find a more efficient way. If you notice a student is doing something in a slow and laborious way and you mention it to the student, if they are a B student, they should be able to improve their own processes and fix their own mistakes.

C students, on the other hand, will need your help to complete tasks. The teacher will have made some suggestions as to how the student can approach the task, and helped them to correct

any mechanical errors along the way. However, the end result will often be error free. Therefore, it will be the process that is a C standard rather than the result.

D students will need teacher guidance at every step of the task.

E students will not have understood the concept at all or have failed to complete the task.

How to give an overall A–E ranking to each studentAt the end of each term or semester, you will end up with a range of assessment results, including rubrics, Tracker Book results, and any other tests that you may have designed and administered.

These items will form the student’s personal folio. From this bank of evidence, teachers will use their knowledge of the student and their judgment to give each student an overall A–E ranking in maths.

The highlighted areas on this rubric show

the result of the student’s performance

in the Understanding, Fluency, Problem

Solving and Reasoning components of the

Proficiency strands.


iMaths 4 Trial Using the program – Differentiation Tasks

© Chris Linthorne, Carolyn Smales, Wayne Lightbourne and Jane Rheeder, Firefl y Education 2013 10ISBN 978 1 74135 172 9 iMaths 4 Teacher Book 17


Differentiation tasksDifferentiation tasks at three levelsEvery Topic in iMaths 4 has a set of Differentiation tasks which can be used to support, consolidate and extend student learning. Differentiation tasks can be downloaded from imathsonline.com.au.

Task code Purpose Description Ideas for using the tasks

Support

These pages contain carefully structured tasks to provide the developmental sequence for students to understand the Topic concept. These tasks are often presented in a more visual, easy to follow and directed manner.

Can be used for:• remedial exercises for students who have

difficulty with the questions in the Student Book• revision at other times of the year• homework.

Consolidation

The tasks on these pages give students additional practice of the Topic concept. The tasks are sequenced from more basic questions to those that require application of the concept in real-life situations.

Can be used for:• extra questions for consolidating the

concept in the Topic• revision at other times of the year• homework.

Extension

These pages contain tasks that are suitable for students who need further challenge. The questions require a higher level of thinking skills and logical thought.

Can be used for:• students who have completed all the

Your turn questions, the challenge and the problem solving task in the Student Book

• homework.

iMaths 4 Differentiation Tasks

ISBN 978 1 74135 209 2 iMaths 4 Differentiation Tasks © Firefl y Education Pty Ltd 2012

1 Look at the pattern. Each time you add one counter. Complete the pattern.

+1+1

+1+1

+1

1 2 3 4 5

1 +1 2 +1 3 +1 4 +1 5 +1

2 a The rule is add two counters. Complete the pattern using counters.

+2

+2

1 3 5

3 Use your calculator for this pattern.

3 5 7

4 Make this pattern with 4 matchsticks.

add 3 matchsticks add 3 matchsticks

Count the number of matchsticks for each.

4 +3 7 +3

5 Continue this pattern with matchsticks.

3 5+2 +2 +2 +2

6 Use your calculator for this pattern. Start at 2 and add on 4.


You will need a calculator, counters and matchsticks.

b Make your own pattern with counters.

6 10

Support activitiesSimplified Topic content to practise the fundamentals.




For each pattern, complete the table of values to the 5th term, describe the change using a rule, then continue the table of values to the 10th term.

2

Term 1 2 3 4 5 6 7 8 9 10Number of matchsticks 5

3

Term 1 2 3 4 5 6 7 8 9 10Number of counters

5

Term 1 2 3 4 5 6 7 8 9 10Number of matchsticks

Term 1 2 3 4 5 6 7 8 9 10Number of matchsticks 5 9

1

4

Term 1 2 3 4 5 6 7 8 9 10Number of matchsticks

Consolidation activitiesAdditional practice activities for the Topic.




1 Continue this pattern of tables and chairs for the fourth and fi fth terms. Complete the table of values to the 5th term, describe the change using a rule, then continue the table of values to the 10th term.

2 How many tables arranged in a line would be needed to seat 50 people?

3 If the tables were arranged in two lines, how many tables would be needed to seat 50 people?

Draw the tables to show the seating arrangements.

4 A classroom uses trapezoid tables. The students are seated in rows. A single table seats 3 or 4 students.

The tables are arranged in long rows.

If the class has 26 students, how could these tables be arranged? Every student must face the front of the room.

Use the drawing tools in a word processing program to show howthese tables would be arranged.

Term 1 2 3 4 5 6 7 8 9 10Number of chairs 5

Extension activitiesExtended higher-order application of the Topic.

iMTB_N4 - 01 Prelims.indd 17 7/04/14 4:17 PM

iMaths 4 Trial Teacher Book pages – Investigation notes

11© Chris Linthorne, Carolyn Smales, Wayne Lightbourne and Jane Rheeder, Firefl y Education 2013

20 iMaths 4 Teacher Book ISBN 978 1 74135 172 920 iMaths 4 Teacher Book ISBN 978 1 74135 243 6

About the InvestigationAbout the InvestigationAbout the Investigation

Planning the Investigation

This Investigation involves the design of a geometric pattern featuring triangles; horizontal, vertical, parallel and intersecting lines; angles and tessellating and transformed shapes. The Investigation is highly engaging as surfboards, skateboards and snowboards appeal to many students. Students will enjoy investigating various designs to produce a colourful model with a geometric pattern that fits the design brief.

Before starting the Investigation, teach the following Topics…

Topics for this Investigation

NA23 Equivalent fractions


MG12 Area

MG13 Area of irregular shapes

MG14 Angles

MG16 Tessellation

Expected duration of Investigation: 3 to 4 weeks

Recommended group size: 2 to 3 students

Students will need:✩ BLMs 1.1–1.3 – Blank board shapes✩ internet access✩ coloured pencils✩ paints✩ ruler✩ surf, skate or snowboard magazines



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Planning the Investigation

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This Investigation involves the design

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Ltessellating and transformed shapes. The Investigation is highly engaging

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LThe Investigation is highly engaging as surfboards, skateboards and

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Curriculum match for Investigation 1 The table below shows how the Topics in Investigation 1 match the content requirements of the Australian Curriculum.

Content descriptions iMaths 4 Topics

Number and Algebra

Fractions and decimals• Investigate equivalent fractions used in contexts. (ACMNA077) NA23 Equivalent fractions

Patterns and algebra• Explore and describe number patterns resulting from

performing multiplication. (ACMNA081)


Measurement and Geometry

Using units of measurement• Compare objects using familiar metric units of area and

volume. (ACMMG290)

MG12 Area

Shape• Compare the areas of regular and irregular shapes by

informal means. (ACMMG087)

MG12 Area


Location and transformation• Create symmetrical patterns, pictures and shapes

with and without digital technologies. (ACMMG091)

MG16 Tessellation

Geometric reasoning• Compare angles and classify them as equal to,

greater than or less than a right angle. (ACMMG089)

MG14 Angles

The table below shows how students will apply the proficiency strands during each task in this Investigation.

Proficiency strands Investigation 1 criteria

Understanding, Fluency and Problem Solving

Step 3: Calculate 34 of the area of the board.

Step 4: Plan a board design using all of the required geometric elements.

Step 4: Transfer the design onto a template of a board.

Reasoning Step 5: Explain the design.

Step 5: Prove that 14 of the board has been left blank for a solid colour.

Step 5: Justify the choice of boards. Explain how they have included all of the geometric elements that were required.

