Australian Curriculum Mathematics - Measurement and Geometry: Year 5 - Ages 10-11 by Teacher Superstore

RIC-6098 6.9/950

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All material identified by is material subject to copyright under the Copyright Act 1968 (Cth) and is owned by the Australian Curriculum, Assessment and Reporting Authority 2013. For all Australian Curriculum material except elaborations: This is an extract from the Australian Curriculum. Elaborations: This may be a modified extract from the Australian Curriculum and may include the work of other authors. Disclaimer: ACARA neither endorses nor verifies the accuracy of the information provided and accepts no responsibility for incomplete or inaccurate information. In particular, ACARA does not endorse or verify that: • The content descriptions are solely for a particular year and subject; • All the content descriptions for that year and subject have been used; and • The author’s material aligns with the Australian Curriculum content descriptions for the relevant year and subject. You can find the unaltered and most up to date version of this material at http://www.australiancurriculum.edu.au/ This material is reproduced with the permission of ACARA.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Foundation) Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 1) Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2) Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3) Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4) Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5) Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 6)

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School Order# (if applicable):

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AUSTRALIAN CURRICULUM MATHEMATICS RESOURCE BOOK: MEASUREMENT AND GEOMETRY (YEAR 5) Foreword Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5) is one in a series of seven teacher resource books that support teaching and learning activities in Australian Curriculum Mathematics. The books focus on the measurement and geometry content strands of the national maths curriculum. The resource books include theoretical background information, resource sheets, hands-on activities and assessment activities, along with links to other curriculum areas.

r o e t s Bo r e p ok u S Contents

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Format of this book ...................................................................... iv – v

Location and transformation .................................................... 58–115

• UUM – 1

• L&T – 1

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Using units of measurement ......................................................... 2–41 Choose appropriate units of measurement for length, area, volume, capacity and mass (ACMMG108)

Use a grid reference system to describe locations. Describe routes using landmarks and directional language (ACMMG113)

– – – – – –

Teacher information ............................................................................... 2–4 Hands-on activities ................................................................................. 5–8 Links to other curriculum areas .................................................................... 9 Resource sheets .................................................................................. 10–16 Assessment ........................................................................................ 17–18 Checklist .................................................................................................... 19

• UUM – 2

Teacher information ........................................................................... 58–59 Hands-on activities ............................................................................. 60–61 Links to other curriculum areas .................................................................. 62 Resource sheets .................................................................................. 63–69 Assessment ............................................................................................... 70 Checklist .................................................................................................... 71

Calculate the perimeter and area of rectangles using familiar metric units (ACMMG109)

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

– – – – – –

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• UUM– 3

• L&T – 3

Compare 12- and 24-hour time systems and convert between them (ACMMG110) – – – – – –

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Teacher information ........................................................................... 28–29 Hands-on activities .................................................................................... 30 Links to other curriculum areas .................................................................. 31 Resource sheets .................................................................................. 32–38 Assessment ............................................................................................... 39 Checklist .................................................................................................... 40

Shape ........................................................................................ 42–57 Connect three-dimensional objects with their nets and other two-dimensional representations (ACMMG111) – – – – – –

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

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Answers .................................................................................. 41 • Shape – 1

Teacher information ........................................................................... 72–74 Hands-on activities ............................................................................. 75–78 Links to other curriculum areas .................................................................. 79 Resource sheets .................................................................................. 80–92 Assessment ........................................................................................ 93–94 Checklist .................................................................................................... 95

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Teacher information .................................................................................. 20 Hands-on activities ............................................................................. 21–22 Links to other curriculum areas .................................................................. 23 Resource sheets .................................................................................. 24–25 Assessment ............................................................................................... 26 Checklist .................................................................................................... 27

Teacher information .................................................................................. 42 Hands-on activities ............................................................................. 43–44 Links to other curriculum areas .................................................................. 45 Resource sheets .................................................................................. 46–53 Assessment ........................................................................................ 54–55 Checklist .................................................................................................... 56

Answers .................................................................................. 57

– – – – – –

Teacher information .................................................................................. 96 Hands-on activities ............................................................................. 97–98 Links to other curriculum areas .................................................................. 99 Resource sheets .............................................................................. 100–110 Assessment .................................................................................... 111–112 Checklist .................................................................................................. 113

Answers ........................................................................ 114–115

Geometric reasoning .............................................................. 116–133 • GR – 1 Estimate, measure and compare angles using degrees. Construct angles using a protractor (ACMMG112) – – – – – –

Teacher information ....................................................................... 116–117 Hands-on activities ......................................................................... 118–119 Links to other curriculum areas ................................................................ 120 Resource sheets .............................................................................. 121–129 Assessment .................................................................................... 130–131 Checklist .................................................................................................. 132

Answers ................................................................................ 133

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5)

R.I.C. Publications® www.ricpublications.com.au

iii

FORMAT OF THIS BOOK This teacher resource book includes supporting materials for teaching and learning in all sections of the Measurement and Geometry content strand of Australian Curriculum Mathematics. It includes activities relating to all sub-strands: Using units of measurement, Shape, Location and transformation and Geometric reasoning. All content descriptions have been included, as well as teaching points based on the Curriculum’s elaborations. Links to the proficiency strands have also been included. Each section supports a specific content description and follows a consistent format, containing the following information over several pages: • teacher information with related terms, student vocabulary, what the content description means, teaching points and problems to watch for • hands-on activities • links to other curriculum areas

• resource sheets • assessment sheets.

• a checklist

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Answers relating to the resource and assessment pages are included on the final page of the section for each sub-strand (Using units of measurement, Shape, Location and transformation and Geometric reasoning).

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The length of each content description section varies.

Teacher information includes background information relating to the content description, as well as related terms, desirable student vocabulary and other useful details which may assist the teacher.

Related terms includes vocabulary associated with the content description. Many of these relate to the glossary in the back of the official Australian Curriculum Mathematics document; additional related terms may also have been added.

What this means provides a general explanation of the content description.

the teacher would use—and expect the students to learn, understand and use—during mathematics lessons.

description.

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The proficiency strand(s) (Understanding, Fluency, Problem solving Solving or Reasoning) relevant to each content description are shown listed. in bold.

