Investigation 10 Radical renovation

94 iMaths 5 Teacher Book ISBN 978 1 74135 173 6

About the Investigation

Planning the InvestigationExpected duration of Investigation: 3 weeks

Recommended group size: Individuals or pairs

Students will need: BLM 10.1 paper or card for frieze craft materials ruler internet access

Topics for this InvestigationBefore starting the Investigation, teach the following Topics…

NA7 Multiplication 3-digit x 2-digit

MG4 Perimeter of rectangles

MG5 Area of rectangles

MG12 Using scale

MG17 Flip, slide, turn

MG18 Enlargement properties of shapes

This Investigation allows students to demonstrate their creativity using colours, lines and shapes. Working in the areas of measurement and geometry, students will create their very own bedroom design using geometric elements.

Investigation 10 Radical renovation

iMTB_N5 - Book.indb 94 3/6/19 1:51 pm

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ISBN 978 1 74135 173 6 iMaths 5 Teacher Book 95

Curriculum match for Investigation 10 The table below shows how the Topics in Investigation 10 match the content requirements of the Australian Curriculum.

Content descriptions iMaths 5 Topics

Number and AlgebraNumber and place value• Solve problems involving multiplication of large numbers

by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies. (ACMNA100)


• Use efficient mental and written strategies and apply appropriate digital technologies to solve problems. (ACMNA291)


Measurement and GeometryUsing units of measurement• Calculate the perimeter and area of rectangles using familiar

metric units. (ACMMG109)MG4 Perimeter of rectanglesMG5 Area of rectangles

Location and transformation• Use a grid reference system to describe locations. Describe

routes using landmarks and directional language. (ACMMG113)

MG12 Using scale

• Describe translations, reflections and rotations of two-dimensional shapes. Identify line and rotational symmetries. (ACMMG114)

MG17 Flip, slide, turn

• Apply the enlargement transformation to familiar two-dimensional shapes and explore the properties of the resulting image compared with the original. (ACMMG115)

MG18 Enlargement properties of shapes

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

Proficiency strands Investigation 10 criteria

Understanding, Fluency and Problem Solving

Steps 2 & 3: Choose a suitable scale and use the grid paper to draw an accurate floor plan of a bedroom, then calculate the area.Step 4: Design a triangular pattern that includes flips, slides and turns. Draw and colour it on the floor planStep 5: Calculate the perimeter of the pattern and show all working.Step 6: Explain where the frieze was to be placed in the room, calculate its length and provide a sample of a geometric pattern.

Reasoning Step 7: Explain the use of flips, slides and turns in the designs and discuss the assumptions that were made when calculating the length of the frieze.

The content strand descriptions © Australian Curriculum, Assessment and Reporting Authority 2015. 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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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.

26 iMaths 5 Student Book ISBN 978 1 74135 180 4

Understanding the Investigation1 Read and plan.

Make sure you understand the meanings of: radical, renovation, frieze, geometric, feature, decorative, actual, combination and represent.

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…

MG12 Using scale .....................................................p106

MG17 Flip, slide, turn ...............................................p116

MG18 Enlargement properties of shapes ............ p118

NA7 Multiplication 3-digit x 2-digit ...........................p44

MG4 Perimeter of rectangles .....................................p90

MG5 Area of rectangles ..............................................p92

Your family has moved into a new home. You are allowed to decorate your bedroom in the colours and design of your choice.

Your room must have a decorative frieze with a geometric pattern around the walls, and a tiled floor with a triangular pattern involving flips, slides and turns in the centre.

Get creative! Investigate which combination of colours and patterns makes for a radical renovation.

Investigation 10Radical renovation

Teacher note• Comprehensive lesson notes,

suggestions and resources are available in iMaths 5 Teacher Book.

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

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 26?

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.

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

radical renovation frieze geometric

feature decorative combination represent




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Fig 10.1 – Example floor plan

Focus questions• What is an appropriate scale for the floor plan?• Why are doors represented on a floor plan with a curved

line?• What are some occupations which might require the use

of floor plans?

For this step of the Investigation, students will each need a copy of BLM 10.1. Students are required to draw the floor plan of a bedroom that measures 6 m x 4 m.