The content strand descriptions © Australian Curriculum, Assessment and Reporting Authority 2012. This material is reproduced with the permission of ACARA. The extract is from the Australian Curriculum. ACARA neither endorses nor verifies the accuracy of the information provided and accepts no responsibility for incomplete or inaccurate information. You can find the unaltered and most up to date version of this material at http://www.australiancurriculum.edu.au/Home


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Compare objects using familiar metric units of area and

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(ACMMG087)

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ocation and transformation

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Geometric reasoning

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Essential word list Students will need to understand the following terms:

The rubricRead and discuss the rubric. Discuss the criteria and have students identify which step of the Investigation each one is describing. The rubric should be revisited after the Understanding the Investigation stage, both during and after the Using maths stage and during the Reasoning and reporting stage.


✩ Australian market✩ company✩ range✩ geometric✩ colour scheme✩ deck designs✩ regular

✩ guidelines✩ patterned✩ enlarge✩ overlapped✩ represent✩ design elements✩ solid colour

Focus questions• What is this Investigation asking you to do?

• Which Topics are really important to this Investigation?

• What do you think you will be good at?

• What do you think you will need help with?

• Do you understand the meanings of the words on page 8?

1 Read and plan.Read the introductory text and discuss the premise of the Investigation.

Teach the Topics (concepts) that provide the knowledge required to complete the Investigation.

Re-read the introductory text and each step of the Investigation. Discuss any procedures to be used, how data will be organised and how solutions will be communicated.

Discuss new terms in the context of the Investigation.

Read and discuss the rubric. Clarify the criteria to be assessed. This rubric should be revisited throughout the investigative process.

Go to imathsonline.com.au and print a copy of the Investigation plan for each student. Work through the plan as a class, in small groups or individually.

ISBN 978 1 74135 179 8

1 Read and plan.

geometric, colourpatterned, enlarge,

and solid colour. solid colour. solid colour

Download your Investigation plan. This will help you with the organisation and understanding of the Investigation.

Topics Before you start the Investigation you need to know…


MG13 Area of irregular shapes ...................... p126

MG14 Angles .................................................... p128

MG16 Tessellation............................................ p132

NA23

NA33

MG12

Teacher note• Comprehensive lesson notes,

suggestions and resources are available in iMaths 4 Teacher Book.

• The BLMs and Investigation plan for this Investigation can be downloaded from imathsonline.com.au.

The iBoards Company is coming to the Australian market. iBoards is famous for making surfboards, skateboards and snowboards.

The company is looking for a talented young designer to create some exciting deck designs for its new Aussie iBoard range.

There are strict guidelines for design – each deck must have no more than 3There are strict guidelines for design – each deck

3There are strict guidelines for design – each deck

4 of its surface covered by design and no less than 1

4 of its surface covered by one solid colour. Investigate a way to prove that your pattern covers as close as possible to 3to prove that your pattern covers as close as

3to prove that your pattern covers as close as

4 of the board.

The designs must be geometric and consist of a specific set of lines and shapes.

Get designing!


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designer to create some exciting deck designs for

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Fig 1.1 – Blank board shapesFor this part of the Investigation, print some sample copies of the blank board shapes from BLMs 1.1–1.3. Students will choose which board shape they want to use. It is suggested that you enlarge these to A3 size for the students.

Students can visit imathskids.com.au, click on Investigation 1 and follow the links to the websites listed to find pictures of boards and their deck patterns. Encourage students to only use these websites to find samples of board designs. These sites have been carefully selected for their suitability. If students are doing a random search of board designs on the internet, it is advisable to carefully monitor the use of these sites as some designs, especially those on commercially produced skateboards, may be unsuitable for students to view.

Ask students to choose which board they would like to design and enlarge a copy of the blank board shape to A3 for them to use (see Fig 1.1). Some students may prefer to design their own board shape.

2 Look at other board designs.

ISBN 978 1 74135 179 8 iMaths 4 Student Book 9

Inve

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Internet access

Inquiry

shapes, sizes, designs and materials.

Guidelines for board designThe board design must include:• 2 small triangles• 2 medium triangles• 2 large triangles• 6 horizontal lines• 6 vertical lines• 3 sets of parallel lines• 4 intersecting lines• an interesting shape that will

tessellate at least 8 times• an unusual shape that is flipped

or reflected• an acute, right and obtuse angle.

2 Look at other board designs. Look at the size and shape of surfboards, skateboards and snowboards. Examine the deck patterns. Are there any with geometric patterns?

Choose your favourite board type and print out the appropriate template from BLMs 1.1–1.3. Keep in mind that only 3appropriate template from

3appropriate template from

4 of the board will be patterned. You may need to enlarge the board template toA3 so you have a bigger design space.

Using maths3 Calculate 3

4 of the board. Use the appropriate blank board shape (BLMs 1.1–1.3) to investigate a method to find 1Use the appropriate blank board shape (

1Use the appropriate blank board shape (

4 of the area of your board.

Once you have 14 , it should be easy to find 3

4 . The area you find will be your design space.

4 Plan and draw your design.Read the guidelines in the box to the right. Experiment with designs that meet the guidelines. Arrange the geometric pattern to cover 3

4 of the board.

When you are happy with your design plan, carefully draw it onto the outline of your board.

Name your creation.

Reasoning and reporting5 Find the most popular, accurate design. Make a class display of all designs. Group the

boards by type.

Explain how you have included all the geometric design elements that were required.

Prove that 14 of your board has been left blank

for the solid colour.

Choose the three boards you would select to submit to iBoards.


Go to imathskids.com.au – the Investigation 1 area contains the Investigation plan, websites and BLMs that you need to complete this Investigation.

BLM 1.1

Board shapes:

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PaintsColoured pencils

iSurf

snowboard magazines


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LISBN 978 1 74135 179 8 iMaths 4 Student Book

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LiMaths 4 Student Book

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Inquiry

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LInquiryInvestigate and list 5 reasons why

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LInvestigate and list 5 reasons why boards come in so many different

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Lboards come in so many different shapes, sizes, designs and materials.

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Lshapes, sizes, designs and materials.

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L3 sets of parallel lines

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L3 sets of parallel lines4 intersecting lines

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L4 intersecting linesan interesting shape that will

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Lan interesting shape that will tessellate at least 8 times

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Ltessellate at least 8 timesan unusual shape that is flipped

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Lan unusual shape that is flipped or reflected

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Lor reflected• an acute, right and obtuse angle.

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L• an acute, right and obtuse angle.

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Find the most popular, accurate design.

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LFind the most popular, accurate design.Make a class display of all designs. Group the

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LMake a class display of all designs. Group the

Explain how you have included all the geometric

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LExplain how you have included all the geometric design elements that were required.

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Ldesign elements that were required.

of your board has been left blank

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L of your board has been left blank

Choose the three boards you would select to

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LChoose the three boards you would select to


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L Give reasons for your choices.

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Students have been asked to investigate a way to cover 34 of their

chosen board with their pattern. Revise the concept of quarters with the class.

Visually represent 14 , 2

4 , 34 and 4

4 . Brainstorm ways students could divide the board into four equal sections (quarters).

If the board is standing upright, it could be divided roughly into four equal parts by ruling down the centre line and then across the middle, forming a cross.

Because of the irregular shape of the boards, it will be difficult to find equal quarters if students rule all horizontal lines or all vertical lines. Lead students to discover this concept by visual demonstration.

The blank board shapes (BLMs 1.1–1.3) have a superimposed squared grid. In order to determine 1

4 , students should count the total squares that cover the board. Some students might be able to join some part squares to form full squares and adjust the total accordingly. The total then needs to be divided by 4. This number of squares will represent 1

4 . Students should multiply this number by 3 to find 3

4 .