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What to look watchforforsuggests suggestsany any difficulties and misconceptions the students might encounter or develop.

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Hands-on activities includes descriptions or instructions for games or activities relating to the content descriptions or elaborations. Some of the hands-on activities are supported by resource sheets. Where applicable, these will be stated for easy reference.

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5)

R.I.C. Publications® www.ricpublications.com.au

FORMAT OF THIS BOOK Links to other curriculum areas includes activities in other curriculum areas which support the content description. These are English, Information and Communication Technology (ICT), Health and Physical Education, History, Geography, the Arts and Languages. This section may list many links or only a few. It may also provide links to relevant interactive websites appropriate for the age group.

r o e t s Bo r e p ok u S Resource sheets are provided to support teaching and learning activities for each content description. The resource sheets could be cards for games, charts, additional worksheets for class use or other materials which the teacher might find useful to use or display in the classroom. For each resource sheet, the content description to which it relates is given.

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Cross-curricular links reinforce the knowledge that mathematics can be found within, and relates to, many other aspects of student learning and everyday life.

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Assessment pages are included. These © R. I . C . Pu b l i cactivities at i ons support activities in the Hands-on or resource sheets. •f orr evi ew pur posesonl y•

o c . che e r o t r s super Each section has a checklist which teachers may find useful as a place to keep a record of the results of assessment activities, or their observations of hands-on activities.

Answers for resource pages (where appropriate) and assessment pages are provided on the final page of each sub-strand section.

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5)

R.I.C. Publications® www.ricpublications.com.au

Sub-strand: Using units of measurement—UUM – 1

Choose appropriate units of measurement for length, area, volume, capacity and mass (ACMMG108)

RELATED TERMS

TEACHER INFORMATION What does it mean

Length

• The measure of a path or object in one dimension from end to end (i.e. 1-D). Area

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• The amount of surface covered (i.e. 2-D; measured in square units).

• The total area of each of the surfaces of an object added together. Volume

• The volume of an object is the total space occupied by the object (i.e. 3-D; measured in cubic units).

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• The amount of matter an object contains, commonly measured in grams, kilograms and tonnes. Weight

• Students are familiar with the common metric units of measurement for each of the attributes.

Teaching points General

• The amount a container can hold. This is different from volume, which is how much space it takes up. An example of this difference is if you consider an esky. The amount of room it takes up in a cupboard is its volume. The amount it can hold is its capacity. Mass

• Students decide the appropriate units for each attribute, rather than the teacher telling them what to use; e.g. students decide whether to use millimetres, centimetres, metres or kilometres to measure the length of a passageway.

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• The force of gravity acting on an object, used to measure mass (actually measured in Newtons) Note 1: It is correct to use the verb ‘to weigh’. Note 2: At this year level, students may use the terms ‘weight’ and ‘mass’ interchangeably, although it is best if the teacher uses the correct terminology.

• Estimate before measuring in all measurement activities.

• The metric units for length are millimetres (mm), centimetres (cm), metres (m) and kilometres (km).

Note: the correct pronunciation of kilometre is ‘KIL-uh-mee-tuh’, not ‘ky-LOM-metre’ or ‘KY-le-metre’. When saying units, the full name is used rather than the letters of the symbols; ‘five kays’ is not really acceptable.

• The common metric units for area are square centimetres (cm2), square metres (m2), square kilometres (km2) and hectares (ha).

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Capacity

• Students are aware that within each of the attributes, there are different units that can be used, dependent of the size of the object and the level of accuracy required. For example, a bridge over a river may be measured in metres, or even kilometres, but engineers designing and building it may need to have a level of accuracy to within millimetres.

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Surface area

• Students are aware of the different attributes of an object that can be measured and that different units are used for each of them.

• The common metric units for volume are cubic millimetres (mm3), cubic centimetres (cm3) and cubic metres (m3). • The metric units for capacity are millilitres (mL), litres (L) and kilolitres (kL).

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Note: the use of the upper case ‘L’ for the abbreviation of litres; it is also used for mL and kL. This is to distinguish it from the number 1.

• The metric units for mass are grams (g), kilograms (kg) and tonnes (t). • A gap is always left between the number of units and the abbreviation of the unit—e.g. 5 cm, 8 kg, 375 mL—and no full stop is used at the end of the abbreviation (unless it is the end of a sentence). • Abbreviations of metric units never use the ‘s’ at the end; e.g. ‘5 cm’ not ‘5 cms’; ‘4 cm2’ not ‘4 cms2’; ’12 m3’ not ’12 ms3’; ‘375 mL’ not ‘375 mLs’; 8 kg’ not ‘8 kgs’. However, if the unit is written in full, the ‘s’ is needed; e.g. ‘5 centimetres’, ‘4 square centimetres’, ‘12 cubic metres’, ‘375 millilitres’ and ‘8 kilograms’. • Students need to be fluent with conversions of common metric units of measure for length, capacity and mass (see page 4). Discussion could centre on needing to know about multiplying and dividing by ten, or powers of ten. Discuss the meanings of the prefixes; e.g. ‘milli’, ‘centi’, ‘kilo’.

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5)

R.I.C. Publications® www.ricpublications.com.au

Sub-strand: Using units of measurement—UUM – 1

Choose appropriate units of measurement for length, area, volume, capacity and mass (ACMMG108)

TEACHER INFORMATION (CONTINUED) Teaching points (continued) Student vocabulary

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centimetres metres millilitres litres square centimetres square metres square kilometres hectares cubic centimetres cubic metres grams kilograms

• Students need to develop ‘referents’ for length, area, volume, capacity and mass. For example, students being aware that their little finger is approximately one centimetre in width; that a big stride is about a metre long; that a square centimetre is about the size of the fingernail on their little finger; that a Base Ten small cube is one cubic centimetre; and that if it was hollow, it would hold one millilitre of water. For mass, when holding an item to be estimated, most people mentally compare the item with something they know such as a tub of margarine or a bag of sugar. Capacity is often problematic because of marketing; a 2-litre cool drink bottle may look as if it holds more than a 2-litre tub of icecream. They may be familiar with the amount of liquid in a normal 375 mL can of soft drink. • Students need to know which units are appropriate for measuring different items. For example, we would not usually measure the length of a room in millimetres, the area of a book cover in square metres, the volume of a room in cubic centimetres, the capacity of a bucket in millilitres, or the mass of a balloon in kilograms.

