Unit 7 measurement
property of length 3
(triangle inequality) for any points A,B, and C AB+BC>or equal to AC. that is, the distance from A to B added to the distance from B to C is greater than or equal to the distance from A to C
volume
........
measurement comparison
A unit is a fixed amount of the measurable attribute by which the ___ will be made
examples of measurable attribute
length, area, perimeter, volume, weight
surface area
...........(first attribute of spatial figures?) -must be measured using square units (because it is a measure of a plane)
property of length 2
AB=BA he distance from A to B equals the distance from B to A
ratios
___ between different units make it possible to convert from one unit to another
accuracy
___ describes how close the measurement is to the actual value of the object being measured
common strategies
___ for finding measure include using estimations, measuring devices, and formulas
area
___ is the amount of plane contained in a two-dimensional shape
estimation
___ is the process of using mental or visual information to arrive at an approximate measure without measuring the object directly using a measuring tool
Cavaleri's Principle
___ is two solids, each having their bases in the same parallel planes, have the same volume if every plane parallel to the bases intersects the solids in cross sections of equal area
measurement formulas
___ often rely on measures that can be taken directly
precision
___ relates to the exactness of the measure. -smaller units lead to more exact measurements -larger units lead to less exact measurements
dimensional analysis
___ uses unit ratios, which are ratios that compare a single unit of measure to the equivalent amount in another unit
property of length 1
____ AB>0 length is always greater than or equal to 0
surface area and volume
____ are the two attributes of spatial figures that are commonly measured
length
____ can be applied to other objects by treating them as if they were segments
measurement
____ is the process of assigning a numerical value to a physical attribute of some object or to a characteristic of some event or situation
nonstandard units
____ such as, pieces of outstretched rope, pencils, toothpicks, and coins can be used to measure length of other objects.
cubic unit
a ___ is the amount of space contained inside a cube that measures one unit along each edge
hectometer(hecto=10^2)
a ___ represents a length that is 100 times longer than a meter, or 1hm=100m
kilometer(kilo=10^3)
a ___ represents a length that is 1000 times longer than a meter, or 1km=1000m
measure of surface area
a ____ is the number of square units required to "cover" the three-dimensional objects
Pythagorean theorem
a formula commonly used to measure length is the ___. in this case two lengths are needed to find the missing length
cubic units
a measure of volume is literally the exact number of ___ required to "fill in" a three-dimensional shape
unitizing
a second method of estimation is ___. the object being measured must have several parts that are roughly the same size. this method proceeds by estimating the size of one part and then multiplying by he number of equivalent parts
measuring tool
a second strategy for measuring is to use a ___. a tool generally allows for much greater precision and accuracy
chunking
a third method of estimating is ____. the object is broken down into small yet related parts, estimate each part, and then add the resulting estimates
use a formula
a third strategy for finding a measure is to ___
power of ten
all larger metric units of length are some___ times longer than the meter
positive
all metric units stem from a basic unit. -larger units are made by multiplying the basic unit by ___ powers of ten -smaller units are made by multiplying the basic unit by negative powers of 10
attribute
an ___ is measurable if it can be quantified in some way
approximation
any measurement taken with a tool is still an ___
lacks precision
because estimation does not rely on measurement tools, it often lacks accuracy and almost always _____
multiplying or dividing
because the common ratio of ten, conversions between metric units can be made by ___ the appropriate power of 10
line
conversions can be aided by placing the metric prefixes along a ___. the direction and number of spaced moved tells us exactly how to move the decimal in the number
unreliable or impracical
estimation is commonly used when more formal measuring devices are ___
examples of attributes that are not measurable
happiness, imagination, pain, success, irritation
measurement process step 1
identify and select an attribute to be measured
property of area
if a planar region A is subdivided into non-overlapping sub-regions B and C, then the area of region A is the sum of the two sub-regions, or area(A)= area(B)+area(C)
length, angles, perimeter, and area
in general, there are four attributes of planar figures that we typically measure. they are ____
unit
measurement determines the size of the object or event relative to some well-known, or easily understood ___
reference unit
one method of estimation is to compare the object to a ___, which is simply the unit we use to find the measure.
one-dimensional
perimeter is a ___ measure of a two-dimensional shape
distance
perimeter is a ___, and so must necessarily be a measure of length. meaning, any measure of perimeter must be done using length units
the measure around (peri-around, meter-to measure)
perimeter literally means "___"
measurement process step 2
select an appropriate unit to measure the attribute
three-dimensional unit
since volume is a measurement of space, it must be measured with a ___, meaning the unit must have a length, width, and depth
ruler postulate
the ___ allows us to make a measure of length
measurement strategy
the ___ is a way to find how many units are equivalent to the attribute being measured
metric system
the ___ is often preferred over the Customary system because it makes use of simple decimal ratios between units
meter
the ___ is the metric system's basic unit of length
perimeter (P)
the ___ of a simple closed curve is the distance around the curve
decimeter(deci=10^-1)
the ___ represents a length that is 1/10 the length of a meter, or one piece from a meter that has been divided into ten equal pieces
centimeter(centi=10^-2)
the ___ represents a length that is 1/100 the length of a meter, or one piece from a meter that has been divided into 100 equal parts
decameter(deca=10^1)
the ___ represents a length that is 10 times longer than a meter, or 1dam=10m
size
the ___of the unit affects the precision and accuracy of the measurement. -precision and accuracy are often used as synonyms, but they are not the same
circumference (C)
the distance, or perimeter, around any circle is called its ___
appropriate type
the first consideration to make when selecting an a unit is- the unit must be the ___, measuring the unit must match the attribute to be measured
2 points
the length of a line segment is the distance between ___
how many
the measure literally describes "___" units are equivalent to the attribute of the object of interest
vary
the problem with nonstandard units is that they can ___from situation to situation leading to different measures of the same object. leading to problems with fairness and communication
appropriate size
the second consideration to make when selecting a unit is- the unit must be of ___. small units should be used to measure small portions of the attribute and large units should be used to measure large portions of the attribute
inverse relationship
there is an ___ between the size of the unit and the measure of the object. -as the unit increases, the measure decreases. -as the unit decreases, the measure increases.
measurement process step 3
use a measurement strategy to determine the measure
creativity
volume is often used incorrectly as a synonym for ___
kind of unit
when we record the results of any measure it is important to include both the number and the ___, as both are needed to clearly communicate the relative size of the measure
irregular shapes
with most ___, the "string" technique is one of the only ways we have of finding the perimeter