Figs 1.2–1.4 show calculations of the areas of the three blank board shapes, based on the number of grid squares that cover each one. Students may calculate different areas, depending on how they estimate the coverage of partial squares.

Before designing their geometric patterns, students should identify the positioning and shape of the area that their design will cover. This will inform the dimensions of their design.

Encourage students to colour (mask) the 14 area of the board that

won't contain the design. The remaining area will make up the space for their design.

Fig 1.4 – Area of skateboard shape

86 whole squares

4 part squares= approx 2 squares

Total squares = 88

14 = 22 squares

34 = 66 squares

50 whole squares


Total squares = 54

14 = 1312 squares

34 = 4012 squares

Focus question• How could you divide the area of your board into

four equal parts?

Fig 1.2 – Area of surfboard shape

57 whole squares


Total squares = 72

14 = 18 squares

34 = 54 squares

Fig 1.3 – Area of snowboard shape

3 Calculate 34 of the board.


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Lto join some part squares to form full squares and adjust the total accordingly. The total then needs to be divided by 4. This

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Ltotal accordingly. The total then needs to be divided by 4. This . Students should multiply this

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Lboard shapes, based on the number of grid squares that cover each one. Students may calculate different areas, depending on

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Lhow they estimate the coverage of partial squares.

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Lidentify the positioning and shape of the area that their design will cover. This will inform the dimensions of their design.

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Lwill cover. This will inform the dimensions of their design.

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L– Area of surfboard shape

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L– Area of surfboard shape

57 whole squares

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30 part squares

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L= approx 15 squares

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LTotal squares = 72

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L – Area of snowboard shape

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Inve

stig

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n 1


Students have been asked to create a geometric design that will cover 3

4 of their boards. This task therefore is multidimensional.

Students must consider where and how to place all the necessary geometric features, which include:

2 small triangles2 medium triangles2 large triangles (these might look interesting overlapped!)6 horizontal lines6 vertical lines3 sets of parallel lines4 intersecting linesAn interesting shape that will tessellate at least 8 timesAn unusual shape that is flipped or reflected An acute, right and obtuse angle.

Students must also consider the fact that the design must only cover 3

4 of the board.

Encourage thoughtful placement of design elements. Placements must have an aesthetic purpose, and not just occur randomly. Geometric features might make an abstract picture or a symmetrical design. Words or symbols might be formed by lines, angles or shapes. The size and shape of the area left after 1

4 of the board shape has been masked will inform the composition of the design.

Problem solving Students could use the draw a picture or diagram problem solving strategy in the design stage to get a better feel for their overall design.

By drawing a rough sketch first and delineating the 34 of the

board they are going to design, students can more easily see how large or small each geometric design element needs to be.

Rough diagrams should be reworked and discarded until students are happy with the overall concept.

Allow students plenty of time to experiment with the use of the geometric elements listed. Students should think about balance, colour, effect and appeal. Students could use a drawing program, basic shapes in a word processing program or hand draw and colour each element.

Encourage students to reflect on the suitability of their designs and check off each of the required elements. They may like to make several sketches before they decide on the final design. Remind students that their designs may contain elements other than those listed, as long as all the listed elements are included.

Final design The final design could be drawn onto the enlarged board shape template (see Fig 1.5), or transferred onto a solid base of cardboard or plywood. Ply or solid card could be painted a base colour. The design could be drawn and cut out, and then glued onto the ply or solid card.

Encourage students to take care when producing their final designs. They should use a ruler to ensure lines are straight.

Before the creations are named, brainstorm vocabulary associated with surfboards, skateboards and snowboards. From these, the students could name their creation, for example Surf Skimmer, Speed Skate or Snow Swish. Allow students to look at samples of brand names before they choose a name and place it on their design.

Fig 1.5 – Example design

4 Plan and draw your design.

Acute angle

Right angle

Reflected shape

Intersecting lines

Parallel lines

14 area blocked out

Vertical lines

Horizontal lines

Large triangle

Medium triangle

Tessellating pattern

Obtuse angle

Small triangle


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IALPlacements must have an aesthetic purpose, and not just

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LPlacements must have an aesthetic purpose, and not just occur randomly. Geometric features might make an abstract

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Loccur randomly. Geometric features might make an abstract picture or a symmetrical design. Words or symbols might be

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Lpicture or a symmetrical design. Words or symbols might be formed by lines, angles or shapes. The size and shape of the

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Lformed by lines, angles or shapes. The size and shape of the

of the board shape has been masked will

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draw a picture or diagram

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Ldraw a picture or diagram problem

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solving strategy in the design stage to get a better feel for their

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Lsolving strategy in the design stage to get a better feel for their

By drawing a rough sketch first and delineating the

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LBy drawing a rough sketch first and delineating the

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Lboard they are going to design, students can more easily see how large or small each geometric design element needs to be.

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Lhow large or small each geometric design element needs to be.

Rough diagrams should be reworked and discarded until

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LRough diagrams should be reworked and discarded until students are happy with the overall concept.

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Lstudents are happy with the overall concept.

Allow students plenty of time to experiment with the use of the

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LAllow students plenty of time to experiment with the use of the geometric elements listed. Students should think about balance,

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Lgeometric elements listed. Students should think about balance, colour, effect and appeal. Students could use a drawing TR

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program, basic shapes in a word processing program or hand draw and colour each element.TR

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LEncourage students to reflect on the suitability of their designs and check off each of the required elements. They may like to TR

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than those listed, as long as all the listed elements are included.

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LThe final design could be drawn onto the enlarged board

), or transferred onto a solid base

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Black Line Masters

Students should submit: draft design plans for their iBoard

final iBoard design, including all required elements

proof that 14 of the board has been left blank

written statement justifying the selection of three iBoards.

Communicating and reflecting The following questions are designed to help you assess students’ understanding of what they have learned in this Investigation. When conferencing with students about their designs, ask:

• Which of your shapes is tessellating? What properties does it have that allow it to tessellate?

• How could you show or prove that these elements are: parallel, tessellating or reflecting?

• How is your design geometric?

• What method did you use to ensure that 14 of the

board was left?

• How much of the board would 13 be?

• If iBoards was really going to turn one of the student designs into a board, why should they choose yours?

The class will arrange a display of their boards grouped by type. The final product should reflect mathematical accuracy and design appeal.

Students could make a table listing all the geometric design elements that were required.

Students should explain the method they used to ensure only 34 of the board was covered.

As a class or group, students will select three boards to submit to iBoards. Individually, students should offer reasons for these choices.

Making connections Discuss the following questions to encourage students to apply what they have learned in this Investigation to other everyday situations.

• Why do you think skateboards, surfboards and snowboards have designs on them?

• What other items contain pattern designs?

• How do design artists use font and colour to create brand names?

• Which of your favourite logos or designs use geometric patterns?

BLM 1.3


BLM 1.3 Investigation 1: Ripper rides

Board shapes: Snowboard

BLM 1.2


Investigation 1: Ripper ridesBLM 1.2

Board shapes: Skateboard

BLM 1.1BLM 1.1


Investigation 1: Ripper rides

Board shapes: Surfboard

Students who need an extra challenge could be engaged in the following activity, which extends the application of the Topics used in this Investigation.

Investigate and list 5 reasons why boards come in so many different shapes, sizes, designs and materials.

A board manufacturer needs to take into account a variety of conditions, such as:

• the age, size, mass and ability of user• the surf, snow or park conditions• the type of use (speed, leisure, accuracy, tricks, technique etc)• transport requirements (light but strong)• the cost• whether they are mass produced• changing trends and fashions• the need for durability, ruggedness and toughness• the appeal of colour, logo and design.