long longer longest short shorter shortest

• National tests usually have questions where students are required to interpret scaled instruments in length, capacity and mass. For this reason, the measuring devices used need to have a scale rather than a digital display. Students need to have had many experiences actually measuring and reading scales, not just watching others do the measuring. There is no skill in reading a digital display on a measuring device.

covers more area covers less area

Length

holds more holds less holds the most holds the least

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heavy heavier heaviest light lighter lightest

• There are 2 types of rulers: dead-end (where the ‘zero’ is level with the end of the ruler) and waste-end (where the ‘zero’ is situated a little way in from the end of the ruler). Dead end ruler

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takes up more space takes up less space

Waste end ruler

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0 1 2 3 4 cm

• Ensure that all students’ rulers are in centimetres and millimetres, not inches. • Students need to be able to express distances in terms of metres and centimetres, or just in centimetres, so that they can record distances using decimals—e.g. 1.3 metres—and know that this is the same as 1 metre and 30 centimetres. • It is impractical for students to measure long distances (i.e. kilometres), but discussion could arise, for example, when going on an excursion. Area • Areas should be measured directly, with formulas being introduced for the area of a square or rectangle arising from this experience. (See UUM–2)

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5)

R.I.C. Publications® www.ricpublications.com.au

Sub-strand: Using units of measurement—UUM – 1

Choose appropriate units of measurement for length, area, volume, capacity and mass (ACMMG108)

TEACHER INFORMATION (CONTINUED) Conversions

Teaching points (continued)

Length

• Finding the surface area of a three-dimensional object involves determining the outside surface area of each face of the object and adding them together. At this stage, use only simple three-dimensional objects such as cubes and rectangular prisms.

10 mm = 1 cm 100 cm = 1 m 1000 mm = 1 m 1000 m = 1 km

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Volume

• Volume is an attribute independent of shape and position. This understanding will take time to develop and will be gained through manipulation and investigation.

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1000 mL = 1 L

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• The use of cubes to investigate volume of different objects enables students to come to the understanding that the same number of cubes (e.g. 12 cubes) can be used to create different-shaped objects that have the same volume (12 units).

Capacity

• There should be no formal use for the formulas for volume of a cube or rectangular prism at this year level.

Mass

1000 g = 1 kg

Capacity

At Year 5 students would not be expected to convert between measures of area or volume.

• Students may need help with strategies for measuring capacity, particularly when not all gradations are marked on a measuring container. Many measuring containers mark only every 5 or 10 millilitres. Mass

• When estimating and measuring mass, the teacher needs to ensure that the masses of the items to be measured are not always obvious (i.e. that students cannot determine comparisons simply by looking). To do this, you need items that have similar masses but different volumes—e.g. a golf ball and a tennis ball—and items that are the same size but have different masses; e.g. lidded tins filled with different materials such as sand and styrofoam.

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• When using metric units for mass, students may use a pan balance and weights, kitchen scales or bathroom scales. Kitchen and bathroom scales may have a dial or a digital readout. It is a useful skill to be able read a dial. There is no skill involved in reading a digital display. • Students should be given every opportunity to handle the standard units of mass. Given such experiences, students will be better able to select appropriate units of measure as well as estimate mass. Parents can be encouraged to help at home by doing regular checks of their child’s mass, and by allowing them to help when weighing ingredients for cooking.

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What to look for

• Students unsure of what attribute to measure; i.e. length, area, volume, capacity or mass. • Students using inappropriate units of measurement.

• Students using inappropriate tools to measure; e.g. using a ruler to measure the length of a basketball court, a medicine measure to calculate the capacity of a bucket or bathroom scales to weigh a pencil case. • Students having useful referents for length, area, volume, capacity and mass.

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5)

R.I.C. Publications® www.ricpublications.com.au

Sub-strand: Using units of measurement—UUM – 1

HANDS-ON ACTIVITIES Length Estimate before measuring in all these activities • Students measure such personal dimensions as hand length (from wrist to fingertip), foot length and length of arm from elbow to wrist. Use these dimensions to look for similarities and differences. For many people, the length of the foot is very similar to the length of their arm from elbow to wrist. Students could investigate how many of their group had that equality, and also investigate any other relationships between the three measures; e.g. is their hand length similar to half of their arm length? Students record their results in ways of their choice.

r o e t s Bo r e p ok u S Foot length > arm length

Foot length < arm length

Greg

Alby

Gemma

Catherine

Nathan

Mark

Adam

Hand half of arm length Lana Flynn

Hand > half of arm length Weng

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Foot length = arm length

Hand < half of arm length Jake Phoebe

• Encourage students to suggest methods of identifying a longer distance; e.g. 500 metres or one kilometre in the school grounds. Students could use a trundle wheel to measure the distance around the oval and work out how many laps of the oval would be needed to make one kilometre.

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• Are you a square or a rectangle? Students measure their height and then measure their outstretched arms from fingertip to fingertip. Compare the width and height. If the width is greater than, or less than the height, the student is a ‘rectangle’. If the height and width are close to the same, the student is a ‘square’. (Note: Some students may be selfconscious about their height. It may be that you only do the comparison for one or two students in each group so that not all students have their measurements taken.)

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• Measuring the length of curved items. Students use pieces of string to determine the lengths of objects that cannot be measured directly using a ruler, then straighten the string out against a ruler to obtain a measurement in millimetres or centimetres. • Students could be given instructions for ruling lines of different lengths. For example, Rule a line that is 5 cm long. Mark the mid-point of the line. This is a different skill from measuring a line. Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5)

R.I.C. Publications® www.ricpublications.com.au

Sub-strand: Using units of measurement—UUM – 1

HANDS-ON ACTIVITIES (CONTINUED) Area Estimate before measuring in all these activities • Polyominoes are puzzle pieces that can be manipulated by joining a specific number of pieces along whole sides, such as dominoes (formed by joining two squares), triominoes (three squares), pentominoes (five squares). Students investigate how many different ways they can find to join five squares (pentominoes; there are 12 different pentominoes shown below). Students explore which of the 12 can be folded along the joins to make open boxes and which cannot. This activity highlights the concept of area, as one pentomino has the same area (5 squares) as each of the others.

