Measuring Up! The MAI Growth Points for Measurement (Time Length Mass) Dianne Rundus Triple M Consulting [email protected] Measurementhas its roots, both historically and in individual development, in significant everyday activity. Thus it can develop in the earliest years from childrens experiences.Further, it spans and connects mathematics and other sciences and thus can ideally integrate subject matter area. Clements, 2003
People numerate in measurement Use the language of measurement appropriate to the task Choose and use measuring tools and instruments appropriate to the task Use estimation techniques Use measurement techniques to solve problems Recognise that some measures are obtained by combining two or more other measures Measurement understandings Measures in common use
Skills needed for everyday purposes Nature of different physical attributes that can be measured The way units are used to quantify amounts of such attributes to needed levels of accuracy Understand units ie decide what needs to be measured and select the appropriate units to use. Directly and indirectly measure ie select and combine measurements, measurement relationships and formulae to determine other measures indirectly. Carry out measurements of length, capacity/volume, mass, area, time and angler to needed levels of accuracy Estimate units ie make sensible direct and indirect estimates and check for reasonableness of results. Three Content Strands Number and Algebra Number and place value
Fractions and decimals Money and financial mathematics Patterns and algebra Measurement and Geometry NOUNS Using units of measurement -Time Length, Mass, Capacity, Volume, Area, Perimeter Shape Geometric reasoning Location and transformation Statistics and Probability Chance Data representation and interpretation
Four Proficiency Strands Understanding Fluency Problem Solving Reasoning VERBS The proficiency strands describe the actions in which students can engage when learning and using the content. The proficiencies are incorporated into the content descriptions of the three strands. While not all proficiency strands apply to every content description, they indicate the breadth of mathematical actions that teachers can emphasise. Measurement language
Comparative statements shorter, taller etc Confusion between volume (the amount of space taken up by an object) and capacity (the amount it can hold) Confusion over the use of mass and weight. Mass is the measure of the inertia of an object. Inertia is the amount of force or push required to move an object. Weight is the force that gravity exerts on an object. The mass of an object remains constant but its weight can vary eg an object weighs more at sea level than on a high mountain. Discussion builds students conceptual and procedural knowledge of measurement and gives teachers valuable information for reporting and
planning next steps. (Principles and Standards for School Mathematics, 2000) Geometric measures Length 1D concept related to direction and line. Includes length, width, depth, thickness, nearness of objects, perimeters. Area 2D concept related to the region (surface) enclosed by a plane shape. The use of formulae to calculate areas of common shapes is the appropriate final stage of the learning sequence. Volume and capacity 3D concept Learning sequence for measurement
Identifying the attribute Comparing and ordering Non-standard units Standard units Applications Three phases for teaching measurement Phase 1 Identifying the attribute Develop the concept of the attribute, use play and practical activities, learn and practise the language, compare objects on the basis of the attribute identified, compare with other attributes, use
informal units. Phase 2 Learning to measure Learn to measure the quantity, usual formal units, estimate measurements. Make the transition from informal to formal units, make and use simplified instruments that highlight key features, measuring objects in various ways with increasing accuracy, acquiring a set of personal benchmarks. Phase 3 Learning to calculate. Converting from one unit to another, calculating instead of direct measuring. Developing formulae from first principles rather than memorisation, converting between units using proportional reasoning. MAI Growth Points for Time and ACM Descriptors GP 0 No apparent awareness of time, its descriptive language, and some features of clock faces. GP 1 Awareness of time, its descriptive language and
some features of clock faces. ACM Compare and order the duration of events using the everyday language of time (ACMMG007) F GP 2 Knowing some clock times, some days of the week and months of the year, and relating key events (personal, community) to these ACM Connect days of the week to familiar events and actions (ACMMG008 F Foundation Achievement Standard. Students connect events and the days of the week. They explain the order and duration of events GP 3 Knowing clock times to half hour, all days of the week and months of the year (in order) ACM Tell time to the half hour ACMMG020) Year 1 Describe duration using months, weeks, days and hours (ACMMG021) Year
