# Estimating and Measuring Key Growth Point 3 and Band 1 LENGTH

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```					                                                            Estimating and Measuring
Key Growth Point 3 and Band 1
LENGTH: Set 1

Key Growth Point 3                                                                                                                                  Band 1
MDS KGP3.1:                                                                                                                                MDS 1.1:
estimate, compare and describe                                                                                                             estimate, compare, describe
length, capacity, area, volume                                                                                                             and measure length, area,
and mass using direct                                                                                                                      capacity, volume and mass
comparison, and length,                                                                                                                    using informal units; estimate
capacity                                                                                                                                   and measure length
and mass using informal units                                                                                                              in cm and m

Resources needed for this set
You will need:
- A range of long thin objects including sticks, straws, paintbrushes, pens, pencils, streamers, rulers etc. including large collections of straws, streamers, sticks etc. cut at
random lengths for ordering
-    Tubs of informal units, eg multilink cubes, popsticks, matchsticks, paperclips
-    Collection of different sized shoes, multilink cubes (or other familiar informal units) prepared recording sheet including objects to be measured, copies of the ‘Use Shoes’
recording sheet
-    Paper/card for chart, trundle wheel, skipping rope (or similar), long tape measure

Estimating and Measuring: Key Growth Point 3 and Band 1: Set 1: Length
Key Growth Point 3                         Estimating and Measuring [Length]                                                        Band 1
MDS KGP3.1:                                                                                                                   MDS 1.1:
estimate, compare and describe                             Lesson 1 of 4: Yardstick                                           estimate, compare, describe
length, capacity, area, volume                                                                                                and measure length, area,
and mass using direct                Main Idea: To compare and order the lengths of objects, including longer,                capacity, volume and mass
comparison, and length,                                  shorter and ‘about the same’.                                        using informal units; estimate
capacity and mass using                                        [Approx. 45 mins]                                              and measure length in cm and m
informal units

Lesson 1: Yardstick
A. Getting Ready - 2 mins:
- Take the students on a ‘stick hunt’ in the playground, emphasising that only dead sticks lying on the ground should be collected, not branches from
trees.

B. Show Me How [Modelling] - 10 mins:
- Students return to the classroom and sit in a circle so everyone
can see three hoops labelled ‘longer’, ‘shorter’ and ‘about the same’.
-   Choose a ‘yardstick’, for example a 30cm ruler.
-   Each child has a turn at comparing one of her/his stick to the yardstick,
firstly indirectly (by eye only) and then directly if necessary (by lining the
stick and the yardstick up next to each other to compare).

C. Help Me Do It [Guided Practice] - 15 mins:
- Repeat the exercise in pairs or small groups using labels (hoops not needed). Students take it in turns to choose the yardstick and the others are
challenged to find something longer, shorter and ‘about the same’.
-   Another variation could involve a group ‘hunt’ to find as many objects as possible that are either ‘shorter’, ‘longer’ or ‘about the same’. In each
instance, focus should be on just one aspect.

D. Let me do it myself [Independent Practice] -10 mins:
- Students take a handful of objects and order them according to length [straws, streamers etc. cut at random lengths are good for this activity]. The
number and variety of objects can vary depending on each child’s ability to compare and order (see indicators below).

