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