1 Name and order months and seasons (ACMMG040 Yr 2 Achievement Standard Yr1. They tell time to the half hour GP 4 Facility with clocks and calendars (can read analogue times to the nearest five minutes and has a good working facility with calendars) ACM Tell time to the quarter-hour, using the language of 'past' and 'to' (ACMMG039) Yr 2 Use a calendar to identify the date and determine the number of days in each month (ACMMG041) Yr 2 Achievement Standard Yr 2. They tell time to the quarter hour and use a calendar to identify the date and the months included in seasons. GP 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)
ACM Tell time to the minute and investigate the relationship between units of time (ACMMG062) Yr 3 Achievement Standard Yr 3. Tell time to the nearest minute. ACM Convert between units of time (ACMMG085) Yr 4 Use am and pm notation and solve simple time problems (ACMMG086) Yr 4 Achievement Standard Yr 4 They solve problems involving time duration. They convert between units of time. ACM Compare 12- and 24-hour time systems and convert between them (ACMMG110) Yr 5 Achievement Standard Yr 5They convert between 12 and 24 hour time. ACM Interpret and use timetables (ACMMG139) Yr 6 Achievement Standard Yr 6 They interpret timetables. The Human Clock In your Growth Points Activities books this activity is on pages 21
and 22 The importance of context Research shows that young children can solve problems in a familiar context but may be unable to solve the same problem if it is in an unfamiliar context. The context provides a framework for exploring mathematical ideas and practising skills. Context provides a strong cognitive structure within which children can recognise and explore inter-relationships. MAI Growth Points for Length and ACM Descriptions GP 0 No apparent awareness of the attribute of length and use of
descriptive language GP 1 Awareness of the attribute of length and use of descriptive language Achievement Standard F They compare objects using mass, length and capacity. GP 2 Comparing, ordering and matching with the attribute of length ACM Use direct and indirect comparisons to decide which is longer, heavier or holds more, and explain reasoning in everyday language ( ACMMG006 F Achievement Standard Yr 1 Students order objects based on lengths and capacities using informal units. GP 3 Quantifying length accurately, using units and attending to measurement principles. Uses uniform units appropriately, assigning number and unit to the measure. ACM Measure and compare the lengths and capacities of pairs of objects using uniform informal units (ACMMG019) Yr 1
ACM Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units (ACMMG037) Yr 2 Achievement Standard Yr 2. Students order shapes and objects using informal units. GP 4 Choosing standard units for estimating and measuring length with accuracy . Uses standard units for estimating and measuring length with accuracy. ACM Measure, order and compare objects using familiar metric units of length, mass and capacity (ACMMG061) Yr 3 Achievement Standard Yr 3 Students use metric units for length, mass and capacity. GP 5 Applying knowledge, skills and concepts of length. Can solve a range of problems involving key concepts of length ACM Choose appropriate units of measurement for length, area, volume, capacity and mass (ACMMG108) Yr 5 ACM Calculate the perimeter and area of rectangles using familiar metric
units (ACMMG109) Yr 5 ACM Connect decimal representations to the metric system (ACMMG135) Yr 6 Achievement Standard Yr 4 Students use scaled instruments to measure temperatures, lengths, shapes and objects. Achievement Standard Yr 5 They use appropriate units of measurement for length, area, volume, capacity and mass, and calculate perimeter and area of rectangles. Achievement Standard Yr 6 Students connect decimal representations to the metric system and choose appropriate units of measurement to perform a calculation. They make connections between capacity and volume. They solve problems involving length and area. Estimating length Activity 1 Everyone lines up. They are asked to move forward eg 25 m. Teacher or leader then moves forward that distance using the