E. What did I learn? - 8 mins:
- Group discussion and jointly constructed text about how to compare objects that are ‘about the same’ in length.
- Include ‘direct comparison’ in this text and the need to line up objects from the same baseline to determine the longer/shorter.
Language & Vocabulary
Assessment                                                           Key Words:
longer, shorter, about the same, nearly the same, longest, shortest
INDICATORS:                                  STRATEGIES and TOOLS:                              Links to L1:
Indigenous people use long and short/ short and tall however most of
these words have these meanings in specific (not general) contexts. In
KGP3 looks and sounds like:                          To gather and record evidence of student
view of this, developing these understandings in L1 & English needs to
learning consider:                                       be done separately. Many Indigenous languages do not have specific
-   uses and responds to descriptive language,                                                                words for comparison (longer/shorter) and superlative
eg long, short                                   -    Using the rubric provided to keep a record of       (longest/shortest) If L1 does have generic descriptive (long/short),
-   uses and responds to comparative language,            student use of descriptive, comparative and         comparative or superlative words for length then the development of
eg longer than, shorter than, taller than             superlative language                                these concepts can be done in both L1 & English at the same time.
-   selects something shorter than/longer than/
about the same length as a given object          -    This rubric can be used in a number of ways,
-   lines up one end of objects to make direct
comparison                                       -    (i) on a particular date/ during a given week
-   compares the lengths of two objects                   by putting student names or initials next to                                  Resources
the appropriate indicator/s                         You will need:
Band 1 looks and sounds like:                                                                                 A range of long thin objects including sticks, straws, paintbrushes,
-    (ii) for an individual learner over a long period   pens, pencils, streamers, rulers etc. including large collections of
of time by indicating the date of observation       straws, streamers, sticks etc. cut at random lengths for ordering.
-   uses and responds to comparative language,
next to the appropriate indicator/s
eg longer, shorter
-   uses and responds to superlative language,
-    A similar rubric could be used for any
Links to Other Materials:
eg longest, shortest, tallest                                                                             Maths Today Series
measurement attribute, eg area, volume,
-   orders objects according to length                    capacity, mass, temperature                         Maths in Aboriginal Schools
-   explains how to effectively compare to objects                                                            NSW Mathematics K-6 syllabus (1989): Length 2 to 7, pages
of similar length                                                                                         112-117.

More Ideas & Notes:
-   The initial activity can be repeated with a different yardstick, eg a pencil, metre ruler.
-   Over a period of a week, build a class collection of objects that are shorter than, longer than or about the same as a given yardstick.
-   In general, lessons addressing Length concepts in L1 should be given at a separate time to these lessons in English and where possible, difference resources
should be used to minimise confusion. Activities similar to these could be used if appropriate however they should be planned by Indigenous staff and, as
such, more culturally appropriate contexts would be selected.
Key Growth Point 3 Extra Support: Limit to comparison rather than ordering. In order to support these learners towards ordering, choose one object shorter
than the yardstick and one longer and using the yardstick as the ‘middle’ length, order these three objects, modelling the language of longest, shortest etc. In
addition, it is helpful of the objects are obviously different lengths rather than objects that are ‘about the same’.
Band 1 Extension: Challenge learners to compare and order objects with their eyes closed – this will amplify the need for direct comparison and using a
common base line.

Estimating and Measuring [LENGTH]: Key Growth Point 3 and Band 1: Lesson 1: Yardstick
Key Growth Point 3                       Estimating and Measuring [Length]                                                          Band 1
MDS KGP3.1:                                                                                                                   MDS 1.1:
estimate, compare and describe                  Lesson 2 of 4: Indirect Comparison                                            estimate, compare, describe
length, capacity, area, volume                                                                                                and measure length, area,
and mass using direct               Main Idea: To compare the lengths of objects without direct comparison,                   capacity, volume and mass
comparison, and length,                              ie using and counting informal units.                                    using informal units; estimate
capacity and mass using                                        [Approx. 45 mins]                                              and measure length in cm and m
informal units

Lesson 2: Indirect Comparison
A. Getting Ready - 7 mins:
- Revisit the jointly constructed text from the previous lesson that identifies the key aspects of ‘direct comparison’ and the need to line up objects
from the same baseline to determine the longer/shorter.
-   Tell students that you can’t always use ‘direct comparison’ and sometimes you need to find other ways to ‘compare’, eg buying a cupboard in Alice
Springs – need to know if it will fit under the window but don’t want to buy it if it won’t fit.
-   Ask for suggestions about how we could compare objects that can’t be put against each other for direct comparison. If no-one suggests, explain
that we can use ‘informal units’ such as multilink cubes, popsticks.
-   Invite students to bring a ‘thin’ object from the previous lesson and sit in a circle on the floor.

