Cloud Object Storage | Store & Retrieve Data Anywhere ... · Web viewDifficulties learning measurement concepts and skills include comprehending; • The attribute (for example, area,

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Growth Point

LearningExperiences

For

MeasurementTime

Length

Mass

Remember that many measurements are closely related to one another and so activities may easily be used for experiences across the content areas.

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Contents Page

ACKNOWLEDGEMENTS PAGE 3-5

TIME GROWTH POINTS PAGE 6-Activities Focusing on Moving Towards:

Growth Point 1 PAGE Growth Point 2 PAGE Growth Point 3 PAGE Growth Point 4 PAGE Growth Point 5 PAGE

Where to next: PAGE

LENGTH GROWTH POINTS PAGE 33-

Activities Focusing on Moving Towards:Growth Point 1 PAGE Growth Point 2 PAGE Growth Point 3 PAGE Growth Point 4 PAGE Growth Point 5 PAGE

Where to next: PAGE

MASS GROWTH POINTS PAGE 46-Activities Focusing on Moving Towards:

Growth Point 1 PAGE Growth Point 2 PAGE Growth Point 3 PAGE Growth Point 4 PAGE Growth Point 5 PAGE

Where to next: PAGE

BIBLIOGRAPHY PAGE 53

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Every effort has been made to contact and obtain copyright on

material quoted in this book, if any involuntary information

infringements have occurred sincere apologies are offered and the owner

of such copyright is requested to contact the publisher.

Measurement and the Mathematics UnderachieverJohn Munro

Difficulties learning measurement concepts and skills include comprehending;• The attribute (for example, area, perimeter, volume); use physical actions or drawings• Relational terms applied to particular attributes• Measurement as matching or comparing with a standard; use physical matching, stepping off

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• Meaning of the lines on a scale; space between two lines represents a tangible physical quantity• A quantity can be described in different ways by converting between scales of measurement• Fractional quantities in measurement

A task analysis of length skills• Use the attribute of length in free play activities with terms such as long, short, little• Use longer, shorter, etc., to relate two lengths• Sort more than two lengths into those that are longer/ shorter than a particular length • Match or cover a particular length by a multiple• Answer "how many (of these blocks) exactly match this (longer length)?• Produce a length that is a certain number of blocks long.• Decide whether two lengths are equal when direct length matching is not possible• Construct and use a length scale of centimetres or blocks, up to 20 cm long initially• Extend this scale to the metre and use the longer scale• Describe the need for the metre; describe a length in both centimetres and metres• Convert between metres and centimetres• Describe the need for the millimetre; modify the scale to include fractions of a cm. The skill to use this scale and to describe a measurement in terms of mm and cm

Area concepts and skills• Distinguish between area and perimeter by using actions• Introduce area as How many are needed to cover this space?• Different shapes have the same area, games such as Area-21 and Tessellations.

Measurement formulae• Derive each formula from several specific instances, using actions• Use drawings, actions etc. to highlight the property to be calculated.• When showing how the formula is derived, encourage actions using cardboard cut-outs etc.

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TIMELEARNING EXPERIENCES FOR GROWTH

POINT 0(No apparent awareness of time, its descriptive language,

and some features of clock-faces)WITH A FOCUS ON MOVING TOWARDS

ACHIEVING GROWTH POINT 1(Awareness of time, its descriptive language, and some

features of clock-faces)(Can describe at least one feature and one purpose of clock-faces)

Challenges Articulation of the purposes of clocks including knowing

when it is time to do something, and understanding that it can be used to work out how long until an event

Responding to the features and purpose of clocks Making simple comments about numbers and hands Making sophisticated comments about the speed at

which the hands move and that the marks between the numbers are minutes

The idea of sequence – what happened first? What happened then?

Key Features of activities

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Lots of experience hearing the features and purposes of clocks

Creating an awareness of time and events in time Play through manipulating the features of clock faces Activities related to everyday experiences Modelling the use of “time” words in context e.g. ‘It is

time to wash our hands’ Employ frequent incidental discussion of daily routines,

times of the day, duration of events, sequence of activities, responding to music through movement and through repeating rhythmic patterns such as body percussio

ACTIVITIESWHAT’S THE TIME MR WOLF?With a group of children, select one child to be Mr Wolf. Mr Wolf turns his back to the rest of children. Draw a line about 2 metres behind Mr Wolf and get the children to stand behind this line. Children then shout, "What’s the time Mr Wolf?" and Mr Wolf shouts "1 o'clock" and turns back. The other children take one-step towards Mr Wolf and freeze when he turns around. Whoever moves must drop out of the game. Repeat until 12 o'clock. Mr Wolf has to catch a child while turning around. Children will have to run back behind the line to avoid being caught.Beware...it can get a bit LOUD!

MUSICAL TIMEUsing percussion instruments students clap out rhythm in music and respond using rhythmic movements to represent particular features e.g. waves. Use a variety of music so the students practise adjusting their rhythmic movements accordingly.

FREE AND DIRECTED PLAYAllow the children to explore the materials available.