Inquiry

5 Find the most popular, accurate design.

Black Line Masters can be downloaded from imathsonline.com.au.


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students’ understanding of what they have learned in this Investigation. When conferencing with students about

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LInvestigation. When conferencing with students about their designs, ask:

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Which of your shapes is tessellating? What properties

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LWhich of your shapes is tessellating? What properties does it have that allow it to tessellate?

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Ldoes it have that allow it to tessellate?

How could you show or prove that these elements are:

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LHow could you show or prove that these elements are: parallel, tessellating or reflecting?

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Lparallel, tessellating or reflecting?

• How is your design geometric?

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L• How is your design geometric?

•

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LWhat method did you use to ensure that

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LIf iBoards was really going to turn one of the student designs into a board, why should they choose yours?

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Ldesigns into a board, why should they choose yours?

How do design artists use font and colour to create

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LHow do design artists use font and colour to create

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Which of your favourite logos or designs use

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LWhich of your favourite logos or designs use

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Students who need an extra challenge could be engaged in the

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LStudents who need an extra challenge could be engaged in the following activity, which extends the application of the Topics

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Lfollowing activity, which extends the application of the Topics used in this Investigation.

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Lused in this Investigation.

Investigate and list 5 reasons why boards come in so many

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different shapes, sizes, designs and materials.

A board manufacturer needs to take into account a variety

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L

iMaths 4 Trial Teacher Book pages – Topic answers



Student Book Answers – Topics


76

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1 2 2 4 4 8

1 22 4

4 8

2 3

2 3

6 94 6 8 12

4 66 9

8 12IS

BN 9

78 1

741

35 1

79 8

iM

aths

4 S

tude

nt B

ook

77

Topic NA23

Chal

leng

e

2 Eq

uiva

lent

frac

tions

can

also

be

show

n on

num

ber l

ines

. Co

mpl

ete

each

pai

r bel

ow.

0

=

b

0

Piec

es o

f eig

ht: H

ow m

any

halve

s in

eigh

t pizz

as?

How

man

y qu

arte

rs in

eig

ht o

rang

es?

How

man

y ei

ghth

s in

eigh

t mel

ons?

0

=

a

01 4

4 4 8 8 3 3 6 62 3

3 W

rite

fract

ions

bel

ow e

ach

pair

of fr

actio

n m

odel

s. Th

e fir

st o

ne h

as b

een

done

for y

ou.

ab

c

de

f

1 32 6

0

=

c

0

10 10 2 25 10

Pizz

a to

ppin

gs: L

ist a

ll of t

he tw

o-to

ppin

g pi

zzas

that

can

be

mad

e w

ith h

am, p

inea

pple

, che

ese

and

olive

s.U

se th

e sp

ace

prov

ided

in iM

aths

4 T

rack

er B

ook

to w

ork

out y

our a

nsw

er.

Prob

lem

solv

ing

task

2 8 4 61 2

2 54 10

3 4 6 8

1 49 36

6 92 3

2 81 4


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LTR

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s

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man

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lves i

n ei

ght p

izzas

? H

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any

quar

ters

in e

ight

ora

nges

?

TRIA

LH

ow m

any

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as?

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man

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rs in

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ht o

rang

es?

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L3

3

TRIA

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Writ

e fra

ctio

ns b

elow

eac

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ir of

frac

tion

mod

els.

The

first

one

has

bee

n do

ne fo

r you

.

TRIA

LW

rite

fract

ions

bel

ow e

ach

pair

of fr

actio

n m

odel

s. Th

e fir

st o

ne h

as b

een

done

for y

ou.

TRIA

LTR

IAL

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1

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L1 3

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List

all o

f the

two-

topp

ing

pizz

as th

at c

an b

e m

ade

with

ham

, pin

eapp

le, c

hees

e an

d ol

ives.

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st a

ll of t

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that

can

be

mad

e w

ith h

am, p

inea

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, che

ese

and

olive

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6

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L6

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L6 9

TRIA

L9

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L2

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L2 3

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L3

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L2

TRIA

L2 8

TRIA

L8

Projectable Student Book answers are also available at

imathsonline.com.au






ISBN

978

1 7

4135

179

8

iMat

hs 4

Stu

dent

Boo

k 9

7

Topic NA33

For

each

pat

tern

, com

plet

e th

e ta

ble

of v

alue

s to

the

5th

term

, des

crib

e th

e ch

ange

usi

ng a

rule

, the

n co

ntin

ue t

he ta

ble

of v

alue

s to

the

10t

h te

rm.

Term

12

34

56

78

910

Num

ber o

f sha

pes

2

Prob

lem

solv

ing

task

Tow

n pl

an: T

oy T

own’

s tow

n pl

an a

llow

s a ‘o

ne sq

uare

’ bui

ldin

g to

be

surr

ound

ed

by o

ne sq

uare

of y

ard

in e

ach

dire

ctio

n. T

his g

ives 8

squa

res o

f yar

d.H

ow m

any

squa

res o

f yar

d is

allo

wed

for a

bui

ldin

g th

at is

10

squa

res l

ong?

Use

the

spac

e pr

ovid

ed in

iMat

hs 4

Tra

cker

Boo

k to

wor

k ou

t you

r ans

wer

.

3 4

Chal

leng

eW

hat’

s th

e 15

th t

erm

? W

ithou

t writ

ing

the

11th

, 12t

h, 1

3th

and

14th

term

s, ca

n yo

u pr

edict

the

15th

term

for e

ach

of th

e gr

owin

g pa

tter

ns a

bove

?

96

iMat

hs 4

Stu

dent

Boo

k IS

BN 9

78 1

741

35 1

79 8

Try

this

NA

33

Inv

estig

atin

g pa

tter

ns

Term

12

34

56

78

910

Num

ber o

f cha

irs4

68

1012

Look

at t

he p

atte

rn o

f tab

les a

nd c

hairs

for a

ban

quet

bel

ow.

Ther

e ar

e tw

o m

ore

chai

rs u

sed

in e

ach

term

so th

e ru

le is

‘add

two

chai

rs’.

Usin

g th

is ru

le, t

he n

ext f

ive te

rms a

re 1

4, 1

6, 1

8, 2

0, 2

2.

1 a

Com

plet

e th

e ta

ble

of v

alue

s to

the

5th

term

.

b

Des

crib

e th

e pa

tter

n us

ing

a ru

le.

c

Cont

inue

the

tabl

e of

val

ues t

o th

e 10

th te

rm.

Term

12

34

56

78

910

Num

ber o

f mat

chst

icks

Add

two

chai

rs

Whe

n in

vest

igat

ing

patt

erns

, a ta

ble

may

be

used

to r

ecor

d in

form

atio

n. T

he ta

ble,

cal

led

a ta

ble

of v

alue

s, lis

ts e

ach

term

and

hel

ps to

id

entif

y a

grow

ing

patt

ern.

A gr

owin

g pa

tter

n in

volve

s a

chan

ge b

etw

een

one

term

and

the

nex

t. Th

is c

hang

e ca

n be

de

scrib

ed u

sing

a ru

le. T

he ru

le m

ay t

hen

be

used

to p

redi

ct fu

rthe

r te

rms.

610

1418

2226

3034

3842

add

4 m

atch

stic

ks

14

710

1316

1922

2528

Term

Num

ber

of m

atch

stic

ks1

23

45

67

89

106

912

1518

2124

2730

33

add

3 sh

apes

add

3 m

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ks

add

2 sq

uare

s

Term

Num

ber

of s

quar

es1

23

45

67

89

101

35

79

1113

1517

19

1416

1820

22


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TRIA

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Tow

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man

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LH

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any

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for a

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g th

at is

10

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ong?