B. Show Me How [Modelling] - 15 mins:
-   Choose a pair of students to sit back to back. Give each student a tub of multilink cubes (or the chosen unit). Ask them to place multilink cubes
along the length of their sticks and count how many they need. Ask students to share their ‘measurements’ and have the class decide which object
is the longer/shorter. Ask them to explain how they know and, where necessary, explain that the bigger number means that the object is longer.
-   Compare the objects by direct comparison to check.
-   Model a sentence explaining the result, eg ‘ Kari’s ruler is longer than Harry’s stick. Harry’s stick is shorter than Kari’s ruler.’ Choose another pair
and repeat as many times as desired.

C. Help Me Do It [Guided Practice] - 15 mins:
- Repeat the exercise in pairs. Ask pairs to record each result on a large sheet of paper

E. What did I learn? - 8 mins:
- Pairs share their results.
Language & Vocabulary
Assessment                                                         Key Words:
longer, shorter, about the same, nearly the same, longest, shortest
INDICATORS:                                 STRATEGIES and TOOLS:                              Links to L1:
Indigenous people use long and short/ short and tall however most of
these words have these meanings in specific (not general) contexts. In
KGP3 looks and sounds like:                           To gather and record evidence of student
view of this, developing these understandings in L1 & English needs to
learning consider:                                      be done separately. Many Indigenous languages do not have specific
-     uses and responds to comparative language,                                                              words for comparison (longer/shorter) and superlative
eg longer than, shorter than, taller than       -   Using the rubric provided to keep a record of       (longest/shortest) If L1 does have generic descriptive (long/short),
-   selects something shorter than/longer than/           student use of descriptive, comparative and         comparative or superlative words for length then the development of
about the same length as a given object              superlative language/ use of informal units         these concepts can be done in both L1 & English at the same time.
-   lines up one end of objects to make direct
comparison                                       -   This rubric can be used in a number of ways,
-     counts informal units to ‘measure’ the length
of an object                                     -   (i) on a particular date/ during a given week
by putting student names or initials next to                                  Resources
Band 1 looks and sounds like:                             the appropriate indicator/s                         You will need:
A range of long thin objects including sticks, straws, paintbrushes,
-   uses and responds to superlative language, eg     -   (ii) for an individual learner over a long period   pens, pencils, streamers, rulers etc. Tubs of informal units, eg
longest, shortest, tallest                           of time by indicating the date of observation       multilink cubes, popsticks, matchsticks, paperclips
next to the appropriate indicator/s
-   orders objects according to length
-    explains how to effectively compare to objects   -   A similar rubric could be used for any
Links to Other Materials:
of similar length                                    measurement attribute, eg area, volume,             Maths Today Series
-    counts informal units to compare the lengths         capacity, mass, temperature                         Maths in Aboriginal Schools
of objects                                                                                               NSW Mathematics K-6 syllabus (1989): Length 6 & 7, pages
116-117.

More Ideas & Notes:
-    .Ask students to brainstorm where they need to measure and can’t directly compare in real life, eg parking a car, fitting furniture through a door or window
when moving it etc.
Key Growth Point 3 Extra Support: Limit to counting and describing the length of objects using informal units rather than comparing. In order to support these
learners towards comparing, choose objects are obviously different lengths rather than objects that are ‘about the same’. Make sure that the number of informal
units to be counted is within the learners’ capacity.

Band 1 Extension: Challenge these students to work out whether a student/teacher desk will fit out the classroom door ‘longways’ and/or sideways. They should
pick an informal unit of their own choice and use their informal measurements to justify their answers.