Use the problem solving strategy act out the problem to visually represent the life-size dimensions of the bedroom in the classroom or playground. Use chalk to mark out the size of the bedroom on a concrete area, or use school bags, books or other objects to demarcate the bedroom. This will give students an idea of the size of the bedroom before they start their scale drawing.

Ask students to collect examples of floor plans. Notice how doors and windows are represented. Locate and discuss the scale.

The most appropriate linear scale for students to use is 1 cm on the grid paper represents 25 cm – this is a scale of 1 cm = 25 cm. Show students this format. Using this scale, the length of 4 squares = 1 metre. Therefore, 16 grid squares will cover an area of 1 m2. This scale will give the largest possible plan.

Students should draw their floor plan on BLM 10.1, and show the scale (see Fig 10.1).

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ISBN 978 1 74135 180 4 iMaths 5 Student Book 27

Materials

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Internet access

InquiryChoose one of the following activities:

• include furniture to scale on your floor plan, or

• calculate the amount of paint you would need to paint this room.

Using maths 2 Draw a floor plan. Your bedroom measures 6 m by 4 m. To draw a floor plan

on an A4 centimetre grid, you need to scale your bedroom measurements. Try making 1 cm (the length of one grid square) represent 1 m. You could also try making 1 cm represent 50 cm, or 1 cm represent 25 cm.

What would 1 cm need to represent so that the floor plan will be a suitable size? This will become your scale. Accurately draw the floor plan on BLM 10.1, and show your scale.

3 Calculate the area. How much floor space does your bedroom have?

Calculate the area of your room and write it on the plan. Show your working.

4 Design the pattern using flips, slides and turns. Try out some triangular patterns that may look good on your

tiled bedroom floor. They must include flips, slides and turns. Decide the size of the feature and mark it on the floor plan.

Colour the pattern to make an attractive feature.

5 Calculate the perimeter of the pattern. The tiles of the pattern need a trim that goes all around the

outside of the pattern. To do this, you need to calculate the perimeter of the patterned feature. Show your working. Round the perimeter to the nearest centimetre. Then, use the scale on your plan to work out the actual perimeter in centimetres.

6 Design the frieze. Calculate the actual length of frieze required to create a

border around the room. Record this on the plan. On A4 paper or card, use geometric shapes, flips, slides

and turns to design a 20 cm section of the frieze.

Reasoning and reporting7 Display and explain. Display your floor plan, calculations and frieze design. Explain how you used flips, slides and turns in your designs.

What assumptions did you make about the room to help you calculate the length of the frieze?

Go to imathskids.com.au – the Investigation 10 area contains the Investigation plan, websites and BLM that you need to complete this Investigation.

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Sample triangular patterned feature using fl ips, slides and turns.

Craft materialsPaper or card

for friezeBLM 10.1ISBN 978 1 74135 180 4 iMaths 5 Black Line Masters © Carolyn Smales, Wayne Lightbourne and Jane Rheeder 2011 Firefl y Education Pty Ltd

BLM 10.1 Investigation 10: Radical renovation

Ruler

scale 1 cm = 25 cm



Students must design a triangular pattern using flips, slides and turns to place on the centre of the bedroom floor. Discuss with students the elements that constitute a pattern, for example: repeated shapes, repeated colours, aesthetically pleasing elements.

Students will need to decide on the size of their floor feature and mark it on their floor plan. Encourage them to use colour to make an attractive feature (see Fig 10.2).

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In this step of the Investigation students must calculate the area of the bedroom and write it on their plan on BLM 10.1. Ensure students show correct working when calculating the area of the bedroom.

Area of the bedroom = L x W = 6 m x 4 m = 24 m2

3 Calculate the area.


Fig 10.2 – Example floor pattern



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Modern friezes are strips of paper or tiles used to decorate the walls of a room. Students may bring samples from home. These friezes can run horizontally or vertically. For the purposes of this Investigation, ask students to create a horizontal frieze.

Students must determine the actual length of frieze required to create a border around their room. The actual perimeter of the room is 20 m, however some students may take into account the size and position of doors and windows when calculating the length, depending on where they plan to place the frieze.