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With permission: Downton, Knight, Clarke and Lewis (2006) Mathematics Assessment for Learning: Rich tasks & Work Samples

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POINT 1Awareness of time, its descriptive language, and some

features of clock faces(Can describe at least one feature and one purpose of clock faces)

WITH A FOCUS ON MOVING TOWARDS ACHIEVING GROWTH POINT 2

Knowing some clock times, some days of the week and months of the year, and relating key events (personal,

community) to these(Knows some clock times, some days of the week and months of the year, and can relate key event to

these)

Challenges Remembering the names of the months of the year Remembering the names of the days of the week Recognising the characteristics of each of the seasons Developing a concept of time Reading and recognising some times on a clock face Matching time spoken to time shown on a clock face

Key Features of activities Lots of experiences with time, reading time and hearing

the days and months of the year Comparing and ordering the duration of events using

the everyday language of time Connecting days of the week to familiar events and

actions Clock faces are presented to students in a clear and

simple way without including confusing information. It should include the following features:

- Numbers 1 to 12- Only minute and hour hand- Marks at one minute intervals

Activities related to everyday experiences Hint: Use geared clocks so children see and learn the

movement of the minute hand in relation to the movement of the hour hand

ACTIVITIESTIME EVENTS

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Children time different events/activities e.g. how many finger clicks can you do in 30 seconds? Tap your foot in one minute? Blink your eyes in 20 seconds? Write your first name in one minute? How long does it take to walk or run or skip or jump 50 meters? To thread 20 beads or build a tower of ten unifix cubes? How any towers of four cubes can you build in 30 seconds?

CLASS CALENDARRecord events on a class calendar - birthdays, school holidays, sports days, excursions, Assemblies etc Find one day before or after an event or given date, progress to a week before/ after.Children write times of events e.g. Assembly from 9.30 to 10.15.Birthdays of class members can be tallied and represented on a bar graph.

BEAN SPROUTSUse days as units of measurement for things such as measuring the growth of bean sprouts.

SEQUENCEING AN EVENTTake photos at different stages of a child building eg a tower of blocks. Spread them out and have the children arrange them back into their correct sequence.Similarly, the could sequence the growth of a plant from seed through to flower/fruit or the sequence of a nursery rhyme or fairy story or story such as Rosie’s Walk by Pat Hutchins.Mark children’s heights at regular times eg the first day of each month or each term – discuss what they notice about it.

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One Minute Game

AIM:To help students put one minute into perspective.OVERVIEW:In this activity, students will explore one minute.WHAT YOU NEED:

A stopwatch A Dr Seuss book such as The Cat in the Hat or Green

Eggs and Ham A list of challenges

TEACHING POINTS:Brainstorm with the students how we measure time. Students might mention such words as day, time, hour, minute, second, clocks, stopwatches. Focus on the words day, hour, minute, and second. Explain to students that

a day = 24 hours, an hour = 60 minutes, and a minute = 60 seconds.

When we say Just a minute, do we mean exactly 60 seconds? We all know that a minute is equal to 60 seconds, but do we really know how long a minute is? The following activities will quickly demonstrate how good a judge of a minute your students are:

Students place their heads on their desks with eyes closed. Say "Go" and then use a stopwatch to measure exactly one minute. When students think one minute is up, they should quietly raise their


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hands without looking up. At the end of the activity, identify those students who raised their hands closest to the 60-second mark.

Try the activity again. Have students place their heads on their desks. This time, ask them to quietly sit up when they think exactly one minute has passed.

Have students repeat the activity in pairs or groups of three, timing one another. Have each student take several turns and record the results. (How many actual seconds had passed when each student indicated a minute was up?) Which students seem to have the best concept of one minute?

Following are more fun activities about time to share with students:

How many of their spelling words can students write/copy in exactly one minute?

Given a sheet of simple addition math facts problems (for example, 4 + 3 and 6+5), how many problems can students solve in exactly one minute? (You might try subtraction, division or multiplication facts to see how students do with those compared to addition facts.)

Have students read aloud a section of familiar text as fast as they can. (One of the popular Dr. Seuss books might be a good book for this activity.) Who can read the most words in exactly 60 seconds?

Give students a list of ten grade-appropriate words to alphabetize. (You might use the same list as used in the previous activity.) When the time begins, they write a 1 next to the word that comes first in alphabetical order, a 2 next to the word that comes second, and so on. How many students accomplished the task in one minute? (For younger students, you might provide a pack of 26 cards with the letters of the alphabet written on them. Have students spread the cards across their desks and, when time begins, arrange those cards in ABC order.)

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Follow-Up Activity

At the end of the one-minute activities, repeat the heads-down test to see if students now have a better concept of the length of a minute.

Challenge Activities We know that a day is made up of 24 hours and an

hour is made up of 60 minutes. But how many minutes are in a day? Have students work in pairs to calculate the total number of minutes in a day. First ask them to estimate how many minutes they think are in one day. When they are done, see which pairs got the correct answer. (24 x 60 = 1440 minutes) Have those teams explain how they got the answer.