Estimating and Measuring [LENGTH]: Key Growth Point 3 and Band 1: Lesson 2: Indirect Comparison
Key Growth Point 3                          Estimating and Measuring [Length]                                                                Band 1
MDS KGP3.1:                                                                                                                           MDS 1.1:
estimate, compare and describe                    Lesson 3 of 4: More than/ Less than                                                 estimate, compare, describe
length, capacity, area, volume                                                                                                        and measure length, area,
and mass using direct                  Main Idea: To estimate (using the more than/less than ‘range’ method)                          capacity, volume and mass
comparison, and length,                              and measure lengths using informal units.                                        using informal units; estimate
capacity and mass using                                          [Approx. 45 mins.]                                                   and measure length in cm and m
informal units

Lesson 3: More than/Less than
A. Getting Ready - 3 mins:
-   Revisit the strategy of using informal units to ‘measure’ objects. Use the same informal units as the previous lesson (multilink cubes or whatever was used), and
a familiar item, eg a 30cm ruler to model the ‘range’ method of estimation as described below.
-   Record the words ‘more than’ and ‘less than’ on the board.

B. Show Me How [Modelling] - 15 mins:
-   Ask students to estimate how many cubes the ruler would be DEFINITELY more than (eg 1, 2, 5, 10). Make sure that all students agree and are confident that
the ruler is definitely longer than that number of cubes and record it on the board.
-   Ask students to estimate how many cubes the ruler would be DEFINITELY less than (eg 50, 40, 30, 25). Make sure that all students agree and are confident that
the ruler is definitely shorter than that number of cubes and record it on the board.
-   Explain that we have agreed as a group that the ruler is ‘more than 5 cubes long and less than 30 cubes long’. If all students agree, confirm that when we check
by measuring, if the answer is between 5 and 30 then we are correct.
-   Check by joining multilink cubes together to measure the ruler. Reinforce the need to have no spaces between units. Celebrate the correct estimation.
-   Repeat the process with a different object or unit (usually best to change the object rather than the unit).

C. Help Me Do It [Guided Practice] - 17 mins:                                                                            Estimate
- In pairs or small groups, ask students to estimate and measure the length of given
Object
More than   Less than
Measure        ☺
objects using a shoe as the informal unit. Students record both their estimate range
Desk
and measurement on a prepared recording sheet. Ensure that each group has a different
sized shoe to use as their unit but make sure that they are all measuring the same objects.
Doorway
-   Move around the room listening to the discussion, encouraging students to use the range
method of estimation prior to measuring.
Blackboard
E. What did I learn? - 10 mins:
- Pairs/groups share results – hang up the recording sheets if necessary. As groups had different sized shoes (measuring units) each group should have different
estimation ranges and measurements. Ask the group why the answers might be different. Band 1 learners (see below) should be able to identify the fact that the
units were different. If possible extend this discussion to consider how they could overcome the problem. At minimum students should be able to suggest using
the same sized shoes. Ideally, some students could suggest using formal units such as centimetres or metres. If not raised by the students it is not necessary to
introduce it at this stage
Language & Vocabulary
Assessment                                                                  Key Words:
longer, shorter, units, more than, less than, longest, shortest, a half, a
INDICATORS:                                       STRATEGIES and TOOLS:
Where available, use L1 to reinforce the notion of ‘more than’ and ‘less
KGP3 looks and sounds like:                                 To gather and record evidence of student
than’ when using the range approach to estimation. Where this is the
learning consider:                                          case, the concept should be developed and consolidated in L1 first
-   counts informal units to ‘measure’ the length                                                                       either by trained Indigenous teachers or by Indigenous team teachers.
of an object                                            -    Using the rubric provided to keep a record of          This will form a solid foundation for using the English concepts. If L1
-   guess how many times a unit will fit along an                student use of informal units                          support is not available, more time and patience will be required to
object                                                                                                              develop the concepts in English only.
-   guess then count informal units of length               -    This rubric can be used in a number of ways,
(such as cubes, paperclips and paces)
-    (i) on a particular date/ during a given week
Band 1 looks and sounds like:                                    by putting student names or initials next to
the appropriate indicator/s                                                        Resources
-    counts informal units to compare the lengths                                                                        You will need:
of objects                                             -    (ii) for an individual learner over a long period       Collection of different sized shoes, multilink cubes (or other familiar
of time by indicating the date of observation           informal units) prepared recording sheet including objects to be
-    use direct comparison to compare objects of
next to the appropriate indicator/s                     measured, copies of the ‘Use Shoes’ recording sheet
similar height/lengths
-    use but recognise the limitations of non-              -    A similar rubric could be used for any
standard units when estimating and/or                       measurement attribute, eg area, volume,
Links to Other Materials:
measuring, eg realise that different sized                  capacity, mass, temperature                             Maths Today Series
shoes will result in different estimates and                                                                        Maths in Aboriginal Schools
measurements                                                                                                        NSW Mathematics K-6 syllabus (1989): Length 6 & 7, pages
116-117.