Students must determine the height and width of any doors and windows in the room. If they decide to put the frieze at a height that is not above the doors and windows, they will need to subtract the width of the doors and windows in order to find the correct length of the frieze. If the frieze is to be placed at floor height, the length of the frieze will be the perimeter of the room (20 m) minus the widths of any doors. If the frieze is to be placed at ceiling height, the length required will be 20 m.

Students will need to create a 20 cm section of the frieze pattern using geometric shapes, flips, slides and turns (see Fig 10.4). It may be advisable for students to submit a draft pattern before producing a final copy on A4 card.

Students must calculate the perimeter of their pattern. They will need to measure and add the length of every edge around the outside of the feature to find the total. The total will be in centimetres and millimetres.

Students will round the perimeter to the nearest centimetre, then use the scale from Step 2 to find the actual length. To do this they will multiply the distance around the outside of the pattern (perimeter) by the scale. Students must show their working.

Alternatively, students could enclose the pattern with straight lines to find a simple perimeter (see Fig 10.3)

The method students use to find the perimeter will vary depending on the pattern they have drawn.

6 Design the frieze.

5 Calculate the perimeter of the pattern.Fig 10.3 – Example perimeter calculations

Fig 10.4 – Example frieze

Scale: 1 cm = 25 cmPerimeter of pattern: 24 cm

x 25 600 cm

The actual perimeter is 6 m.

Focus questions• What impact does the position of the frieze on the wall

have on your calculations?• Will any object, gap or structure interrupt your frieze?

Discussion starterDiscuss and list some geometric shapes that are suitable for flipping, sliding and turning. Squares, isosceles triangles, pentagons and hexagons are all suitable.

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

Choose one of the following activities:• include furniture to scale on your floor plan, or• calculate the amount of paint you would need to paint this

room.

Example floor plan with furniture

In order to calculate the paint required for the room, students must calculate the area of each wall first, and then add these areas. This will necessitate measuring the floor to ceiling height of their bedroom at home. The standard ceiling height of a residential home is 8 feet (2.4384 metres), however students can round up to 2.5 metres.

Next, the area of each window and the door must be calculated, and subtracted from the total wall area. They then need to multiply the total wall area by the number of coats applied. Students should make allowances for at least two coats of paint.

Students may also have to account for painting the ceiling.

Note: 1 litre of paint will cover approximately 15 m². However, students can check the coverage for a particular type of paint on the label of the can.


&RPPXQLFDWLQJ�DQG�UHÀHFWLQJ�The following questions are designed to help you assess students’ proficiency in reasoning.• How did you use flips, slides and turns in your floor

pattern and wall frieze?• Which factors did you take into account when you

calculated the length of the wall frieze?• What assumptions did you make about the room?• A house plan usually has a scale of 1 cm = 100 cm.

How would the size of a house plan change if the scale was 1 cm = 50 cm?

• How did you calculate the perimeter of the pattern?• How did you calculate the area of the bedroom? • If the bedroom was 1 metre longer, how would this

affect the area?

Students should present their floor plans to the class, explaining their patterns. They must explain how they used flips, slides and turns to create their patterns, pointing out examples of each. Students will have different sized floor plans, depending on the scale they used. The perimeter of the feature will also vary. Check students’ calculations for accuracy.

Students should also be able to identify any assumptions they made about the room when calculating the length of the frieze. These assumptions could include:• the room has a door and windows• the number of windows• the size of windows and door.The friezes would make a great display around the classroom.

7 Display and explain.

Students should submit a floor plan for a bedroom drawn on centimetre grid paper (BLM 10.1). The floor plan must be marked with the following:

• a suitable scale • calculated area of room (including working out) • a triangular flip, slide and turn pattern in the centre of

the floor • calculated perimeter of the pattern • calculated length of wall frieze (including working out)

a 20 cm frieze pattern on an A4 card, using geometric shapes, flips, slides and turns.



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Black Line Masters

BLM 10.1

ISBN 978 1 74135 180 4 iMaths 5 Black Line Masters © Carolyn Smales, Wayne Lightbourne and Jane Rheeder 2011 Firefl y Education Pty Ltd

BLM 10.1 Investigation 10: Radical renovation

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

Notes and strategies




Notes and strategies


Documents

Investigation 10 Radical renovation