If that was too easy, have students calculate the number of seconds in a day. (1440 x 60 = 86,400 seconds)


POINT 2Knowing some clock times, some days of the week and months of the year, and relating key events (personal,

community) to these

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(Knows some clock times, some days of the week and months of the year, and can relate key event to these)


Knowing clock times to half-hour, all days of week and months of year (including order)

Challenges Remembering the names and the order of the months of

the year Remembering the names and order of days of the week Recognising the characteristics of each of the seasons

Key Features of activities Describing duration using months, weeks, days and

hours Telling time to the half-hour Naming and ordering days, months and seasons Characteristics of the seasons – you might look at the

characteristics of the Aboriginal seasons Activities related to everyday experiences Estimating, measuring, comparing and ordering

intervals of timeACTIVITIESSONGSSing songs about the months of the year, days of the week and the four seasons.http://www.youtube.com/user/HarryKindergartenhttp://www.songsforteaching.com/calendarseasons.htm

FOLLOW ME LOOP CARDSEach student has a card and on each card it has ‘I have....., who has......?’ The teacher starts by first reading their card, the students need to listen out for the question to which they have the answer on their card. The class read their cards out in the correct order. For example,

'I have 1 o’clock. Who has 3 o’clock?''I have 3 o’clock. Who has 5 o’clock?''I have 5 o’clock. Who has 1 o’clock?'

It continues like this until the end card is reached. An undercurrent of murmuring is what you want as the

http://www.songsforteaching.com/calendarseasons.htm

http://www.youtube.com/user/HarryKindergarten

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students will be working out the answer and looking round to see who has got it. This activity can be modified for times to half-hour, or times to the nearest five minutes, as well as digital and analog times.Or see Growth Point 4, for another adaptation.

On the next page is a template you may use to make your own Loop Cards.

I have

Who has 3 o’clock?

I have

Who has ?

I have

Who has ?

I have

Who has ?

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I have

Who has ?

I have

Who has ?

I have

Who has ?

I have

Who has ?

I have

Who has ?

I have

Who has ?


POINT 3Knowing clock times to half-hour, all days of week and

months of year (including order)WITH A FOCUS ON MOVING TOWARDS

ACHIEVING GROWTH POINT 4Facility with clocks and calendars

(Can read analogue clock times to the nearest five minutes and has a good working facility with calendars)

Challenges Relationship between units of time, intervals of time and

reading and writing times

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Converting between 24-hour time and 12-hour time; Telling time to the quarter-hour; using the language of ‘past’ and ‘to’

Key Features of activities Using a calendar to identify the date and determine the

number of days in each month Activities related to everyday experiences Estimating, measuring, comparing and ordering

intervals of time

ACTIVITIESREADING AND RECORDINGRead and record starting and finishing times for common tasks and particular activities. This assists the children’s understanding of what can be done in a specified period of time (e.g. 1 minute, 5 minutes, 10 minutes, 20 minutes……).

“We began our measuring game at 11.04 a.m. and had to stop at 11.28 a.m. I won today”.

TWENTY-FOUR HOUR TIMEPractise reading from a twenty-four hour clock. Relate these to the public utilities which use this type of clock. Relate the number of hours in a day to the rotation of the Earth. Time lines (marked in hours) can be made by students.

MONTHLY KNUCKLESCount the months on your knuckles and the grooves between your knuckles. Leave out your thumb knuckle. Every month that lands on a knuckle is 31 days, every month that lands on a groove between knuckles is 30 days (or 28 for February).

1st knuckle: Jan (31 days)Groove: Feb (28 or 30 days)2nd knuckle: March (31 days)Groove: April (30 days)3rd Knuckle: May (31 days)Groove: June (30 days)4th Knuckle: July (31 days)

1st Knuckle: August (31 days)Groove: September (30 days)2nd Knuckle: October (31 days)Groove: November (30 days)3rd Knuckle: December (31 days)

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CALENDARSCollect different calendars and discuss the similarities and differences.Make a collection of calendars from several different years. Notice e.g. when your birthday is on each of them, or what day Christmas Day was etc. Speculate why they are different. Can you predict what day of the week your birthday will be on next year; in ten years’ time; when you will turn 21?Cut up a calendar (cut out each month and then cut the month into strips so children can see e.g. a week in a strip with the name of the day) and have the children work in groups to put it back together - like a jig saw. Explain their thinking and reasoning.

YOUR CLASS IS A CLOCKThis activity is designed to allow the children to ‘become’ the clock face and physically show the various times. All children can be involved – there are roles for everyone and the roles may be redistributed several times during the activity. You need a reasonably large space!Children sit in a circle of 12 wearing their role cards i.e. the numbers 1-12, behind them, as appropriate sit other children wearing the 5 minute cards and the quarter/half/past/to/o’clock cards. Two children lie on the floor forming the minute and hour hands. Remaining children call out the times from the time cards and the children work together to make sure the ‘hands’ show the correct time.

Roles (use the templates, laminate and attach string so they loop over the child’s head.)The numbers on the clock face – 1-12The quarter and half hour times i.e. quarter past, half past, quarter to, o’clockThe five minute times e.g. 5 minutes, 10 minutes and so on.Big hand (minute hand), small hand (hour hand)A set of time cards – both analogue and digital.

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Template: Clock face 1-12, quarter to, quarter past, half past, o’clock, big hand, small hand

1 2 34 5 67 8 9

10 11 12O’CLOCK HALF

PASTQUARTE

RTO

QUARTER

PAST

BIG HAND(MINUTE HAND)

SMALL HAND

(HOUR HAND)

Template: set of time cards

12 o’clock

1 o’clock 2 o’clock 6 o’clock 9 o’clock

Half past 5

Half past 10

Quarter to 9

Quarter past 8

Half past 4

2:30 5:00 6:45 7:15 8:00

12:30 3:00 4:45 12:15 11:00

EARTH’S ROTATIONDiscuss the alternation of day and night - can be related to Earth's rotation if children are ready.

SHADOWS

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Observation of shadows can be related to am and pm times e.g. shadow stick.