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Investigate how many ways six squares can be joined together. Some of these hexominoes can be folded along the lines to make a closed box (a cube); others cannot. Students investigate which ones can, and how you can determine this just by looking at the arrangement of the squares. You would not expect every student to find all 35 solutions, although they can be found on the internet. (Of the 35 hexominoes, 11 can be folded to form a cube.)

• Tangrams are another way to manipulate shapes but not alter the area of the original square from which they are formed (as long as all pieces are used and there are not overlaps). What is the same about the two shapes below? (Area) What is different? (Shape)

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• Students use nets to investigate the surface area of simple three-dimensional objects such as cubes and rectangular prisms. Once they have drawn a net for a cube, they can work out the surface area of one of the faces, then multiply this by six to determine the total surface area of the cube. Although it can be useful to have ready-made nets of objects for students to follow, it is also necessary for students to work out for themselves what the nets may look like. In the example of the hexominoes above, students will find there are a number of different nets for a cube; but often nets of cubes are only presented in one format. This activity links to the unit Shape–1 where students look at nets as twodimensional representations of three-dimensional objects. • The area of regular and irregular shapes can be measured by placing them under a transparent grid and counting the squares and part squares. The teacher could print 1 cm2 grid paper onto overhead transparencies (see page 11). Students could then use these to overlay any shapes and work out the areas. It may help to put the transparencies and the shape into a plastic sleeve. This would hold the shape steady so it’s easier for students to count the squares.

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• Groups of students could investigate how large a square metre is by joining sheets of newspaper together with sticky tape or masking tape and using metre rulers to check for accuracy. Prior to doing this, students could be asked to estimate the area of a room, then when they see the size of a square metre, be allowed to revise their estimations. If each group lay their square metres alongside each other, a physical count of the area can be made. • Once students have made their square metre of newspaper, they can investigate what happens to the area if they cut and rearrange their squares (they will all still be one square metre). This may help overcome a common misconception that a square metre must be in the shape of a square.

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5)

R.I.C. Publications® www.ricpublications.com.au

Sub-strand: Using units of measurement—UUM – 1

HANDS-ON ACTIVITIES (CONTINUED) Volume Estimate before measuring in all these activities • Allow students to experiment with cubes by using them to fill boxes and other containers, then counting the number of cubes used. • Have students make various shapes using the same number of cubes. Discuss the fact that changing the layout of the cubes in the shape does not alter the number of cubes or the amount of space they take up (the volume). This may help to develop an intuitive understanding of the relationship of volume to length, width and height. At this year level, formulas for determining the volume of solids are not used.

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• Count and record the number of cubes used to fill various boxes in layers to calculate volume. Layers of cubes

1 3

Volume in cubes

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Cubes per layer

• Relate the use of Base Ten small cubes to the activities above, and discuss that each of these cubes is one cubic centimetre (1 cm3). So if they have determined that a box has a volume of 24 Base Ten small cubes, it can also be said that it has a volume of 24 cm3. • Another way to compare the volumes of their boxes would be to line the cubes for each box up alongside each other. This is a very visual way to show the different volumes.

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• Use metre sticks or sticks that are a little longer than one metre and join 12 of them with rope or tape to make a cubic metre. (There are commercial kits with joiners that can be used to a construct a cubic metre.) Prior to doing this, students could be asked to estimate the volume of a room, then when they see the size of a cubic metre be allowed to revise their estimations. It is quite difficult to move a cubic metre around the room to try to work out its actual volume, but seeing the dimensions of a cubic metre will give the students a better idea of what the volume might be.

Capacity

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• Compare various containers of fairly similar size for capacity. It would be good if there were some short, wide containers as well as tall, narrow ones. Students seriate (place in order) the containers from ‘holds the least’ to ‘holds the most’. Allow students to revise their estimates after measuring the first container. My estimate

Actual capacity

500 mL

275 mL

450 mL 250 mL

175 mL

Bottle

700 mL 500 mL

375 mL

Glass

400 mL 200 mL

200 mL

Mug Jar

We thought the glass would hold the least amount of water, but it was the jar, then the glass, then the mug. The bottle held the most.

• Investigate how many of a small container of known capacity will fill larger containers and use this to compare volumes. For example, use a 500 mL measuring jug to fill a bucket, a plastic tub and a large fruit bowl. Students convert capacities to litres. My estimate

Number of jugs

Total capacity (mL)

Total capacity (L)

Bucket Plastic tub Fruit bowl Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5)

R.I.C. Publications® www.ricpublications.com.au

Sub-strand: Using units of measurement—UUM – 1

HANDS-ON ACTIVITIES (CONTINUED) Mass Estimate before measuring in all these activities • Compare the masses of objects in the same containers; e.g. a yoghurt container of sand, water, gravel, styrofoam etc. This will reinforce the reality that we cannot estimate the mass of an object by just looking at it; we need to actually pick it up or handle it in some way. • Bathroom scales can be made available so students’ mass can be recorded at regular intervals. Be aware that some students may be sensitive to having their mass disclosed. For this reason, it may preferable to weigh other items such as a class pet. However, this is unlikely to offer the opportunity to measure in kilograms on bathroom scales, so other heavier objects will need to be found for weighing; e.g. a bucket of sand, a box of Base Ten Blocks, a box of books.

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• Students experiment with making their own balance scales using two plastic cups, a coat hanger, ruler and string. There are many suggestions on the internet. 1

RULER

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• Students construct lists of objects that have a similar mass. For example: What can they find that has the same mass as 500g? (2 potatoes, or 3 bananas etc.)

• Ask the students to choose the appropriate unit, grams or kilograms. ‘Which of these would we weigh in grams or kilograms? A piece of paper, a chair, a calculator, a bag of marbles, a person?’ • Compare the masses of various substances. One cup of ...