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er B

ook

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4

TRIA

L4

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IAL

With

out w

ritin

g th

e 11

th, 1

2th,

13t

h an

d 14

th te

rms,

can

you

pred

ict th

e

TRIA

LW

ithou

t writ

ing

the

11th

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h, 1

3th

and

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term

s, ca

n yo

u pr

edict

the

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IAL

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Inv

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g pa

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ns TRIA

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Inv

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IAL

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23

45

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10

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45

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23

45

67

89

10

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L1

23

45

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10

TRIA

LW

hen

inve

stig

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g pa

tter

ns, a

tabl

e ma

y be

TRIA

LW

hen

inve

stig

atin

g pa

tter

ns, a

tabl

e ma

y be

us

ed to

rec

ord

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rmat

ion.

The

tabl

e, c

alle

d TRIA

Lus

ed to

rec

ord

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rmat

ion.

The

tabl

e, c

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d ta

ble

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ts e

ach

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and

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ps to

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Lta

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of v

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A gr

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one

term

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the

nex

t. Th

is c

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e ca

n be

TRIA

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rm a

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he n

ext.

This

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IAL

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IAL

Term

TRIA

LTe

rmN

umbe

r of

mat

chst

icks

TRIA

LN

umbe

r of

mat

chst

icks

add

3 m

atch

stic

ks

TRIA

Ladd

3 m

atch

stic

ks

add

2 sq

uare

s

TRIA

Ladd

2 sq

uare

s

Term

TRIA

LTe

rmN

umbe

r of

squ

ares

TRIA

LN

umbe

r of

squ

ares

Num

ber

of s

quar

es

TRIA

LN

umbe

r of

squ

ares

1

TRIA

L12

TRIA

L23

TRIA

L34

TRIA

L45

TRIA

L56

TRIA

L61

TRIA

L13

TRIA

L35

TRIA

L57

TRIA

L79

TRIA

L911

TRIA

L1113

TRIA

L13






ISBN

978

1 7

4135

179

8

iMat

hs 4

Stu

dent

Boo

k 1

25

Topic MG12

Chal

leng

e

My

dog

can’

t sw

im. D

o yo

u kn

ow

wha

t I c

alle

d hi

m?

2 W

ork

out t

he a

rea

of e

ach

shap

e, th

en w

rite

the

lett

er th

at

mat

ches

the

answ

er in

the

boxe

s bel

ow.

69

710

125

84

12

Tetr

omin

oes:

Dra

w a

ll the

shap

es th

at h

ave

an a

rea

of fo

ur

squa

res.

If yo

u fli

p or

turn

a sh

ape,

it d

oes n

ot c

ount

as a

noth

er

shap

e. T

here

are

five

to d

raw.

3 Fin

d th

e ar

ea o

f gra

ss a

t the

fron

t of

the

hous

e an

d at

the

back

of t

he h

ouse

.

W

ork

out b

oth

area

s of g

rass

. G

ive y

our a

nsw

er in

num

ber o

f squ

ares

.

cubb

y

gara

geFron

t gr

ass

Bac

k gr

ass

Fron

t gra

ss

Shed

Back

gra

ss

E V

A D

O L

N R

squa

res

squa

res

squa

res

squa

res

squa

res

squa

res

squa

res

squa

res

124

iM

aths

4 S

tude

nt B

ook

ISBN

978

1 7

4135

179

8

Try

this

MG

12 A

rea

To fi

nd th

e ar

ea o

f eac

h 2D

shap

e, c

ount

the

num

ber o

f squ

ares

insid

e th

e bo

unda

ry. T

he a

rea

of th

e sp

otte

d sh

ape

is 7

squa

res.

1 Fi

nd th

e ar

ea o

f eac

h sh

ape.

a Th

e ar

ea o

f sha

pe 1

is

squa

res

.

b Th

e ar

ea o

f sha

pe 2

is

.

c Th

e ar

ea o

f sha

pe 3

is

.

Area

is t

he a

moun

t of

spa

ce

insi

de t

he b

ound

ary

of a

2D

sha

pe. A

squ

ared

grid

is

usef

ul fo

r me

asur

ing

area

. All

the

squa

res

are

the

same

size

an

d th

ey fi

t to

geth

er s

o th

at

ther

e ar

e no

gap

s.

1

2

31

2

3

5

8 sq

uare

s

5 sq

uare

s

LA

ND

RO

VE

R

17 s

qua

res

15 s

qua

res

5 8

9 10

5 6

7 12


TRIA

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IAL

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IAL

69

710

125

84

12

TRIA

L6

97

1012

58

412

69

710

125

84

12

TRIA

L6

97

1012

58

412

69

710

125

84

12

TRIA

L6

97

1012

58

412

69

710

125

84

12

TRIA

L6

97

1012

58

412

69

710

125

84

12

TRIA

L6

97

1012

58

412

69

710

125

84

12

TRIA

L6

97

1012

58

412

69

710

125

84

12

TRIA

L6

97

1012

58

412

Dra

w a

ll the

shap

es th

at h

ave

an a

rea

of fo

ur

TRIA

LD

raw

all t

he sh

apes

that

hav

e an

are

a of

four

sq

uare

s. If

you

flip

or tu

rn a

shap

e, it

doe

s not

cou

nt a

s ano

ther

TRIA

Lsq

uare

s. If

you

flip

or tu

rn a

shap

e, it

doe

s not

cou

nt a

s ano

ther

3

TRIA

L3

TRIA

L F

ind

the

area

of g

rass

at t

he fr

ont o

f

TRIA

LFi

nd th

e ar

ea o

f gra

ss a

t the

fron

t of

the

hous

e an

d at

the

back

of t

he h

ouse

.

TRIA

Lth

e ho

use

and

at th

e ba

ck o

f the

hou

se.

W

ork

out b

oth

area

s of g

rass

.

TRIA

L

Wor

k ou

t bot

h ar

eas o

f gra

ss.

Give

you

r ans

wer

in n

umbe

r of s

quar

es.

TRIA

LG

ive y

our a

nsw

er in

num

ber o

f squ

ares

.

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IAL

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IAL

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IAL

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LgarageTR

IALgaragegarage

TRIA

LgaragegarageTR

IALgarage

TRIA

LFron

t gr

ass

TRIA

LFron

t gr

ass

Fron

t gr

ass

TRIA

LFron

t gr

ass

Fron

t gr

ass

TRIA

LFron

t gr

ass

Fron

t gr

ass

TRIA

LFron

t gr

ass

Fron

t gr

ass

TRIA

LFron

t gr

ass

Fron

t gr

ass

TRIA

LFron

t gr

ass

TRIA

LB

ack

gras

s

TRIA

LB

ack

gras

sB

ack

gras

s

TRIA

LB

ack

gras

sB

ack

gras

s

TRIA

LB

ack

gras

s

TRIA

LTR

IAL

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IAL

Fron

t gra

ss

TRIA

LFr

ont g

rass

Back

gra

ss

TRIA

LBa

ck g

rass

TRIA

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IAL

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IAL

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IAL

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IAL

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IAL

V

TRIA

LV

TRIA

LTR

IALD

TRIA

LD

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IAL

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LTR

IAL

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Lsq

uare

s

TRIA

Lsq

uare

s

TRIA

LTR

IAL

squa

res

TRIA

Lsq

uare

ssq

uare

s

TRIA

Lsq

uare

s

TRIA

LTR

IALsq

uare

s

TRIA

Lsqua

res

squa

res

TRIA

Lsqua

res

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

L

TRIA

LL

A

TRIA

LAN

TRIA

LND

TRIA

LDR

TRIA

LRO

TRIA

LOV

TRIA

LV

17 s

qua

res

TRIA

L17

sq

uare

s15

sq

uare

s

TRIA

L15 s

qua

res

5

TRIA

L5 8

TRIA

L8

10

TRIA

L10





Topi

cs M

G12

–MG

13

ISBN

978

1 7

4135

179

8

iMat

hs 4

Stu

dent

Boo

k 1

27

Chal

leng

e

Topic MG13

Chal

leng

e

Surr

ound

ing

area

: Cal

cula

te th

e ar

ea o

f the

cen

timet

re g

rid a

bove

that

is n

ot c

over

ed b

y yo

ur h

and.