PHASES OF THE MOONInvestigating information telling phases of the moon, tides, moonrise and set.

CANDLE CLOCKMake and use a candle clock. Get 2 identical tall candles. Start burning one when the first bell/siren sounds. Mark the significant parts of the school day on the other candle e.g. bell times or lesson times and break times. On the next day cover the classroom clock, remove any watches and monitor the day’s time according to the candle clock. Discuss the pros and cons.Children could also make a sun dial and/or a water clock.

CLOCKS OVER TIMESet up a classroom project display showing different clocks over time e.g. alarm clocks, Big Ben, watches, travelling clocks, sun dials, analog and digital clocks, clepsydra, candle clock, stop watch, atomic clocks, hour glass, egg timer etc. This could be an ICT research project. Highlight similarities and differences, and discuss advantages and disadvantages of each device. This could also include an investigation of how ancient peoples and different civilisations monitored the passage of time.

Research the origins of the names of the seasons, months, days. Research the phases of the moon; discover why we have night and day.Research the way Indigenous peoples of Australia monitor time and the seasons of the year.

TIME LINESStudents create time lines e.g. of their life, or their family, of their city or country since settlement, of Bible events, of historical events of a particular town or country as

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appropriate. An excellent resource is “My Place” by Sally Morgan.


POINT 4Facility with clocks and calendars

(Can read analogue clock times to the nearest five minutes and has a good working facility with calendars)


Extending and applying knowledge, skills and concepts with time

(Can solve a range of problems involving duration, and digital and analogue time to the nearest minute)

Challenges Learning that duration requires a starting and finishing

time Comparing 12-hour and 24-hour time systems and

convert between them Uses am and pm notation and solves simple time

problemsKey Features of activities

Converting between units of time Activities related to everyday experiences Estimating, measuring, comparing and ordering

intervals of time Telling time to the nearest five minutes

ACTIVITIESELAPSED TIMEStudents need to have experience with calculating elapsed time and relate it to their experiences. Examples could include reading and interpreting time tables and television guides, cooking times, sporting events, swimming and athletics records. Students could use stop watches to time each other for activities such as running 50m, swimming one length of the pool etc.

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THE PASSAGE OF TIME'I have 1 o’clock. Who has 3 o’clock?''I have 3 o’clock. Who has 5 o’clock?'

'I have 5 o’clock. Who has 1 o’clock? 'I have 1 o’clock. Who has 3 o’clock?'

'I have 3 o’clock. Who has 5 o’clock?''I have 5 o’clock. Who has 1 o’clock?Present activities to help children develop an idea of the passage of time e.g. it is five minutes until recess, how many pages of our book can I read in that time? How many times can you jump (hop, tap your head, click your fingers, blink, tap your foot, write letters of the alphabet, write three letter words etc ) in one minute (30 seconds, ten seconds, 45 seconds etc.) Estimate first then check.

CHALLENGE IDesign a device (not a candle, water clock or sun dial) which accurately and consistently measures a set amount of time.

FOLLOW ME LOOP CARDSEach student has a card and on each card it has ‘I have....., who has......?’ The teacher’s starts by first reading their card, the students need to listen out for the question to which they have the answer on their card. The class read their cards out in the correct order. For example,

'I have 1 o’clock. Who has 3 o’clock?''I have 3 o’clock. Who has 5 o’clock?''I have 5 o’clock. Who has 1 o’clock?

It continues like this until the end card is reached. An undercurrent of murmuring is what you want as the students will be working out the answer and looking round to see who has got it. This activity can be modified - see Growth Point 2, for an easier version.

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12:00I have twelve o’clock. Who

has ten minutes later?

12:10I have ten past

twelve. Who has five

minutes later?

12:15I have quarter past twelve. Who has 10

minutes later?

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Worksheet Danger Distance1. I think that a moving car should

be……………………....... before I can safely cross the road outside the school.

2. I think I would take about……………second to cross ‘the road’.

3. My actual time to cross the road was seconds.

4. A car travelling at 60km/h covers metres in 1 second.

5. My danger distance is

x =……………..

metres.

TIME

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LEARNING EXPERIENCES FOR GROWTH POINT 5

Extending and applying knowledge, skills and concepts with time

(Can solve a range of problems involving duration, and digital and analogue time to the nearest minute)

Extend children’s vocabulary of time related words such as decade, century, Anno Domini (AD), Before

Current Era (BCE), chronological order, Daylight Saving.

Where to next? Consolidation of skills and understandings Developing fluency reading both digital and analogue

time, readily converting between 12 and 24 hour time, calculating elapsed time, exploring time zones and the International Date Line. What is Greenwich Mean Time?

Solve authentic problems involving time. Incorporate informal activities based on sequences of

events such as days in the week, months in the year, days in the current month, annual events, regular events (eg Class Assemblies), the four seasons, day and night, the length of shadows over a day, the longest day, the shortest day, the equinoxes.

Research why December which has the ‘dec’ prefix meaning ‘ten’ is the twelfth month. Similarly find out why August, September, October and November are not where you would expect them to be on the calendar according to their prefix.

Create a time line of the history of the Earth showing significant events (suggested by the children) in chronological order

Make a model of the Earth’s orbit around the sun, explaining it in relation to the days, months and seasons

Explore the idea of a century Explore life cycles How far back can you trace your family tree? Visit the local cemetery and look at the gravestones.