Estimated mass in grams

Actual mass in grams

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Rice Marbles Sand

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• Use real objects to explore the relationships between grams and kilograms and their multiples. Using balances pans to compare two 500 g bags of flour with one 1 kg bag. • Once students have experience with numbers to three decimals places, they can convert masses in grams and kilograms to just kilograms and vice versa. I kg and 500g is the same as 1.5 kg 2 kg and 225g is the same as 2.225 kg 3.2 kg is the same as 3 kg and 200 grams 1.375 kg is the same as 1 kg and 375 grams

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5)

R.I.C. Publications® www.ricpublications.com.au

Sub-strand: Using units of measurement—UUM – 1

LINKS TO OTHER CURRICULUM AREAS English • Read Is the blue whale the biggest thing there is? by Robert E Wells. This book compares the sizes of things starting with the blue whale, which is the largest animal that ever lived. The book compares the size of a blue whale with the height of Mt Everest, then to the size of the Earth, the Sun, the star Antares, the Milky Way and the Universe.

Information and Communication Technology • A YouTube site with instructions on how to build your own balance scales can be found at <http://www.youtube.com/ watch?v=12760IJwMuU>

r o e t s Bo r e p ok u S

• Use measurement of capacity to make Oobleck. This is named after a substance described in a Dr Seuss’ book, Bartholomew and the Oobleck. The Oobleck is a strange goo that acts as both a liquid and solid, made from cornflour and water (and food colouring, if desired). A recipe and short video clip can be find at <http://www.instructables.com/ id/Oobleck/>

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Health and Physical Education

• Students measure the lengths of sports events such as long jump, high jump and triple jump.

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• Students measure the distance a ball or beanbag has been thrown.

• If students have swimming lessons or a swimming carnival, discuss how long the pool is. For longer distances, students could work out how many laps of the pool would make one kilometre. • For Sports Day and practices beforehand, students could help with measuring out the course for a 50-metre race, a 100-metre race etc. Students could use this knowledge to look at longer distances. We had a 100-metre race. There were 10 of us in the race. Altogether we ran 1 kilometre.

Science

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• Students measure the length of shadows at different times of day. A metre stick could be set up and students could take measurement every hour from 9:00 to 3:00.

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• Grow plants with a fairly rapid growth pattern such as bean sprouts or broad beans. Students record the growth of the plant every day, either in a diary, logbook, or on a graph using paper tape. My plant was 4 cm tall yesterday, but today it is nearly 5 cm tall. It is about 47 mm high. • Students measure ingredients to make various recipes.

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5)

R.I.C. Publications® www.ricpublications.com.au

Sub-strand: Using units of measurement—UUM – 1

RESOURCE SHEET

(b) 2. (a) (b)

paperclips

Join the paperclips and find out.

paperclips

Estimate how many you would need to equal one metre.

paperclips

Use your ruler to work out how many you would need.

paperclips

How many do you think you would need for 1 kilometre?

paperclips

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3. (a)

Estimate how many joined paperclips you would need to make a chain as long as your ruler.

(c)

How did you work this out?

4. (a)

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Waist Head (b)

more than many others

fewer than many others

Use joined paperclips to fill in the chart below.

Distance Wrist

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(b)

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My estimate

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Number of paperclips

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1. (a)

Difference (+ or –)

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Were your estimates more or less than your measurements?

Remember: Separate the paperclips before packing them away.

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5)

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Choose appropriate units of measurement for length, area, volume, capacity and mass

Paperclip chains

Sub-strand: Using units of measurement—UUM – 1

RESOURCE SHEET

Teac he r

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r o e t s Bo r e p ok u S

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CONTENT DESCRIPTION: Choose appropriate units of measurement for length, area, volume, capacity and mass

1 cm2 grid paper

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5)

R.I.C. Publications® www.ricpublications.com.au

Sub-strand: Using units of measurement—UUM – 1

RESOURCE SHEET Ambitious areas

You will need:

1 cm2 grid paper Ruler, pencil and scissors

1. (a)

Cut a 4 x 3 rectangle from your grid paper.

(b)

Draw in the diagonal.

(c)

Cut along the diagonal.

(d)

Place one piece over the other until they fit together exactly.

r o e t s Bo r e p ok u S

Area of rectangle equals 2 squares Area of triangle equals 1 square

2. Use diagonals across different sized rectangles in these shapes to work out the areas of the shaded parts.

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(a)

. t e (d) squares o c . ctwo e 3. Work out the areas of the shaded pictures. hethe r o Hint: look for the diagonals and rectangles t r s super cut in half.

(a) 12

squares

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5)

(b)

squares

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Choose appropriate units of measurement for length, area, volume, capacity and mass

Here is another example:

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You have shown: The diagonal cuts the AREA of a rectangle into two equal parts.

Sub-strand: Using units of measurement—UUM – 1

RESOURCE SHEET Boxes of eight

You will need:

8 x 1 cm3 cubes Surface area

Length

Width

Height

8 cm3

34 cm2

8 cm

1 cm

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Volume

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CONTENT DESCRIPTION: Choose appropriate units of measurement for length, area, volume, capacity and mass

Sketch

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1. (a)

(b)

o c . Build as many different rectangular prisms as you can, each using 8 cubes, and c e h r sketch each one one the table above. Considero the length, width and height of t r s s r a cube to be 1 centimetre.u pe

Write the dimensions of each prism into the table. The first example is done for you.

2. When you have built as many prisms as you can: (a)

What do you notice about the volume of them all.

(b)

What do you notice about the surface area?

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5)

R.I.C. Publications® www.ricpublications.com.au

Sub-strand: Using units of measurement—UUM – 1

RESOURCE SHEET Mystery tour

Start at the bus on the map on the next page. At each crossroad there is a letter. Find that letter on the list below, then work out which would be the most suitable unit to use to measure the item listed next it. Once you have decided on the unit, follow the road that has that unit until you get to the next intersection. Where will the Mystery tour take you?

The mass of an orange

How far it is between the shelves on a bookcase The area of your fingernail

The length of an ant

The capacity of a glass

The mass of a golf ball

The length of a running track

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The distance from Sydney to Newcastle

The height of a room

M N P

The area of grass on a football oval

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How heavy a sack of potatoes is

The area of the screen on a computer

How much a water tank holds

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5)

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Choose appropriate units of measurement for length, area, volume, capacity and mass

Teac he r

The mass of a person

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5)

mm2

cm2

L mL

cm2 cm

LOST!