Squ

ares

com

plet

ely

insid

e yo

ur h

and

c

m2

O

ther

com

bine

d sq

uare

s +

cm

2

To

tal a

rea

2 F

ind

the

area

of y

our h

and.

Put

you

r fin

gers

clo

se to

geth

er a

nd p

lace

you

r ha

nd o

n th

is ce

ntim

etre

grid

. Tra

ce a

roun

d th

e ou

tline

then

cal

cula

te th

e to

tal a

rea.

126

iM

aths

4 S

tude

nt B

ook

ISBN

978

1 7

4135

179

8

A ha

lf is

one

par

t of

tw

o eq

ual p

arts

.

Try

this

A sq

uare

cen

timet

re (c

m2 ) h

as a

leng

th

of 1

cm

and

a w

idth

of 1

cm

.

To fi

nd a

reas

onab

le e

stim

ate

of th

e ar

ea o

f an

irreg

ular

shap

e, lik

e Le

af A

bel

ow:

• co

unt t

he n

umbe

r of s

quar

e ce

ntim

etre

s com

plet

ely

insid

e th

e le

af (1

3 cm

2 )

• co

mbi

ne o

ther

par

ts in

to sq

uare

cen

timet

res (

5 cm

2 )

• ad

d to

find

the

tota

l are

a (1

8 cm

2 ).

Leaf

Le

af

1 cm

2

13 c

m2

(1 c

m2 )

(1 c

m2)

(1 c

m2)

(1 c

m2)

(1 c

m2)

AB

1 Fi

nd a

reas

onab

le e

stim

ate

of th

e ar

ea o

f Lea

f B.

a Sq

uare

s com

plet

ely

insid

e th

e le

af

c

m2

b O

ther

com

bine

d sq

uare

s +

cm

2

c To

tal a

rea

Area

is t

he a

moun

t of

spa

ce in

side

th

e bo

unda

ry o

f a 2

D sh

ape.

To

mea

sure

are

a w

e ca

n us

e sq

uare

cen

timet

res

(cm2 ) a

nd

squa

re m

etre

s (m

2 ).A

squa

re m

etre

1 cm

1 cm

1 m

1 m

MG

13 A

rea

of ir

regu

lar

shap

es

7 5 12 c

m2



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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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LTR

IAL

Area

is t

he a

moun

t of

spa

ce in

side

TRIA

LAr

ea is

the

amo

unt

of s

pace

insi

de TR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

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LTR

IAL

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IAL

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IAL

A sq

uare

met

re

TRIA

LA

squa

re m

etre

1 mTR

IAL

1 m

1 mTR

IAL

1 m

1 mTRIA

L1

m

Are

a of

irre

gula

r sh

apes TRIA

L

Are

a of

irre

gula

r sh

apes TRIA

L






ISBN

978

1 7

4135

179

8

iMat

hs 4

Stu

dent

Boo

k 1

29

Topic MG14

Chal

leng

e

a A

n ob

tuse

ang

leb

An

acut

e an

gle

e A

righ

t ang

le

c A

stra

ight

ang

led

An

obtu

se a

ngle

Wha

t do

you

cal

l a s

nail o

n a

boat

?

2 To

solve

the

riddl

e, c

hoos

e fro

m e

ach

pair

of a

ngle

s the

one

that

mat

ches

th

e la

bel.

Writ

e th

e le

tter

from

the

corr

ect a

ngle

in th

e bo

x be

low.

The

firs

t on

e is

done

for y

ou a

s an

exam

ple.

The

othe

r an

gle:

Lab

el th

e ot

her a

ngle

in e

ach

pair

of a

ngle

s abo

ve.

a

b

c

d

e

f

g

h

ab

cd

ef

gh

A

3 Fi

nd e

xam

ples

in th

e cla

ssro

om a

nd a

roun

d th

e sc

hool

of t

he fo

llow

ing

kinds

of a

ngle

s.

a Ri

ght a

ngle

s

b Ac

ute

angl

es (l

ess t

han

a rig

ht a

ngle

)

c O

btus

e an

gles

(mor

e th

an a

righ

t ang

le)

f A

stra

ight

ang

leg

A ri

ght a

ngle

h A

n ac

ute

angl

e

B

A

T

S

I

JP

O

ONB A

KL

S

R

128

iM

aths

4 S

tude

nt B

ook

ISBN

978

1 7

4135

179

8

Try

this

MG

14 A

ngle

s

Whe

n an

y tw

o st

raig

ht lin

es m

eet,

an

angl

e is

form

ed. T

he lin

es a

re c

alle

d ar

ms. T

he p

oint

whe

re t

hey

meet

is c

alle

d th

e ve

rtex

.Th

e am

ount

of t

urn

betw

een

the

arms

ch

ange

s th

e siz

e of

the

ang

le.

The

angl

e at

the

cor

ner

of a

squ

are

is

righ

t an

gle.

1 La

bel e

ach

of th

ese

angl

es a

s a ri

ght a

ngle

, les

s tha

n a

right

ang

le,

mor

e th

an a

righ

t ang

le o

r a st

raig

ht a

ngle

.

a b

c d

Obt

use

angl

esTh

ese

blun

t ang

les a

re m

ore

than

a

quar

ter t

urn.

The

y ar

e m

ore

than

a ri

ght a

ngle

.

Stra

ight

ang

les

Thes

e an

gles

are

hal

f tur

ns

(exa

ctly

two

quar

ter t

urns

). Th

ey a

re st

raig

ht a

ngle

s.

Acut

e an

gles

Thes

e sh

arp

angl

es a

re le

ss th

an

a qu

arte

r tur

n. T

hey

are

less

than

a

right

ang

le.

Righ

t an

gles

Th

ese

angl

es a

re ri

ght a

ngle

s. A

right

ang

le is

also

kno

wn

as a

qu

arte

r tur

n.

vert

exar

m

arm

angl

e

rig

ht a

ngle

less

tha

n a

rig

ht a

ngle

mor

e th

an

a ri

ght

ang

lest

raig

ht a

ngle

SN

AI

LO

R

SS

N

A

LOO

R


TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

Le

TRIA

Le

A ri

ght a

ngle

TRIA

L A

righ

t ang

le

TRIA

LLa

bel t

he o

ther

ang

le in

eac

h pa

ir of

ang

les a

bove

.

TRIA

LLa

bel t

he o

ther

ang

le in

eac

h pa

ir of

ang

les a

bove

.

TRIA

Lc

TRIA

Lc

TRIA

Lg

TRIA

Lg

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

a

TRIA

La

bc

de

fg

h

TRIA

Lbc

de

fg

hb

cd

ef

gh

TRIA

Lbc

de

fg

hb

cd

ef

gh

TRIA

Lbc

de

fg

hb

cd

ef

gh

TRIA

Lbc

de

fg

h

A

TRIA

LA

3

TRIA

L3

Find

exa

mpl

es in

the

class

room

and

aro

und

the

scho

ol o

f the

follo

win

g kin

ds o

f ang

les.