Look for the oldest grave. Who lived the longest? Who lived the shortest?

Research calendars used in other cultures or religions. Investigate rate and speed. Debate the benefits or disadvantages of Daylight

Saving.

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LENGTHLEARNING EXPERIENCES FOR GROWTH

POINT 0(No apparent awareness of the attribute of length and use

of descriptive languageWITH A FOCUS ON MOVING TOWARDS

ACHIEVING GROWTH POINT 1

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(Awareness of the attribute of length and use of descriptive language)

Challenges Becoming aware of the attribute of length Identifying the attributes of length Developing methods for gaining more accurate

measures eg placing materials end to end without any ‘gaps’, starting at one edge and moving to another in a straight line

Use of appropriate language e.g. longer than, shorter than, about

Key Features of activities Hands-on, concrete learning activities Children use a variety of arbitrary units to measure a

given object. Children begin to make estimates after consideration of

results.ACTIVITIES

‘LENGTH’ WORDSExplicit teaching of ‘length’ words through direct, hands-on activities - long, longer, longest, short, shorter, shortest, distance, height, depth, low, high, far, near, all round, tall, straight, crooked, curved, line etc

ATTRIBUTES OF LENGTHEnsure children understand which attribute is length.

SORTING ACTIVITIESSort familiar objects according to length.

TREASURE HUNTShow a familiar object, children tell or find one that is longer of shorter or about the same length. While the children are doing this, ask questions such as “How do you know it is longer (shorter)?” “What does the same mean?’’ ‘’What does shorter (longer) mean?”

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ORDERING OBJECTSOrder objects according to length, for example choose 3 crayons that are different colours, put them in order from longest to shortest and draw them in that order. Check to see if the children line them up so that the bases are even. Now challenge them to order them in a different way – are they in the same order? (Try ordering the objects according to width.+)

CIRCLE GAMEChildren sit in a circle. Give each child one or two objects that can easily be ordered by length. Tell the children that they are going to put all of them in order from the shortest to the longest. Teacher places first object. Discuss why it is important to line them up for example along a join in the carpet. Call on a child to estimate where his/her object will go and place it there. Discuss after each object and see if the class agrees. Objects may be moved after they have been placed to ensure they are in order.

INFORMAL UNITSUse informal units for measurement e.g. paper plates, leaves, lids, books, handprints etc. Discuss which unit best suits the shape to be measured.

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POINT 1(Awareness of the attribute of length and use of

descriptive language)WITH A FOCUS ON MOVING TOWARDS

ACHIEVING GROWTH POINT 2(Comparing, ordering and matching with the attribute of

length)Challenges

Identifying the attributes of length Use of appropriate language Alignment of starting point – for accurate comparison

Key Features of activities Children need lots of practice, with a wide variety of

materials, using non-standard units BEFORE they move on to standard measures

ACTIVITIESMAKE LENGTHSInvite children to make lengths of e.g. 5 paper clips, pop-sticks, match sticks, tooth picks etc. compare with their partner. Why might they be different lengths? Ensure

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children realise they need to have no gaps or overlaps and they need to line them up so the bottom of each object is on the same line. Challenge the children to find which objects provide more reliable measures and discuss which features make these arbitrary units more reliable.

TRAINSShow children 'trains' of unifix cubes - have one train where the blocks are butted together and one that has the same number of blocks but with the blocks slightly apart. Discuss the differences and similarities. Ask why they look different. Try this with paper clips - make one train with separate clips and one which has the same number of clips but joined together.

WRIGGLY WORMSMake a set of “worms” of different lengths. Each child takes a worm and decorates it. Then sort them according to length from smallest to longest, working together and discussing. Once the whole class agrees, glue them in place. Remember to line up their ‘tails’!

NAMESTeacher writes a long name in tall skinny letters, all squashed together, and a short name in fat, spread out letters so it is actually longer than the first name. Ask children which name is longer and why. Once the children have come up with the idea that the letters should be the same size, discuss how this could be done. Give them a grid paper and ask them to write their own name (you may need to demonstrate how to use the squares). Line up names and glue them in place.

FEET Children trace around one of their feet and cut it out. Measure length of their feet with e.g. cubes, discuss and compare. Now measure with e.g. paperclips, discuss and

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compare, why are the numbers (e.g. of the cubes and paperclips) different?

HOW MANY?Children identify objects in the environment which are about three handspans (or five handspans, or seven paperclips etc.) in length, less than........more than....... Children then check for accuracy.

FOLLOW THE PATHChildren follow curved and winding paths, make string pictures to experience the length of a path that is not straight.

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POINT 2(Comparing, ordering and matching with the attribute of

length)WITH A FOCUS ON MOVING TOWARDS

ACHIEVING GROWTH POINT 3(Quantifying length accurately, using units and attending

to measurement principles)(Uses uniform units appropriately, assigning number and unit to the measure)

Challenges Being sure to have a standard starting point eg all paper

clips in line Being clear about what is being measured ie the

attribute of length To measure accurately, children need to be aware that a

specific length has a start and end point.Key Features of activities

Use of appropriate length language eg longer, shorter, taller.

Use of a wide range of materials eg straws, paper streamers, pop sticks, string, ribbon, tape, rope, blocks etc

ACTIVITIESPAPER STREAMERSUse paper streamers to measure e.g. length of arm, leg, foot, height, walking paces, jump, neck, waist, perimeter of head etc. Each child writes their name on their piece of streamer. Display as a graph – remember to establish the base line. Describe the information e.g. Who has the longest legs? Who has the shortest head perimeter? Do you come in the same place in each data set?