Shop

YOU ARE

cm2

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C A R PA R K A

NOT HERE!

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Church

GO BACK!

MARKET

E mm

OOPS!

IES MOV

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CIRCUS

START HERE

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NOWHERE!

cm2 J

g L

MOVIE S

m m2

km2

N E

STABLES

Scale: 1 cm = 1 km 13

m2 L

r o e t s Bo r e p ok u S

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CONTENT DESCRIPTION: Choose appropriate units of measurement for length, area, volume, capacity and mass Sub-strand: Using units of measurement—UUM – 1

RESOURCE SHEET

Mystery tour map

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Sub-strand: Using units of measurement—UUM – 1

RESOURCE SHEET Units of length

1. Which measuring tool would you use to measure the length of each of these? trundle wheel

pedometre

0 17723

1 m ruler

(d)

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2. Write three things you would measure using each unit of measurement.

(a)

kilometres

(b)

metres

(c)

centimetres

(d)

millimetres

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5)

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Choose appropriate units of measurement for length, area, volume, capacity and mass

(c)

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(e)

30 cm ruler

r o e t s Bo r e p ok u S (b)

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(a)

tape measure

Assessment 1

Sub-strand: Using units of measurement—UUM – 1

NAME:

DATE: Units of length

1. Fill in your estimates for each of the items below. Think about what equipment you will need to measure each of them and what units of measurement you will use. Item

Estimate

Actual length

Difference

Length of the classroom

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Width of the classroom

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Height of the classroom Length of the board Height of the board Height of the door

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Write it into your table and work out the difference between your estimate and the actual measure.

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CONTENT DESCRIPTION: Choose appropriate units of measurement for length, area, volume, capacity and mass

Width of the door

3. Go back and change the estimates you made for the rest of the list if you need to. Do you need to make the distances greater or smaller?

. te o c Were these estimates more accurate? . che e r o t r s super

4. Measure the rest of the items and work out the differences.

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5)

R.I.C. Publications® www.ricpublications.com.au

Assessment 2

Sub-strand: Using units of measurement—UUM – 1

NAME:

DATE: Boxes and more boxes about 40 x 1 cm3 cubes

You will need: 1. (a)

Build this rectangular prism. How many cubes did you use? This is its volume (24 cm3).

r o e t s Bo r e p ok u S (b)

Now look at this rectangular prism. What is its volume?

(c)

What do you notice about the two rectangular prisms? Their

is the same, but their

2. (a)

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cm3

are different.

Build the three prisms below. Prism 1

Prism 2

Prism 3

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(b)

Complete this table:

Prism 1 2 3 (c)

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Length

Width

Height

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Volume

Surface area

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Write about what you found.

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5)

R.I.C. Publications® www.ricpublications.com.au

Checklist

Sub-strand: Using units of measurement—UUM – 1

Choose appropriate units of measurement for length, area, volume, capacity and mass (ACMMG108) Choose appropriate units of measurement for ... Length

Area

Volume

Capacity

Mass

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Teac he r

STUDENT NAME

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5)

R.I.C. Publications® www.ricpublications.com.au

Sub-strand: Using units of measurement—UUM – 2

Calculate the perimeter and area of rectangles using familiar metric units (ACMMG109)

RELATED TERMS

TEACHER INFORMATION What does it mean

Perimeter

• A measure of the distance around the boundary of a two-dimensional shape. Area

• There is no direct relationship between the area and perimeter of rectangles. Two rectangles with the same area may have different perimeters and two rectangles with the same perimeter may have different areas.

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• It is not necessarily the case that, as the perimeter of a rectangle is increased or decreased, the area of the rectangle is increased or decreased.

Familiar metric units

• Students should be led to ‘discover’ the formula for calculating the perimeter or area of a rectangle.

• For perimeter, use centimetres, metres and kilometres. For area, use square centimetres, square metres and square kilometres. Large areas of land may also be measured in hectares, though students would not be expected to work with this unit at this year level.

Teaching points

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• The amount of surface covered (i.e. 2-D; measured in square units).

• Students may measure the lengths of the four sides of a rectangle and add them together to obtain the perimeter. They may then ‘discover’ that a more efficient way to calculate the perimeter is to double the lengths of the two different sides and add them together.

• Students will have had experience in finding the areas of rectangles by counting squares. The next step is to find the number of squares in each row and then work out how many rows there are. Students should explore the relationships rather than the teacher simply telling them a formula.

• Teachers need to stress that the formulas for working out the perimeters and areas of rectangles only pertain to rectangles and are not necessarily appropriate for other shapes.

Student vocabulary perimeter

What to look for

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• Use the language ‘square centimetres’ not ‘centimetres squared’; they mean different things. For example, 2 cm2 (2 square centimetres) means 2 lots of 1 cm x 1 cm squares. Two centimetres squared means a square with a length of 2 cm and a width of 2 cm (which is actually 4 square centimetres).

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• Students confused about the difference between perimeter and area.

• Students believing that there is a direct relationship between the perimeter and area of a rectangles.

area centimetres metres kilometres square centimetres square metres square kilometres

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5)

R.I.C. Publications® www.ricpublications.com.au

Sub-strand: Using units of measurement—UUM – 2

HANDS-ON ACTIVITIES • Students construct rectangles on 1 cm2 grid paper (see page 11). They record the size of the length and widths and add them together to determine the perimeter. Students can be ‘led’ to realise that if they double the size of the length and the size of the width, then add those two figures together, they have found an efficient way to calculate the perimeter of a rectangle. Another method for calculating the perimeter of a rectangle is to add the size of the length and width together and double the result. 5 cm 3 cm

3 cm

The perimeter is 5 + 5 + 3 + 3, which is 16 cm. This is the same as 10 cm (2 x 5) + 6 cm (2 x 3).

r o e t s Bo r e p ok u S The length of the rectangle is 5 cm, the width is 3 cm.