TRIA

L F

ind

exam

ples

in th

e cla

ssro

om a

nd a

roun

d th

e sc

hool

of t

he fo

llow

ing

kinds

of a

ngle

s.

a

TRIA

La

Righ

t ang

les

TRIA

LRi

ght a

ngle

s

TRIA

LTR

IAL

Acu

te a

ngle

s (le

ss th

an a

righ

t ang

le)

TRIA

L A

cute

ang

les (

less

than

a ri

ght a

ngle

)

TRIA

LTR

IAL

Obt

use

angl

es (m

ore

than

a ri

ght a

ngle

)

TRIA

LO

btus

e an

gles

(mor

e th

an a

righ

t ang

le)

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

B

TRIA

LB

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LJ

TRIA

LJ

TRIA

LTR

IALK

TRIA

LK

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LW

hen

any

two

stra

ight

lines

mee

t, an

TRIA

LW

hen

any

two

stra

ight

lines

mee

t, an

an

gle

is fo

rmed

. The

lines

are

cal

led

TRIA

Lan

gle

is fo

rmed

. The

lines

are

cal

led

arms

. The

poi

nt w

here

the

y

TRIA

Lar

ms. T

he p

oint

whe

re t

hey

meet

is c

alle

d th

e TRIA

Lme

et is

cal

led

the TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

vert

ex.

TRIA

Lve

rtex

.ve

rtex

.TR

IAL

vert

ex.

vert

ex.

TRIA

Lve

rtex

.ve

rtex

.TR

IAL

vert

ex.

vert

ex.

TRIA

Lve

rtex

.ve

rtex

.TR

IAL

vert

ex.

vert

ex.

TRIA

Lve

rtex

.Th

e am

ount

of t

urn

betw

een

the

arms

TR

IAL

The

amou

nt o

f tur

n be

twee

n th

e ar

ms

chan

ges

the

size

of t

he a

ngle

.TR

IAL

chan

ges

the

size

of t

he a

ngle

.Th

e an

gle

at t

he c

orne

r of

a s

quar

e is

TRIA

LTh

e an

gle

at t

he c

orne

r of

a s

quar

e is

TRIA

LTR

IAL

righ

t an

gle.TRIA

Lri

ght

angl

e.ri

ght

angl

e.TRIA

Lri

ght

angl

e.ri

ght

angl

e.TRIA

Lri

ght

angl

e.ri

ght

angl

e.TRIA

Lri

ght

angl

e.ri

ght

angl

e.TRIA

Lri

ght

angl

e.TRIA

LTR

IAL

TRIA

LAc

ute

angl

esTRIA

LAc

ute

angl

esTh

ese

shar

p an

gles

are

TRIA

LTh

ese

shar

p an

gles

are

less

than

TRIA

Lle

ss th

an

a qu

arte

r tur

nTRIA

La

quar

ter t

urn.

The

y ar

e

TRIA

L. T

hey

are

less

than

TRIA

Lle

ss th

an

a rig

ht a

ngleTRIA

La

right

ang

le.TRIA

L.TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IALS

TRIA

LSN

TRIA

LNA

TRIA

LAI

TRIA

LIL

TRIA

LL

TRIA

LTR

IAL

TRIA

LI

TRIA

LI

TRIA

L






ISBN

978

1 7

4135

179

8

iMat

hs 4

Stu

dent

Boo

k 1

33

Topic MG16

Chal

leng

eTe

ssel

lati

on li

st: T

here

are

tess

ella

ting

shap

es a

ll aro

und

us. M

ake

a lis

t of t

he te

ssel

latio

ns th

at y

ou fi

nd.

Insid

e, lo

ok fo

r row

s of c

upbo

ards

, dra

wer

s, w

indo

ws a

nd sh

elve

s. Lo

ok fo

r pat

tern

s on

floor

s, w

alls

and

even

ce

ilings

. Out

side,

look

for p

aver

s, pa

ths,

wal

ls, w

indo

ws a

nd th

e ro

of. Y

ou’ll

find

plen

ty m

ore!

3 N

ow tr

y yo

ur h

and

at th

is te

ssel

latio

n. C

ompl

ete

the

scho

ol o

f fish

, ad

d so

me

scal

es a

nd c

olou

r the

com

plet

ed te

ssel

latio

n.

2 Ea

ch o

f the

shap

es in

this

grid

will

tess

ella

te. C

ontin

ue th

e te

ssel

latin

g pa

tter

ns b

y dr

awin

g fiv

e m

ore

of e

ach

shap

e. S

hade

eac

h pa

tter

n in

con

tras

ting

colo

urs.

132

iM

aths

4 S

tude

nt B

ook

ISBN

978

1 7

4135

179

8

Try

this

MG

16 T

esse

llatio

n

Man

y sh

apes

will

tess

ella

te, i

nclu

ding

all t

riang

les a

nd q

uadr

ilate

rals.

Equi

late

ral t

riang

les,

squa

res a

nd h

exag

ons a

re th

e on

ly re

gula

r po

lygo

ns th

at w

ill te

ssel

late

by

them

selve

s.

1 Co

ntin

ue th

is te

ssel

latin

g

patt

ern

until

the

area

is

co

mpl

etel

y co

vere

d.

Tess

ella

tion

is t

he r

epea

ted

patt

erni

ng o

f 2D

shap

es. L

ike

tiles

in a

bat

hroo

m or

thi

s ho

neyc

omb,

tess

ella

ting

shap

es

fit to

geth

er s

o th

at t

hey

cove

r an

are

a co

mplet

ely,

with

no

gap

s or

ove

rlapp

ing

of s

hape

s.

Lang

uage

rem

inde

rA

regu

lar p

olyg

on h

as a

ll sid

es e

qual

and

all a

ngle

s equ

al.

A qu

adril

ater

al is

a 2

D sh

ape

with

four

side

s and

four

ang

les.


TRIA

LTR

IAL

TRIA

LTR

IAL

The

re a

re te

ssel

latin

g sh

apes

all a

roun

d us

. Mak

e a

list o

f the

tess

ella

tions

that

you

find

.

TRIA

L T

here

are

tess

ella

ting

shap

es a

ll aro

und

us. M

ake

a lis

t of t

he te

ssel

latio

ns th

at y

ou fi

nd.

Insid

e, lo

ok fo

r row

s of c

upbo

ards

, dra

wer

s, w

indo

ws a

nd sh

elve

s. Lo

ok fo

r pat

tern

s on

floor

s, w

alls

and

even

TRIA

LIn

side,

look

for r

ows o

f cup

boar

ds, d

raw

ers,

win

dow

s and

shel

ves.

Look

for p

atte

rns o

n flo

ors,

wal

ls an

d ev

en

ceilin

gs. O

utsid

e, lo

ok fo

r pav

ers,

path

s, w

alls,

win

dow

s and

the

roof

. You

’ll fin

d pl

enty

mor

e!

TRIA

Lce

ilings

. Out

side,

look

for p

aver

s, pa

ths,

wal

ls, w

indo

ws a

nd th

e ro

of. Y

ou’ll

find

plen

ty m

ore!

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

3

TRIA

L3

Now

try

your

han

d at

this

tess

ella

tion.

Com

plet

e th

e sc

hool

of f

ish,

TRIA

LN

ow tr

y yo

ur h

and

at th

is te

ssel

latio

n. C

ompl

ete

the

scho

ol o

f fish

, ad

d so

me

scal

es a

nd c

olou

r the

com

plet

ed te

ssel

latio

n.