trundle wheel. Discuss how accurate their estimates were. Return to starting point and estimate a different distance. Activity 2 Give a few children pedometers and ask them to wear them for the whole day. At the end of the day record the number of steps they have taken. Calculate the length of an average pace for each child. Calculate the total distance they have covered. Use a map to work out where they could have travelled eg from Geraldton to _______. They can work in teams over a period of time, to see if they could walk from Perth to Broome..;.. (This involves lots of place value work as well as measurement, scale, direction etc MAI Growth Points for Mass and ACM Descriptions GP 0 No apparent awareness of the attribute of mass and use of
descriptive language GP 1 Awareness of the attribute of mass and use of descriptive language GP 2 Comparing, order and matching with the attribute of length ACM Use direct and indirect comparisons to decide which is longer, heavier or holds more, and explain reasoning in everyday language ( ACMMG006 F Achievement Standard F. They compare objects using mass, length and capacity GP 3 Quantifying mass accurately, using units and attending to measurement principles. Uses uniform units appropriately, assigning number and unit to the measure. ACM Compare masses of objects using balance scales (ACMMG038 Yr 2 Achievement Standard Yr 2. Not mentioned. Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units
(ACMMG037) Yr 2 GP 4 Choosing standard units for estimating and measuring mass with accuracy. ACM Compare masses of objects using balance scales (ACMMG038 Yr 2 Measure, order and compare objects using familiar metric units of length, mass and capacity (ACMMG061) Yr 3 Achievement Standard Yr 3. Students use metric units for length, mass and capacity. GP 5 Applying knowledge, skills and concepts of mass. Can solve a range of problems involving key concepts of mass. ACM Use scaled instruments to measure and compare lengths, masses, capacities and temperatures (ACMMG084) Yr 4 Achievement Standard Yr 4. Students use scaled instruments to measure temperatures, lengths, shapes and objects. Choose appropriate units of measurement for length, area, volume, capacity and mass (ACMMG108) Yr 5
Achievement Standard Yr 5. They use appropriate units of measurement for length, area, volume, capacity and mass, and calculate perimeter and area of rectangles. ACM Connect decimal representations to metric system (ACMMG135) (Yr 6) Convert between common metric units of length, mass and capacity (ACMMG136) Yr 6 Achievement Standard Yr 6Students connect decimal representations to the metric system and choose appropriate units of measurement to perform a calculation. Estimating mass On your table are five bags containing various amounts of sand. By hefting them, place them in order from lightest to heaviest. Discuss what you are doing. Do you all agree on the order? What language did you use?
What criteria were you using? Tony Ryans Thinkers Keys y e K Reverse Key n o i t s e Qu y W e K
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Ad r ge g i B ce a l ep An idea to make it more challenging! Question Key The answer is 1000m. What might the question be?
Reverse Key Improvements Key List 10 things you would Design a new ruler to NOT measure using measure height. centimetres. Explain your changes. What if? Key What if there were no km signposts on highways? Construction Key Construct a measuring
tape that can be used to measure things around your size. Alphabet Key List words from A to Z which relate to measurement. BAR Key (Bigger Add Replace) Discuss the use of a tape measure and suggest ways you could improve it. Alternatives Key List ways you could measure the length of
the classroom without using a ruler or tape measure. Order them from least to most effective. Brainstorming Key Brainstorm all the different ways you could measure something. A possible planning sequence Identify the topic Examine curriculum content and proficiency statements Use data to inform decisions on emphasis and
specific content needs Select, then sequence, appropriate activities Identify the mathematical actions in which you want students to engage Identify and explicitly teach and model the required language Model the effective use of any instruments required Teach LENGTH, AREA, VOLUME in that order. Possible approach: Prepare a 4 or 5 lesson sequence and teach that before moving onto the next sub-strand. Allow children to practise their skills, language and understandings. Begin every lesson by discussing the attribute to be measured, the appropriate units of measurement, the measurement device to use and the recording
method. Ask questions which help them to see connections. Does the measurement instrument match the attribute to be measured?
Colorimetric Tubes and Sampling Pump. Colorimetric Gas Detection Tubes. GRAB SAMPLING - ADVANTAGES - After collection, frequently . analyzed immediately by GC or direct-reading instruments. - Therefore, quick decisions . made in field/site about source of leaks;
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