More Ideas & Notes:
- Estimation is an overriding skill required in all types of calculation and related applications in measurement and space. Without estimation skills, the accuracy of a child’s solution to
any problem remains a mystery until evaluated by someone else, usually the teacher. In order to be numerate, an individual needs to be able to independently estimate. The ‘range
method’ described in this lesson helps to overcome students’ reluctance to estimate as the chance of being correct is greatly increased and the notion of estimation is properly
represented. If you have observed students being unwilling to estimate or recording their estimate after the task has been completed (so it is ‘correct’) then it could take a number of
attempts at the ‘range method’ before they feel comfortable. It is important to persist in order for effective estimation skills to be developed.

Key Growth Point 3 Extra Support: Make sure that students have a clear image of the unit to be used and the object being measured. Where needed, place the units
alongside the object being measured. This will limit the degree to which the estimate is an estimation rather than a measurement but it will support the learners.
Band 1 Extension: Challenge these students to decide what the ‘correct’ results are and what should be reported to another group/class/audience. Alternatively, ask them to
choose a unit that would be useful for these measurements. This needs to take into account both the size of the unit (ie a paperclip is not a useful unit for measuring long objects
such as a blackboard) and the availability of the unit (ie there need to be enough of the unit available so that each group can have the same unit).

Estimating and Measuring [LENGTH]: Key Growth Point 3 and Band 1: Lesson 3: More than/Less than
Key Growth Point 3                            Estimating and Measuring [Length]                                                                     Band 1
MDS KGP3.1:                                                                                                                                 MDS 1.1:
estimate, compare and describe                           Lesson 4 of 4: Paces for Races                                                     estimate, compare, describe
length, capacity, area, volume                                                                                                              and measure length, area,
and mass using direct                              Main Idea: To recognise the need for standard informal                                   capacity, volume and mass
comparison, and length,                                    (or formal) units to measure distance.                                           using informal units; estimate
capacity and mass using                                              [Approx. 45 mins]                                                      and measure length in cm and m
informal units

Lesson 4: Paces for Races
A. Getting Ready - 3 mins:
- Revisit issues relating to the different sized shoes used in the previous lesson. Ask students to suggest important ‘tips’ or ‘rules’ for effective measurement of
length. These should include: (i) Having a clear starting and finishing point; (ii) Measuring the shortest, most direct distance (straight line); (iii) There should be no
gap or overlap between units; (iv) Units should be of the same size if comparisons are to be made. Record these on a chart for future reference (within and
beyond this lesson).
-   Explain to students that today’s lesson will be outdoors, that they will be working in pairs and that each pair will need some chalk or appropriate markers

