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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 bit left, about INDICATORS: STRATEGIES and TOOLS: Links to L1: 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: Links to L1: 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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Estimating and Measuring Key Growth Point 3 and Band 1 LENGTH ...

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