HAND SPANS

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Use uniform arbitrary units such as hand spans to measure and compare e.g. children's heights, arm lengths etc; dimensions of classroom, playground equipment, distance to canteen or Principal's Office etc. Discuss why different children get different results – this is a vital aspect of this level.

STUDENT MADE MEASURING TAPES

Allow children to make their own tapes by gluing pop-sticks or toothpicks onto a paper strip. They use these to measure themselves, their classmates, various things inside and outside the room. Discuss the advantages or disadvantages of using this sort of ruler, then have them make another tape by accurately marking the pop-stick (or toothpick) lengths on a paper strip. Use this to repeat the measuring and discuss the advantages/disadvantages over using the first strip.

AWKWARD LENGTHS

Measure awkward lengths with a ruler e.g. a table leg, a drink bottle, around their upper arm or waist, around a wheel or a (clean) rubbish bin. Ask them if they can think of a better way to measure them. Let them try again with a piece of string or a paper strip and then measure that length using the ruler (children could mark the paper strip in 1cm units). Discuss the results in terms of the accuracy of each and the ease of measurement.Examples of probing questions:What did you use to measure that? Why did you choose it? What difficulties did you encounter? How did you overcome them? How did you work it out? Show me what you counted? Where did you start counting from?

PAPER PLANE CHALLENGE

Students use one A4 sheet of paper to make a paper glider. Launching their planes from the same place they measure how far they flew to see which design flew best. Discuss what they will use as the unit of measurement.

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Should they all use the same unit to measure how far their planes flew? Why?

CLASSIFICATION ACTIVITYChildren are given a wide range of materials and are asked to sort and order them according to length, height, width, distance around. They can draw or photograph their results or they can measure them with string or paper streamers and glue these on a chart or graph in order.

PERSONAL DIMENSION – THIS IS ME!Children use paper streamers to show their personal dimensions – height, length of arm, length of leg, waist, neck, head, arm span. Children could work in a group of five with each child having a different coloured streamer. Paste streamers onto chart or graph eg Heights, Waists etc. Teacher asks challenging questions such as Is your streamer in the same spot on each chart? Why do you think that is (or is not)? What do you notice when you compare your arm span with your height?

ESTIMATIONSUse stimulating activities to get the children estimating and measuring egHow far can you throw a bean bag? How high do the steps on the climbing frame go?How far can you jump with five jumps?


POINT 3(Quantifying length accurately, using units and attending

to measurement principles)(Uses uniform units appropriately, assigning number and unit to the measure)


(Choosing standard units for estimating and measuring length, with accuracy)

(Uses standard units for estimating and measuring length, with accuracy)

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Challenges Use of appropriate language-metre, centimetre,

perimeter Recognising and using the abbreviations eg mm, cm Understand the need for standard units of measure Recognising the difference between area and perimeter Recognising that two shapes may have the same

perimeter but their area is different and vice versa.Key Features of activities

Accurate measures Using measurement tools accurately and effectively Using appropriate language and correct terminology eg

perimeter, area.

ACTIVITIESMETRE STICKMeasure longer distances with a metre stick, estimating first.

ONE METRE GAME Each child has a metre stick or metre tape measure. In the centre of the table place an assortment of coloured Cuisenaire rods or MAB 'longs' and 'ones'. Players take turns to select pieces according to the roll of a die or dice and place them alongside the tape/stick. First child to make a metre is the winner. Highlight the relationship between centimetres and metres.

PREIMETER OF OBJECTSMeasure the perimeter of a range of objects. Discuss how different shapes may have the same perimeter. Make sure children understand that perimeter is the distance around a closed figure. Ensure the start and end point is obvious.

ALPHABET LETTERSUse graph paper to draw all the letters of the alphabet with the same perimeter e.g. 20 - or the same area. Discuss what they notice.

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RECTANGLESUse graph paper to draw as many different rectangles which have a perimeter of e.g. 30. How many different triangles can you make with the same perimeter as the rectangles?

FOOT PERIMETERSMeasure, compare and order the foot perimeters of everyone in the class. Discuss any challenges this may raise.

GEOBOARDSUse geoboards to link area and perimeter e.g. use 6 squares to make as many different shapes as possible. This can be linked to flips, slides and turns. What is the perimeter of each? What is the area of each?

TESSELLATIONSInvestigate tessellations – history, where they are seen in the children’s surroundings, which shapes tessellate and why, which shapes do not tessellate and why.

2 METRES LONGStudents use 2m long paper strips and orange rods or MAB 'longs' and calibrate the strip in 10 cm lengths (decimetres). Discuss where to write the labels for each decimetre and what will you write at the end of each metre? Students work in pairs to Measure a variety of things and discuss their findings. Did they arrive at the same answer? Why or why not?

HOW FAR IS……..?Line children up eg on the outside of the netball court. Ask them to go and stand where they think 37 metres is. Teacher uses the trundle wheel while children count the clicks and stops on 37. Children see who is closest to 37 m. Repeat with different distances.

