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Week 1: Measurement & Geometry (Intro to Measurement (MM is about the…
Week 1: Measurement & Geometry
Intro to Measurement
MM is about the
comparison of diff attributes
Apply MM to
solving real world probs
. MM skills are essential for
coping with every day experiences
- approach from mm PoV is less daunting than just focusing on numbers
Allows us to
quantify the world, desire to compare
Key to all MM ideas -
notion of comparison, focus on comparative language
All measurement is
approximate
Estimation i
mportant - not just focus on numbers
*
Print Scope and Sequence from lecture slides
Standard Units - An agreed measure, handy when MMs must be recorded for later use, are transported, are communicated and are used for calculation e.g. minutes, cms, kgs
Rarely taught inside the classroom - integrates well with other LA's
Non-std units - useful for prior lng b4 std units, translates well, meaningful learning
Choosing appropriate units
BIG IDEAS about measurement
1.
ID the attribute to be measured
(manipulate, discuss, explore, make comparisons). Involves dev awareness of the attribute and adopting any new assoc. lang
2.
Compare and order
(language - tall, taller, tallest.... heavy, heavier, heaviest... slow, slower, slowest). Reinforces dev of concepts assoc with attribute being used as unit of mm.
Use non-std units -
from every day experiences, natural and fun. Before introduced most mm principles can be dev. naturally using non-std units (must not change, comparisons performed by having all mm's in same unit)
Use std units
- metric units. Becoming familiar with quantity in each unit, correct language and symbols, using measuring devices, making estimations in real life sitchs, mastering equivalences between units. Show the connection between units of mm.
Application of MM
- only when comfortably and efficiently measuring using appropriate std units - end of process (use of mm formula as powerful formal tools for generalisation, applications of mm to other situations). Lng exp be directed towards wide range of authentic mm apps and to the power that comes from use of mm formulae.
Developing Formal MM
Should not be intro until comparison and estimation skills well experienced
Direct comparison - using matching but no number
Use of non-std units as well as std units
In connection with number skills
Classroom Activities
Make a measuring jug using water from a cup and labelling the jug (cut off plastic bottle)
Measure me! Complete questionairre e.g. how tall are you? How long is your leg? How big is your head?
Which is the longer line - use non std units to measure e.g. paper clips, cubes)
Working out which banana is longer using a piece of string the measuring string with a ruler.
Compare and order different instances of an attribute:
directly: comparing length by lying objects directly in line with each other
indirectly: comparing volumes by pouring sand from one container to another.
Length scavenger hunt - practice making indirect mm comparisons using non-std units of mm - pairs get strip of card of particular length and have to find items that are longer/shorter/same length of card.
Attributes
If sts deeply understand one attribute they can transfer knowledge to other attributes
Mass
Length - linked to number, good way to teach all areas of mm, introduce numbers in contextual format
Area
Volume
Capacity
Time
Temperature
Qu. 1: Define and compare and contrast standard and non-standard units.
Units of MM enable sts to measure and compare quantities that are separated by time or space, and to give a numerical value to such quantities.
Std units
universally employed is the metric units
and are the same size regardless of who uses them.
Agreed accepted units of measurement
. Handy when measurements must be recorded for later use, are
transported, are communicated and are used for calculation
.
(Siemon et al., 2015)
sts need to become fam with characteristics of, and quantities involved in, each unit, the correct language for naming the units, and correct conventions for writing measures using recognised notations.
provide practical examples in use of forming measuring devices, estimating quantities in real-world applications, and mastering proportionality between the units (10mm = 1cm).
Non-std units are
created for a particular purpose
, and used before standard units are formally introduced in Year 3 to
dev MM sense
.
Make it easier to focus on attribute being measured (discuss what it means to measure rather than actual official length of object).
Avoid use of large numerical values. Measurement needs to be communicated. A fun and engaging way to develop measurement understandings.
-
Informal everyday language
used to
estimate
mm - bigger, longer, heavier, using uniform objects (have a lot of them)
(Siemon et al., 2015)
Sts should be provided with
many opps
to measure using informal, non-std units in order to
prep for measuing with formal, std units.
Provides opps to
estimate quantity
of the attribute b4 mm is made, to
make choices
about the most app unit to use, and judge degree of accuracy approp for sitch.
Leads to
establishing **
need to stdise units** in order to eliminate ambiguities and miscommunication and enhance precision.
(Siemon et al., 2015)
Jump from measuring with non-std units to measuring in std units using measuring devices is challenging.
To assist sts in mnging transition provide them with opp to
create own simple measuring tools using non-std units
e.g. make your own ruler.
More likely they will understand how such instrument makes formal mm.
Qu. 2 Why is measurement of length fundamental to developing other measurement understandings?
Refers to how long something is.
Understanding of length is foundational to building the concepts of area and volume, it is the first of the MM attributes to be introduced in Year 1.
Linked to number, good way to teach all areas of MM and introduce numbers in a contextual format.
Length (1st dimension), Area (2nd dimension) & Volume (3rd dimension)
If sts deeply understand one attribute they can transfer knowledge to other attributes
Natural leads to making comparisons and use of comp. lang - reinforces awareness of length attribute and preps sts for mm activities involving use of units.