C. Help Me Do It [Guided Practice] - 30 mins:
-   Ideally this lesson would be held on a large concrete or asphalt area with a clear baseline such as a basketball court, tennis court etc. If the best space is a
grassed area, mark the baseline with a long skipping rope or similar.
-   Each pair of students is going to mark out a 100 pace straight running ‘track’. Amend the number of paces according to the available space – this could be as few
as 10 paces however the more paces, the more obvious the differences will be.
-   Each pair must commence at the same baseline and ‘mark out’ the same number of paces. Both the starting and ending point must be marked.
-   One student in the pair paces it out while the other (or both) counts the given number. Each pair then ‘checks’ their course by having the other student pace the
distance. Depending on the paces taken, there should be some variety in the lengths of the ‘tracks’ even though they took the same number of paces.
-   Once all pairs have marked their course, ask them to start at their marker and run to their end marker. Once they reach the end marker they must sit on it so you
can see who finishes first.
-   Bring the group together to discuss whether or not the race was ‘fair’. Points raised are likely to include that races usually have one finishing point. Ask students
to explain why the endpoints were all different – Band 1 learners should be able to do this. Another point could be that it is fairer for shorter or younger students
to have shorter ‘tracks’ so the uneven finish line is justified.
-   Ask students to help decide where the finish line should be. There are a number of possible solutions including: choose one student (or the teacher) to pace out
the ‘track’; use a trundle wheel to count out the given number of ‘clicks’. Whatever way of pacing the track is decided, mark it with a streamer or skipping rope
across the width of the space. Have a couple of races to ‘celebrate’ the running ‘track’.

E. What did I learn? - 12 mins:
- Ask students to write and/or draw the aspect of the lesson that was most important/ significant to them. The language from charts and jointly constructed texts
from earlier in this series of lessons should be pointed out as environmental print and used in their recordings.
Language & Vocabulary
Assessment                                                           Key Words:
further, not as far, closer, not as close, shorter, longer, paces, steps,
distance, race, track
INDICATORS:                                    STRATEGIES and TOOLS:
Where available, use L1 to reinforce the notion of ‘nearer’ and ‘further’
KGP3 looks and sounds like:                             To gather and record evidence of student
when discussing the different ‘track’ endpoints. Where this is the
learning consider:                                      case, the concept should be developed and consolidated in L1 first
-   counts informal units to ‘measure’ the length of                                                            either by trained Indigenous teachers or by Indigenous team teachers.
an object                                          -   Using the rubric provided to keep a record of       This will form a solid foundation for using the English concepts. If L1
-   guess how many times a unit will fit along an           student use of informal units                       support is not available, more time and patience will be required to
object                                                                                                     develop the concepts in English only.
-    guess then count informal units of length          -   This rubric can be used in a number of ways,
(including handspans and paces)
-   (i) on a particular date/ during a given week
Band 1 looks and sounds like:                               by putting student names or initials next to
the appropriate indicator/s                                                     Resources
-   counts informal units to compare the lengths of                                                              You will need:
objects                                            -   (ii) for an individual learner over a long period    Paper/card for chart, trundle wheel, skipping rope (or similar), long
of time by indicating the date of observation        tape measure
-   use direct comparison to compare objects of
next to the appropriate indicator/s
similar height/lengths
-    use but recognise the limitations of non-          -   A similar rubric could be used for any
Links to Other Materials:
standard units when estimating and/or                  measurement attribute, eg area, volume,              Maths Today Series
measuring, eg realise that different sized             capacity, mass, temperature                          Maths in Aboriginal Schools
shoes will result in different estimates and                                                                NSW Mathematics K-6 syllabus (1989): Length 6 & 7, pages
measurements                                                                                                116-117.

More Ideas & Notes:
- Take the chart outside so that you can refer to it as students pace out their ‘tracks’.
- An ideal place to conduct this lesson is on a sporting field (grassed or concreted). It is important that the area is flat (for safety) and that it is wide enough for all
pairs to spread out and mark their ‘tracks’.
Key Growth Point 3 Extra Support: Make sure that the number of paces is within the capacity of these learners. If necessary, partner them with a learner who
has demonstrated solid evidence of Band 1 – this is a great lesson to used multi-level buddies/pairs.
Band 1 Extension: Challenge these students to measure the distances in metres (using a trundle wheel or a long measuring tape). They might be able to
measure the ‘track’ length of each pair and/or the longest and shortest tracks and calculate the difference between them. If these students suggested that
younger/shorter students should be able to run on a shorter track to make the race fair, ask them to suggest ‘handicaps’ where the older/taller students start at the
baseline while others had an agreed ‘head-start’

Estimating and Measuring [LENGTH]: Key Growth Point 3 and Band 1: Lesson 4: Paces for Races

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