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POINT 4(Choosing standard units for estimating and measuring

length, with accuracy)(Uses standard units for estimating and measuring length, with accuracy)


(Applying knowledge, skills and concepts of length)(Can solve a range of problems involving key concepts of length)

Challenges Choosing the most appropriate units of measurement Measuring accurately – starting point, accurate counting

etcKey Features of activities

ACTIVITIESProblem Solving with LengthTry ESTIMATING THE HEIGHT OF A TREEThis activity requires students to estimate indirectly the height of a tree by incorporating reasoning and

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mathematical understanding in a creative and efficient way.Investigation 1: (based on a Native American method) Students work in pairs. Student A starts at the base of the tree and walks away from it, stopping at regular intervals to bend forward and look through his/ her legs at the tree. Student stops at the point where they can see the whole tree between their legs. Student B uses a tape or trundle wheel to measure the distance from Student A to the base of the treethis is the approximate height of the tree. (This can be represented as a right angled isosceles triangle)Investigation 2:Students work in pairs, they need a pencil and a measuring tape or trundle wheel. Student A stands at the base of the tree. Student B slowly walks away from the tree until the length of the pencil (held at arm's length) matched the height of Student A. Count how any pencil lengths would be needed to reach the height of the tree. Measure the height of Student A and multiply this by the number of pencils counted earlier. Swap jobs and repeat the activity using the same tree.

Investigation 3Students can work singly or in pairs. They need a long stick/dowel (or a metre ruler) and a tape measure. Poke the stick into the ground and measure how much of it protrudes from the ground and measure its shadow. Record it. Measure the shadow cast by the tree. Record it. Calculate the estimated height of the tree using knowledge of ratio. The ratio of the shadows should be the same as the ratio of the heights of the objects ratio e.g. if the stick's height above the ground is 100 cm and its shadow is 40cm, the ratio of shadow to actual height is 40:100 or 4:10

Based on an activity in APMC 16 (2) 2011 A Primary Classroom Investigation: Estimating the Height of a Tree.

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POINT 5(Applying knowledge, skills and concepts of length)

(Can solve a range of problems involving key concepts of length)

Where to next Consolidation of skills and understandings Developing fluency Relate activities with length to other measures.

Key Features of activities Problem Solving – suggesting possible strategies,

carrying out their plan, checking results for reasonableness.

ACTIVITIESSCHOOL GARDENWe want to make a school garden to grow vegetables which can then be used by school families. To protect the vegetables we need to put a fence around the garden. We could only afford to buy 26 panels of 1m fencing. How many different shaped gardens could we build with a fence 26m long? Which one would you recommend? Remember you can only have a perimeter of 26m.

MASS

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LEARNING EXPERIENCES FOR GROWTH POINT 0

(No apparent Awareness of the attribute of mass and use of descriptive language)


(Awareness of the attribute of mass and use of descriptive language)

Challenges Identify and describe measurable attribute of mass Use appropriate mass language Shape and re-shape modelling material and discuss size,

shape and mass as appropriate Predicting which objects will be heaviest/lightest/ about

the same In evaluating mass, sight may be misleading so it is vital

for children to handle the materialsKey Features of activities

Children explore, measure and experience mass through activities such as hefting and comparing different objects

Children use balance scales to compare objects Use of appropriate mass language – less, more, same,

same as, heavy, heavier, heaviest, lighter, lightest, balance,

Use purchased as well as improvised balances Practise estimating before handling Allow the children to freely select activities such as

balancing, throwing, rolling, carrying, building, constructing, cooking, modelling, shaping etc and observe when you can ask a question or direct a learning experience.

Note: a gram is one thousandth of a kilogram (0.001kg). One ml of water (a cubic centimetres of it) also has a mass of 1gram

ACTIVITIESMass is a measure of the amount of matter present in an object. The idea of mass can be described as the general “heaviness” of an object. Mass is measured in milligrams, grams, kilograms and tonnes. Children need direct experience with a wide range of materials such as – stone, metal, blocks, plastics, foam, cork, rubber, polystyrene, peas, beans, seeds, marbles, toys, bricks, logs, planks, full and empty containers, see-saw, balance.

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SOME POSSIBLE QUESTIONSWhich one feels heavier?Which one feels lighter?Which jar feels heavier/lighter when they are both empty?Can you make two balls of dough the same mass?How can we check they have the same mass?How does the balance scale show us which is the heaviest?How can you tell which one has more mass without using the balance?Can you find a pair of objects which balance?How will you know if the two objects have the same mass?Why do you think that one of them will be heavier?

MASSWhat objects can you find that weigh less than your water bottle?What objects can you find that weigh more than you water bottle?Discuss “how can we know for sure which one weighs more?How does and objects’ size affect its weigh? Does bigger always mean heavier?