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• Students investigate how to calculate the perimeter of a square, which is a ‘special’ type of rectangle. They could use the above method, but may realise that as all four sides of a square are equal, they only need to work out the length of one side and multiply it by four. • Find the perimeter of Geoboard shapes. These do not need to be just one rectangle or square, but can be combinations, as below.

The perimeter is 12 units

The perimeter is 18 units

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• Use eight squares and investigate how many different shapes can be made. Some examples are shown below. Discuss which shape has the longest perimeter. Why are some of the perimeters different if all the shapes are made with eight squares? What types of shapes have the longer/shorter perimeters?

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5)

R.I.C. Publications® www.ricpublications.com.au

Sub-strand: Using units of measurement—UUM – 2

HANDS-ON ACTIVITIES (CONTINUED) • Students work out the area of a rectangle by counting the total number of squares, one at a time. Next, they count the number of squares in one row and work out how many rows there are altogether. Students then investigate any relationship between the sets of figures. To assist in this, a table could be drawn up.

r o e t s Bo r e p ok u S There are 3 rows; so the area of the rectangle is 15 cm2

Rectangle

Number of squares in each row (length)

Number of rows (width)

Total area

15 cm2

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Teac he r

Area of each row of the rectangle is 5 cm2

2 3

• Students may use a similar format to the one above, but include a column for calculating and recording the perimeters. Rectangle

Number of squares in each row (length)

Number of rows (width)

Perimeter

Total area

10 + 6 = 16 cm

15 cm2

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3 • Using a Geoboard, students investigate area and perimeter of various shapes.

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The perimeter is 8 units and the area is 3 square units.

The perimeter is 12 units and the area is 6 square units.

The perimeter is 18 units and the area is 9 square units.

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5)

R.I.C. Publications® www.ricpublications.com.au

Sub-strand: Using units of measurement—UUM – 2

LINKS TO OTHER CURRICULUM AREAS Information and Communication Technology • Students can calculate the perimeters of shapes on the website <http://www.bgfl.org/custom/resources_ftp/client_ftp/ ks2/maths/perimeter_and_area/index.html> • A shape surveyor that looks at area and perimeter of rectangles can be found at <http://www.funbrain.com/cgi-bin/ poly.cgi> • The Shape Explorer can be found at <http://www.shodor.org/interactivate/activities/ShapeExplorer/> You can choose to have only rectangular shapes for this activity. It also has the option of looking at the areas and perimeters of the shapes students have worked with in table format.

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• A catchy YouTube™ song on perimeter and area can be found at <http://www.youtube.com/watch?v=D5jTP-q9TgI> It goes straight to multiplication for working out the area of a rectangle, so this could be used after students have ‘discovered’ how the formula works. • A perimeter rap song can be found on YouTube™ at <http://www.youtube.com/watch?v=wynwRcc5q_U&feature=relat ed> It shows some of the measurements in inches and others in centimetres.

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• An activity where students use perimeter and area to launch a ship can be found at <http://pbskids.org/cyberchase/ math-games/airlines-builder> The instructions are a little unclear, but students will soon get the hang of it. • A Design a Party planning activity where students look for particular rectangles with given areas and perimeters can be found at <http://www.mathplayground.com/PartyDesigner/PartyDesigner.html>

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5)

R.I.C. Publications® www.ricpublications.com.au

Sub-strand: Using units of measurement—UUM – 2

RESOURCE SHEET Area the same

Materials:

Examples:

8 square tiles

• This square is 1 unit long and 1 unit wide. Its perimeter is 4 units.

1 cm2 grid paper

1 unit 1 unit 1 unit

• Tina the tiler has 8 tiles. She must use all the tiles so she always has an area of 8 square units.

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• She has arranged her tiles like this to get a perimeter of 12 units.

1 unit

4 units

2 units

2 units 4 units

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Teac he r

1. Do the same with your tiles. Make a copy of Tina’s floor on your grid paper.

(a)

a perimeter of 12 units (different from the one above)

(b)

a perimeter of 14 units

(c)

a perimeter of 16 units

Shape

(b) (c)

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Area

Perimeter

8 square units

12 units

8 square units

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(d) and (e) two different floors with a perimeter of 18 units.

o c . che e r 8 square units o t r s super 8 square units

(d)

8 square units

(e)

8 square units

3. Write about your results.

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5)

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Calculate the perimeter and area of rectangles using familiar metric units

2. Help Tina by making these 5 different floors, using all 8 tiles for each one and copy each floor on grid paper.

Sub-strand: Using units of measurement—UUM – 2

RESOURCE SHEET Perimeter the same

Materials:

Examples:

8 square tiles

• This square is 1 unit long and 1 unit wide. Its perimeter is 4 units.

1 cm grid paper

1 unit 1 unit

• Arrange 8 tiles like this.

4 units

r o e t s Bo r e p ok u S • The area is 8 square units The perimeter is 12 units.

2 units

4 units

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Teac he r

1. Do the same with your tiles. Make a copy of this floor on your grid paper. 2. Make the perimeter stay at 12 units by removing different numbers of tiles, then copy each floor on grid paper: (a)

1 tile

(b)

2 tiles

(c)

3 tiles

(a)

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12 units

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8 square units

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CONTENT DESCRIPTION: Calculate the perimeter and area of rectangles using familiar metric units

Write the area and perimeter next to each shape and complete the table to show your results.

12 units

o c . (c) 12 units che e r o t r s super 3. Write about your results. (b)

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5)

12 units

R.I.C. Publications® www.ricpublications.com.au

Assessment 1

Sub-strand: Using units of measurement—UUM – 2

NAME:

DATE: Twelve squares Find the area and perimeter of each shape below.

(b)

Which shapes have the same perimeter?

(c)

Which shapes have the same area?

(i)

(ii)

2. (a) (b)

r o e t s Bo r e p ok u S cm

cm2

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(iv)

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(iii)

(v)

cm2

3. Materials: 12 square tiles Make the three different rectangles that are possible with 12 tiles.

(b)

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(c)

Draw the rectangles in the first column of the table.

Complete the table.