TRIA

Lad

d so

me

scal

es a

nd c

olou

r the

com

plet

ed te

ssel

latio

n.

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

Man

y sh

apes

will

tess

ella

te, i

nclu

ding

all t

riang

les a

nd q

uadr

ilate

rals.TR

IAL

Man

y sh

apes

will

tess

ella

te, i

nclu

ding

all t

riang

les a

nd q

uadr

ilate

rals.TR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

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LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

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LTR

IAL

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LTR

IAL

TRIA

LTR

IAL

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IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

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LTR

IAL

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LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

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LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

LTR

IAL

TRIA

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IAL

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LTR

IAL

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LTR

IAL

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LTR

IAL

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IAL

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IAL

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IAL

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LTR

IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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IAL

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L

iMaths 4 Trial Teacher Book pages – Challenge answers


Additional answers

iMaths 4 Teacher Book ISBN 978 1 74135 179 8

Challenge answers


Pieces of eight: How many halves in eight pizzas? How many quarters in eight oranges? How many eighths in eight melons?

Answer: 16, 32, 64


What’s the 15th term? Without writing the 11th, 12th, 13th and 14th terms, can you predict the 15th term for each of the growing patterns on page 97 of the Student Book?

Answer: 43 shapes, 48 matchsticks, 29 squares

MG12 Area

Tetrominoes: Draw all the shapes that have an area of four squares. If you flip or turn a shape, it does not count as another shape. There are five to draw.


Surrounding area: Calculate the area of the centimetre grid on page 97 of the Student Book that is not covered by your hand.

MG14 Angles

The other angle: Label the other angle in each pair of angles above.

Answer: a right b obtuse c acute d straight e obtuse f acute g acute h obtuse

MG16 Tessellation

Tessellation list: There are tessellating shapes all around us. Make a list of the tessellations that you find. Inside, look for rows of cupboards, drawers, windows and shelves. Look for patterns on floors, walls and even ceilings. Outside, look for pavers, paths, walls, windows and the roof. You’ll find plenty more!

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Without writing the 11th, 12th, 13th and 14th terms, can you predict the

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LWithout writing the 11th, 12th, 13th and 14th terms, can you predict the 15th term for each of the growing patterns on page 97 of the Student Book?

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L15th term for each of the growing patterns on page 97 of the Student Book?

If you flip or turn a shape, it does not count as another shape.

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LIf you flip or turn a shape, it does not count as another shape.

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LCalculate the area of the centimetre grid on page 97 of the Student Book

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LCalculate the area of the centimetre grid on page 97 of the Student Bookthat is not covered by your hand.

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Lthat is not covered by your hand.

Label the other angle in each pair of angles above.

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LLabel the other angle in each pair of angles above.

acute

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Lacute d

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Ld straight

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Lstraight e

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Le obtuse

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Lobtuse f

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Lf acute

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Lacute g

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Lg acute

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Lh obtuse

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Lobtuse

There are tessellating shapes all around us. Make a list of the tessellations that you find.

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LThere are tessellating shapes all around us. Make a list of the tessellations that you find. Inside, look for rows of cupboards, drawers, windows and shelves. Look for patterns on

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LInside, look for rows of cupboards, drawers, windows and shelves. Look for patterns on floors, walls and even ceilings. Outside, look for pavers, paths, walls, windows and

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Lfloors, walls and even ceilings. Outside, look for pavers, paths, walls, windows and the roof. You’ll find plenty more!

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Lthe roof. You’ll find plenty more!

Projectable Tracker Book answers are also available at

imathsonline.com.au

iMaths 4 Trial Teacher Book pages – Problem Solving Task answers


Additional answers

ISBN 978 1 74135 179 8 iMaths 4 Teacher Book

Problem solving task answers


Pizza toppings: List all of the two-topping pizzas that can be made with ham, pineapple, cheese and olives.

Answer: ham and pineapple

pineapple and cheese

cheese and olives

pineapple and olives

ham and cheese ham and olives

1 Guess and check 6 Check for relevant or irrelevant information

2 Make a table or chart 7 Find smaller parts of a large problem

3 Draw a picture or diagram 8 Make an organised list

4 Act out the problem 9 Solve a simpler problem

5 Find a pattern or use a rule 10 Work backwards


Town plan: Toy Town’s town plan allows a ‘one square’ house to be surrounded by one square of yard in each direction. This gives 8 squares of yard. How many squares of yard is allowed for a house that is 10 squares long?

Answer: 26 squares of yard

HOUSE

1 Guess and check 6 Check for relevant or irrelevant information

2 Make a table or chart 7 Find smaller parts of a large problem

3 Draw a picture or diagram 8 Make an organised list

4 Act out the problem 9 Solve a simpler problem

5 Find a pattern or use a rule 10 Work backwards

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LCheck for relevant or irrelevant information

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LFind smaller parts of a large problem

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LMake an organised list

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LSolve a simpler problem

Toy Town’s town plan allows a ‘one square’ house to be surrounded by one

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LToy Town’s town plan allows a ‘one square’ house to be surrounded by one square of yard in each direction.

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L square of yard in each direction. How many squares of yard is allowed for a house that is 10 squares long?

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LHow many squares of yard is allowed for a house that is 10 squares long?

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L6 Check for relevant or irrelevant information

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7

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LFind smaller parts of a large problem

8

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LMake an organised list

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L9 Solve a simpler problem

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LSolve a simpler problem

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LFind a pattern or use a rule 10

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L10 Work backwards

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LWork backwards

iMaths 4 Trial Teacher Book pages – Tracker Book answers


Additional answers

iMaths 4 Teacher Book ISBN 978 1 74135 179 8

Tracker Book answersNA23 Equivalent fractionsa 2

8 = 14 b 1

3 = 39 c 2

6 = 13 d 2

3 = 46 e 2

10 = 15

f 24 g 2

6 h 46 i 6

8

j 24

1020

816

13

50100

48

910

714

510

36 20

404

401530


a Term 1 2 3 4 5 6 7 8 9 10Number of matchsticks 3 5 7 9 11 13 15 17 19 21

add 2 matchsticks

b Term 1 2 3 4 5 6 7 8 9 10Number of matchsticks 4 8 12 16 20 24 28 32 36 40

add 4 matchsticks

MG12 Area

a 8 squares b 18 squares c 10 squaresd 9 squares e 15 squares f 9 squaresg 30 squares h 20 squares i 10 squaresj 60 squares


a 6 cm² b 12 cm² c 18 cm²d 10 cm² e 6 cm²

f–j

MG14 Angles

a acute angle b right angle c obtuse angled–f R R

O

A

g 3 h 3 i 2 j Clock hands at 9 o’clock

MG16 Tessellation

a b

c d

e f kitchen floor tiles g a brick wall h a chess board i honeycombj

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L Clock hands at 9 o’clock

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27

WANT TO TALK TO SOMEONE?Let us know if there’s anything we can do to support you. Speak to an education consultant today.

Phone: 07 5445 5749 www.fireflyeducation.com.au/contact

WANT TO FIND OUT MORE?• Download our Australian Curriculum match.

• Take a test-drive of iMaths Online.

• Understand our program better at imaths.com.au.

WANT SUPPORT?• Watch our tutorial videos.

• Read our case studies.

• Book an iMaths Introduction Workshop at imaths.com.au/support.

WANT TO SEE BOOKS?• Order inspection copies to show your team.

• Visit your local bookseller to browse books.

• Take a look at sample pages at imaths.com.au.

Copyright © Firefl y Education 2015

trial - firefly education · this trial provides you with everything you need to complete an imaths...

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