*Collect materials so that children may have experience with ;

a large object that has less mass than a small one a large object that has more mass than a small one a large object that has the same mass as a small one objects which appear to be of the same size and have

similar masses objects which appear to have the same size but have

different masse

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MASSLEARNING EXPERIENCES FOR GROWTH

POINT 1(Awareness of the attribute of mass and use of descriptive

language)WITH A FOCUS ON MOVING TOWARDS

ACHIEVING GROWTH POINT 2(Comparing, ordering and matching with the attribute of

mass)Challenges

Identify and describe measurable attribute of mass Use appropriate mass language Shape and re-shape modelling material and discuss size,

shape and mass as appropriate Predicting which objects will be heaviest/lightest/ about

the sameKey Features of activities

Children explore, measure and experience mass through activities such as hefting and comparing different objects

Children use balance scales to compare objects Use of appropriate mass language – less, more, same,

same as, heavy, heavier, heaviest, lighter, lightest, balance,

Use purchased as well as improvised balances Practise estimating before handling Identify the attribute of mass Use mass language appropriately Hands-on, concrete experiences and free exploration

ACTIVITIESSHOE BOX

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Make a “shoe box” balance, you will need a shoe box lid or similar, a can and some blu-tac. Place a blob of blu-tac on the table, place the can into it so the can doesn’t move (press it down into the blob). Balance (no blu-tac) the lid on the can. Students need to practise making it balance- firstly empty, but then with a range of materials. Talk about how a see-saw works. Use their balances to find objects that weigh the same.Use this activity before introducing ‘real’ balances.


POINT 2(Comparing, ordering and matching with the attribute of

mass)

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(Quantifying mass accurately, using units and attending to measurement principles)

(Uses uniform units appropriately, assigning number and unit to the measure)

Challenges Realising that the mass of an object is not

directly related to its size. Compare two attributes of

measurement eg length and mass so that children can see that sometimes the two are related but with other objects they are independent of each other.

Key Features of activities Hands on experiences with a wide range

of objects and materials. Much discussion and explanation of their

thinking and conjecturing.

ACTIVITIESESTIMATION BY HAND Picking up objects one at a time to decide which requires more effort.

HEFTING Comparing small objects by holding one in each hand to compare which has more pull on your arm muscles. Change hands.

ORDERING

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Take 4 or 5 lunch bags (not transparent) and put different amounts of e.g. sand, sugar, rice etc. into each. Fold down top of bag and staple in place. Students need to heft the bags and place them in order from lightest to heaviest.

COLLECT A RANGE OF OBJECTS OF DIFFERENT MASSES

1. Compare objects and order them according to their mass. Ask ”Which one weighs the most?” watch to see how they keep track of their explorations. Good for students to work in groups for this activity.

2. What objects can you find that weigh the same as an eraser?

3. Choose an object, how many cubes does it take to balance your object? Can also use bears etc. Talk to them about why you need to use the same object e.g. cubes, bears.

4. Ask students to explain how a balance works.

Set some problems to explore e.g. I have six bears on one side of my balance and nine on the other side. How can I make it balance?

DIRECTLY COMPARE MASS AND SIZEChildren use balance scales to compare the mass of a range of objects which have the same length.

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POINT 3(Quantifying mass accurately, using units and attending to

measurement principles)(Uses uniform units appropriately, assigning number and unit to the measure)


(Choosing standard units for estimating and measuring mass, with accuracy)

(Uses standard units for estimating and measuring mass, with accuracy)

Challenges Use of appropriate language Understand the need for standard units of measure

Key Features of activities Accurate measures Using measurement tools accurately and effectively

ACTIVITIESBALANCE SCALESUse balance scales to compare one object with one object (e.g. nuts, beans); one object with many (household items, pencil cases), beans) and varied sets of identical units

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(e.g. bottle tops, nails); many objects with many objects (e.g. marbles balanced with gum nuts) 4. Balance blocks, books, marbles etc against a 1 kg mass or 250g, 500 g, 100 g etc. children write lists e.g. 3 potatoes balance with 1 kg.


POINT 4(Choosing standard units for estimating and measuring

mass, with accuracy)(Uses standard units for estimating and measuring mass, with accuracy)


(Applying knowledge, skills and concepts of mass)(Can solve a range of problems involving key concepts of mass)

Challenges Developing the skills necessary for

reading calibrated instruments accurately

Making informed decisions about the most appropriate measurement tool

Key Features of activities Introduction and experience with using

grams and kilograms

ACTIVITIESGRAMSSome objects to weigh in grams include paper clips, leaves, feathers, coffee beans, rice, macaroni, sheets of

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paper, nails, screws, pattern blocks, shells, buttons, ails, cotton reels, buttons etc


POINT 5(Applying knowledge, skills and concepts of mass)

(Can solve a range of problems involving key concepts of mass)

Where to next Consolidation of skills and understandings Developing fluency Recognising the inter-relationships between formal units

of measurement and with the number system Understanding that the prefix kilo indicates 1000 (1 000

g = 1 kilogram and 1 000 kg = 1 tonne) Knowing and using the appropriate abbreviations – g,

kg, t. Solving problems which deal with mass Accurately reading calibrated instruments Inventing ways to accurately weigh a mass when you do

not have access to a set of scales or weights.

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BibliographyDownton, A. Linking Multiplication and Division in Helpful and Enjoyable Ways for Children. Australian Catholic University, St Patrick’s Campus.

Gervasoni, A. (2004). Chapter 5 EMU Program Activities. Extending mathematical understanding intervention program specialist teacher manual. Australian Catholic University, Ballarat: Heritage Services.

Downton, A. Knight, R. Clarke, D. and Lewis, G. (2006). Mathematics Assessment for Learning: Rich tasks & Work Samples. ACU and CEO Melbourne, Australia.

The Australian Association of Mathematics Teachers Inc. (2011). Australian Primary Mathematics Classroom Vol. 16 no. 2. Adelaide, Australia.

Documents

Cloud Object Storage | Store & Retrieve Data Anywhere ... · Web viewDifficulties learning measurement concepts and skills include comprehending; • The attribute (for example, area,