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Sketch of rectangle

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(a)

12 square o c units . che e r o t r s super Length

Width

Perimeter

12 units

1 unit

26 units

Area

4. Write about what you found.

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5)

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Calculate the perimeter and area of rectangles using familiar metric units

1. (a)

Checklist

Sub-strand: Using units of measurement—UUM – 2

Compares area and perimeter of rectangles

Understands how to calculate the area of rectangles

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Teac he r

STUDENT NAME

Understands how to calculate the perimeter of rectangles

Calculate the perimeter and area of rectangles using familiar metric units (ACMMG109)

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5)

R.I.C. Publications® www.ricpublications.com.au

Sub-strand: Using units of measurement—UUM – 3

Compare 12- and 24-hour time systems and convert between them (ACMMG110)

RELATED TERMS

TEACHER INFORMATION

am (ante meridiem)

What does it mean

pm (post meridiem)

• It is expected students can tell the time to the nearest minute, but previously, have only used 12-hour clocks.

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• Converting between 12-hour and 24-hour times can be difficult because of the non-metric nature of time. So 1630 is not 6:30 pm, but 4:30 pm. • Calculations of time difference can be quite difficult, again because of the non-decimal nature of time. For example, if using a timetable and calculating how long before the next bus, a calculator may actually hamper the process. If the bus arrives at 1625 and it is currently 1547, you cannot simply key 1625 into a calculator and subtract 1547; the result would be 78, which a child could incorrectly interpret as 78 minutes. In this case, the number of minutes until 1600 would be calculated first (13 minutes), and the extra 25 minutes until the desired time (1625) added to give a total waiting time of 38 minutes.

Teaching points

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(From the Latin words meaning before and after noon)

• Standard abbreviations for units for time are seconds (s), minutes (min) and hours (h). The other units do not have standard abbreviations. Note: ‘sec’ and ‘hr’ are commonly used abbreviations for second and hour, but they are not the correct ones.

Student vocabulary o’clock half past quarter past quarter to xx:25 (e.g. 3:25) xx:52 (e.g. 3:52) clockwise

am (ante meridiem) pm (post meridiem)

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• When writing 12-hour time, we use a colon between the hours and minutes; for example, two o’clock should be 2:00 not 2.00. When writing 24-hour time we generally do not use a colon, but use four digits; for example, 4:33 pm would be written as 1633. For times before 10 am, there is a zero at the start in 24-hour time in the written form; e.g.0730 for 7:30 in the morning. Whether we say ‘oh’ or ‘zero’ depends on community practice. (Note: some sources do use a colon in 24-hour time.) • Telling the time in both 12- and 24-hour formats should be practised daily and treated incidentally whenever the opportunity arises.

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• Classrooms should have both an analogue clock and a digital clock, preferably side-by-side. Regularly seeing the two different displays for the same time of day helps students realise there are two equally valid ways to read the time. There are some large clocks available commercially that clearly show the time in both formats. Clocks that display 24-hour time would also be useful. • It is generally recommended that ‘quarter to an hour’ is the only time that students deal with times to the next hour. For example, we would use 5:52 rather than 8 minutes to 6. These times ‘to’ an hour may be dealt with informally as the need arises. • The spoken time reflects the written digital time; e.g. in 12-hour time format, 11:28 would be said as eleven twenty-eight, not twenty-eight minutes after/past eleven. The time 7:31 would be said as seven thirty-one, not twenty-nine minutes to 8 or thirty-one minutes after/past seven. With times such as 11:05, whether we say oh instead of zero or whether we verbalise the zero at all, depends on community practice. However, the zero must be used in the written form. When ‘am’ and ‘pm’ are used, they are simply spoken as the letters am or pm.

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5)

R.I.C. Publications® www.ricpublications.com.au

Sub-strand: Using units of measurement—UUM – 3

Compare 12- and 24-hour time systems and convert between them (ACMMG110)

TEACHER INFORMATION (CONTINUED) Teaching points (continued) • When using the 24-hour time format, times on the hour generally are said as ‘hundred’; e.g. 1100 would be eleven hundred, and 0500 would be zero/oh five hundred. Other times with a zero at the end would be spoken in tens; e.g. 1120 would be eleven twenty, and 0530 would be zero/oh five thirty.

r o e t s Bo r e p ok u S What to look for

• Students unable to convert from 12- to 24-hour time

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• National tests usually have several questions on time, including calculating time differences.

• Students not using four digits when writing 24-hour time; e.g. writing 815 instead of 0815 for 8:15 am. • Students using the wrong base (e.g. Base 10) for time calculations. • Students using a calculator inappropriately when subtracting one time from another to find the duration of an event. • Students unable to decide which operation is appropriate when calculating time problems.

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o c . che e r o t r s super Proficiency strand(s): Understanding Fluency Problem solving Reasoning

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5)

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Sub-strand: Using units of measurement—UUM – 3

HANDS-ON ACTIVITIES • Students count the times on the hour in 12-hour and then 24-hour times, saying one am, two am, three am, four am, five am, six am, seven am, eight am, nine am, ten am, eleven am, twelve am, one pm, two pm etc. Then zero one hundred, zero two hundred, zero three hundred, zero four hundred, zero five hundred, zero six hundred, zero seven hundred, zero eight hundred, zero nine hundred, ten hundred (not one thousand and of course, no longer needing the leading zero), eleven hundred, twelve hundred etc. They would see the fact that in 24-hour format, times after noon carry on from the 12:00 midday time. If viewed in isolation, students may assume, for example, 1400 in 24-hour time is 4:00 pm. • When converting from the 12-hour to the 24-hour clock for any time after 12:59 pm (that is in the afternoon), we add 12; so 5:00 pm becomes (5 + 12) which is 1700 and 11:13 pm becomes (11 + 12, and the 13 minutes) which is 2313. • Read and record start and finish times for events whenever possible, using both 12- and 24-hour time. This gives students the opportunity to see both formats for the same times. Our maths classes usually start at 9:20 am, which is 0920 in 24-hour time. The cross-country race started at 2:05 pm and finished at 2:37 pm. We could write that as 1405 for the start and 1437 for the finish.

r o e t s Bo r e p ok u S

• Students list activities, recording in both 12- and 24-hour times.

24-hour time

Got out of bed